Mayrin has rectangular rug with an area of 36 square feet. The area is represented by the equation f(x)= x2 + 5x – 36 and this rug is 5 feet longer than it is wide. What are the dimensions of the rug?

Answers

Answer 1

Answer:

B)  width = 4 ft

    length = 9 ft

Step-by-step explanation:

Area = 36 ft²

Let width = x

⇒ length = x + 5

Area of a rectangle = width × length

⇒ 36 = x(x + 5)

⇒ x² + 5x - 36 = 0

⇒ x² + 9x - 4x - 36 = 0

⇒ (x² + 9x) + (-4x - 36) = 0

⇒ x(x + 9) - 4(x + 9) = 0

⇒ (x + 9)(x - 4) = 0

⇒ x = -9, x = 4

As distance is positive, x = 4 only

Therefore,

width = x = 4 ft

length = x + 5 = 4 + 5 = 9 ft


Related Questions

In the following figure, the square ABCD is inscribed in the circle centered at point P. What is the area of the circle?

Answers

Answer:

[tex]A_{Circle} \approx 39.24\: units^2[/tex]

Step-by-step explanation:

Square ABCD is inscribed in a circle with center P such that BC = 5 units.

BD will be diagonal of the square as well as diameter of the circle.

[tex]BD = BC\times\sqrt 2[/tex]

[tex]\implies BD = 5\sqrt 2[/tex]

-> Diameter of the circle [tex](d) = 5\sqrt 2[/tex]

-> Radius of the circle [tex](r) = 2.5\sqrt 2=3.535\: units[/tex]

[tex]A_{Circle} =\pi(r)^2[/tex]

[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]

[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]

[tex]\implies A_{Circle} =39.2381465[/tex]

[tex]\implies A_{Circle} \approx 39.24\: units^2[/tex]

Solve for x: √(32^0 + 2/3)=(0.6)^2-3x​

Answers

Step-by-step explanation:

Given: √{32⁰ + (2/3)} = (0.6)²⁻³ˣ

Asked: Find the value of x = ?

Solution: Given that √{32⁰ + (2/3)} = (0.6)²⁻³ˣ

⇛√{1 + (2/3)} = (0.6)²⁻³ˣ

⇛√{(1/1) + (2/3) = (0.6)²⁻³ˣ

⇛√{(1*3 + 2*1)/3} = (0.6)²⁻³ˣ

⇛√{(3 + 2)/3} = (0.6)²⁻³ˣ

⇛√(5/3) = (0.6)²⁻³ˣ

Squaring on both sides then

⇛{√(5/3)}² = {(0.6)²⁻³ˣ}²

⇛√(5²/3²) = {0.6}(²⁻³ˣ)²

⇛√{(5*5)/(3*3)} = {0.6}(²⁻³ˣ)²

⇛5/3 = {0.6}(²⁻³ˣ)²

[[tex]\mathsf{\because}[/tex] (aᵐ)ⁿ = aᵐⁿ]

⇛5/3 = (0.6)²*²⁻³ˣ*²

⇛5/3 = (0.6)⁴⁻⁶ˣ

⇛5/3 = (6/10)⁴⁻⁶ˣ

⇛5/3 = {(6÷2)/(10÷2)})⁴⁻⁶ˣ

⇛5/3 = (3/5)⁴⁻⁶ˣ

⇛(3/5))⁻¹ = (3/5)⁴⁻⁶ˣ

[[tex]\mathsf{\because}[/tex] a⁻ⁿ = 1/aⁿ]

Base are the same, so the exponents must be equal.

[tex]\mathsf{\therefore}[/tex] -1 = 4 - 6x

Shift the number 4 from RHS to LHS, changing it's sign.

⇛-1 - 4 = -6x

⇛-5 = -6x

⇛x = {(-5)/(-6)}

[tex]\mathsf{\therefore}[/tex] x = 5/6

Answer: Hence, the value of x for the given problem is 5/6.

