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Rama09 [41]
3 years ago
8

The amount of money and dollars that it cost to purchase x square feet of the carpet is given by f(x)= 8x the insulation feet is

$125 more than 8% of the cost of the carpet right function of g that represents the insulation fee then use the function to find the insulation fee for 175 square feet of carpet
Mathematics
1 answer:
nadezda [96]3 years ago
7 0

Answer:

The insulation fee for 175 square feet of carpet is $237.

Step-by-step explanation:

The amount of money, f(x), that it cost to purchase x square feet of the carpet is:

f(x)= 8x

The insulation fee,g(x), is $125 more than 8% of the cost of the carpet,f(x), we have

g(x)=8% of f(x)+125

\Rightarrow=\frac{8}{100}\times (8x)+125

\Rightarrow=0.64x+125

The insulation fee for 175 square feet of carpet,

i.e for x=175

g(x=175)=0.64\times175+125=237

Hence, the insulation fee for 175 square feet of carpet is $237.

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Answer:

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Step-by-step explanation:

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What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)
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Solve 8.2 w less-than-or-equal-to 29.52. Which of the following must be true about the inequality and the resulting graph? Selec
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A, B, E

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Can someone please explain how to do this!!!
DedPeter [7]

Hi there!

So we are given that:-

  • tan theta = 7/24 and is on the third Quadrant.

In the third Quadrant or Quadrant III, sine and cosine both are negative, which makes tangent positive.

Since we want to find the value of cos theta. cos must be less than 0 or in negative.

To find cos theta, we can either use the trigonometric identity or Pythagorean Theorem. Here, I will demonstrate two ways to find cos.

<u>U</u><u>s</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>I</u><u>d</u><u>e</u><u>n</u><u>t</u><u>i</u><u>t</u><u>y</u>

\large \displaystyle{ {tan}^{2}  \theta + 1 =  {sec}^{2}  \theta}

Substitute tan theta = 7/24 in.

\large \displaystyle{ {(  \frac{7}{24}) }^{2}  + 1 =  {sec}^{2} \theta }

Evaluate.

\large \displaystyle{ \frac{49}{576}  + 1 =  {sec}^{2}  \theta} \\  \large \displaystyle{ \frac{625}{576}  =  {sec}^{2}  \theta}

Reminder -:

\large \displaystyle{ sec \theta =  \frac{1}{cos \theta} }

Hence,

\large \displaystyle{ \frac{576}{625}  =  {cos}^{2}  \theta} \\  \large \displaystyle{ \sqrt{ \frac{576}{625} }  = cos  \theta} \\  \large \displaystyle{ \frac{24}{25}  = cos \theta}

Because in QIII, cos<0. Hence,

\large \displaystyle \boxed{ \blue{cos \theta =  -  \frac{24}{25} }}

<u>U</u><u>s</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>P</u><u>y</u><u>t</u><u>h</u><u>a</u><u>g</u><u>o</u><u>r</u><u>e</u><u>a</u><u>n</u><u> </u><u>T</u><u>h</u><u>e</u><u>o</u><u>r</u><u>e</u><u>m</u>

\large \displaystyle{ {a}^{2}  +  {b}^{2}  =  {c}^{2} }

Define c as our hypotenuse while a or b can be adjacent or opposite.

Because tan theta = opposite/adjacent. Therefore:-

\large \displaystyle{ {7}^{2}  +  {24}^{2}  =  {c}^{2} } \\  \large \displaystyle{49 + 576 =  {c}^{2} } \\  \large \displaystyle{625 =  {c}^{2} } \\  \large \displaystyle{25 = c}

Thus, the hypotenuse side is 25. Using the cosine ratio:-

\large \displaystyle{cos \theta =  \frac{adjacent}{hypotenuse}}

Therefore:-

\large \displaystyle{cos \theta =  \frac{24}{25} }

Because cos<0 in Q3.

\large \displaystyle \boxed{ \red{cos \theta =  -  \frac{24}{25} }}

Hence, the value of cos theta is -24/25.

Let me know if you have any questions!

8 0
2 years ago
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