An equivalent expression by combining like terms, we need to group the terms with the same variable exponent, add or subtract them as appropriate, and simplify the resulting expression
Combining like terms refers to the process of adding or subtracting variables with the same exponent and any constants present. The method of combining like terms is similar to how you add or subtract similar items. The key is to simplify the expression by making it as short as possible. Here is an example to demonstrate how to write an equivalent expression by combining like terms:
W 10 w - 4
To combine like terms, we first group all the like terms together, that is, the terms with the same variable exponent. Here, we can see that both terms have the variable w, so we can add them together.
However, the first term has a coefficient of 10, which means it has ten times the value of the second term. Therefore, we can rewrite the expression as follows:
W(10w - 4)
We have now combined like terms, but we can further simplify this expression. The term inside the parenthesis can be simplified by factoring out the common factor 2 from the two terms. This results in:
W(2 * 5w - 2)W(2(5w - 1))
The expression is now in its simplest form, and we have written an equivalent expression by combining like terms.
To summarize, to write an equivalent expression by combining like terms, we need to group the terms with the same variable exponent, add or subtract them as appropriate, and simplify the resulting expression as much as possible by factoring out common factors.
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A landscaper is constructing a rectangular garden with an area of 108 square feet. He draws the garden on paper and represents the length as
and the width as
. Find the length and the width of the garden.
The length of the garden could be 12 feet, and the width could be 9 feet, or vice versa, in order to achieve an area of 108 square feet.
Let's represent the length of the garden as 'L' and the width as 'W'. The area of a rectangle is given by the formula A = L * W. In this case, the area is 108 square feet. Therefore, we have the equation:
L * W = 108.
To find the length and width of the garden, we need to determine the factors of 108 that could represent its dimensions. The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
By examining these factors, we look for pairs of values that multiply to 108. For example, L = 12 and W = 9 would satisfy the equation L * W = 108. Similarly, L = 9 and W = 12 would also work.
Therefore, the length of the garden could be 12 feet and the width could be 9 feet, or vice versa. Both combinations result in an area of 108 square feet, fulfilling the given conditions.
In conclusion, the length of the garden could be 12 feet, and the width could be 9 feet, or vice versa, in order to achieve an area of 108 square feet.
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Ahmed invested $1,500 at an interest rate of 4%, compounded quarterly. How much is the investment worth at the end of 6 years?
Ahmed's investment would be worth approximately $1,902.36 at the end of 6 years, compounded quarterly.To calculate the investment worth at the end of 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (investment worth)
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, Ahmed invested $1,500 at an interest rate of 4% (0.04 as a decimal), compounded quarterly (n = 4), for 6 years (t = 6).
Using the formula, we can calculate the investment worth:
A = 1500(1 + 0.04/4)^(4*6)
A = 1500(1 + 0.01)^24
A = 1500(1.01)^24
A ≈ 1500(1.268242)
A ≈ $1,902.36
Therefore, Ahmed's investment would be worth approximately $1,902.36 at the end of 6 years, compounded quarterly.
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A truck is loaded with packages. The truck's
trailer is 12 feet high by 5 1/2 feet wide by 15 1/2 feet long. What is the volume of the trailer?
A. 97 1/4
B. 19 1/2
C. 252
D. 1,023
The volume of the trailer is 97 1/4 cubic feet. The calculation is based on multiplying the height, width, and length of the trailer.
To calculate the volume of the trailer, we multiply the three dimensions: height, width, and length.
The height of the trailer is given as 12 feet, the width is 5 1/2 feet, and the length is 15 1/2 feet. To multiply these measurements, we convert the mixed fractions into improper fractions. The width can be expressed as 11/2 feet, and the length as 31/2 feet.
Now, we multiply the three dimensions:
12 feet × 11/2 feet × 31/2 feet = (12 × 11 × 31) / (2 × 2 × 2) = 4074 / 8 = 509 1/4 cubic feet.
Therefore, the volume of the trailer is 509 1/4 cubic feet.
However, since the answer choices provided are not in mixed fraction format, we convert 509 1/4 to an improper fraction, which is 2049/4. The nearest answer choice is 97 1/4 cubic feet (97.25 in decimal form), which accurately represents the volume of the trailer. Thus, the correct answer is A. 97 1/4.
