The area of the opening of a rectangular window is to be 120 square feet. If the length is to be 2 feet more than the width, what are the dimensions

Answers

Answer 1

Answer:

Width = 10ft

Length = 12ft

Step-by-step explanation:

For a rectangle of length L and width W, the area is calculated as:

A = L*W

In this case, we know that:

The area is 120 ft^2.

The length is 2 ft more than the width.

Then we can write:

L = W + 2ft.

If we use these two equations and replace them in the equation for the area of a rectangle, we get:

A = 120ft^2 = W*L = W*(W + 2ft)

120ft^2 = W*(W + 2ft)

Now we can solve this for W

120 ft^2 = W^2 + 2ft*W

Now we can rewrite this as:

W^2 + 2ft*W - 120ft^2 = 0

The solutions of this equation can be found by the Bhaskara's formula.

We know that for an equation of the form:

a*x^2 + b*x + c = 0

The two solutions are given by:

[tex]x = \frac{-b +\sqrt{b^2 - 4*a*c} }{2*a}[/tex]

in our case, we have:

a = 1

b = 2ft

c = -120ft^2

Then the solutions for the equation W^2 + 2ft*W - 120ft^2 = 0 are:

[tex]W = \frac{-2ft + -\sqrt{(2ft)^2 - 4*1*(-120ft^2)} }{2*1} = \frac{-2ft +- 22ft}{2}[/tex]

Then the two solutions are:

W = (-2ft - 22ft)/2 = -12ft  (this is a negative measure, does not have a real meaning in this case, so this solution can be discarded)

The other solution is:

W = (-2ft + 22ft)/2 = 10ft  (this is the correct solution)

Then the width is 10ft, and we know that the length is 2 ft longer than the width, then the length is:

L  = W + 2ft = 10ft + 2ft = 12ft


Related Questions

Please help me with this I really need it my grades are trash. Look at the file attached. just tell me which ones are equivalent thanks!

Answers

Answer:

Top left, top right, bottom right

Step-by-step explanation:

Combine all of them together. I'll use the top left and middle left as my example. We will need to end up with 2 positive x's, 5 negative y's and the number 3.

x + x - y + 1 + 1 + 1 - y - y - y -y

We can see here there are 2 positive x's, 5 negative y's, and the number 3.

If we were to write that into an equation it would be 2x - 5y +3

With the middle left we have

-5y - x -x + 2 + 1

Here we have 2 negative x's, 5 negative y's, and the number 3.

If this were simplified it would be -2x - 5y + 3. We don't want the 2x to be negative therefore it is incorrect.

I kinda need I’ll give you 100 points

Answers

Answer:

the second one makes more sense

Answer:

This question answer is defenetily answer B ( there is a slight association between hieght and weight)

Step-by-step explanation:

Because of how the number line is set up I do believe your answer will be B  Just remember the way the number line is set up when you put the number line there and how the dots of where the number line goes plays a huge part in finding your answers. :)

Hope this helps!!!!!!!!! :)

Please I really need help!

Answers

Answer:

26 if we not adding then -12

Step-by-step explanation:

6. 10 X 10 X 10
exponent form:
word form:

Answers

Answer:

the exponent is 10 ^ 3 and the word form is ten times ten times ten

Step-by-step explanation:

if you need more help just ask

A window is in the form of a rectangle capped by a semicircle. The width of the rectangular portion is equal to the diameter of the semicircle. If the total perimeter of the window is 20 feet, what is the maximum possible area of the window

Answers

Answer:

The answer is below

Step-by-step explanation:

Let x be the diameter of the semicircle. radius = x/2

The window is a combination of a rectangle and semicircle.

Width of window = diameter = x, let length of the window = y.

Perimeter of semicircle = πr = πx/2

Perimeter of window = x + y + y + πx/2

20 = x + 2y + πx/2

2y + x + πx/2 = 20

2y = 20 - x(1 - π/2)

y = 10 - x(1 - π/2)/2

Area of semicircle = (1/2)πr² = (1/2)π(x/2)²

Area of window = xy + (1/2)π(x/2)²

A = x(10 - x(1 - π/2)/2) + πx²/8

A = 10x - x² - πx²/4 + πx²/8

A = 10x - x² - πx²/8

The maximum area is at dA / dx = 0

dA / dx = 10 - 2x - 2πx/8

0 = 10 - 2x - πx / 4

2x + πx / 4 = 10

2.785x = 10

x = 3.59 feet

Maximum area = 10x - x² - πx²/8 = 10(3.59) - 3.59² - π(3.59²) / 8

Maximum area = 17.95 feet²

history on our 50% of 32 less than a hundred greater than 100 but less than 150 or greater than 150 ​

Answers

Answer:

I'm not sure I understand this. elaborate a bit more and I can help tho :)

Which tables shows a proportional relationship between X and Y.

