Answer:
Linear function: y = x + 7.75
Step-by-step explanation:
A store sells packages of comic books with a poster. We are told that:
A poster and 4 comics books cost $11 75.A poster and 11 comics books cost $18.75.Let p be the cost of one poster.
Let c be the cost of one comic book.
Write a system of equations using the given information and the defined variables:
[tex]\begin{cases}p + 4c = 11.75\\p + 11c = 18.75\end{cases}[/tex]
Subtract the first equation from the second equation to eliminate p:
[tex]\begin{array}{crcrcl}&p&+&11c&=&18.75\\-&(p&+&4c&=&11.75)\\\cline{2-6}&&&7c&=&\;\;7.00\\\cline{2-6}\end{array}[/tex]
Solve for c:
[tex]7c=7.00[/tex]
[tex]c=1.00[/tex]
Therefore, the cost of one comic book is $1.00.
Substitute the found value of c into one of the equations and solve for p:
[tex]\begin{aligned}p+4(1.00)&=11.75\\p+4.00&=11.75\\p&=7.75\end{aligned}[/tex]
Therefore, the cost of one poster is $7.75.
Now we know the cost of one poster and one comic, we can write a linear function that models the cost y of a package containing x number of comic books:
[tex]y = 1.00x + 7.75[/tex]
[tex]y =x + 7.75[/tex]
We are told that another store sells a similar package modeled by a linear function rule with initial value $6.99. The initial value is the y-intercept of each function, i.e. the cost of the package when zero comics are sold. So the linear function for this package is:
[tex]y = x + 6.99[/tex]
To determine which store has the better deal, we need to compare the y-intercepts (the initial values). The store with the lower initial value provides a better deal because it charges less for the basic package (when the number of comic books is zero).
Since 6.99 is less than 7.75, the other store offers a better deal, as it has a lower initial cost for the basic package.
Answer:
[tex]\Huge \boxed{ \texttt{\bf{y = x + 7.75} }}[/tex]
Step-by-step explanation:
To find the linear function rule that models the cost [tex]\texttt{y}[/tex] of a package containing any number [tex]\texttt{x}[/tex] of comic books, we can use the given information:
A poster and 4 comics cost $11.75A poster and 11 comics cost $18.75Let's denote the cost of a poster as [tex]\texttt{P}[/tex] and the cost of a comic book as [tex]\texttt{C}[/tex]. Then, we can write two equations:
[tex]\texttt{ P + 4C = 11.75}[/tex] (Equation 1) [tex]\texttt{P + 11C = 18.75}[/tex] (Equation 2)To solve these equations, we can use the method of elimination. Let's use this method to eliminate [tex]$$P$$[/tex]:
[tex]\texttt{(P + 11C) - (P + 4C) = 18.75 - 11.75}[/tex][tex]\texttt{7C = 7}[/tex][tex]\texttt{C = 1}[/tex]Now, substituting the value of [tex]\texttt{C}[/tex] back into equation 1:
[tex]\texttt{P + 4(1) = 11.75}[/tex][tex]\texttt{P = 11.75 - 4}[/tex][tex]\texttt{P = 7.75}[/tex]Now that we have the cost of a poster (P) and a comic book (C), we can write the linear function rule as:
[tex]\Large \boxed{\texttt{y = x + 7.75}}[/tex]
[tex]\texttt{y}[/tex] is the total cost of a package [tex]\texttt{x}[/tex] is the number of comic books in the package.Now, suppose another store sells a similar package modelled by a linear function rule with an initial value of $6.99. This means that the cost of a poster at the other store is $6.99. Since the cost of a comic book is the same at both stores ($1), the linear function rule for the other store is:
[tex]\Large \boxed{ \texttt{y = x + 6.99}}[/tex]
Comparing the two linear function rules, we can see that the second store has a better deal because the initial cost of a poster is lower ($6.99) compared to the first store ($7.75).
________________________________________________________
A triangle has side lengths of (9v-7w)(9v−7w) centimeters, (7v+10x)(7v+10x) centimeters, and (8x+5w)(8x+5w) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Perimeter of triangle is P= 18x+16v-2w.