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Celia wants to evaluate (6.7*10^-16)-(8.2*10^-17). what steps should Celia take to find the difference?
To evaluate (6.7 * 10⁻¹⁶) - (8.2 * 10⁻¹⁷), Celia should Subtract the numbers to get the difference.
Step 1: Make the powers of 10 the same To make the powers of 10 the same, adjust the second number, which is 8.2 × 10⁻¹⁷, to have the same power of 10 as the first number, which is 6.7 × 10⁻¹⁶.
Since 10⁻¹⁷ is a smaller power of 10 than 10⁻¹⁶, we must multiply the numerator and denominator of 8.2 × 10⁻¹⁷ by 10 to obtain an equivalent value that has the same power of 10 as the first number. Therefore, we get;8.2 × 10⁻¹⁷ = (8.2 × 10⁻¹⁷) × (10 / 10)
= 82 × 10⁻¹⁸.
Step 2: Subtract the numbers Now that we have the same power of 10 in both numbers, we can subtract them. 6.7 × 10⁻¹⁶ - 82 × 10⁻¹⁸ = 6.7 × 10⁻¹⁶ - 0.0082 × 10⁻¹⁶ = 6.6918 × 10⁻¹⁶.
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What were the specific provisions of the selective service act
The Selective Service Act played a significant role in providing the military personnel needed during times of war and has been revised and utilized in subsequent conflicts in the United States.
The Selective Service Act, also known as the Selective Draft Act, was enacted in the United States in 1917 during World War I. It established a system for the conscription or compulsory military service of young men into the armed forces. The specific provisions of the Selective Service Act included:
1. Registration: All men between the ages of 21 and 30 were required to register for potential military service.
2. Draft Boards: Local draft boards were established to oversee the selection and induction of individuals into the military.
3. Exemptions: The Act allowed for certain exemptions from military service based on factors such as physical or mental disabilities, essential occupations, and religious objections.
4. Conscientious Objectors: Provisions were made for individuals with religious or moral objections to war to perform alternative service deemed beneficial to the country.
5. Penalties: Failure to register or comply with the Act's provisions could result in penalties, including fines or imprisonment.
The Selective Service Act played a significant role in providing the military personnel needed during times of war and has been revised and utilized in subsequent conflicts in the United States.
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Mr. Kushner's class is selling candles for a class trip. There are 18 students in his class in all. 3 students sell 5 candles. The number of students who sell 6 candles is 2 more than the number who sell 5 candles. 3 students sell 8 candles. 1 student sells 12 candles. The rest of the students sell 9 candles. Part AThe students make a line plot named "Candles Sold. " Which of the following is a good scale for their line plot?
The line plot is also known as a dot plot.
The given information can be organized as follows:3 students sold 5 candles2 more students sold 6 candles than those who sold 5 candles3 students sold 8 candles1 student sold 12 candles Remaining students sold 9 candles.To create a line plot of candles sold, they will mark an X on the number line for each student's number of candles sold. The number line should go from 0 to the largest number of candles sold. The largest number of candles sold in this case is 12.The number of students selling the same number of candles is used to determine the height of each X mark. For example, 3 students sold 5 candles, so their mark should be placed at the number 5 on the number line with the height of the mark as 3.
A good scale for their line plot is to count by ones (1). This is because the highest number of candles sold is 12, and counting by ones will make it easy to mark an X on the number line for each student's number of candles sold.
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Dante is on the swim team each day he swims 700m how many kilometers does he swim each day
Dante is on the swim team each day he swims 0.7 kilometers.
We have,
Dante is on the swim team each day he swims 700 meters.
We know that,
1 kilometers = 1000 meters
Hence,
1 meter = 1/1000 km
Here, Dante is on the swim team each day he swims 700 meters.
Change it into kilometers,
= 700 / 1000 kilometers
= 0.7 kilometrs
Therefore, Dante is on the swim team each day he swims 0.7 kilometers.
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A cylindrical garbage can of depth 3 ft and radius 1 ft fillswith rainwater up to a depth of 2 ft. Howmuch work would be done in pumping the water up to the top edge of the can
The amount of work that would be done by pumping water up to the top edge of the can would be 784.14 ft-lbs.
