A museum curator needs to frame a rectangular painting. The painting is 30 inches by 17 inches. If the frame has a width of x on all sides, what is the quadratic function that models the area of the painting and frame?

Answers

Answer 1

Answer:

(30 + 2x) * (17 + 2x)

Step-by-step explanation:

Dimension of painting = 30 by 17 inches

Width of frame on all sides = x

Painting and frame takes the shape of a rectangle :

Area of rectangle = Length * Width

Area of painting = (30 * 17)

Area of frame ;

Length = (x + x) = 2x ;

Width = (x + x) = 2x

Area of frame = 2x * 2x

Equation for the Area of painting and frame :

(30 + 2x) * (17 + 2x)


Related Questions


Landen's front lawn measures 20 feet by 80 feet. He counts to find that there are
120 blades of grass per square inch. How many blades of grass are in the entire
lawn?

Answers

Answer:

[tex]27,648,000[/tex]

Step-by-step explanation:

The area of a rectangle is given by [tex]l\cdot w[/tex]. Landen's 20 feet by 80 feet front lawn therefore has an area of [tex]20\cdot 80 = \fbox{$1600\: \mathrm{ft^2}$}[/tex].

He counts there are 120 blades of grass per square inch. There are [tex]12^2=144[/tex] square inches in one square foot.

Therefore, his lawn has an area of [tex]1600\: \mathrm{ft^2}\cdot \frac{144\:\mathrm{in^2}}{1\:\mathrm{ft^2}}=230,400\:\mathrm{in^2}[/tex].

Thus, there are [tex]230,400\:\mathrm{in^2}\cdot 120=\fbox{$27,648,000$}[/tex] blades of grass in the entire lawn.

PLEASE HELP I WILL GIVE BRAINLEIST PLEASE ALSO SHOW STEPS!!!!!!
Write the equation of a line that passes through the point (-1,5) and has a slope of -7. Your answer should be given in the form y = mx + b

Answers

Answer:

The equation of a line that passes through the point (-1,5) and has a slope of -7 will be:

y = -7x-2

Step-by-step explanation:

The slope-intercept form of the line equation

[tex]y = mx+b[/tex]

where

m is the slopeb is the y-intercept

Given

The point (-1, 5)Slope m = -7

substituting m = -7 and the point (-1, 5) in the slope-intercept form of the line equation

[tex]y = mx+b[/tex]

5 = -7(-1) + b

5 = 7+b

b = 5-7

b = -2

Thus, the y-intercept is: b = -2

now substituting b = -2 and m = -7 in the slope-intercept form of the line equation

y = mx+b

y = -7x+(-2)

y = -7x-2

Therefore, the equation of a line that passes through the point (-1,5) and has a slope of -7 will be:

y = -7x-2

Suppose translating triangle ABC by 5 units to the right and 5 units down results in a new triangle A'B'C. Which statements are
correct?

Answers

Answer: ABC

Step-by-step explanation:

I took it

Answer:

A) segments AB is parallel to segment A’B’.

B) A and A’ have the different coordinates.

C) <C and <C’ have the same measures.

Step-by-step explanation:

Which equation represent a circle with a center at (2,-7) and a radius of 4 units ?

Answers

Answer:

[tex] {(x - 2)}^{2} + {(y + 7)}^{2} = 16[/tex]

Step-by-step explanation:

[tex] {(x - 2)}^{2} + {(y + 7)}^{2} = 16[/tex]

An airplane is flying from knoxville to new york. The distance it travels in miles, d, is related to the time in seconds, t, by the equation: d=0.12t. How many miles is it flying per second?

Answers

Answer:

0.12 miles is it flying per second.

Step-by-step explanation:

The distance d is related to time t in seconds is given by the equation as follows :

d =0.12 t

We need to find how many miles is it flying per second.

[tex]\dfrac{d}{t}=0.12\\\\\dfrac{\text{miles}}{\text{second}}=0.12[/tex]

So, the speed of the airplane is 0.12 miles per second, Hence, 0.12 miles is it flying per second.

A shipping box has the dimensions shown 1/4 1/4 and 1/2, What is the volume of the box in cubic yards.

First 3 people get a brainly

Answers

Step-by-step explanation:

what is the unit of measurement for the 1/4, 1/4, and 1/2?

The diagram shows a trapezoid prism.
The area of the cross-section is 55cm.
The volume of the prism is 330cm
Find the length of the prism.​

Answers

Given:

The area of the cross-section is 55cm².

The volume of the prism is 330cm³.