Answers

Answer:

the secound option :)

What is the area of an rectangle with sides lengths of 5/12 foot and 2/3 foot​

Answers

Answer:

The area of given rectangle is 5/18 square feet.

Step-by-step explanation:

Let l be the length of rectangle and w be the width of the rectangle.

Given information is:

Length = l = 5/12 foot

Width = w = 2/3 foot

The area of a rectangle is given by the formula

[tex]Area = Length*Width\\A = l*w[/tex]

Putting the values for width and length

[tex]A = \frac{5}{12} * \frac{2}{3}\\= \frac{10}{36}\\=\frac{5}{18}[/tex]

The area is 5/18 square feet.

Hence,

The area of given rectangle is 5/18 square feet.

please help me i am stuck trying to figure this out ​

Answers

I believe the answer is C

I think it is C I hope that it

The total area of the polygon is 176 square feet. Find the value of x.

Answers

Answer:

x = 6 ft

Step-by-step explanation:

Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3

Area of triangle 1 = Area of triangle 3 = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                                              = [tex]\frac{1}{2}(x)(8)[/tex]

                                                              = 4x square feet

Area of rectangle 2 = Length × Width

                                 = 16 × 8

                                 = 128 square feet

Total area of the given polygon = 4x + 128 + 4x

176 = 8x + 128

8x = 176 - 128

x = [tex]\frac{48}{8}[/tex]

x = 6 ft

Answer:

The answer is six to one of the sides

Step-by-step explanation:

Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3

Area of triangle 1 = Area of triangle 3 =

                                                             =

                                                             = 4x square feet

Area of rectangle 2 = Length × Width

                                = 16 × 8

                                = 128 square feet

Total area of the given polygon = 4x + 128 + 4x

176 = 8x + 128

8x = 176 - 128

x =

x = 6 ft

1. Solve using polynomial long division x? - 4x² + 2x + 5 Divide: X-2​

Answers

Answer : x^2 - 4x^2 - 2x^2 + 3

Please help easy maths and quick. Please explain the answer first or last and make sure to say the answer is: Or something like that

Answers

Answer:

15

Step-by-step explanation:

Answer is 15 becouse these two degrees are equal

60 - 45 = 15

the answer is 15 x - 15

please answer number 3. what does the y int mean in the context of this problem?

Answers

Answer:

ıts increase

Step-by-step explanation:

help me please thanks

Answers

I think b ! I’m not sure tho

Which pair of sides in this shape are parallel? R S P T RS and ST RS and PT QR and QP QR and ST​

Answers

Answer:

RS and PT

Step-by-step explanation:

Judging by looks, RS and PT are going the exact same direction, and look like they don't touch. Also, if RSTP is a square, then those two are definitely parallel.

Solve for x:
1 ½ - ( 5/6x + ⅓ ) = 8/9

Answers

Answer:

its x=1/3 :)))

Help please! This is timed!

Answers

Answer: 14

Step-by-step explanation:

think of it like a right triangle

a²+b²=c²

13²+5²=194

ladder length= √194= 13.92≈14

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 150 engines and the mean pressure was 6.3 pounds/square inch (psi). Assume the population variance is 0.49. If the valve was designed to produce a mean pressure of 6.2 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications?

Answers

Answer:

We are given that The valve was tested on 150 engines and the mean pressure was 7.7 lbs/square inch.

We are also given that the valve was designed to produce a mean pressure of 7.6 lbs/square inch

So,  

Null hypothesis:  

Alternate hypothesis :  

Since n > 30 and population standard deviation is given

So, We will use z test

Formula :  

Substitute the values

refer the z table for p value

so, p value is 0.9927

Since it is a two tailed test So, p = 2(1-  0.9927) = 0.0146

α = 0.1

p value< α

So, we reject null hypothesis

Hence There is  sufficient evidence at the 0.1 level that the valve does not perform to the specifications

Step-by-step explanation:

No, there is insufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Step-by-step explanation:

We are given that an engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 170 engines and the mean pressure was 7.5 pounds/square inch (psi). Assume the population variance is 0.36 and the valve was designed to produce a mean pressure of 7.4 psi.