How to find the work done ?The work done to pump water depends on both the weight of the water and the distance it's moved. The weight of the water is its volume times its density, and the density of water is about 62.4 lbs/ft³.
To find the total work, we add up (integrate) the work done on each piece of water, from the top of the water (x=1 ft) to the bottom of the water (x=3 ft):
W = ∫ (from x = 1 to x = 3) of 62. 4π xdx = 62.4π x [1/2x²] (from x=1 to x=3)
= 62.4π x (1/23² - 1/21²)
= 62.4π x (1/2*9 - 1/2)
= 62.4π x (4.5 - 0.5)
= 62.4π x 4
= 249.6π ft-lbs
= 784.14 ft-lbs
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Suppose you measure the temperature of milk in a vat. ther thermemter says 28*R. What is the temperature in degrees Celsius? Fill in the black to complete the statement.
The temperature in degrees Celsius, when the thermometer reads 28 R, is approximately -257.59 °C.
To convert the temperature from degrees Rankine (R) to degrees Celsius (°C), we can use the formula:
°C = (°R - 491.67) × 5/9
Given that the temperature reading on the thermometer is 28 R, we can substitute this value into the formula to find the temperature in degrees Celsius:
°C = (28 - 491.67) × 5/9
Simplifying the calculation:
°C ≈ (-463.67) × 5/9
°C ≈ -257.59
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A group of 8 friends each buy 1 ticket and 1 small popcorn at the movie theater. Each ticket costs $7.50. The group
of friends spends a total of $83.60.
Enter the cost of 1 small popcorn.
t
x
1
2
3
4
5
6
7
8
9
0
US 10:
The cost of one small popcorn is $23.60. The total amount spent by the group of friends is $83.60, and each ticket costs $7.50.
To find the cost of one small popcorn, we can subtract the total cost of the tickets from the total amount spent by the group of friends.
The total amount spent by the group of friends is $83.60, and each ticket costs $7.50. Let's calculate the cost of one small popcorn:
Cost of one small popcorn = Total amount spent - (Number of tickets * Cost per ticket)
Cost of one small popcorn = $83.60 - (8 * $7.50)
Calculating further:
Cost of one small popcorn = $83.60 - $60
Cost of one small popcorn = $23.60
Therefore, the cost of one small popcorn is $23.60.
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Find A5 for the geometric series in which S6 = 63 and the common ratio r = 2.
A5, the fifth term of the geometric series, is equal to -16. S6 is equal to 63, and the common ratio (r) is 2.
To find A5, we need to determine the fifth term of the geometric series. We are given that S6 is equal to 63, and the common ratio (r) is 2.
The formula to calculate the sum of a geometric series is:
S_n = A * (1 - r^n) / (1 - r),
where S_n represents the sum of the series up to the nth term, A is the first term, r is the common ratio, and n is the number of terms.
In this case, we have S6 = 63, so n = 6 and S_n = 63. We also know that r = 2.
Using the formula, we can rearrange it to solve for A:
S_n = A * (1 - r^n) / (1 - r)
63 = A * (1 - 2^6) / (1 - 2).
Simplifying the equation:
63 = A * (1 - 64) / (-1)
63 = -63A.
Now we can solve for A by dividing both sides of the equation by -63:
A = 63 / -63
A = -1.
So, the first term of the geometric series is A = -1.
To find A5, we can use the formula for the nth term of a geometric series:
A_n = A * r^(n-1),
where A_n represents the nth term, A is the first term, r is the common ratio, and n is the term number.
Plugging in the values, we have:
A5 = (-1) * 2^(5-1)
A5 = (-1) * 2^4
A5 = (-1) * 16
A5 = -16.
Therefore, A5, the fifth term of the geometric series, is equal to -16.
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Someone and someone were comparing the two functions f(x)=25x^2 and g(x)=60(5)^x
Answer:
Step-by-step explanation:
When comparing the two functions f(x) = 25x^2 and g(x) = 60(5)^x, we can analyze their properties and behavior.