How do triangles work?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a single point.
The triangle's three angles add up to a total of 180 degrees.
.
side lengths of a triangle are (9v-7w),(7v+10x),(8x+5w) centimetres.
We know that perimeter of the triangle is sum of all the three sides.
So here perimeter p= addition of all sides of a triangle.
Therefore ,
P = ( 9v - 7w) + (7v + 10x ) + ( 8x + 5w)
= 9v - 7w + 7v + 10x + 8x + 8w
= 18x + 16v - 2w
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Convert 940 hours into a year Round answer to the nearest hundredth
Answer:
0.41 years
Step-by-step explanation:
940 hours is equivalent to 0.41 years. When rounded to the nearest hundredth, that would be 0.00 years. It is not possible to convert hours directly to years because they are different units of time measurement. Years are a measure of the time it takes for the Earth to orbit around the Sun, while hours are a measure of time within a day. To convert hours to years, you would need to know the number of hours in a year, which can vary depending on the number of days in the year and the number of hours in a day.
Answer:
Hi!
I think the answer you might be looking for is 0.11
I hope this helped you :)
a. 1 /2 + 5 12 greater than 1 less than 1 b. 2 7/8 – 1 7/9 greater than 1 less than 1.
Find the area of the figure.
The area of the figure in the first, second, and third cases will be 76 square ft, 120 square cm, and 87.5 square in, respectively.
What is a trapezoid?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.
The area of the trapezoid will be calculated as,
A = 1/2(sum of parallel sides) x height
8. The area of the figure is calculated as,
A = 1/2 (6 + 6 + 7) x 8
A = 76 square ft
9. The area of the figure is calculated as,
A = 1/2 (8 + 4) x 4 + 8 x 12
A = 24 + 96
A = 120 square cm
10. The area of the figure is calculated as,
A = 1/2 (5 + 10) x 5 + 5 x 10
A = 37.5 + 50
A = 87.5 square in
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HELP ME PLEASE!!!!!!!!!
The length of a cell phone is 1.41.4 inches and the width is 3.43.4 inches. The company making the cell phone wants to make a new version whose length will be 1.541.54 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:7.48521878104
Question 1 of 7 ✓
Question 1
>
The relationship between the amount of time a car is parked, in hours, and the cost of parking, in dollars, can be described with a function. Which
statements about the function are true? Select all that apply.
A
The parking cost is the function of the amount of time the car is parked and for 1 hour the cost of parking is $3 with a maximum amount of $12 for parking. The correct statements are C and D.
What is a function?A function is a relationship between the dependent and independent variables. The independent variables are function inputs, while the dependent variables are function outputs. The value of a dependent variable is determined by the input.
Here in the graph, the cost of parking is varying with time. It means that the cost of parking is dependent on the time of parking but the maximum amount for parking is $12 for any number of hours of car parking.
Hence, the correct statements are C and D.
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make g the subject of 3e+4g=7+9eg
Answer:
the answer is g = (7 - 3e) / (4 - 9e)
Step-by-step explanation:
The subject of an equation is the value or values being solved for. An equation typically consists of two parts: an expression on the left side of an equal sign and an expression on the right side of the equal sign.
The given equation subject of equation is 3e + 4g = 7 + 9eg
Subtraction of 9eg from both sides of the equation
3e + 4g - 9eg = 7 + 9eg - 9eg
3e + 4g - 9eg = 7
Subtract 3e on both sides of the equation
3e + 4g - 9eg - 3e = 7 - 3e
4g - 9eg = 7 - 3e
Factorize g on left side of the equation,
g (4 - 9e) = 7 - 3e
Then divide (4 - 9e) on both sides of the equation,
g = (7 - 3e) / (4 - 9e)
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Jeremy spent a total of $79.16 on a shirt and one pair of jeans. He knows the jeans cost $49.95 but he does not know the cost of the shirt, s. He created the model shown to find the cost of the shirt.