We have to test if there sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Let, NULL HYPOTHESIS, H_0H

0

: \muμ = 7.4 psi {means that the valve perform to the specifications}

ALTERNATE HYPOTHESIS, H_1H

1

: \mu\neqμ

= 7.4 psi {means that the valve does not perform to the specifications}

The test statistics that will be used here is One-sample z-test;

T.S. = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }

n

σ

X

ˉ

−μ

~ N(0,1)

where, \bar X

X

ˉ

= sample mean pressure = 7.5 psi

\sigmaσ = population standard deviation = \sqrt{Variance}

Variance

= \sqrt{0.36}

0.36

= 0.6

n = sample of engines = 170

So, test statistics = \frac{7.5-7.4}{\frac{0.6}{\sqrt{170} } }

170

0.6

7.5−7.4

= 2.173

Now, at 0.02 significance level z table gives critical value of 2.3263. Since our test statistics is less than the critical value of z so we have insufficient evidence to reject null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the valve perform to the specifications and there is not sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

can somebody help me with these, i will mark you brainliest :)

Answers

Answer:

1). sin 30°=5/x

1/2=5/x

x=10

2)sin 30°=y/18

1/2=y/18

y=9°

cos 30°=x/18

√3/2=x/18

x=93

3) option D is correct

because cosine ratio is base / hypotenuse.

4) option c is correct.

PERIMETER OF A RECTANGLE
1.5m height
2.0m width

Answers

THE ANSWER IS:
THE PERIMETER IS 3.5 :) have a nice night or day

Answer:

7.0m

Step-by-step explanation:

=2h ×2w

=2(1.5m)+2(2.0m)

=7.0m

Which equations passes through point (5, 1) with an x-intercept of 4?
O y=x-4
O y = 5x + 1
Oy - 4x + 1
O y = x + 5

Answers

It is the first one

What fraction below is NOT equivalent to 1/5? *

5/25

2/10

3/8

4/20

3/4 _______ 9/12 *


=

In the problem, 156 divided by 12 = 13, what number is the "divisor?" *

156

12

13

The fractions 4/7 and 12/21 are equivalent fractions. *

True

False

What is the "difference" between 73.51 and 6.392? *

What is the "product" of 30 and 6? *

36

24

180

5

What is 4 2/5 written as an improper fraction? *

18/5

11/5

22/5

42/5

1/9 _______ 1/12 *


=

What fraction below is NOT a proper fraction. *

7/4

4/7

6/11

8/9

The fractions 2/16, 3/24, and 4/32 are ALL equivalent to what fraction? *

1/3

1/4

1/6

1/8

Giving Brainliest, It'll mean much if you'll try to help me with this! And correct me if i'm wrong but, Brainliest is VERY usefull! And yeah good luck! :D

Answers

1.3/8 I THINK
2.12
3.True
4.67.118
5. 180
6. 22/ 5
7. 7/4
8.1/8

I hope It'll help you!

I GIVEEEEEEEEEEEEEE BRAINLILSTTT

Answers

Answer:

(x,y) → (x -3, y-8)

Step-by-step explanation:

jsienzis

The size of a cylinder changes with time. If r increases at the rate of 2 cm/min and h decreases at the rate of 7 cm/min, at what rate is the volume changing at the instant when r

Answers

Answer:

The volume of the cylinder with time is increasing approximately at a rate of 16.493 cubic centimeters per minute.

Step-by-step explanation:

The statement is incomplete: The size of a cylinder changes with time. If r increases at the rate of 2 cm/min and h decreases at the rate of 7 cm/min. ¿At what rate is the volume changing at the instant when r = 1 cm and h = 7 cm?

The volume of the cylinder ([tex]V[/tex]), measured in cubic centimeters, is expressed by the following formula:

[tex]V = \frac{\pi}{4}\cdot r^{2}\cdot h[/tex] (1)

Where:

[tex]r[/tex] - Radius, measured in centimeters.

[tex]h[/tex] - Height, measured in centimeters.

The rate of change of the volume ([tex]\frac{dV}{dt}[/tex]), measured in cubic centimeters is obtained by deriving (1) in time:

[tex]\frac{dV}{dt} = \frac{\pi}{2} \cdot r\cdot h\cdot \frac{dr}{dt} + \frac{\pi}{4}\cdot r^{2}\cdot \frac{dh}{dt}[/tex] (2)

Where:

[tex]\frac{dr}{dt}[/tex] - Rate of change of the radius, measured in centimeters per minute.