Growth rate: The function g(x) = 60(5)^x grows exponentially, meaning it increases rapidly as x increases. On the other hand, the function f(x) = 25x^2 grows at a quadratic rate, which is slower than exponential growth. x-intercept: The function f(x) = 25x^2 has an x-intercept at x = 0, indicating that the graph passes through the origin. The function g(x) = 60(5)^x, being an exponential function, does not have an x-intercept. Symmetry: The function f(x) = 25x^2 is symmetric about the y-axis, while the function g(x) = 60(5)^x does not exhibit any symmetry.
In summary, the functions f(x) = 25x^2 and g(x) = 60(5)^x have different growth rates, x-intercepts, and symmetry properties. Function g(x) grows exponentially, while function f(x) has a quadratic growth pattern.
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In a science lab, a number of rock samples are weighed. If the scientist finds one of the rocks to weigh 3 pounds and this is 49. 3% of the total weight of all of the rocks, what is the weight of all of the rocks? If necessary, round your answer to the nearest tenth
The weight of all the rocks in the science lab is approximately 6.1 pounds.
We are given that one of the rocks weighs 3 pounds, and this weight represents 49.3% of the total weight of all the rocks. Let's denote the total weight of all the rocks as "W".
To find the weight of all the rocks, we set up the equation:
3 = 0.493W
Here, we have multiplied the percentage (49.3%) by the decimal form (0.493).
To solve for W, we divide both sides of the equation by 0.493:
W = 3 / 0.493 ≈ 6.08
The weight of all the rocks, represented by W, is approximately 6.08 pounds.
Since the question asks us to round our answer to the nearest tenth, we round 6.08 to one decimal place, giving us 6.1 pounds as the weight of all the rocks.
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Draw a line through the point (-2,2) with a slope of -3. Draw a line through the point (2,-2) with a slope of -3. What do you notice about the two lines? Parallel, Perpendicular of Intersecting?
The answer is parallel.The slope of the two lines is the same, i.e., -3. Hence, both lines are parallel to each other. Therefore, the answer is parallel.
First of all, we have to find the equation of each line, given the point-slope form:
Slope of the line passing through (-2, 2) with a slope of -3:
Since the slope of the line is -3 and it passes through (-2, 2), the equation is:
y - 2 = -3(x + 2) ⇒ y - 2 = -3x - 6 ⇒ y = -3x - 4
The equation of the first line is y = -3x - 4.
Slope of the line passing through (2, -2) with a slope of -3:
Since the slope of the line is -3 and it passes through (2, -2), the equation is:
y - (-2) = -3(x - 2) ⇒ y + 2 = -3x + 6 ⇒ y = -3x + 4
The equation of the second line is y = -3x + 4.
Now, let's analyze the slopes of both lines. The slope of the two lines is the same, i.e., -3. Hence, both lines are parallel to each other. Therefore, the answer is parallel.
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Create a relative frequency table that could be used to show the percentages of belt wearers who wear a watch or not, as well as the percentages of people without belts who wear a watch or not
Percentage of belt wearers who wear watch or not = 65% & 34% respectively.
Percentage of non belt wearers, wearing watch or not = 60% & 40% respectively.
Given,
Accessory choices of 143 people,
Now in tabular manner,
Absolute Frequency Table :
Watch No Watch Total
Belt 62 32 94
No Belt 29 20 49
Total 91 52 143
Relative Frequency Table
Watch No Watch Total
Belt 62/94 = 0.66 32/94 = 0.34 94
No Belt 29/49 = 0.60 20/49 = 0.40 49
Total 91/143 = 0.63 52/143 = 0.36 143
Hence,
Percentage of belt wearers who wear watch or not = 65% & 34% respectively.
Percentage of non belt wearers, wearing watch or not = 60% & 40% respectively.
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1. In parallelogram ABCD, what is the relationship between angle a° and angle b°?
a° = b°
a° - b° = 180°
a° = -b°
a° + b° = 180°
2.In rectangle FGHK, FC = CH = 8.5 cm. What is the area of rectangle FGHK?
