A portrait has dimensions of 30“ x 60“ and is surrounded by a frame of uniform width. If the total area (Portrait plus frame) is 2584 square inches, find the width of the frame

Answers

Answer 1

Answer:

The width of the is 4 inches

Step-by-step explanation:

Assume that the width of the frame is x

The width of the fame is x inches

→ That means each dimension will increase by 2x ⇒ x from each side

∵ The portrait has dimensions of 30“ x 60“

∴ Its dimensions including the frame = (30 + 2x) × (60 + 2x)

The total area of the portrait plus frame = (30 + 2x)(60 + 2x)

→ Multiply the brackets

∵ (30 + 2x)(60 + 2x) = 30(60) + 30(2x) + 2x(60) + (2x)(2x)

∴ (30 + 2x)(60 + 2x) = 1800 + 60x + 120x + 4x²

→ Add the like terms

∴ (30 + 2x)(60 + 2x) = 1800 + 180x + 4x²

The total area of the portrait plus frame = 4x² + 180x + 1800

∵ The total area of the portrait plus frame = 2584 square inches

→ Equate the two right sides of the area

4x² + 180x + 1800 = 2584

→ Subtract 2584 from both sides

∴ 4x² + 180x + 1800 - 2584 = 0

→ Add the like terms in the left side

∴ 4x² + 180x - 784 = 0

→ Divide all terms by 4 to simplify

x² + 45x - 196 = 0

→ Factorize it to find the value of x

∵ x² + 45x - 196 = (x - 4)(x + 49)

→ Equate the right side by 0

(x - 4)(x + 49) = 0

→ Equate each factor by 0

∵ x - 4 = 0  

→ Add 4 to both sides to find x

x = 4

∵ x + 49 = 0

→ Subtract 49 from both sides to find x

∴ x = -49 ⇒ refused it x can not be -ve (no negative dimensions)

The width of the is 4 inches


Related Questions

which model represents a fraction greater than 3/5? ​

Answers

Answer:

The last one is your answer :))

Step-by-step explanation:

Answer:

Blue circle.

Step-by-step explanation:

I hope it helps, if my answer is correct, please give BRAINLEST!

All swimming equipment is on sale with a 40% discount. A snorkeling set regularly sells for $45. Find the discount.

Answers

The discount is $18 if the all swimming equipment is on sale with a 40% discount. A snorkeling set regularly sells for $45.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

All swimming equipment is on sale with a 40% discount. A snorkeling set regularly sells for $45.

The regular price = $45

The discount is worth = 40% of 45

= (40×45)/100

= $18

Thus, the discount is $18 if the all swimming equipment is on sale with a 40% discount. A snorkeling set regularly sells for $45.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ1

The length of a rectangle exceeds its width by 1
inch and the area is 132 square inches. What
are the length and width of the rectangle?

Answers

Answer:

Width equals 11, and length equals 12.

Step-by-step explanation: It is helpful to memorize your multiplication tables up to 12. I personally couldn't figure out a formula for this, but I knew that 12 x 11 equals 132, and the length is greater than the width, so length is 12 and width is 11. Hopefully somebody else can figure it out. P.S. I meant the formula, not the answer, my answer is correct.

Answer:

[tex]l(l - 1) = 132[/tex]

[tex] {l }^{2} - l - 132 = 0 [/tex]

[tex](l - 12)(l + 11) = 0[/tex]

[tex]l = 12 \: or \: l = - 11[/tex]

[tex]length \: must \: be \: postive[/tex]

[tex]integers[/tex]

[tex]l = 12 \: and \: w = l - 1 = 11[/tex]

plato

Twice a number x minus 18

Answers

Step-by-step explanation:

Here is the answer...

Hope this helps you

Write the equation in slope-intercept form.
- 4x – 10y = -7

Answers

Answer:

The answer will be in the form y=mx+b

y= - [tex]\frac{2}{5}[/tex] x + [tex]\frac{7}{10}[/tex]

Brainliest please

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The equation of -4x - 10y = -7 in slope-intercept form is

y = (-2/5)x + (-7/10)

What is slope intercept form?

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The equation of a line in slope intercept form is given by:

y = mx + c

m = slope

c = y-intercept

We have,

-4x - 10y = -7

Add 4x on both sides.

-4x - 10y + 4x = 7 + 4x

-10y = 7 + 4x

Multiply -1/10 on both sides.

y = -1/10 ( 7 + 4x )

y = -7/10 - (4/10)x

y = (-2/5)x + (-7/10)

Thus the equation of -4x - 10y = -7 in slope-intercept form is

y = (-2/5)x + (-7/10)

Learn more about the equation of a line here:

https://brainly.com/question/21298390

#SPJ2

the sum of the first six terms of a geometric series is 21/16 . if the common ratio is -1/2 , what is the first term?

