Subtract 7x from both sides.
5=-x
Therefore,
x=-5
Answer:
Total Area = ![104+16\,\sqrt{13}](https://tex.z-dn.net/?f=104%2B16%5C%2C%5Csqrt%7B13%7D)
Step-by-step explanation:
If T.A. stands for Total Area, then we need to add the area of two equal right angle triangles of base 6' and height 4', which give : 2 * (6' * 4'/2) = 24 square feet. tothe area of three rectangles (the lateral faces of this triangular base prism):
![(8')*(4')+(8')*(6')+(8')*(\sqrt{6^2+4^2})= 32+48+8\,\sqrt{52} =80+8\,*\,2\,\sqrt{13}=80+16\,\sqrt{13}](https://tex.z-dn.net/?f=%288%27%29%2A%284%27%29%2B%288%27%29%2A%286%27%29%2B%288%27%29%2A%28%5Csqrt%7B6%5E2%2B4%5E2%7D%29%3D%2032%2B48%2B8%5C%2C%5Csqrt%7B52%7D%20%3D80%2B8%5C%2C%2A%5C%2C2%5C%2C%5Csqrt%7B13%7D%3D80%2B16%5C%2C%5Csqrt%7B13%7D)
Therefore the total area of the prism is:
![24+80+16\,\sqrt{13} =104+16\,\sqrt{13}](https://tex.z-dn.net/?f=24%2B80%2B16%5C%2C%5Csqrt%7B13%7D%20%3D104%2B16%5C%2C%5Csqrt%7B13%7D)
Answer:
A local maximum of the function f(x) occurs when x =Step-by-step explanation:
Answer:
∠1 is 90° because it is a right angle
To find angle 2, we must add the given angles and x then make the equation equal to 180°, which we next solve for x;
x + 90 + 30 = 180
x + 120 = 180
-120 -120
x = 60, ∠2 = 60°
Angle 5 is vertical to angle 1 which equals 90 degrees, and <u>vertical angles are congruent</u> meaning that they measure the same degrees so therefore ∠5 = 90°
Angles 4 and 40° are <u>vertical</u> to angle 2 which measures 60 degrees;
40 + x(where x equals angle 4) = 60
-40 -40
x = 20, ∠4 = 20°
Specified earlier, angles <u>40° and 4 are equal to 60°</u>, this means that angle three added to angles 40° and 4 will be equal to 90 degrees since angle 1 is 90 degrees and the other three angles will have to equal 90 degrees because they are supplementary.
So we set up the equation;
40 + 20(angle four) + x = 90
60 + x = 90
-60 -60
x = 30, ∠3 = 30°
I think the answer would be 1:2 because 15 is half of 30 so the simplest form is a half