Suppose that a rectangular picture is surrounded by a frame of uniform width of x
inches as depicted below. The dimensions of the picture are 8 inches (width) by
10 inches (length). Find a simplified expression that represents the area of the
picture and frame.
Type your simplified answer for the area of the picture and frame along with your
work in the box below. To receive any partial credit, you must include all your work.

Answers

Answer 1

Answer:

Ok so the area of the frame is 18*12 = 216cm^2

Let’s suppose the width of the frame is x

The total area (painting and frame) is (2x+18)(2x+12) and this is equal to 432

4x^2 + 60x + 216 = 432

4x^2 + 60x - 216 = 0

x^2 + 15x - 54 = 0

(x+18)(x-3) = 0

Therefore x = {-18,3}

Since width of the frame has to be positive, the width has to be 3cm Step-

i hope i helped!


Related Questions

A math class consists of 26 students, 14 women, 10 men, and 2 non-binary. Two students are selected at random to participate in a probability experiment. Compute the probability that:

Answers

Answer:

there's a higher probability for females

Kumar is opening a lemonade stand. He spent $4.50 to build the stand and $2.50 for lemons and sugar. He has enough ingredients to make 20 glasses of lemonade. How much should he charge for one glass of lemonade to cover his expenses and make $10 in profit?

Round to the nearest cent.

Timed test

Answers

Answer:

profit = revenue - cost

10 = 20x - (4.5 + 2.5)

10 = 20x - 7

10 + 7 = 20x

17 = 20x

17/20 = x

0.85 = x

check...

profit = revenue - cost

10 = 20(0.85) - 7

10 = 17 - 7

10 = 10 (correct)

so he would have to sell each cup at 0.85 ccents to make a profit of $ 10

Step-by-step explanation:

Answer:

I cant find the next one hehrh

Which coordinate pair is a solution of the linear
equation below?
-X + 3y = 21
Click on the correct answer.
(3,-8)
(-3,8)
(3,8)

Answers

Answer:

slope is 4/3 and y intercept is -7

Step-by-step explanation:

3y+21=4x.........now subtract 21 from each side

3y=4x-21......now divide all terms by 3

y=%284%2F3%29x-7......there ya go ...slope is 4/3 and y intercept is -7

Answer:

B (-3,8)

Step-by-step explanation:

awnser A is incorrect because if you switch out the x for 3 and the y for -8. The equation would look like -3+3×(-8)=21. and after multiplying 3×-8 which equals -24. The equation turns into -3+(-24)=21 . And after adding -3 and -24 you get -27=21

awnser B is correct because if you switch out the x for -3 and the y for 8. The equation would look like -3+3×8=21. After multiplying 3×8 which equals 24. The equation turns into -3+24=21. And after adding -3and 24 which is pretty much subtracting you get 21=21.

Best apologies if incorrect

Martha earns $24 in four hours. How much would she
earn in 10 hours?

Answers

Answer:

$60

Step-by-step explanation:

24/4=6

6*10=60

Answer:

$60

Step-by-step explanation:

24 ÷ 4 = 6

6 × 10 = 24

she makes $6 an hour. $60 in ten hours.

HELP ME PLEASE I ALREADY GRAPHED IT BUT PLEASE ANSWER THE QUESTION BELOW


Answers

Answer:

32ed

Step-by-step explanation:

A dentist sees a patient every 20 minutes. He works an average of 60 hours per week. How many patients does he see in a year. He takes 3 weeks vacation. Round your answer down.

Answers

Answer:

1040

Step-by-step explanation:

a pizzeria had 4 cans of tomato sauce how many pizzas could they make with the cans if each pizza took one fourth of a can​

Answers

Answer:

16 pizzas.

Step-by-step explanation:

That is 4 divided by 1/4

= 4 * 4/1

= 16.

Answer:

16

Step-by-step explanation:

There are 4 pizzas per can and you have 4 cans.

4 x 4 = 16

Which point represents the opposite of –2?

