Solving a system of equations we can see that the length is 22 feet and the width is 16 feet.
How to find the length and the width?
For a rectangle of length L and width W, the area is given by the formula:
A = L*W
Here we know that the rectangular room has an area of 352 square feet, and we also know that the length of the room is 6 feet mroe than the width of the room, then we can write a system of equations:
352 = L*W
L = W + 6
To solve that system, we can substitute the second equation in the first one, we will get:
352 = (W + 6)* W
352 = W^2 + 6W
W^2 + 6W - 352 = 0
So we have a quadratic equation, the solutions give:
[tex]W = \frac{-6 \pm \sqrt{6^2 - 4*1*(-352)} }{2} \\\\W = \frac{-6 \pm 38 }{2}[/tex]
We take the positive value as the with, so:
W = (-6 + 38)/2
W = 16
And the length is 6 feet longer than that, so:
L = 16 + 6 = 22
Then the length is 22 feet, and the width is 16 feet.
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the function f(x) goes through the point (-2,6). which of the following translation of f(x) will go through the point (3,5)?
option 1; f(x-5)+1
option 2; f(x+5)-1
option 3; f(x-5)-1
option 4; f(x+5)+1
Answer:
Option 3: the function that goes through the point (3, 5) is f(x-5)-1
Step-by-step explanation:
To find which function goes through the point (3, 5), we can substitute 3 for x and solve for the value of f(x).
For option 1, f(x-5)+1, we have:
f(3-5)+1 = f(-2)+1 = 6+1 = 7
For option 2, f(x+5)-1, we have:
f(3+5)-1 = f(8)-1 = ?
For option 3, f(x-5)-1, we have:
f(3-5)-1 = f(-2)-1 = 6-1 = 5
For option 4, f(x+5)+1, we have:
f(3+5)+1 = f(8)+1 = ?
What is the value of 5/9 ÷ 5/6? Responses
Answer:
2/3 or 0.667
Step-by-step explanation:
5/9 ÷ 5/6
5/9 * 6/5
1/3 * 2/1 (after cancelling off)
= 2/3
I need some with this I would really appreciate if you could be able to help me with this.
I don't see the picture. Can you send it in the message.
The sum of the digits of a certain two digit number is 13. Twice the tens digit exceeds the unit digit by 2. What is the number?
Answer:
Step-by-step explanation:
6.5
Naomi's car used \frac{2}{5} 5 2 of a gallon to travel 15\tfrac{1}{2}15 2 1 miles. how many miles can the car go on one gallon of gas?
Answer:
To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 miles. We are told that the car used \frac{2}{5} 5 2 of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 to get the total number of gallons used:
\frac{2}{5} \cdot 15\tfrac{1}{2} = 9
Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:
15\tfrac{1}{2} \div 9 = \frac{31}{18}
This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:
\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}
Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:
\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}
Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.
A parallelogram in a coordinate plane is translated, rotated, and then reflected. Which of the following statements about the parallelogram and its final image are true？
The true statements about the image of the parallelogram are,
The corresponding sides have different lengths.
The parallelograms are congruent.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A parallelogram in a coordinate plane is translated, rotated, and then reflected.
In the case of translation, rotation and reflection would only change its coordinate points, and the preimage and image will be congruent.
The coordinate points of the vertices would only change if given.
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luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?
Luka will require 24 cups of water to make lemonades as calculated from the data given.
The quantity of sugar which he use is twice the amount of lemon which he us ,
= 2 x 3 = 6
and ,
as we know the amount of water is 4 times as much as lemon juice
Therefore, amount of water
= 4 * 6
= 24
A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.
A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.
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Solve for e.
2e + 3 + 7 = 2
e = [?]
One morning, Adrian stood tall and had a friend measure his shadow on the sidewalk. Adrian's friend also measured from the top of Adrian's head to the tip of his shadow. The diagram below shows these measurements. How tall is Adrian? A 4.5 ft B 5 ft C 5.5 ft D 6 ft
The length of Adrian's shadow measured by his friend and the distance directly from Adrian's head to the tip of his shadow can be used to find Adrian's height using Pythagorean Theorem. Using an example of the measurement values, Adrian's height is about 5.5 feet
What is Pythagorean Theorem?Pythagorean Theorem states that the sum of the square of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse side.
The diagram in the question appears left out. Please find attached a drawing made using the measurement lengths in the following example, created with MS Word.