[tex]\frac{dh}{dt}[/tex] - Rate of change of the height, measured in centimeters per minute.

If we know that [tex]r = 1\,cm[/tex], [tex]h = 7\,cm[/tex], [tex]\frac{dr}{dt} = 2\,\frac{cm}{min}[/tex] and [tex]\frac{dh}{dt} = -7\,\frac{cm}{min}[/tex], then the rate of change of the volume is:

[tex]\frac{dV}{dt} = \frac{\pi}{2}\cdot (1\,cm)\cdot (7\,cm)\cdot \left(2\,\frac{cm}{min} \right) + \frac{\pi}{4}\cdot (1\,cm)^{2}\cdot \left(-7\,\frac{cm}{min} \right)[/tex]

[tex]\frac{dV}{dt} \approx 16.493\,\frac{cm^{3}}{min}[/tex]

The volume of the cylinder with time is increasing approximately at a rate of 16.493 cubic centimeters per minute.

Find the average rate of change for the given function over the indicated values of x. If necessary, round your final answer to two decimal places.


f(x)=x^2+6x, where x goes from 5 to 7.

Answers

Answer:

The average rate of change of the function in this interval is of 18.

Step-by-step explanation:

The average rate of change of a function [tex]f(x)[/tex] in an interval from a to b is given by:

[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]

In this question:

[tex]f(x) = x^2 + 6x[/tex]

Where x goes from 5 to 7.

This means that [tex]b = 7, a = 5[/tex]. So

[tex]f(7) = 7^2 + 6(7) = 49 + 42 = 91[/tex]

[tex]f(5) = 5^2 + 6(5) = 25 + 30 = 55[/tex]

The rate of change is:

[tex]A = \frac{f(7) - f(5)}{7 - 5} = \frac{91 - 55}{2} = 18[/tex]

The average rate of change of the function in this interval is of 18.

The rate of change of a function over a given interval is required.

The average rate of change is 18

Rate of change

The given function is

[tex]f(x)=x^2+6x[/tex]

The interval is between [tex]x=5[/tex] to [tex]x=7[/tex]

Finding the corresponding [tex]y[/tex] values

[tex]y=5^2+6\times 5=55[/tex]

[tex]y=7^2+6\times 7=91[/tex]

The two points are

[tex](5,55),(7,91)[/tex]

The slope is

[tex]m=\dfrac{\Delta y}{\Delta x}\\\Rightarrow m=\dfrac{91-55}{7-5}\\\Rightarrow m=18[/tex]

Learn more about rate of change:

https://brainly.com/question/8728504

Determine whether the following is an example of a sampling error or a non sampling error.

12% of all people are left handed. A researcher randomly selected 200 people and found that 16% of them were left handed. No mistakes were made in the data collection or data recording. The 4% difference is due to ...

Answers

Answer:

Sampling Error

Step-by-step explanation:

We are told that 12% of all people are left handed.

Now, from the sampling done, we are told that 16% of them were left handed.

This is a 4% difference.

However, we are told that no mistakes were made in the data collection or data recording.

This means that it is likely the error came from the fact that the 200 people sampled didn't reflect the total population because the 12% reflects the true population.

Thus, this is clearly a sampling error.

Solve log x = 2 by changing it to exponential form.
a. X = -20
C. X=20
B x=10^2
D x=2^10

Answers

Answer:

Option B

Step-by-step explanation:

log x=2

x = 10^2

Therefore, the exponential form is the one in option B

Answer:

B

Step-by-step explanation:

Convert to Exponential Form log of x=-2. log(x)=−2 log ( x ) = - 2. For logarithmic equations, logb(x)=y log b ( x ) = y is equivalent to by=x b y = x such that x>0 x

if ⅚ of a certain number is -6⅔. what is the number?​

Answers

The answer would be -3 4/3

Step-by-step explanation:

ok ok ok ok I'm very sorry if i get it wrong at least I tried on this app most of the people don't even do the homework they do it to cheat.

Answer:

Dan and Paul share some money in the ratio 13:5.

Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.

How much did Paul originally have

HELLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

What is the distance between (3, 5.25) and (3, –8.75)?
6 units
8.25 units
11.75 units
14 units

Answers

Answer:

14

Step-by-step explanation:

Answer:

D 14

Step-by-step explanation:

ILL MARK BRAINLIST , PLS HELL

Answers

Answer:

All the four steps are correct

Step-by-step explanation:

All the four steps are correct

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