A number line going from negative 5 to positive 5. Point A is at negative 2, point B is between negative 1 and 0, point C is between 0 and 1, and point D is at 2.
A
B
C
D

Answers

Answer:

Point D

Point D is at 2, the absolute value of -2.

2 is the opposite of -2, and D is at 2.

So, the answer must be option D.

Hope this helps!

Answer:

d

Step-by-step explanation:

The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years.

Required:
a, What was the initial population P0?
b. How fast is the population growing at t = 10?

Answers

Step-by-step explanation:

Let the initial population of a community be P0 and the population after time t is P(t).

If the population of a community is known to increase at a rate proportional to the number of people present at time t, this is expressed as:

[tex]P(t) = P_0e^{kt}[/tex]

at t = 5 years, P(t) = 2P0

substitute:

[tex]2P_0 = P_0e^{5k}\\2 = e^{5k}\\ln2 = lne^{5k}\\ln2 = 5k\\k = \frac{ln2}{5}\\k = 0.1386[/tex]

If the population is 9,000 after 3 years

at t = 3, P(t) = 9000

a) Substitute into the formula to get P0

[tex]9000 = P_0e^{0.1386\times 3}\\9000 = P_0e^{0.4158}\\9000 = 1.5156P_0\\P_0 = \frac{9000}{1.5156}\\ P_0 = 5938.24[/tex]

Hence the initial population is approximately 5938.

b) In order to know how fast the population growing at t = 10, we will substitute t = 10 into the formula as shown:

[tex]P(10) = 5938.24e^{0.1386(10)}\\P(10) = 5938.24e^{1.386}\\P(10) = 5938.24(3.9988)\\P(10) = 23,745.97[/tex]

Hence the population of the community after 10 years is approximately 23,746

I need help with this ASAP !! I’m failing !!!

Answers

Answer:

c=130,b=50

Step-by-step explanation:

[tex]c = 180 - 50 = 130[/tex]

[tex]b = 180 - 130 = 50[/tex]

i think this is the answer

Intro:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

<b and 50° are vertical angles so that means they are congruent.  So that means <b is 50.

<c and 50° are supplementary angles which means when you add them you should get 180. So if do 180 - 50 we will get 130. So that means <c is 130°.

3. Determine if the graph below is a function.
Explain your reasoning.

Answers

Answer:

A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. "x causes y"), but does not *necessarily* exist.

Step-by-step explanation:

point Q was rotated about the origin (0,0) by 180

Answers

Answer:B

Step-by-step explanation:

The coordinates of the image of the rotation of the point Q is:

Q' = (4, 2)

What is the image of the rotation?

We can see that the original coordinates of point Q are (-4, 0).

If we apply a rotation of 180° about the point (0, 0), it is equivalent to a reflection around the y-axis.

It only changes the sign of the x-component.

Then the image of the rotation is:

Q' = (4, 0)

If you want to learn more about rotations:

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If the points P(5,2),Q(0,7) and R(-5,2) are drawn on coordinate plane,where must point S be located so that figure PQRS is square.

Answers

Answer:

(0, -7) i think

hope this helps :3

sorry if im wrong

how many times can 130 go into 22? DIVIDE

Answers

130 cannot go into 22.

22 can go into 130 5 times

130 can not go into 22 idk if u meant 22 into 130

What is m<KNL?
Enter your answer in the box

Answers

The measurement of ∠KNL   is 102°

First, you must set up an equation to find x.

[tex]5x+2=[3(x+14)[/tex]

Then, you must simplify both sides of the equation.

[tex]5x+2=3x+42[/tex]

Next, subtract 3x on both sides.

[tex]2x+2=42[/tex]

Then, subtract 2 on each side.

[tex]2x=40[/tex]

Next, divide 2 on each side.

[tex]x=20[/tex]

Now that we have the value of x, we can substitute it in for angle KNL.

[tex][3(20+14)][/tex]

[tex][3(34)][/tex]

[tex]102[/tex]

[tex]102[/tex]°

How many pounds are in 80 kilograms? Round your answer to the nearest whole number. Note: There are approximately 2.2lbs in a kg.