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(3^-2 × 4^-2)^-3 = 12^x In the given expression find the value of x. https://brainly.com/question/25746273?referrer

please help i dont take links or files
What do all of the numbers have in common
1.) 13%
2.) 0.125
3.) 1
----
5
4.) 10%

PLEASE HELP I DONT TAKE LINKS OR FILES AND PLEASE SHOW YOUR WORK

Answers

Answer: They are all less than 1

13% = 0.13 is less than 1

So is 0.125

And so is [tex]\frac{1}{5} = 0.2[/tex]

Same goes for 10% = 0.10

They are all less than 1

(PLS help I’ll give brainliest to whoever can answer right nobody has been able to. )

A company makes piñatas for special events such as birthday parties. One of their piñatas is in the form of a cone-shaped hat. How much space do they have inside the piñata for candy if the piñata is 2 feet tall and 1.5 feet wide? Round to the nearest hundredth.

Answers

Volume of a cone = 3.14 x 0.75^2 x 2/3
= 3.14 x 0.5625 x 2/3
= 1.76625 x 2/3
= 1.1775 = 1.18 feet^3

PLS HELP I am giving 25 points here is the question

A shopkeeper sold 12 bags of potatoes for $2.99 each. He bought the potatoes for $1.90 for each bag what was his total profit

Answers

Find theFind tha amount of profit per bag by subtracting:

2.99 - 1.90 = 1.09

He made $1.09 profit per bag.

Now multiply the profit per bag by the number of bags:

1.09 x 12 = 13.08

Total profit = $13.08 amount of profit per bag by subtracting:

2.99 - 1.90 = 1.09

He made $1.09 profit per bag.

Now multiply the profit per bag by the number of bags:

1.09 x 12 = 13.08

Total profit = $13.08

Sold 12 bags for $2.99 each
Shopkeeper makes $1.09 profit for each bag
1.09 x 12 = 13.08
The shopkeeper makes $13.08 profit.

What is the slop of the line?
5(y+2)=4(x-3)

A. 3/2
B. 2/3
C. 4/5
D. 5/4

Answers

Answer:

c. 4/5

Step-by-step explanation:

Note: Images may not be drawn to scale
Square A'BC V' is a ditation of square ABCD.
What is the scale factor?
Enter your answer in the box
C
Be
7
8
9
11
4
5
6
6
1
2
3
V
:
$
0
*

Answers

Answer:

  1/3

Step-by-step explanation:

The scale factor is the ratio of image lengths to original lengths. For this pair of figures, the scale factor is ...

  A'B'/AB = 2/6 = 1/3

The scale factor is 1/3.

CAN SOMEBODY SOLVE THE PROBLEM IVE BEEN STUCK ON IT I WILL GIVE BRAINIEST


The diameter of a cylinder is 3 yd. The height is 12 yd.Find the volume of the cylinder.

Answers

Answer:

84.78cube.yd

Step-by-step explanation:

Volume of cylinder= πr^2h

3.14 × 1.5 × 1.5 × 1284.78 cube.yd

Solve the equation for x


Answers

Answer:

5x-18=4x+7 ( vertical opposite angle)

5x-4x=7+18

x=25

Constants are numbers without letters attached.
What is the constant in the equation x/2 - 3?


answers:
2
-3

Answers

Answer:

constant = - 3

Step-by-step explanation:

[tex]\frac{x}{2}[/tex] - 3 = [tex]\frac{1}{2}[/tex] x - 3

the number without letters attached is the constant - 3

Answer:

-3

Step-by-step explanation:

The answer is -3 because 2 has a letter attached to it which is x/2 -3 is without a letter.

hope dis helps):

Please help me!!! I don't know!
txcfygvubhjnlkm

Answers

Answer:

See explanation

Step-by-step explanation:

look photo

Can an isosceles triangle be a right triangle? Why or why not?

Answers

Answer: Yes

Step-by-step explanation:

It can have angles of 90 degrees, 45 degrees, and 45 degrees.

Yes, a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.

What is the isosceles triangle?

The Isosceles Right Triangle has one of the angles exactly 90 degrees and two sides, which are equal to each other.

Since the two sides are equal it makes the corresponding angle congruent.

An Isosceles triangle is a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.

Hence, Yes, a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.

Read more on isosceles triangle;

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#SPJ4

Y+1.27=7.23 solve for y

Answers

Answer:

y=5.96

Step-by-step explanation:

You can do a reverse equation and do 7.23 - 1.27 = 5.96

how do i find slope in standard form?