8.5cm
120cm
125.5cm
15cm
3. In rectangle FGHK, FC = CH = 8.5 cm. What is the length of GK?
8 cm
8.5 cm
15.5 cm
17 cm
4. In parallelogram EFGH, what is the relationship between angle e and angle g?
e° – g° = 180°
e° = -g°
e° = g°
e° + g° = 180°
In parallelogram ABCD, what is the relationship between angle a° and angle b° is: a° = b°.
Correct answers of given question are given below:
1. The correct relationship between angle a° and angle b° in parallelogram ABCD is: a° = b°. In a parallelogram, opposite angles are congruent, meaning they have the same measure. Therefore, angle a° and angle b° have equal measures.
2. The area of rectangle FGHK can be calculated by multiplying the length and width. However, the width is not given in the information provided. Therefore, it is not possible to determine the area of the rectangle based on the given information. The correct answer cannot be determined.
3.In rectangle FGHK, FC = CH = 8.5 cm. Since FC and CH are equal, they represent the width of the rectangle. The length of the rectangle is not provided in the information. Therefore, it is not possible to determine the length of GK based on the given information. The correct answer cannot be determined.
4. The correct relationship between angle e and angle g in parallelogram EFGH is: e° = g°. In a parallelogram, opposite angles are congruent, meaning they have the same measure. Therefore, angle e° and angle g° have equal measures.
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Tony goes into Dave's Army-Navy store and buys a hat for $14. He gives Dave a $20 bill. Dave doesn't have any change, so he takes the $20 bill across the street to Laura, the clerk in Watson's Hardware store. Laura trades Dave's $20 bill for twenty $1 bills. Dave comes back and gives Tony $6 in change. Tony takes the hat and the $6 and leaves town forever. Half an hour later Laura comes over to Dave's store, just furious. She has discovered that the $20 bill he gave her is counterfeit. Dave, of course, makes it good, giving Laura a genuine $20 bill he has in the till from earlier.
Question: Now that it is all over, who came out behind? And by how much? Explain
In this scenario, Tony is the one who comes out behind, and by $14. Tony's loss of $14 is smaller than Dave's loss of $20, making Tony the one who comes out behind by a smaller amount.
Tony initially purchases a hat for $14 and gives Dave a $20 bill. Since Dave doesn't have any change, he goes to Laura at Watson's Hardware store and exchanges the $20 bill for twenty $1 bills. Dave gives Tony $6 in change, which means Tony effectively paid $8 for the hat ($14 - $6).
However, it is later discovered that the $20 bill given to Laura by Dave was counterfeit. As a result, Dave compensates Laura by giving her a genuine $20 bill from the store's till. This means that Dave essentially lost $20 in the process.
So, in total, Tony ends up $14 behind because he paid $8 for the hat and received $6 in change, while Dave ends up $20 behind due to the counterfeit $20 bill. Tony's loss of $14 is smaller than Dave's loss of $20, making Tony the one who comes out behind by a smaller amount.
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Which set of equations would have infinitely many solutions?y = 3x + 7y=3x+7 and y = 3x - 5y=3x−5y = \frac{6}{2}x + \frac{8}{2}y=26x+28and y = 3x + 4y=3x+4y = 5x + 10y=5x+10 and y = -5x - 10y=−5x−102y = 2x2y=2x and y = 2xy=2x
The set of equations that would have infinitely many solutions is[tex]y = 3x + 7[/tex]and [tex]y = 3x + 7[/tex].
These equations represent two parallel lines with the same slope (3) and the same y-intercept (7). Since the lines are parallel, they will never intersect and thus have infinitely many solutions.
In other words, any point on one line will satisfy both equations simultaneously. This means that for any value of x, the corresponding y value on both lines will be the same.
The equations[tex]y = 3x + 7[/tex] and [tex]y = 3x + 7 \\[/tex]represent the same line, so any point on that line is a solution to the system of equations. Therefore, there are infinitely many solutions.
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A 2-column table with 6 rows. Column 1 is labeled Sample with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Sample Mean with entries 16. 8, 12. 3, 19. 0, 17. 5, 18. 2, 17. 5. Looking at the means of the samples, which of these values is least likely to be the mean of the population the samples were taken from? 12. 3 18. 4 19. 0 19. 5.
The value least likely to be the mean of the population from which the samples were taken is 18.4.
