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1 year ago

A building in a city has a rectangular base. The length of the base measures 75 ft less than three times the width. The

Mathematics

1 answer:

MariettaO [177]1 year ago

7 0

The dimensions of the rectangular base of the building with the given perimeter are 120ft and 285ft.

<h3>What are the dimensions of the rectangle base?</h3>

The perimeter of rectangle is expressed as;

P = 2( l + w )

Given the data in the question;

Let x represent the width of the rectangular base.

Width w = x
Length = l = 3x-75
Perimeter P = 810ft

Plug these values into the equation above.

P = 2( l + w )

810 = 2( (3x-75) + x )

810 = 6x - 150 + 2x

810 = 8x - 150

8x = 810 + 150

8x = 960

x = 960/8

x = 120

Hence,

Width of the rectangle = x = 120ft

Length of the rectangle = 3x-75 = 3(120) - 75 = 285ft

Therefore, the dimensions of the rectangular base of the building with the given perimeter are 120ft and 285ft.

Learn more about rectangles here: brainly.com/question/17043956

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kumpel [21]

Answer:

see the explanation

The graph in the attached figure

Step-by-step explanation:

we have

$y=3x+4$

This is a linear equation (the graph is a line)

The y-intercept is the point (0,4) ---> value of y when the value of x is equal to zero)

The x-intercept is the point (-4/3,0) ---> value of x when the value of y is equal to zero)

The slope is m=3

If the slope is changed to m=1/3

we have

$y=(1/3)x+4$

This is a linear equation too (the graph is a line)

The y-intercept is the point (0,4) ---> is the same

The x-intercept is the point (-12,0) ---> the x-intercept is different

The slope is m=1/3

The second line becomes a lot less steep

Remember that the slope is the ratio between the rise and the run

In the first line the ratio rise/run is 4/1

In the second line the ratio rise/run is 1/3

see the attached figure to better understand the problem

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2 years ago

Pls helpppppp thanks!!!!!!!<br> :)

Lena [83]

Answer:

If i did this right the answer would be 69

I converted the inches to feet (might be my first mistake)

so i get 2.5 X 1 X 1 to get 2.5

i then multiply that by 62.4 to get 156

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Step-by-step explanation:

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2 years ago

If using the method of completing the square to solve the quadratic equation

lara [203]

Answer:

x² + 7x + 10 = 0

Subtract 10 from both sides

x² + 7x = -10

Use half the x coefficent (7/2) as the complete the square term

(x + 7/2)² = -10 + (7/2)²

note: the number added to "complete the square" is (7/2)² = 49/4

(x + 7/2)² = -10 + 49/4

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x + 7/2 = ±3/2

Subtract 7/2 from both sides

x = -7/2 ± 3/2

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2 years ago

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Find the length of the third side. If necessary, write in simplest radical<br> form.<br> 8<br> 17

statuscvo [17]

Answer:

Step-by-step explanation:

so we know that its a right triangle and 8 and $\sqrt{17}$ are not the hypotenuse.

the equation for this is $a^{2}$ + $b^{2}$ = $c^{2}$ with c being the hypotenuse.

$8^{2}$ + $\sqrt{17} ^{2}$ = $c^{2}$

64+17= $c^{2}$

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2 years ago

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Construct a 95% confidence interval for the population mean, µ. Assume the population has a normal distribution. A sample of 25

bixtya [17]

Answer:C. (77.29, 85.71)

Step-by-step explanation:

We want to determine a 95% confidence interval for the mean test score of randomly selected students.

Number of sample, n = 25

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Standard deviation, s = 10.2

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

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= mean +/- z ×standard deviation/√n

It becomes

81.5 +/- 1.96 × 10.2/√25

= 81.5 +/- 1.96 × 2.04

= 81.5 +/- 3.9984

The lower end of the confidence interval is 81.5 - 3.9984 =77.5016

The upper end of the confidence interval is 81.5 + 3.9984 =85.4984

Therefore, the correct option is

C. (77.29, 85.71)

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