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3 years ago

A rectangle with an area of 120 in2 has a length 8 inches longer than two times its width. What is the width of the rectangle

Mathematics

2 answers:

Anni [7]3 years ago

6 0

Answer:

6 inches

Explanation:

Area of a rectangle with length, l and breadth, b = l⋅b

Given l=2b+8 and A=120

Area A = l⋅b=(2b+8)⋅b=2b2+8b=120 =>

2b2+8b−120=0 =>b2+4b−60=0 =>b2+10b−6b−60=0 =>b(b+10)−6(b+10)=0 =>(b−6)(b+10)=0; =>b=6 as b cannot be −10.

Width is 6 inches

Westkost [7]3 years ago

6 0

L x W = 120
L = 2 x W + 8

(2W + 8) x (W) = 120
2W^2 + 8W = 120
W^2 + 4W - 60 = 0
(W+ 10) x (W-6) = 0
W= -10, 6
(( shouldn't be negative, so therefore W = 6 ))

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Sveta_85 [38]

I'll do Problem 8 to get you started

a = 4 and c = 7 are the two given sides

Use these values in the pythagorean theorem to find side b

$a^2 + b^2 = c^2\\\\4^2 + b^2 = 7^2\\\\16 + b^2 = 49\\\\b^2 = 49 - 16\\\\b^2 = 33\\\\b = \sqrt{33}\\\\$

With respect to reference angle A, we have:

opposite side = a = 4
adjacent side = b = $\sqrt{33}$
hypotenuse = c = 7

Now let's compute the 6 trig ratios for the angle A.

We'll start with the sine ratio which is opposite over hypotenuse.

$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(A) = \frac{a}{c}\\\\\sin(A) = \frac{4}{7}\\\\$

Then cosine which is adjacent over hypotenuse

$\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(A) = \frac{b}{c}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\$

Tangent is the ratio of opposite over adjacent

$\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(A) = \frac{a}{b}\\\\\tan(A) = \frac{4}{\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{(\sqrt{33})^2}\\\\\tan(A) = \frac{4\sqrt{33}}{33}\\\\$

Rationalizing the denominator may be optional, so I would ask your teacher for clarification.

So far we've taken care of 3 trig functions. The remaining 3 are reciprocals of the ones mentioned so far.

cosecant, abbreviated as csc, is the reciprocal of sine
secant, abbreviated as sec, is the reciprocal of cosine
cotangent, abbreviated as cot, is the reciprocal of tangent

So we'll flip the fraction of each like so:

$\csc(\text{angle}) = \frac{\text{hypotenuse}}{\text{opposite}} \ \text{ ... reciprocal of sine}\\\\\csc(A) = \frac{c}{a}\\\\\csc(A) = \frac{7}{4}\\\\\sec(\text{angle}) = \frac{\text{hypotenuse}}{\text{adjacent}} \ \text{ ... reciprocal of cosine}\\\\\sec(A) = \frac{c}{b}\\\\\sec(A) = \frac{7}{\sqrt{33}} = \frac{7\sqrt{33}}{33}\\\\\cot(\text{angle}) = \frac{\text{adjacent}}{\text{opposite}} \ \text{ ... reciprocal of tangent}\\\\\cot(A) = \frac{b}{a}\\\\\cot(A) = \frac{\sqrt{33}}{4}\\\\$

------------------------------------------------------

Summary:

The missing side is $b = \sqrt{33}$

The 6 trig functions have these results

$\sin(A) = \frac{4}{7}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\\tan(A) = \frac{4}{\sqrt{33}} = \frac{4\sqrt{33}}{33}\\\\\csc(A) = \frac{7}{4}\\\\\sec(A) = \frac{7}{\sqrt{33}} = \frac{7\sqrt{33}}{33}\\\\\cot(A) = \frac{\sqrt{33}}{4}\\\\$

Rationalizing the denominator may be optional, but I would ask your teacher to be sure.

7 0

1 year ago

6) If 1 Inch = 2.54cm, then set up and solve a proportion that finds how many

Roman55 [17]

Answer:

3.93700787402, almost 4

Step-by-step explanation:

10 ÷ 2.54

3 × 2.50 = 7.50

3 × 0.04 = 0.12

7.50 + 0.12 = 7.65

7.65 + 2.54 = 10.19

The precise number is use calculator.

7 0

3 years ago

Pls help!!!! i have eight more minutes to answer eeeeeeeeee

Sati [7]

Answer: B) 16 units

Step-by-Step Explanation:

As we can observe from the graph,

Length (l) = 5 units
Breadth (b) = 3 units

Perimeter = 2(l + b)

Therefore,
= 2(l + b)
= 2(5 + 3)
= 2(8)
= 2 * 8
=> 16

Perimeter = 16 units

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2 years ago

Please answer 2 3 and 4 thank you have a great day

Fudgin [204]

For number two it’s Milton,Laredo,France Because all you have to do is add the number of water and see which one is bigger and which one is smaller and put them in order

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3 years ago

A skateboard ramp is 40 feet long and rises from the ground at an angle of 33 degrees. How tall is the ramp?

olga_2 [115]

Answer:

The ramp is 21.8 ft tall.

Step-by-step explanation:

If you convert this into a triangle, 40 ft is the hypotenuse, 33° is the angle next to the right angle (on the horizontal line) and we need to find how tall the ramp is, which will be x. It is very helpful to draw a picture.

We will use the sine ratio because, starting from the given degree of 33, we have the hypotenuse value and need to find the value opposite the degree:

$sine=\frac{opposite}{hypotenuse}$