Answers

Answer:

The standard form of a linear equation is Ax + By = C. When we want to find the slope of the line represented by this equation, we have two options. We can put the equation in slope-intercept form and identify the slope that way, or we can use the formula m = -A/B.

Answer:

m = -A/B

The standard form of a linear equation is Ax + By = C.

[tex]hope \: it \: will \: help \: [/tex]

12 , − 7 , − 20 , − 9 , − 5 , 6 , 2 , − 12 , 15 , 16 State the median.

Answers

To find the median, we must order the numbers from least to greatest and find the middle number which will be the median.

     List in order: -20, -12, -9, -7, -5, 2, 12, 15, 16

The number in the middle position is -5 <-- median

Hope that helps!

PLS HELP WILL GIVE BRAINLIEST

Answers

Answer:

y = 1/2x - 1

Step-by-step explanation:

The x value is divided by 2 and then has 1 subtracted from it.

also for future posts, put the question in the title that way people know what you need and can click if they know the answer.

I don't know how to solve this

Answers

Answer:

7

Step-by-step explanation:

List out possible numbers that would add to the answer choices and see which has most possibilities

7

3 + 4

5 + 2

1 + 6

10

5 + 5

4 + 6

11

5 + 6

12

6 + 6

I think the answer is 7. If it’s not, the answer is 10. Sorry if I’m wrong!

What is 8 * 8?
8*8 =
A. 64
B. 24
C. 91
D. 8

Answers

Answer: A. 64

Step-by-step explanation:

8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 64

James has 13. 7 ounces of trail mix. He shares the trail mix equally with his sister. How much trail mix does each person get?
6. 35 oz
6. 85 oz
7. 35 oz
7. 7 oz

Answers

Answer: 6.85 ounces

Step-by-step explanation:

13.7 divide by 2 because he and his sister are sharing the trail mix.13.7 = 2x6=12 so 13-12=1 and bring down the 7 so 2x8=16 17-16=11 so 2x5=10 11-10=1. But don't put 6.851 put 6.85 ounces.

how to multiply and divide decimals with whole numbers

Answers

If this helps: 10 x .5 would be the same as 50% of 10. Also: 40 x .12 would be the same as 12% of 40.

you buy a sandwich for $6.965, a salad for $3.25, and a drink for $1.79. if sales tax is 7%, how much change do you receive from $20 bill, rounded to the nearest cent?

Answers

6.965 + 3.25 + 1.79 = 12.005, now, let's apply a 7% taxation on that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 12.005}}{\left( \cfrac{7}{100} \right)12.005}\implies 0.84035~\hfill \underset{total~bill}{\stackrel{12.005~~ + ~~0.8435}{12.84535}} \\\\\\ 20~~ - ~~12.84535\implies 7.15465~~\approx ~~ \$7.15[/tex]

Consider the function defined by f(x) lnx/x^4 for x > 0 and its graph y = f(x).
The graph of f has a horizontal tangent at point P. Find the coordinates of P.

Answers

Answer:

[tex]\sqrt[4]{e};\frac1{4e}[/tex]

Step-by-step explanation:

The first derivative of [tex]f(x)[/tex] will give, for each x, the slope of the tangent at that specific x. Let's calculate the derivative, applying the quotient rule.

[tex]D(\frac AB) = \frac{A'B-AB'}{B^2}\\f'(x)= \frac1{x^8}[(\frac1x)x^4-(lnx)(4x^3)]=\frac1{x^8}[x^3(1-4lnx)]=\frac{1-4lnx}{x^5}[/tex]

Now, to find the point with an horizontal tangent (called "stationary points"), we set the first derivative equal to 0. Considering that we're working with [tex]x > 0[/tex] we deal only with the numerator.

[tex]1-4lnx = 0 \rightarrow lnx= \frac14\\x=e^\frac14 =\sqrt[4]{e}[/tex]

At this point we Replace the value we found in the equation to find it's y coordinate

[tex]f(\sqrt[4]e) = \frac{ln\sqrt[4]e}{\sqrt[4]e^4}= \frac{\frac14}{e} = \frac1{4e}[/tex]

Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?

The function is decreasing on the interval (0, ∞).
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (0, ∞).
The function is increasing on the interval (–∞, 0).

Answers

Using translation concepts, it is found that the correct statement about h(x) is:

The function is decreasing on the interval (0, ∞).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is:

[tex]f(x) = \sqrt{x}[/tex]

Which is increasing on (0, ∞).