To find:

The length of the prism.​

Solution:

We have,

Area of the cross-section = Area of base = 55 cm²

Volume of the prism = 330cm³.

Let x be the length(height) of the prism.

We know that,

[tex]\text{Volume of prism}=\text{Base area}\times height[/tex]

[tex]330=55\times x[/tex]

[tex]\dfrac{330}{55}=x[/tex]

[tex]6=x[/tex]

Therefore, the length of the prism is 6 cm.

What number should go in the space?
Multiplying by 0.76 is the same as decreasing by ____%.

Answers

Answer:

76%

Step-by-step explanation:

Do turn decimals into percentages you just gotta multiply by 100.

0.76×100=76

Answer:

24

Step-by-step explanation:

HELP: The table shows the relationship between x, the number of hours driven
and y, the total miles traveled. Find the value of y when x is 5.

Answers

I’m pretty sure the answer is 270 when x is 5

Pleasee helpp with this
!:))

Answers

Answer:

[tex]x=42[/tex]

Step-by-step explanation:

Use this to remember the trigonometry ratios:

SOH-CAH-TOA

Because:

Sine=Opposite/Hypotenuse → SOH

Cosine=Adjacent/Hypotenuse → CAH

Tangent=Opposite/Adjacent → TOA

Use the inverse of the tangent ratio since you need to find the angle measure.

:D Tehe

Answer:

x approximately equals 42.0

Step-by-step explanation:

give other person brainliesttt

. The sum of two consecative integers is three times of their difference. what is the
smoller number
3
2
4
1​

Answers

Answer:

The smallest number is 1

Step-by-step explanation:

1+2=3

2-1=1

1•3=3

21
Select the correct answer.
Which will help you when you file a claim for home insurance?
A.
home loan
B.
home budget
C.
home inventory
Reset
Next

Answers

Answer:

Home inventory lol

Step-by-step explanation:

Convert the following repeating decimal to a fraction in simplest form.
.27

Answers

27/100 would be simplest form

y=6x + 100

help i don’t know this
what is the rate of change for this equation

Answers

Answer:6

Explanation: the slope (6) is the same thing as rate of change

ABCD is a parallelogram. Find the value of x, y, w, and z.

Answers

Answer:

Summary:

The value of x = -14The value of y = 18The value of w = 14The value of z = 14

Step-by-step explanation:

Given

The parallelogram ABCDAD = x-28BC = 3xAB = 12CD = 2/3y

We know opposite sides of a parallelogram are equal.

Therefore,

AD = BC AB = CD

now subtitute AD = x-28 and BC = 3x in AD = BC

AD = BC

x-28 = 3x

switch sides

3x = x-28

subracting x from both sides

3x-x = x-28+x

2x = -28

divide both sides by 2

2x/2 = -28/2

x = -14

Therefore,

The value of x = -14

Now subtitute AB = 12 and CD = 2/3y in AB = CD

AB = CD

12 = 2/3y

switching sides

2/3y = 12

y = 3/2 × 12

y = 18

Therefore,

The value of y = 18

We also know that the opposite angles of a parallelogram are equal.

Therefore,

5w = 70°

divide both sides by 5

5w/5 = 70°/5

w = 14

Therefore,

The value of w = 14

We know that the sum of the measures of the adjacent angles of a parallelogram is 180°.

Here,

m∠B = 70°.

m∠A = (3w+2z)°

As m∠B is adjacent to m∠A.

so

m∠A + m∠B = 180°

so substituting m∠B = 70° and m∠A = (3w+2z)° in the equation

70° + (3w+2z)° =  180°

now substituting w = 14 in the equation

70° +  (3(14) + 2z)° = 180°

70° + (42+2z)° =  180°

70° + 42 + 2z = 180°

112 + 2z = 180°

2z = 180° - 112

2z = 68

divide both sides by 2

2z/z = 68/2

z = 34

Therefore,

The value of z = 14

Summary:

The value of x = -14The value of y = 18The value of w = 14The value of z = 14

Which ordered pair is not a solution to the equation y = 2x?

Answers

Answer:

Step-by-step explanation:

Y=1/2y

A House needs to some maintenance one sink is dripping water every 10 minutes and the other sink is dripping every 12 minutes if both sink dripped at the same time how many minutes until they both drip at the same time again

Answers

Answer:

60 minutes

Step-by-step explanation:

We solve this question using Lowest Common Factor method

Find and list multiples of each number of minutes( 12 and 10 minutes) until the first common multiple is found. This is the lowest common multiple.