Answers

Answer:

176.37 orrrr 176

Step-by-step explanation:

Answer:

176 pounds

Step-by-step explanation:

Which of the following is equal to the opposite of −45?

−|45|
−|−45|
−(−45)
−45








Which of the following statements does not represent the same value as the others?

the absolute value of 9
the absolute value of negative 9
the opposite of 9
the distance between 0 and −9











All of the following are true statements except _____.

|−93| = −93
|−93| = 93
−|93| = −93
|93| = 93













If you move from zero to 15 on the number line, you are representing all of the following except _____.

the absolute value of 15
the distance between zero and 15
the opposite of −15
the opposite of 15














All of the following expressions are equal to N except _____.

−(− N )
− N
| N |
|− N |

Answers

Answer:

The first one

Step-by-step explanation:

1. -(-45)
2. “The opposite of 9”
3. -93
4. “ the opposite of 15”
5. -N

ANSWER ONE PLS :(

Beyonce’s fish tank holds 180 gallons of water and is leaking at a rate of 8 gallons per day. Jay Z’s fish tank holds 160 gallons of water and is leaking at a rate of 6 gallons per day. At how many days will the two fish tanks have the same amount of water in them?

Justin Bieber’s sand castle is 180cm tall but the wind is blowing away sand at a rate of 8cm per minute. Taylor Swift’s sand castle is 160cm tall and she it adding sand to it at a rate of 6cm per minute. After how many minutes will their sand castles be the same height?

Answers:
1) 160 + 8x = 180 + 6x

2) 160 + 6x = 180 - 8x

Answers

The fish tank problem:

x = # of days

180 - 8x = 160 - 6x

Add 8x to both sides and subtract 160 from both sides.

20 = 2x

Divide both sides by 2

10 = x

It will take 10 days for the fish tanks to have the same amount of water in them.

The sand castle problem:

x = # of minutes.

180 - 8x = 160 + 6x

Add 8x to both sides and subtract 160 from both sides.

20 = 14x

Divide both sides by 14

x = 10/7 mins

After 10/7 mins their sand castles will be the same height

Convert 2 days into months. Round your answer to the nearest hundredth.

Answers

Answer:

0.0657534

Step-by-step explanation:

divide 2 by 30.417

7) Order the numbers from least to greatest.
A. 6.66
B. 6.07
C. 7
D. 6.32

Answers

the Answear is B,D,A,C

1. Darla's piggy bank is full, so she plans to empty out all of the coins, roll as many as possible to deposit

into her savings account, and put the remaining coins back into the piggy bank. Rolls of pennies and

dimes consist of 50 coins each, while rolls of nickels and quarters consist of 40 coins each.

(9 points: Part 1 - 2 points; Part II - 2.5 points; Part III - 2 points; Part IV - 2.5 points)

Part II: How much will Darla deposit into her savings account?

U.S.)

Answers

Answer:

The number of coins is missing, so I looked for a similar question:

Darla counted 472 pennies, 319 nickels, 436 dimes, and 271 quarters

Darla can make:

9 rolls of pennies (worth $4.50)

7 rolls of nickels (worth $14)

8 rolls of dimes (worth $40)

6 rolls of quarters (worth $60)

total amount of money = $118.50

If a polygon is a pentagon, then it has 5 sides hypothesis conclusion

Answers

Answer:

Hypothesis

 

Step-by-step explanation:

 a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.

hope this helps

The sum of two consecutive numbers is 253. Which of the following equations
describes this situation?
A) 3n-1= 253
D) 2n+2= 253
B) 2n+1= 253
E) n+2= 253
C) 2n= 253

Answers

Answer:

EEEEEEEEEEEEEEEEEEEEEEEEEEE

Step-by-step explanation:

EEEEEEEEEEEEEEEEEEEEEEEEE

The situation is a linear equation, and the equation that describes the situation is 2n + 1 = 253

How to determine the equation of the situation?

Let the smaller number be n.