The measurements Adrian had his friend to do are;
The length of Adrian's shadow on the sidewalk and the length from Adrian's head to the tip of the shadow.
Let x represent the length of Adrian's shadow, let r represent the distance from Adrian's head to the tip of the shadow, and let y represent Adrian's height
According to Pythagorean Theorem, we get;
r² = x² + y²
Therefore, the Adrian's height, h = √(r² - x²)
When r ≈ 8.14, and x = 6, we get;
h = √(8.14² - 6²) ≈ 5.5
Adrian's height is about 5.5 feet in the example situation
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What is the cubic polynomial with zeros (3,0), (-6,0), and (1,0)?
Question 15
The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:
D. x³ + 2x² - 21x + 18.
How to obtain the cubic polynomial?We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.
The zeros of the polynomial are given as follows:
x = 3, x = -6, x = 1.
Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:
(x - 3)(x + 6)(x - 1)
(x² + 3x - 18)(x - 1)
x³ + 2x² - 21x + 18.
Meaning that option D is correct.
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What is the sum of x + y for the system of equations
below?
y=-3x-1
y = -2/3x + 6
O-24
-3
O-11
O5
The sum of x and y is 5.
What is an equation?An equation is a statement of two expressions connected by equal sign.
Given that, the system of equations, y=-3x-1 and y = -2/3x + 6
Simplifying the equations,
-3x-1 = -2x/3+6
Multiplying the both sides by -3
9x +3 = 2x-18
7x = -21
x = -3
Put x = -3 in any one of the equations,
y = -3(-3)-1
y = 9-1
y = 8
Hence, the sum is 5
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cross-tabulation can only be used for two variables; each variable must have well-defined labels. true false
The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false
The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that that present the results of the entire group of respondents
The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "
The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables
The cross tabulation can be used for two or more variables
Therefore, the the given statement is false
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2. Divide. Write the answer in simplest
form.
6 2/3 divided by 4 1/5
Answer:
100/63
Step-by-step explanation:
6 2/3 ÷4 1/5
20/3÷21/5
20/3×5/21
1 37/63 or 100/63 or 1.587301587
so the answer is one (whole number) thirty seven over sixty three
1. Find the measure of y.
110°
z
yº
100°
87°
Answer:
97.8263768112
Step-by-step explanation:
Geometric Mean is denoted as 'x'
x = √(110×87)
x = √9570
∴ x = 97.8263768112
Define Geometric MeanThe Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. For instance, the geometric mean for a given pair of numbers, say 3 and 1, is equivalent to (3 + 1) = 3 = 1.732.In other terms, the geometric mean is the product of n numbers divided by the nth root. The geometric mean differs from the arithmetic mean, as is noted. As a result of the fact that in arithmetic mean, the data values are added before being divided by the total number of values. However, when calculating the geometric mean, we multiply the provided data values before taking the root of the entire number of data values using the radical index. Take the square root, for instance, if there are two data points, the cube root if there are three, the fourth root if there are four, and so on.To learn more about Geometric Mean refer https://brainly.com/question/28347817
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These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two yellow marbles if the first one is placed back before the second draw. Write your answer as a ratio. Reduce to simplest terms
The probability of drawing two yellow marbles if the first one is placed back before the second draw is 1/25.
Explain the term probability with replacement?For queries where the results are repeated in the sample space, probability with replacement is utilized. This indicates that the item is replaced with in sample space after being picked, keeping the sample space's total number of items constant.The formula for the probability;
probability = favourable outcome/total outcome
The bag contains the marbles as;
yellow marbles: 2pink marble: 3blue marble: 5Total marble: 10Thus, probability of drawing 1st yellow marble.
probability(1st yellow) = 2/10 = 1/5
As the ball is placed again in the bag.
probability(2nd yellow) = 2/10 = 1/5
So, probability of drawing two yellow marble = 1/5 x 1/5 = 1/25.
Thus, the probability of drawing two yellow marbles if the first one is placed back before the second draw is 1/25.
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Find two consecutive positive integers such that the square of the first decreased by 21 equals 6 times the second
The given two consecutive positive integers are 9 and 10.
What is an integer?It is a whole number that can be positive, negative, or zero.
Let consider x and x+1 as two consecutive positive integers.