Answers

Answer:

-84

Step-by-step explanation:

The formula for the nth term of a geometric progression is

Un = ar^n- 1

The sum of the first six terms of a geometric series (U6) = 21/16

Common ratio = -1/2 ,

a = First term ??

21/16 = a × (-1/2 )^6- 1

21/16 = a ×(-2^-1)^5

21/16 = a × -2^-6

Cross Multiply

16 × a × -2^-6 = 21

a = 21/16 × -2^-6

a = 21/16 ×- 1/2⁶

a = 21/16 × -1/64

a = 21 ÷(-1/4)

a = 21 × -4

a = -84

The first term = 84

HELP FAST I NEeD THIS

Answers

Answer:

1. x=7.16304347

2.x=11.2

Step-by-step explanation:

What number divided by 6 leaves a remainder of 5, divided by 5 leaves a remainder of 4, divided by 4 leaves a remainder of 3, and divided by 3 leaves a remainder of 2?

Answers

Answer:

59

Step-by-step explanation:

If a number is divided by [tex]n[/tex] and leaves a remainder [tex](n-1)[/tex], then the number [tex](n+1)[/tex] will be completely divisible by [tex]n[/tex].

Therefore, when we say a number [tex]x[/tex], when divided by 6, it leaves a remainder 5, then ([tex]x+1[/tex]) will be a multiple of 6.

When we say a number [tex]x[/tex], when divided by 5, it leaves a remainder 4, then ([tex]x+1[/tex]) will be a multiple of 5.

When we say a number [tex]x[/tex], when divided by 4, it leaves a remainder 3, then ([tex]x+1[/tex]) will be a multiple of 4.

When we say a number [tex]x[/tex], when divided by 3, it leaves a remainder 2, then ([tex]x+1[/tex]) will be a multiple of 3.

So, [tex]x+1[/tex] is a common multiple of 3, 4, 5 and 6.

Taking LCM of 3, 4, 5 and 6, we get 60.

So, the number 60 - 1 = 59 is the least such number.

Mandy has an annual salary of $37,580. Each month she has a car payment of $265 and a student loan of $120. If she applies for a home loan, how likely is it Mandy will be approved based on her debt-to-income ratio?

Answers

Answer: Not likely; recurring debt is higher than what is allowed.

Step-by-step explanation:

The options are:

a. Very likely; recurring debt is less than what is allowed.

b. Somewhat likely; recurring debt is equal to what is allowed.

c. Not likely; recurring debt is higher than what is allowed.

d. There is not enough information given to determine the answer.

Annual salary = $37,580

Car loan payment annually = $265 × 12 = $3180

Annual student loan= $120 × 12 = $1440

Annual loan payment will be:

= $3180 + $1440

= $4620

Based on the above, Mandy is already paying 12.3% (4620 / 37580)× 100 as loan every month. Coupled with the fact that he'll still have some amount to pay as loan every month, he won't be given as the recurring loan is higher than what will be allowed.

Answer:

c. Not likely; recurring debt is higher than what is allowed.

Step-by-step explanation:

got it right

3x+14=2(2x-3), steps to solve

Answers

Answer:

20

Step-by-step explanation:

3x+14=2(2x-3)

3x+14=4x-6

3x-4x=-6-14

-x=-20

X=20

So the valueof X is 20

please help with this question will give brainlyest if you get it right
the answer choices are
9 and 22/40
9 and 3/28
10 and 22/40
10 and 11/13
please help!!!!!!!

Answers

We need to first make these improper fractions. 5 = 40/8, so 40/8+6/8 = 46/8. Similarly, 4 = 20/5, so 20/5+4/5=24/5.

So we need to find the value of 46/8+24/5. Multiply the first fraction by 5/5 and second fraction by 8/8 to get the same denominator. We get (46*5+24*8)/8*5 = 422/40. This is equal to 400/40 + 22/40 = 10+22/40.

So the third answer choice is correct.

Hope that helped!

Each big square below represents one whole,
What percent is represented by the shaded area?
%

Answers

The first square is 100% and the second square is 55% filled in

Kelly currently has a checking account balance of $172.14. She makes a deposit of $27.45, and then spends $17.89 on dinner. How much money does she have now? *

Answers

Answer:

126.8 Hope this helps

PLEASE HELP WHO KNOWS THIS?