So, the consecutive numbers are n and n + 1

When the numbers are added, we have:

Sum = n + n + 1

This gives

Sum = 2n + 1

The sum is 253.

So, we have:

2n + 1 = 253

Hence, the equation that describes the situation is 2n + 1 = 253

Read more about linear equations at:

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which direction would the graph of y=|x+5|-1 open?

a. down
b.up
c.right
d.left ​

Answers

The answer fam is.......... "b.up"

According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123]


Compute the probability that a randomly selected peanut M&M is not yellow.


Compute the probability that a randomly selected peanut M&M is brown or red.


Compute the probability that three randomly selected peanut M&M’s are all brown.


If you randomly select three peanut M&M’s, compute that probability that none of them are blue.


If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

P(brown) = 12% = 0.12

P(Yellow) = 15% = 0.15

P(Red) = 12% = 0.12

P(blue) = 23% = 0.23

P(orange) = 23% = 0.23

P(green) = 15% = 0.15

A.) Compute the probability that a randomly selected peanut M&M is not yellow.

P(not yellow) = P(Yellow)' = 1 - P(Yellow) = 1 - 0.15 = 0.85

B.) Compute the probability that a randomly selected peanut M&M is brown or red.

P(Brown) or P(Red) :

0.12 + 0.12 = 0.24

C.) Compute the probability that three randomly selected peanut M&M’s are all brown.

P(brown) * P(brown) * P(brown)

0.12 * 0.12 * 0.12 =0.001728

D.) If you randomly select three peanut M&M’s, compute that probability that none of them are blue.

P(3 blue)' = 1 - P(3 blue)

P(3 blue) = 0.23 * 0.23 * 0.23 = 0.012167

1 - P(3 blue) = 1 - 0.012167 = 0.987833

If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.

P(1 blue) + p(2 blue) + p(3 blue)

(0.23) + (0.23*0.23) + (0.23*0.23*0.23)

0.23 + 0.0529 + 0.012167

= 0.295067

Vanessa and Tia buy a printer. Vanessa pays $90 for her printer and each replacement ink cartage cost $25. The equation T=80+20c can be used to find the total cost, T, Tia pays for her printer plus C number of ink cartridges. Who buys the less expensive printer

Answers

Answer:

Vanessa, she only needs to buy one ink cartridge according to the question

where Tia has to buy more? I need more info on the question

Step-by-step explanation:

Tia bought less expensive printer.

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Vanessa and Tia buy a printer. Vanessa pays $90 for her printer and each replacement ink cartage cost $25. The equation T = 80 + 20c can be used to find the total cost, T, Tia pays for her printer plus C number of ink cartridges.

Equation that represents the cost for Vanessa's printer is -

V = 90 + 25c

Equation that represents the cost Tia's printer is -

T = 80 + 20c

For {c} = 1, the cost for Vanessa's printer is -

V(1) = $115

For {c} = 1, the cost for Tia's printer is -

T(1) = 80 + 20 = $100

Therefore, Tia bought less expensive printer.

To solve more questions on algebraic expressions, visit the link below -

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the measure of an angle is 79.7 what is the measure of its complementary angle

Answers

Answer:

10.3

Step-by-step explanation:

Answer:

10.3°

Step-by-step explanation:

complementary angles are angles that sum up to 90°.

Therefore the complement of 79.7

= 90-79.7

=10.3°

Round 24.9652 to
1 decimal Place​

Answers

Answer:

2.5 one decimal rounding off means to make it to one decimal place.the no is 24.9652 if you want to round of then you have to put decimal after 2 only then it will be one decimal place .this is because when we see a number after the point greater than 5 then we add 1 to the right side .now if we add 1 to the right side of 24.9652 by rounding off and making it to one decimal place then it will be 2.5.

Use substitution to solve the following systems of equations:
-3x -4y = 2
5x + 5y = -5
O (4,3)
O (-3, 2)
O (3, 2)
O (-2, 1)

Answers

The answer is (-2,1)

2x + 7 = 13
Please help

Answers

Answer:

x=3

Step-by-step explanation:

Hope this helps u..

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