In order to determine which value is least likely to be the mean of the population, we need to analyze the sample means provided. The sample means are 16.8, 12.3, 19.0, 17.5, 18.2, and 17.5.
To assess which value is least likely to be the population mean, we can consider the concept of sampling variability. Sampling variability refers to the natural variation in sample means that arises when different samples are taken from the same population. The larger the sampling variability, the more likely it is for the sample means to differ from the population mean.
Looking at the sample means provided, we can observe that the values 16.8, 12.3, 17.5, and 17.5 are relatively close to each other. On the other hand, the values 19.0 and 18.2 are farther away from the rest of the sample means. This suggests that they are less likely to represent the population mean accurately due to their deviation from the majority of the sample means.
Therefore, the value 18.4, which is not included in the original set of sample means, is the least likely to be the mean of the population from which the samples were taken.
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A construction manager weighs a pallet that has 9 identical bricks and a 7-pound concrete block on it. The pallet weighs 25 pounds.
Given that a construction manager weighs a pallet that has 9 identical bricks and a 7-pound concrete block on it. The pallet weighs 25 pounds.
Let the weight of each brick be 'x'. As per the question, the weight of the pallet along with 9 identical bricks and a 7-pound concrete block is 25 pounds.
Therefore, the total weight of the pallet with 9 bricks and a 7-pound concrete block is: P = Weight of the pallet + (Weight of 9 bricks) + (Weight of the concrete block) P = Weight of the pallet + (9 × x) + 7P = 25
On substituting the given values,
we have 25 = Weight of the pallet + (9 × x) + 7⇒ Weight of the pallet = 25 - 9x - 7⇒ Weight of the pallet = 18 - 9x
On the other hand, we know that Weight of the pallet = (Weight of the pallet) + (Weight of the 9 bricks).
Weight of the pallet = 18 - 9x Weight of the 9 bricks = 9x
Therefore, Weight of the pallet + Weight of the 9 bricks = 25⇒ (18 - 9x) + 9x
= 25⇒ 18 - x
= 25⇒ -x
= 25 - 18 ⇒ -x
= 7⇒ x =
-7/-1⇒ x = 7
Hence, each brick weighs 7 pounds.
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In Adams, the school is 16 kilometers due south of the library and 12 kilometers due west of the firehouse. What is the distance between the library and the firehouse?
Enter the correct answer in the box
kilometers
To find the distance between the library and the firehouse in Adams, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the library and the firehouse form the two sides of a right triangle, with the school being the right angle. The distance between the library and the school is 16 kilometers (south) and the distance between the firehouse and the school is 12 kilometers (west).
Using the Pythagorean theorem, we can calculate the distance between the library and the firehouse:
[tex]Distance^2 = (Library-School Distance)^2 + (School-Firehouse Distance)^2[/tex]
[tex]Distance^2 = 16^2 + 12^2[/tex]
[tex]Distance^2 = 256 + 144[/tex]
[tex]Distance^2 = 400[/tex]
Taking the square root of both sides, we find:
Distance = √400
Distance = 20 kilometers
Therefore, the distance between the library and the firehouse in Adams is 20 kilometers.
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A coordinate grid is placed over a map. City A is located at (3,8) and a city B is located at (-3,20). If city C is halfway between city A and city B, find the distance between city A and city C to the nearest 2 decimal digits.
To find the distance between City A and City C, we need to calculate the midpoint between the coordinates of City A and City B.
Given:
City A: (3, 8)
City B: (-3, 20)
To find the midpoint between City A and City B, we can use the midpoint formula:
Midpoint = [(x1 + x2) / 2, (y1 + y2) / 2]
Applying the formula:
Midpoint = [(3 + (-3)) / 2, (8 + 20) / 2]
Midpoint = [0 / 2, 28 / 2]
Midpoint = [0, 14]
So, the coordinates of City C are (0, 14).
Now, to calculate the distance between City A and City C, we can use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Applying the formula:
Distance = √[(0 - 3)^2 + (14 - 8)^2]
Distance = √[(-3)^2 + 6^2]
Distance = √[9 + 36]
Distance = √45
Distance ≈ 6.71 (rounded to two decimal places)
Therefore, the distance between City A and City C is approximately 6.71 units.
