Answer: 136 square feet
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Explanation:
The front face is a triangle with base 6 and height 4.
The area is 0.5*base*height = 0.5*6*4 = 12 square feet
The back face is also 12 square feet since the front and back faces are identical triangles.
So far we have 12+12 = 24 square feet of surface area.
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The bottom face, that runs along the floor or ground, is a rectangle that is 6 ft by 7 ft. So we have 6*7 = 42 square feet of surface area here. This adds onto the 24 we found earlier to get 24+42 = 66 square feet so far.
To find the left and right upper faces, we'll need to find the length of the hypotenuse first. The 6 ft cuts in half to 3 ft. The right triangle on the left has side lengths of 4 ft and 3 ft as the two legs. Use the pythagorean theorem to find the hypotenuse is 5 ft. We have a 3-4-5 right triangle.
This means the upper left face is 5 ft by 7 ft leading to an area of 5*7 = 35 square feet. The same can be said about the upper right face.
So we add on 35+35 = 70 more square feet to the 66 we found earlier to get a grand total of 70+66 = 136 square feet of surface area.
Answer: The required simplified answer in standard form is 
Step-by-step explanation: We are given to multiply the following polynomials and write the answer is standard form :
To multiply the given polynomials, we need to multiply each term of one polynomial to each term of the other polynomial.
From (i), we have
Thus, the required simplified answer in standard form is
Answer:
25. x=19
26. 16=x
27 28=x
28. 24=x
Step-by-step explanation:
25. The two angles make a straight line (180 degrees)
6x-17 + 3x+26 = 180
Combine like terms
9x +9 = 180
Subtract 9 from each side
9x+9-9=180-9
9x = 171
Divide by 9
9x/9 = 171/9
x=19
26. These angles are corresponding angles and corresponding angles are equal if the lines are parallel
4x+20 = 6x-12
Subtract 4x from each side
4x-4x+20 = 6x-4x-12
20 =2x-12
Add 12 to each side
20+12 = 2x-12+12
32=2x
Divide by 2
32/2 = 2x/2
16=x
27 These are alternate interior angles and alternate interior angles are equal if the lines are parallel.
4x+30 = 6x-26
Subtract 4x from each side
4x-4x+30 = 6x-4x-26
30 = 2x-26
Add 26 to each side
30+26 =2x-26+26
56= 2x
Divide by 2
56/2 = 2x/2
28=x
28. These are corresponding angles and corresponding angles are equal if the lines are parallel.
99=3x+27
Subtract 27 from each side
99-27 = 3x+27-27
72 = 3x
Divide by 3
72/3 = 3x/3
24=x
Answer: 11.1 m
Step-by-step explanation:
This can be solved by the Pythagorean theorem where;
c² = a² + b²
c is the hypotenuse which is the distance from the top of the building to the tip of the shadow.
a is the height
c is the length
32² = 30² + b²
b² = 32² - 30²
b² = 1,024 - 900
b² = 124
b = √124
b = 11.1 m