Answers

Answer:

I don't know how you would submit this but I do know it's a transformation. So you would move it across the x-axis 4 or 5 times depending on the shape. So I would maybe just write out each individual number like 3,4,5

Step-by-step explanation:

please help me!!!!!!!!!!​

Answers

Answer:

HFHBEHFBHEHHEHHHHH

Step-by-step explanation:

Question 1 of 60
Find an underestimate for 32 x 67 by adjusting each factor down to the next
ten.
A. 2800
B. 2100
C. 1800
D. 2400

Answers

Answer:

2100

Step-by-step explanation:

30 x 70 = 2100

32 rounds to 30. 67 rounds to 70.

Answer:

[tex]2100[/tex]

Step-by-step explanation:

Estimate:

Change numbers 32 and 67 to the next factor:

[tex]30 and 70[/tex]

Multiply together:

[tex]2100[/tex]

So your answer is B:

[tex]2100[/tex]

2. What number is equal to five units + three tenths? Circle the correct answer.
0.53
0.35
5.3
3.5
53
35

Answers

Answer:

35

Step-by-step explanation:

5*1+3*10

5+30 = 35

what type of angle is 1​

Answers

Answer:

Step-by-step explanation:

A right angle

0.01 is blank times as much as 0.001 please answer i will brainliest ​

Answers

Answer:

100

Step-by-step explanation:

10 times as much

0.001 * 10 = 0.01

Use the power property to rewrite log3x9.

Answers

Answer:

[tex]\log _3\left(x^9\right)=9\log _3\left(x\right)[/tex]

Step-by-step explanation:

Given the expression

[tex]\log _3\:x^9[/tex]

now rewriting the expression

[tex]\log _3\:x^9[/tex]

[tex]\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0[/tex]

[tex]=9\log _3\left(x\right)[/tex]

Therefore,

[tex]\log _3\left(x^9\right)=9\log _3\left(x\right)[/tex]

Answer:

B

Step-by-step explanation:

edge


HELP ME PLEASEE ASAPAPAP PLEASE PLEASE PLEASE PLEASE!!!!!!!!!!!

Answers

Answer: AEC = 80

              X=30

YW ;)

explain BRAINLIEST PLZ HELP!!!!100. Given B(-4,-6), under which reflections is B'(4,6)?
a. reflected in the x-axis
b. reflected in the origin
c. reflected in the y-axis
d. reflected in the line y=x

Answers

Under b. reflected in the origin  B(-4, -6) would be B'(4, 6).

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.

Point B(-4, - 6) is given lies on the third quadrant.

Now, If we reflect along y = x it would be (- 6, - 4).

But if we reflect point B(-4, - 6) along the origin it would be B'(4, 6).

learn more about transformations here :

https://brainly.com/question/20954335

#SPJ1

Which of the following pairs of functions are inverses of each other?

Answers

Answer:

The answer is (B).

Step-by-step explanation:

A). y = f(x) = 6(x - 2) + 3 ⇔ y = 6x - 12 + 3 ⇔ 6x = y + 9 ⇔ x = [tex]\frac{y+9}{6}[/tex]

g(x) = [tex]\frac{x+9}{6}[/tex] is inverse function of f(x) and ≠ [tex]\frac{x+2}{6}[/tex] - 3

B). y = f(x) = [tex]\frac{5x}{4}[/tex] - 3 ⇔ 4y = 5x - 12 ⇔ x = [tex]\frac{4y+12}{5}[/tex]  

g(x) = [tex]\frac{4(x + 3)}{5}[/tex] is inverse of f(x)

1.5.3

6x+7

To solve for the lengths of the right triangle sides, which equation is correct?

A. x² = (4x - 1)² + (6x + 7)?

B. x2 +(6x + 7)2 = (4x - 1)2

c. x² = (4x - 1)² – (6x + 772

D.x² + (4x - 1)2 = (6x + 7)?

4x-1

To solve for the lengths of the right triangle sides, equation is correct.

(Type A, B, C, or D.)

Answers

Answer:

A. [tex]x^2 = (4x - 1)^2 + (6x + 7)^2[/tex]

Step-by-step explanation:

The question seems to be incomplete. However, we'll make the following assumption.

[tex]Opposite = 6x + 7[/tex]

[tex]Adjacent = 4x - 1[/tex]

[tex]Hypothenuse = x[/tex]

Pythagoras theorem states that:

[tex]Hypothenuse^2 = Opposite^2 + Adjacent^2[/tex]

Substitute values for Hypothenuse, Opposite and Adjacent.