Multiples of 10:

10, 20, 30, 40, 50, 60, 70, 80

Multiples of 12:

12, 24, 36, 48, 60, 72, 84

Therefore,

LCM(10, 12) = 60

The number if minutes until they both drip again is 60 minutes

marking Brainlist 7-9g+3g

Answers

Answer:

7-6g

Then you do the 1 step equation.

Divide both sides by 6.

1.16=g

I'm not sure if it's right.

Which of the following is the equation of the line shown graphed below?

Answers

Answer:

Is the 4

Step-by-step explanation:

pls i need help what is 1 plus 1?

Answers

1+1 = 84, explanation is quite simple. i should get brainliiest

I would really appreciate it if someone could help and explain too, please

Answers

Answer:

A. $101/month

Step-by-step explanation:

From January to February, it changes by 195

From February to March, it changes by -72

From March to April, it changes by 180.

Now, you just find the average of these three numbers.

195 - 72 + 180 = 303

303 / 3 = 101

This means that the answer is A. $101/month

PLEASE ANSWER I WILL MARK AS BRAINLIESTTTTTT
Simplify the expression by combining like terms.

43a−12b+13a+52b
Enter your answer as an expression, like this: 42x+53

Answers

Answer:

56a + 40b

Step-by-step explanation:

hope this helps!

Answer: 56a + 40b

Step-by-step explanation:

43a - 12b + 13a + 52b

Bring like terms together

43a + 13a - 12b + 52b

Combine like terms

56a + 40b

Hope that helped!

The sum of two consecutive integers is 471.

what is the equation

Answers

Answer:

x+(x+1)=471

Step-by-step explanation:

By leading figure estimation, approximate the value of 5 850÷22

Answers

265.9090909090909 is the answer

I NEED ANSWERS TO THESE QUESTIONS IT WAS DUE 5 mins ago and i have TILL 8:30 TO GET THEM DONE SOMEONE HELP A GIRL OUT

Answers

6. A

7. C

8. C

9. B

-FWEW

It took 4 hours to drive 240 miles. At this rate, how long does it take to drive 150 miles?

Answers

Answer:

The correct answer is 11/2.

Answer:2 hours and 30 minutes

Step-by-step explanation:

they drive 60 miles in a hour.

You buy a house that costs $345,000. You put down a downpayment of 20%. You borrow the rest from the bank, who charges an annual interest rate of 4.6%. If you pay this back in 30 years, how much did the house cost you in total? A=p(1+rt) format

Answers

Answer:

Total cost of the house = $725,880

Step-by-step explanation:

This can be calculated as follows:

Down payment = $345,000 * 20% = $69,000

Amount borrowed = $345,000 * (100% - 20%) = $276,000

The total amount of loan repaid can be calculated using the following formula:

A = p(1  + rt) .................... (1)

Where;

A = Total amount of loan repaid = ?

p = Principal or amount borrowed = $276,000

r = annual interest rate = 4.6% = 0.046

t = number of years = 30

Substitute the values into equation (1), we have:

A = $276,000 * (1  + (0.046 * 30)) = $656,880

The total cost of the house can now be calculated as follows:

Total cost of the house = Down payment + Total amount of loan repaid = $69,000 + $656,880 = $725,880

A square was altered so that one side is increased by 9 inches in the other side is decreased by 2 inches. The area of the resulting rectangle is 6o in 2 what was the area of the

Answers

Answer:

area of the original square = 36 in²

Step-by-step explanation:

given data

one side is increased = 9 inches

other side is decreased = 2 inches

area of the resulting rectangle = 60 in²

solution

we consider here x as the length of any one side

and

longer side of the resulting rectangle = x + 9

and

the shorter side x - 2

so that area of this rectangle is (s+9) × (s-2) = 60 in²

standard form of equation is  x² + 7x - 18 = 60   .....................1

it will be

x² + 7x - 78 = 0

(s+13) (s-6) = 0

so that here x  = -13

and  x = 6

here we Discard x = -13 because the side length cannot be negative.

so x = 6

and area of the original square = 36 in²

Given g(x) = -5x + 5, solve for 2 when g(x) = -10

Answers

Answer:

Set up the composite function and evaluate.

g(−5x+5)=25x−20

Step-by-step explanation:

Show if 2 is a SOLUTION or NOT a SOLUTION to the equation 0.5(x + 0.8) = 1.4

Answers

Step-by-step answer:

0.5(x+0.8)=1.4

0.5x+0.4=1.4

0.5x+0.4-0.4=1.4-0.4

0.5x=1

0.5x/0.5=1/0.5

x=2

Plzzzzz give me Brainliest!!!!!  

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