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3 years ago

Find the value of the variable.

Mathematics

1 answer:

Artist 52 [7]3 years ago

8 0

Answer:

x=8

base side of isosceles triangle

y=√{8²+8²}=8√2

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its 76 degrees fahrenheit at the 6000-foot level of a mountain, and 49 degrees Fahrenheit at the 12000-foot level of the mountai

brilliants [131]

$T = \frac{-9}{2}x + 103$ is the linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet.

<em><u>Solution:</u></em>

The linear equation in slope intercept form is given as:

T = cx + k ------ (i)

Where "t" is the temperature at an elevation x

And x is in thousands of feet

<em><u>Given that its 76 degrees fahrenheit at the 6000-foot level of a mountain</u></em>

Given, when c = 6 thousand ft and $T = 76^{\circ}$ fahrenheit

This implies,

From (i)

76 = c(6) + k

76 = 6c + k

⇒ k = 76 - 6c ----- (ii)

<em><u>Given that 49 degrees Fahrenheit at the 12000-foot level of the mountain</u></em>

Given, when c = 12 thousand ft and $T = 49^{\circ}$ fahrenheit

This implies,

From (i)

49 = c(12) + k

49 = 12c + k

Substitute (ii) in above equation

49 = 12c + (76 - 6c)

49 = 12c + 76 - 6c

49 - 76 = 6c

6c = -27

$c = \frac{-9}{2}$

Substituting the value of c in (ii) we get

$k = 76 - 6( \frac{-9}{2})\\\\k = 76 + 27 = 103$

Substituting the value of c and k in (i)

$T = \frac{-9}{2}x + 103$

Where "x" is in thousands of feet

Thus the required linear equation is found

5 0

3 years ago

Gabriel wants to paint the model. How

enyata [817]

Answer:

<h2>The area of the base is 144 square inches.</h2><h2>The area of each triangular face is 66 square inches.</h2><h2>Grabiel needs 408 square inches of paint.</h2>

Step-by-step explanation:

The complete problem is attached.

Notice that the figure is a square pyramid, where its base dimensions are 12 inches by 12 inches, which represents an area of

$B=12 \times 12 = 144 \ in^{2}$

The slant height of the pyramid is 11 inches, which allow us to find the area of each triangle face

$A=\frac{1}{2}bh =\frac{1}{2}(12)(11)= 66 \ in^{2}$

But there are four triangle faces, so $A_{faces} =4(66)=264 \ in^{2}$ .

Therefore, the area of each triangular face is 66 square inches.

So, the total surface area would be the sum

$S=144+264=408 \ in^{2}$

Therefore, Gabriel needs 408 square inches to paint the whole model.

4 0

3 years ago

PLEASE SOLVE DUE RIGHT NOW!!!!!!!!!!!!

erma4kov [3.2K]

Solution:

$Area \ of \ triangle = \dfrac{1}{2} \times Base \times Height$

<em>Since we are already given the base and the height, we can substitute them into the formula to find the area of the triangle.</em>

$Area \ of \ triangle = \dfrac{1}{2} \times 18 \times24$

<u>Cancel out the "2" by dividing it by 18.</u>

$Area \ of \ triangle = 9 \times24$

<u>Simplify the multiplication.</u>

$\bold{Area \ of \ triangle = 216 \ ft^{2}}$

6 0

2 years ago

I am having trouble with number 2. Please show how the answer was gotten.

Andrews [41]

We know how we got 90, since a right angle is 90 degrees,

180 degrees are in a triangle.

180-90=90

Find the pair that equals 90 so you get 180 degrees!

If you have more questions don’t have hesitation to ask!

Or add all number to get 180 degrees!

4 0

3 years ago

What is -2k + (-4k) + 5

zavuch27 [327]

If you want it simplified -6k+5, if you need the answer lmk

8 0

3 years ago

Read 2 more answers