Given that,
[tex]x^{2} -21=6(x+1)[/tex]
[tex]x^{2} -6x-27=0[/tex]
It can be written in fractional form like,
(x-9)(x+3)=0
so the values of x are 9 and -3.
Here, only positive integers are considered.
Hence 9 and 10 are the two consecutive positive integers.
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the mass of a radioactive substance follows a continuous exponential decay model. a sample of this radioactive substance has an initial mass of and decreases continuously at a relative rate of per day. find the mass of the sample after two days.
The initial mass of the sample after two days = 8483.45 kg
Given that,
It is known as exponential decay when a population or group of something is deteriorating and the quantity of decline is proportional to the size of the population. In an exponential decay, the overall value falls but the percentage that departs stays the same throughout time.
The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula.
The standard formula for this type of behavior which is written below:
A = [tex]Pe^{-rt}[/tex]
Where
A refers the amount left after time t
P refers the initial amount at t = 0
r refers the rate
Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day.
A sample of this radioactive substance was taken after two days.
And we need to find if the sample has a mass of today, then the initial mass of the sample.
Now, we have to substituting the values,
Let us assume,
P = 9575 kg
r = 0.12
t = 1
Then we get the equation as,
A = (9575 kg) [tex]e^{-0.12*1}[/tex]
When we simplify this one, then we get,
A = (9575 kg) [tex]e^{-0.12}[/tex]
A = (9575 kg) 0.886
A = 8483.45 kg
Therefore,
The initial mass of the sample after two days = 8483.45 kg
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Select the number of the algebraic expression for "The room capacity does not exceed 250".
c>250
c≥250
c<250
c≤250
c≠250
The algebraic expression for "The room capacity does not exceed 250" is D. c≤250
How to illustrate the inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
It should be noted that "the room capacity does not exceed 250" simply means it should be less than or equal to 250. This will be c≤250.
In conclusion, the correct option is D.
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Here is part of a recipe for different-size cakes, showing the ratio of eggs to flour.
Make a table that represents the same situation.
eggs : 0 2 4 6
flour (cups) : 0 1.5 3 4.5
question, we have to calculate the ratio by dividing a by b we will get the ratio as [tex]\frac{4}{3}[/tex].
What is a ratio formula?Using the ratio formula, ratios can be represented as a fraction. The ratio formula for any two quantities says a and b, is a:b = a/b. Because a and b are individual amounts for two portions, the total quantity is given as (a + b).
How do you calculate the ratios of a recipe?Known Total Amount
Determine the total quantity to be produced.
Determine the total number of parts in the ratio.
Divide the total quantity made by the total number of parts to get the amount per part.
Calculate the amount of each ingredient by multiplying each component by the amount per part.
Given:
Here is the ratio of eggs to flour
Eggs(a) 0 2 4 6
Flour(b) 0 1.5 3 4.5
For the table look at the image.
as per the question, we have to calculate the ratio by dividing a by b we will get the ratios as [tex]\frac{4}{3}[/tex].
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please please please help i’m desperate!!!!
Answer:
parallel
Step-by-step explanation:
You want to know the parallel/perpendicular status of the lines described by the equations ...
2x -5y = 25y = 2/5x +3Parallel linesParallel lines have the same slope. The slope is the coefficient of x when the equation is written in the form ...
y = mx +b
as is the second equation.
The first equation can be put in that form by solving for y.
2x -5y = 25 . . . . . . given equation
2x -25 = 5y . . . . . . add 5y -25
2/5x -5 = y . . . . . . divide by 5
The coefficient of x (slope) is 2/5, same as the second equation.
The lines are parallel.
__
Additional comment
Your graphing calculator can help you figure this out, too. The graphed lines are parallel.
ayden deposits $2000 into a savings account with an annual interest rate of 3%. If he makes no further deposits or withdrawals, which graph shows the growth of his account balance?
$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.
How to resolve our equation?Ayden deposits $2000 into a savings account with an annual interest rate of 3%.
To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest.
A = $2,060.00
I = A - P = $60.00
A is equal to P(1 + rt).
First, convert R percent to r a decimal; for example, R/100 is 3%/100, or 0.03 per year.
A = 2000(1 + (0.03 × 1)) = 2060 \sA = $2,060.00
$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.
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Find the volume of the pyramid.