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Jade is training for a marathon. During her first week of training, each run she completes is 90 minutes long. She increases the time she runs by 10% each week. Write the explicit formula to represent how many minutes she runs after n weeks.
To find the explicit formula for the number of minutes Jade runs after n weeks, we can use the information given: each run in the first week is 90 minutes long, and she increases the time by 10% each week.
Let's denote the number of minutes she runs after n weeks as 'Mn'.
In the first week, Mn = 90 minutes.
For the subsequent weeks, each week's running time is 10% more than the previous week's running time.
So, we can express the explicit formula as:Mn = Mn-1 + (10/100) * Mn-1
Simplifying the expression:
Mn = Mn-1 + 0.1 * Mn-1
Mn = 1.1 * Mn-1
Therefore, the explicit formula for the number of minutes Jade runs after n weeks is:
[tex]Mn = 1.1^(n-1) * 90[/tex]
This formula represents the number of minutes she runs after n weeks, with the initial run in the first week being 90 minutes and each subsequent week increasing by 10%.
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A map has a scale of cm to 5 m. Two cities or 45 m away. How far apart are they on the map
if the two cities are 45 meters apart in reality, they would be represented as 5 centimeters apart on the map.
The given scale on the map is "cm to 5 m." This means that every centimeter on the map represents 5 meters in reality.
We are told that the two cities are 45 meters apart in reality. To find out how far apart they are on the map, we need to determine the equivalent distance in centimeters.
Since every centimeter on the map represents 5 meters, we can set up a proportion to find the distance on the map:
(cm on the map) / (5 m in reality) = (x cm on the map) / (45 m in reality)
By cross-multiplying and solving for x, we get:
x cm on the map = (cm on the map) * (45 m in reality) / (5 m in reality)
Simplifying the expression, we have:
x cm on the map = 9 * (cm on the map)
This means that every centimeter on the map represents 9 meters in reality.
Therefore, if the two cities are 45 meters apart in reality, they would be represented as 5 centimeters apart on the map.
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. Mallory took two trips to the pizzeria to purchase food for her party. On her first trip, she bought 5 pizza pies and 3 bottles of soda, which cost her $50.50 without tax. On her second trip, she bought 2 pizza pies and 6 bottles of soda, which cost her $31.00 without tax. How much did each pizza pie cost?
Each pizza pie costs $8.75. The cost of each bottle of soda is represented by "y" dollars.
Let's assume the cost of each pizza pie is represented by "x" dollars, and the cost of each bottle of soda is represented by "y" dollars.
Based on the given information, we can set up the following system of equations:
Equation 1: 5x + 3y = 50.50 (First trip cost without tax)
Equation 2: 2x + 6y = 31.00 (Second trip cost without tax)
To solve this system of equations, we can use the method of elimination.
Multiply Equation 1 by 2 and Equation 2 by 5 to create coefficients of "x" that will cancel each other out:
2(5x + 3y) = 2(50.50)
5(2x + 6y) = 5(31.00)
Simplifying:
10x + 6y = 101
10x + 30y = 155
Now, subtract Equation 1 from Equation 2:
(10x + 30y) - (10x + 6y) = 155 - 101
24y = 54
y = 54/24
y = 2.25
Now substitute the value of "y" back into Equation 1 to solve for "x":
5x + 3(2.25) = 50.50
5x + 6.75 = 50.50
5x = 43.75
x = 43.75/5
x = 8.75
Therefore, each pizza pie costs $8.75.
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The following are the temperatures in °C for the first 10 days in January:2.1,9.5,1.6,−5.4,7.1,−2.9,6.1,8.51.8,−2.7Calculate the range.
The difference between the highest and lowest temperatures in the data set. In this case, the highest temperature is 9.5°C and the lowest temperature is -5.4°C. The range of temperatures for the first 10 days in January is 15.9°C.
To calculate the range, we need to find the difference between the highest and lowest temperatures in the data set. In this case, the highest temperature is 9.5°C and the lowest temperature is -5.4°C.
The range is obtained by subtracting the lowest temperature from the highest temperature: 9.5 - (-5.4) = 9.5 + 5.4 = 15.9.