The model to show the cost of the shirt is x+49.95=79.16. Therefore, the cost of shirt is $29.21.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Jeremy spent a total of $79.16 on a shirt and one pair of jeans.
Let the cost of shirt be x.
The jeans cost is $49.95
Now, the cost of shirt + the cost of jeans = Total cost
⇒ x+49.95=79.16
⇒ x=79.16-49.95
⇒ x=$29.21
Therefore, the cost of shirt is $29.21.
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AHH PLEASE HELP I NEED TO HAVE THIS DONE IN 30 MIN AND THIS IS THE QUESTION I NEED HELP WITH I WILL GIVE 95 POINTS AND MARK BRAINLIEST
A linear relationship is given.
The slope of the linear relastionship is ?
The slope of the linear relationship is 15.
Define slope.Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). The slope of a line tangent to a function's graph in differential calculus is determined by the derivative of that function and serves as a representation of the function's instantaneous rate of change with regard to changes in the independent variable. The slope of a tangent line in the graph of a position function, which plots the distance travelled by an object against the passage of time, corresponds to the object's instantaneous velocity.
Given
A linear relationship is given.
y₁ = -9
y₂ = 6
x₁ = 0
x₂ = 1
Slope:
m = y₂ - y₁/x₂ - x₁
m = 6 + 9/1 - 0
m = 15/1
m = 15
The slope of the linear relationship is 15.
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Answer:
Slope = 15
Step-by-step explanation:
Now we have to,
→ find the slope of linear relationship.
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Coordinates we use from table,
→ x1 = 0, y1 = -9
→ x2 = 1, y2 = 6
Then the required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (6 -(-9))/(1 - 0)
→ m = (6 + 9)/1
→ m = (15)/1
→ [ m = 15 ]
Hence, the required slope is 15.
in 12 years a man will be twice as old as he was 12 years ago . find his present age
His present age is 36 years.
Let his present age = x
Given,
2(x − 12) = x +12
2x - 24 = x + 12
2x - x = 12 + 24
x = 36
Therefore, his present age is 36 years.
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A game uses an unbiased die with faces numbered 1 to 6. The die is thrown once. If it shows an even number this number is doubled to get the final score. If an odd number is thrown then the die is thrown again and the final score is the sum of the numbers shown on the two throws.
Given that the dice was thrown twice. What is the probability that the final score is 8
Can you please give me the answer you don’t have to solve all but please!!!!!!
Answer: Reduction: 1/3
Step-by-step explanation:
Remember that if you are dilating it to be larger, it will be a whole number. If it is less than one, then it is dilating to be smaller.
Answer: Reduction 1/3.
Step-by-step explanation: When a shape is transformed into a smaller version of the original, it's a reduction. Reductions are less than 1 so the answer I provided above is what you're looking for.
Have a great day! :)
9. Solve for x.
12x + 3
11x +9
a. x = 9
b. x = 12
C. X = 6
d. x = 23
each student at william elementary can only participate in one fall activity. there are 65 students on the football team and twice that number in band. there are 61 students on each of the two soccer teams. how many students participate in fall activities
Answer:191
Step-by-step explanation:
65x2=130
130+61=191
what is the difference between a squared number and a cubed number
this is the explanation above with some examples
find f(20) if f(x)=[tex]\frac{1}{4}x+5[/tex]
Answer:
f(20) = 10
Step-by-step explanation:
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
Determine the distance between the Trolley Train and the Silly Slide.
25 units
7 units
5 units
3 units
The distance between the Trolley Train and the Silly Slide is 5 units. The 3rd option is the answer
How to determine the distance between the Trolley Train and the Silly Slide?From the map, the coordinate of the Trolley Train is (-2, -6) and the coordinate of the Silly Slide is (2, -3)
The formula for finding the distance between the two points is given as:
d=√(x₂ – x₁)² + (y₂ – y₁))²).
where
x₁ = -2,
y₁ = -6 (Trolley Train)
x₂ = 2
y₂ = -3 (Silly Slide)
d = √((2 – (-2))² + (-3 – (-6))²)
d = √((4)² + (3)²)
d = √25
d = 5 units
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The true statements about the circle are
The radius of the circle is 3 units.The center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. How to determine the true statements about the circle?From the question, we have the following parameters that can be used in our computation:
x² + y² - 2x - 8 = 0
Generally, To convert this equation to standard form, we need to complete the square.