Answer:
180 ft^3
Step-by-step explanation:
volume of the pyramid = (1/3)(area of base) (height)
v= 1/3×(10×12÷2)×(9)
= 180 ft^3
Answer:
answer on the picture.....
ow many ways can you get exactly six heads and exactly six tails if after six tosses you have had three tails and three heads?
The number of possible combinations available as calculated from the given data is 259200.
Coin just has a head and a tail.
The potential configuration is (6! * 6!)/2.
Divide by two because each coin has two faces.
The potential configuration is (6! * 6!)/2.
The potential configuration is (( 720 x 720)/2
The potential configuration is 259200.
259200 different combinations are available.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data.
Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.
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9x + 2 = 10x +7
solve for x
Answer:
The value of x is (-5)
Step-by-step explanation:
9x + 2 = 10x + 7
9x - 9x + 2 - 7 = 10x - 9x + 7 - 7
(-5) = x
x = (-5)
Thus, The value of x is (-5)
In AABC, b = 620 cm, ZC=106° and ZA=48°. Find the length of a, to the nearest
centimeter.
The length of A in the triangle is obtained as follows:
a = 282.74 cm.
How to obtain the missing side length?The first step in obtaining the missing side length is obtaining the measure of the missing angle.
The sum of the measures of the internal angles of a triangle is of 180º.
The angle measures for this triangle are given as follows:
106º.48º.26º. (as the sum of the three measures is of 180º).Then we have that:
The length of 620 cm is opposite to the angle of 106º.The length of a is opposite to the angle of 26º.Then the length of a is obtained applying the law of sines as follows:
sin(26º)/a = sin(106º)/620
Applying cross multiplication, we have that:
a = 620 x sin(26º)/sin(106º)
a = 282.74 cm.
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Answer:
the real answer is 1051
Step-by-step explanation:
What is the cubic polynomial with zeros (3,0), (-6,0), and (1,0)?
(Question 15)
Answer:
D
Step-by-step explanation:
when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.
f(x) = (x - 3)(x + 6)(x - 1)
we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :
-3 × +6 × -1 = +18
and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).
solve the system if x = 2y + 3 and 4x - 5y = 9
The solution of the system of equations:
x = 2y+ 3
4x - 5y = 9
Is x = 1, y = -1.
How to solve the system of equations?Here we have the following system of equations:
x = 2y+ 3
4x - 5y = 9
To solve it, we can notice that the variable x is already isolated on the first equation, then we can take it and replace it on the other equation, then we will get:
4*(2y + 3) - 5y = 9
Now we can solve that equation for y:
4*(2y + 3) - 5y = 9
8y + 12 - 5y = 9
8y - 5y = 9 - 12
3y = -3
y = -3/3
y = -1
And the value of x is:
x = 2y + 3
x = 2*(-1) + 3
x = -2 + 3 = 1
So the solution is x = 1 and y = -1.
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FINALS PLEAZ HEL One year after you start a savings account you have $480 in the account. You were adding $120 each year write a linear function in the form y=mx+b that models your savings account a each year t after you start the account
Answer:
y = 120t + 480
Step-by-step explanation:
what are the three strategy of cube roots
i need explanation pls
Answer:
look at the explanation below
Step-by-step explanation:
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing the same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number not a perfect cube and we cannot find the cube root of that number
i hope this helps
1-36) what is the sum of 2 + (1/5 + 1/5² + 1/5³ +...,.. +... 1/(5 to power n) ..)
help how
Answer:
[tex]\displaystyle \frac{9}{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} )[/tex]
The second term of this sum is an Infinite Geometric Progression
To find the sum of an Infinite Geometric Progression,
- Find the first term ( 1/5 ) of the progression and call it a
- Find the common ratio, (divide any term by it's predecessor. i.e [tex]\displaystyle \frac{\frac{1}{5^2} }{\frac{1}{5} } = \frac{5}{5^2} = \frac{1}{5}[/tex]) and call it r
Finding the sum of given Geometric Progression:
Sum of Infinite GP: [tex]\displaystyle \frac{a}{1-r}[/tex]
Plugging our values in this equation, we get:
Sum of Geometric Progression = [tex]\displaystyle \frac{\frac{1}{5} }{1 - \frac{1}{5} } = \frac{\frac{1}{5} }{\frac{5 - 1}{5} } = \frac{1}{4}[/tex]
Adding to find the actual answer:
[tex]\displaystyle (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = 2 + \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{9}{4}[/tex]