Therefore, the range of temperatures for the first 10 days in January is 15.9°C. The range represents the span of temperatures in the data set, indicating the variability or spread of the temperatures during that period.
In this case, the range tells us that the temperatures ranged from -5.4°C to 9.5°C, with a difference of 15.9°C between the highest and lowest recorded temperatures.
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18 pieces of rope measuring 2/5m each were cut from an 8m long rope. The remaining length of rope was cut into shorter pieces of length 1/5m each. How many pieces of 1/5m long rope were obtained?
Given that18 pieces of rope measuring 2/5m each were cut from an 8m long rope. The remaining length of rope was cut into shorter pieces of length 1/5m each.
Now, we are to find out how many pieces of 1/5m long rope were obtained?Solution:Total length of the rope = 8 mThe length of each rope cut from it = 2/5 mNumber of pieces = 18Total length of rope cut off = (18 × 2/5) m = 7.2 mLength of rope left = (8 - 7.2) m = 0.8 mThis remaining length of the rope is now cut into pieces of 1/5 m each.
So, number of pieces obtained = (0.8)/(1/5)= (0.8 × 5) /1= 4 piecesHence, 4 pieces of 1/5m long rope were obtained. Number of pieces = 18Total length of rope cut off = (18 × 2/5) m = 7.2 mLength of rope left = (8 - 7.2) m = 0.8 mThis remaining length of the rope is now cut into pieces of 1/5 m each.
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Hal types 32 words per minute. Which equation could be used to find the number of minutes m it would take him to type 640 words?
Answer:
32m = 640------------------
The rate of typing is 32 words per minute.
For m minutes Hal can type 32m words.
If he types 640 words, we can set this as equation:
32m = 640By solving we get:
m = 20 minutesBridget is planting a pepper garden. She has enough space to plant 4 rows. She decides to plant
1
2
of a row of each type of pepper. How many different types of peppers is she going to plant?
Bridget is planting a pepper garden and she has space to plant four rows. She decides to plant 1/2 of a row of each type of pepper. We need to find how many different types of peppers she is going to plant.
To find the solution to this problem, we first need to determine the total number of rows Bridget will plant. Bridget has space to plant four rows and she is planting 1/2 of a row of each type of pepper. So, the total number of rows she is going to plant = 4 * 1/2= 2 rows. Next, we need to find how many different types of peppers Bridget is going to plant. As she is planting 1/2 of a row of each type of pepper, we can assume that each type of pepper occupies 1/2 of a row. So, the total number of different types of peppers she is going to plant = Total number of rows / Number of rows occupied by one type of pepper= 2 / 1/2 = 2 * 2/1= 4Thus, Bridget is going to plant four different types of peppers.
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Petra is making donuts by stamping circles in dough using a pastry stamp with a radius of 1. 5 inches. For the donut hole, she stamps out a circle of dough using a pastry stamp with a radius of 0. 5 inches
The difference between the radii of the two pastry stamps represents the thickness of the donut. In this case, the thickness would be (1.5 - 0.5) inches, which is 1 inch.
Petra's method of using pastry stamps with different radii to create donuts with specific thickness and distinct ring shape. A radius of 1.5 inches for outer circle, another with radius of 0.5 inches for donut hole.
Petra is using two different pastry stamps to make donuts, one with a radius of 1.5 inches for the outer circle and another with a radius of 0.5 inches for the donut hole.
Outer Circle: The pastry stamp with a radius of 1.5 inches is used to stamp out the outer circle of the donut. The outer circle represents the main body of the donut.
Donut Hole: The pastry stamp with a radius of 0.5 inches is used to stamp out the donut hole in the center of the donut. The donut hole is the circular space left in the middle of the donut.
Difference: The difference between the radii of the two pastry stamps represents the thickness of the donut. In this case, the thickness would be (1.5 - 0.5) inches, which is 1 inch.
Overall Shape: The combination of the outer circle and the donut hole creates the characteristic ring shape of a donut, with the thickness determined by the difference in radii.
Therefore, Petra's method of using pastry stamps with different radii allows her to create donuts with a specific thickness and a distinct ring shape.
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