First, we can rearrange the terms on the left-hand side of the equation so that all the x terms are together and all the y terms are together:
x² - 2x + y² - 8 = 0
Then, we need to add and subtract a value that allows us to rewrite x² - 2x term as a perfect square.
To do this, we take half of the coefficient of the x term (which is -2), square it, and add it to both sides of the equation:
So, we have
x² - 2x + (1²) + y² - 8 = 0 + (1²)
Evaluate
(x - 1)² + y² - 8 = 1
Finally, we can rearrange the terms
So, we have
(x - 1)² + y² = 9
Express 9 as the square of 3
(x - 1)² + y² = 3²
So, the standard form of the equation is (x - 1)² + y² = 3²
The standard equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
When these equations are compared, we have
Center = (a, b) = (-1, 0)
Radius = r = 3
The point (-1, 0) lies on the x-axis
This means that the center is on the x-axis.
Also, it means that the radius of the circle is 3 units
This radius is the same for a circle that has the form x² + y² = 9
This is so because 9 can be expresses as the square or 3, and r = 3
Hence, the correct statements are (a), (b) and (e)
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Complete Question
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true?
Select three options.
The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Which expression is equivalent to −6(b − 7)? −6b − 42 −6b + 42 −6b − 7 6b + 7
The expression that is equivalent to −6(b − 7) is: B. -6b + 42.
How to Find Equivalent Expressions?Expressions that are equivalent to each other will give the same value when simplified and solved in their simplest forms.
Simply put, two expressions will be equivalent if they have the same number of terms or they will give the same quantity when you plug in the values of all the variables that are given in the expressions.
Given the expression, -6(b - 7), the steps below shows how we can simplify to determine the expression that is equivalent to it
-6(b - 7) [given]
Open the parentheses by using the distributive property of equality, which involves multiplying each of the terms within the parentheses by the term outside of the parentheses:
-6(b) -6(-7) [distributive property]
-6b + 42
-6b + 42 is the equivalent expression of -6(b - 7).
Thus, the answer is: B. -6b + 42.
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Simplify the fractions, show your work
35/90
3/36
Answer:
Step-by-step explanation:
35/90 gets devided by 5
7/18
3/36 gets devided by 3
1/12
Answer:35/90 = 7/18
3/36=1/12
Step-by-step explanation:
for 35/90 you divide both sides by 5 giving you 7/18 and 3/36 you divde both by 3 giving you 1/12.
Hope this helped
The r in the simple interest formula stands for rate which best describes how to use rate in formula
The best option is to Convert it to a decimal and multiply is the best way to describe rate in simple interest formula. The correct option is A.
What is simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest (S.I.) is a method for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount. The correct option is A.
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Match each theorem with its description.
(3) Isosceles triangle Theorem
(8) Same side Interior angle Theorem
(2) Triangle sum Theorem
(1) Vertical angle Theorem
(7) Alternate exterior angle Theorem
(5)Corresponding angle Postulate
(6)Alternate exterior angle Theorem
(4) Triangle midsegment Theorem
What is isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Isosceles triangle Theorem: A triangle's opposite angles are also congruent if its two sides are.
Same side Interior angle Theorem:
The same side interior angles are additional when two parallel lines are cut by a transversal.
Triangle sum Theorem:
According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
Vertical angle Theorem:
When two straight lines collide, two sets of linear pairs with identical angles are created.
Alternate exterior angle Theorem:
The alternate interior angles or alternate exterior angles that emerge from cutting two parallel lines by a transversal are congruent.
Corresponding angle Postulate:
The related angles are equivalent if a transversal cuts two parallel lines.
Alternate exterior angle Theorem:
The alternate interior angles or alternate exterior angles that emerge from cutting two parallel lines by a transversal are congruent.