After the translation, the function is:

[tex]h(x) = -2\sqrt{x}[/tex]

It was multiplied by a negative number, which means that it was reflected over the x-axis, and it will be decreasing on the interval (0, ∞).

More can be learned about translation concepts at https://brainly.com/question/4521517

I need the assistance of smarter beings than I..... I'm so lost.....

Answers

Answer:

[tex]\sf \bold{ 1 * (-3)^{n-1}}[/tex]

Explanation:

first term, a₁ = 1

difference between the terms: -3

used geometric formula : [tex]\bold{\sf a_1 * (r)^{n-1}}[/tex]

where "a₁ is first term" and "r refers to common difference"

formula for this nth term: [tex]\sf \bold{ 1 * (-3)^{n-1}}[/tex]

Lita must find the area of the sector enclosed by central angle QCR in circle C.

Points Q and R lie on circle C. The measure of angle Q C R is 74 degrees and the radius of circle C is 1 foot.


What steps should Lita take to correctly solve this problem?

A: Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360∘, so the portion of the area she wants to find is 74∘360∘. Therefore, she must multiply 74∘360∘ times the area, which is πr2.Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360 degrees textsf comma so the portion of the area she wants to find is 74∘360∘. Therefore, she must multiply 74∘360∘ times the area, which is πr2.

B: Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360∘, so the portion of the area she wants to find is 74∘360∘, so she must multiply 74∘360∘ times the area, which is 2πr.Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360 degrees textsf comma so the portion of the area she wants to find is 74∘360∘, so she must multiply 74∘360∘ times the area, which is 2πr.

C: Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360∘, so she should subtract 74∘ from 360∘. The portion of the area she wants to find is 286∘360∘, so she must multiply 286∘360∘ times the area, which is 2πr.Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360 degrees textsf comma so she should subtract 74 degrees from The portion of the area she wants to find is 286∘360∘, so she must multiply 286∘360∘ times the area, which is 2πr.

D: Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360∘, so she should subtract 74∘ from 360∘. The portion of the area she wants to find is 286∘360∘, so she must multiply 286∘360∘ times the area, which is πr2.

Answers

To find the area of the sector, Lita must multiply 74°/360° times the area of the circle, which is πr² (Option A).

What is the Area of the Sector of a Circle?

Area of sector = ∅/360 × πr², where ∅ = central angle, and r = radius of the circle.

Given the following:

∅ = m∠QCR = 74°r = 1 ft.

The area of the circle she wants to find is: 74°/360°.

Since the area of the whole circle is, πr², therefore, to find the area of the sector, Lita must multiply 74°/360° times the area of the circle, which is πr² (Option A).

Learn more about area of sector on:

https://brainly.com/question/22972014

Which of the following notes is G?

Answers

G in bass clef is the answer D!

Can anyone solve this?

Answers

Would it be 40.25????

Answer:

  54 cubic inches

Step-by-step explanation:

Just as the area of a triangle is half the area of a rectangle with the same dimensions, the volume of a triangular prism is half the volume of a rectangular prism with the same dimensions:

  V = 1/2(LWH)

  V = (1/2)(9 in)(4 in)(3 in) = 54 in³

The volume of Phil's block of cheese is 54 in³.

Name the circle
Will give a lot of points!!! ASAP

Answers

Circle KJI center L, radius LK/diamter KI?

Write the following series in sigma notation.
7 + 16 + 25 +34 +43 +52 + 61

Answers

The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series

The sigma notation of the series is: [tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

How to write the series in sigma notation?

The series is given as:

7 + 16 + 25 +34 +43 +52 + 61

The above series is an arithmetic series, with the following parameters

First term, a = 7Common difference, d = 9Number of terms, n = 7

Start by calculating the nth term using:

a(n) = a + (n - 1) * d

This gives

a(n) = 7 + (n - 1) * 9

Evaluate the product

a(n) = 7  - 9 + 9n

Evaluate the difference

a(n) = 9n - 2

So, the sigma notation is:

[tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

Read more about arithmetic series at:

https://brainly.com/question/6561461

Write x=2 in Slope intercept form

Answers

Answer:

y= 2/1 + 0

Step-by-step explanation:

If there's not a y-int. it'll be 0.

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