This gives

[tex]x^2 = (6x + 7)^2 + (4x - 1)^2[/tex]

or

[tex]x^2 = (4x - 1)^2 + (6x + 7)^2[/tex]

From the list of given options.

A answers the question

Will mark as brainliest if correct!

Answers

Answer:

the answer is A

Step-by-step explanation:

48/50 x 100% = 96% of student wearing tennis shoes

100% - 96% = 4% students not wearing tennis shoes

HELP FAST ITS AN IMAGE

Answers

Answer:

3

Step-by-step explanation:

the answer is 3 because there are three units between each point of the triangle!

Five less than the area of a square is 59 square feet. Find the side length of the square.​

Answers

Answer:

4 feet

Step-by-step explanation:

Let the side length of the square be x feet.

x^2 - 5 = 59

x^2 = 64

x = ±4 (reject - 4 since length > 0)

Topic: Areas of polygons

If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

Let the function f be defined by f(x) = 12 -5x


4. Is it true that f(0) = 0?


5. Explain why or why not?

ILL MARK YOU BRAINLIEST if you answer xx

Answers

4. It is not true
5. This is because if you substitute f(0) the equation would be f(x) = 12-0 or f(x) = 12
Hope this helps, if it does can I get brainliest ?

4+4
[tex]4 + 4[/tex]

Answers

Answer:

4+4 = 8.

Step-by-step explanation:

Or 44, depends on whether you're trolling. XD

Hope this helped...

[tex] \huge \: Your \: answer \: is \: 8[/tex]

helpppppp pleaseeeee

Answers

Answer:

A: 24

B: 40.04

Step-by-step explanation:

A=L*W

8*3=24

5.2*7.7=40.04

part a is 8(3)=24 units² and part b is 5.2(7.7)=40.04 units²
Other Questions
Find the variable :4t + 5.25 = 35.25 Order the following integers from least to greatest -25,-41,36,28,and16 SOMEONE PLZ HELP ME WITH THIS?!?!? What does r-a-c-e mean How to do this question plz answer me 1. Adjacent angles are two angles in the same plane with a commonand a commonbut no common interior points. Which item most likely symbolizes danger?O A. A lightning stormB. A lightbulbO C. A four-leaf cloverO D. A snake In 1792 the radicals took control of the Assembly, abolished the monarchy, and A.) Rejected the constitutional governmentB.) Declared France a republicC.) Surrendered to the Prussian ArmyD.) Ended the war with the other nations of Europe why did Naacp support lawsuits against public institutions such as university of oklahoma? how did these lawsuits realated to the issue of intergation Who are most likely the suspects Steve refers to in the following passage (Paragraph 24)?STEVE. Go ahead, whats my wife said? Lets get it all out. Lets pick out every idiosyncrasy of every man, woman, and child on the street. And then we might as well set up some kind of kangaroo court. How about a firing squad at dawn, Charlie, so we can get rid of all the suspects? Narrow them down. Make it easier for you.A. Neighbors who appear different from other neighborsB. Criminals who have been caught in the neighborhoodC. City officials that control the neighbors lightsD. A family that moves into a new house paragraph on water cycle Recent research by Ravizza and colleagues suggests that students may spend as much as one-typical class hour browsing the internet.halfthirdfifthquarterNeed help on this question? Help me ASAP please Solve the system of equations algebraically.5x - 3y = 66x - 4y = 2a. many solutionsC.no solutionb. (8, 14d. (9. 13)Please select the best answer from the choices provided A skier rides horizontally off of a 200 meter high cliff. If he lands 25 meters away from the base of the cliff, how fast was he skiing as he went off the edge?A. 0.91 m/sB. 2.91 m/sC. 3.91 m/sD. 25.91 m/s write the short note on durable and non durable materials Two cards are drawn in succession from a standard 52-card deck.1. What is the probability that the first card is red and the second card is black(A) If the cards are drawn without replacement?(B) If the cards are drawn with replacement?2. Two balls are drawn in succession out of a box containing 3 red and 5 white balls. Find the probability that at least 1 ball was red, given that the first ball was(A) Replaced before the second draw(B) Not replaced before the second drawContext Header: Conditional ProbabilityContext Section:Conditional Probability is a calculation of the likelihood of an occurrence provided that another event has already occurred. Conditional probability A provided B is generally written as:P(A/B)=P(AB)P(B) Isabel company offers other programs and incentives to help employees with their savings and expenses. To be tilted to the side is? in art/dance class You have been mowing grass in the hot sun and perspiring heavily, and depletion of liquids from your body has made you very thirsty. This state of arousal is referred to as: a. an incentive. b. homeostasis. c. a need. d. a drive.