Triangle midsegment Theorem:
The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.
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A man spends 70% of his income and craves rs 2580 What is his income? Full explanation please
Answer:
• Statement of the given problem,
⚫ A man spends 70% of his income and saves Rs. 2550. What is his income?
According to above data,
⚫ the required income of the
given man
= 2550/(1 - 70/10)
☐ = 2550/0.30
= 8,500 (Rs) [Ans]
In a school Auditorium, there are three types of rows arrangement
possible for watching programs: rows of 20 students per row, or rows
of 25 students ver row, or rows of 40 students per row. Find the least
number of students required for any one of these arrangements so
that all the students can be accommodated in each of these
arrangements.
I think
it should be 200 as it's the first common multiple of 20 40 and 25
An elected official surveyed residents of a town to assess their satisfaction with city services. the survey includes both those who own and those who rent their homes. level of satisfaction high medium low total owners 26 34 18 78 renters 15 12 5 22 total 41 46 23 110 what proportion of those surveyed have low satisfaction with city services? 0.2091 0.2308 0.2644 0.3727
The proportion we get is 0.291 and that matches up with our first choice that we see.
What is proportion?A proportion simply means the amount or quantity of a thing present in another thing taken as whole.
What are the applications of proportion?The main purpose of stating stuff in proportions is to compare shares. If 2 people receive shares in a 1:1 proportion, it means they have exactly equal shares. If 2 people invest in something and one partner invests $3 for every $2 the other invested, the major partner would expect the profits to be divided 3:2 in their favor.
This issue informs us that a town's residents were polled by an elected official to see how satisfied they were with the town's services. Both homeowners and renters were included in the survey. The following charts show the percentage of respondents that are unsatisfied with city services. In order to calculate the percentage of surveys with low satisfaction, we only need to consider the third column to the right, which is labeled "low satisfaction," and the number we are interested in is the 1, which corresponds to the row labeled "total," because it represents the total number of survey respondents who have low satisfaction, whether or not they are home owners or renters. This number is 23 points.
But that only represents the whole population of those with low levels of satisfaction. We can find the total number of respondents in the cross section between the total column and the total row, giving us 110 points. We wish to multiply that total for the low level by the entire number of respondents. Therefore, if we want that proportion right away, we need divide 23 by 110 points. When we round off to four decimal places, the result is 0.291, which corresponds to our initial option that we see.
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Answer:
A - 0.2091
Step-by-step explanation:
I took it
There are 30 students in Mrs. Woodward's class and 1/5 of the class has their own cell phone. Of the students that have cell phones, 1/2 of them are allowed to use social media. How many of the students have a cell phone and can use social media?
Answer: 3 people
Step-by-step explanation:
1/5 of 30 will give us the number of students.
6
1/2 of 6, will give us the number of people who can use social media.
3 people.
Solve the inequality.
$-12
[140,166,132,165,152,168,181,158,173,180,182,163,177,180,142,147,149,178]
Answer: Mode: 180
Quartiles:
Q1 --> 149
Q2 --> 165.5
Q3 --> 178
Mean: 162.944....
Median: 165.5
Step-by-step explanation:
Find the sum of the finite arithmetic sequence.
Sum of the first 80 positive odd integers
Answer:
6400
Step-by-step explanation:
We have 1 + 3 + 5 + ... + 155 + 157 + 159.
We can use Gauss's strategy.
Since we are adding 80 numbers, there are 40 pairs. Each pair adds up to 1 + 159 = 160. (Notice that 3 + 157, 5 + 155 = 160)
Thus, because there are 40 pairs and each pair adds up to 160, we have 160 * 40 = 6400.
I hope this helps!
PLEASE HELP!
determine the truth value of each conditional.
1. Explain your reasoning or give a counterexample. if a figure has four congruent angles then the figure is a square.
2. if the sidewalks are wet, then it has been raining.
3. Write a biconditional for the following conditional. Determine the truth value of the new statement. If two lines have the same slope, then they are parallel.