Answer:
121 square feet
Step-by-step explanation:
The area of a triangle is the height multiplied by the base divided by 2. Since this is a right triangle, you can simply use the two legs for this. The area of this triangle is therefore:
![\dfrac{24.2\cdot 10}{2}=\dfrac{242}{2}=121](https://tex.z-dn.net/?f=%5Cdfrac%7B24.2%5Ccdot%2010%7D%7B2%7D%3D%5Cdfrac%7B242%7D%7B2%7D%3D121)
Hope this helps!
Answer:
Step-by-step explanation:
an (the nth term ) = a1 + d(n - 1)
= 6 + 3(n - 1).
a17 = 6 + 3(17-1)
= 6 + 48
= 54.
Answer:
![x=1](https://tex.z-dn.net/?f=x%3D1)
Step-by-step explanation:
Here first open the inner parentheses and use the distributive property,
![4(x+5)=4x+20\\\\(x+4(x+5))=(x+4x+20)=(5x+20)\\\\3(x+4(x+5))=3(5x+20)=15x+60\\\\(x+3(x+4(x+5)))=(x+15x+60)=16x+60\\\\2(x+3(x+4(x+5)))=2(16x+60)=32x+120\\\\x+2(x+3(x+4(x+5)))=x+32x+120=33x+120\\\\\\Hence\ x+2(x+3(x+4(x+5)))=x+32x+120=33x+120\\\\\Rightarrow 33x+120=153\\\\33x=153-120\\\\33x=33\\\\x=1](https://tex.z-dn.net/?f=4%28x%2B5%29%3D4x%2B20%5C%5C%5C%5C%28x%2B4%28x%2B5%29%29%3D%28x%2B4x%2B20%29%3D%285x%2B20%29%5C%5C%5C%5C3%28x%2B4%28x%2B5%29%29%3D3%285x%2B20%29%3D15x%2B60%5C%5C%5C%5C%28x%2B3%28x%2B4%28x%2B5%29%29%29%3D%28x%2B15x%2B60%29%3D16x%2B60%5C%5C%5C%5C2%28x%2B3%28x%2B4%28x%2B5%29%29%29%3D2%2816x%2B60%29%3D32x%2B120%5C%5C%5C%5Cx%2B2%28x%2B3%28x%2B4%28x%2B5%29%29%29%3Dx%2B32x%2B120%3D33x%2B120%5C%5C%5C%5C%5C%5CHence%5C%20x%2B2%28x%2B3%28x%2B4%28x%2B5%29%29%29%3Dx%2B32x%2B120%3D33x%2B120%5C%5C%5C%5C%5CRightarrow%2033x%2B120%3D153%5C%5C%5C%5C33x%3D153-120%5C%5C%5C%5C33x%3D33%5C%5C%5C%5Cx%3D1)
Answer:
A. Because the measure of the angle
is
and the angles
and
are Vertical angles. Therefore, they are congruent (
)
B. ![m\angle BCD=19\°](https://tex.z-dn.net/?f=m%5Cangle%20BCD%3D19%5C%C2%B0)
Step-by-step explanation:
<h3> <em><u>The missing figure is attached.</u></em></h3><h3 />
You can observe in the figure that the parallel lines
and
are intersected by a another line
(this is a transversal).
Let's begin with PART B:
Observe that the angles
and
are located inside the parallel lines and they alternate sides of the transversal. Therefore, we can determine that these angles are "Alternate Interior Angles".
Since the lines
and
are parallel, we know that the Alternate Interior Angles are congruent. Then:
![m\angle ABC=m\angle BCD=19\°](https://tex.z-dn.net/?f=m%5Cangle%20ABC%3Dm%5Cangle%20BCD%3D19%5C%C2%B0)
Now we can solve the PART A.
Observe the figure.
Since the angle
and the angle
share the same vertex, they are "Vertical angles" and, therefore, they are congruent:
![m\angle BCD=m\angle ECF =19\°](https://tex.z-dn.net/?f=m%5Cangle%20BCD%3Dm%5Cangle%20ECF%20%3D19%5C%C2%B0)
Answer:
The solution of the given set in interval form is
.
Step-by-step explanation:
It is given in the question an inequality as
.
It is required to determine the solution of the inequality.
To determine the solution of the inequality, solve the inequality
and, ![$x-4 \leq-8$](https://tex.z-dn.net/?f=%24x-4%20%5Cleq-8%24)
Step 1 of 2
Solve the inequality ![$x-4 \geq 8$](https://tex.z-dn.net/?f=%24x-4%20%5Cgeq%208%24)
![$$\begin{aligned}&x-4 \geq 8 \\&x-4+4 \geq 8+4 \\&x \geq 12\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%26x-4%20%5Cgeq%208%20%5C%5C%26x-4%2B4%20%5Cgeq%208%2B4%20%5C%5C%26x%20%5Cgeq%2012%5Cend%7Baligned%7D%24%24)
Solve the inequality
.
![$$\begin{aligned}&x-4 \leq-8 \\&x-4+4 \leq-8+4 \\&x \leq-4\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%26x-4%20%5Cleq-8%20%5C%5C%26x-4%2B4%20%5Cleq-8%2B4%20%5C%5C%26x%20%5Cleq-4%5Cend%7Baligned%7D%24%24)
Step 2 of 2
The common solution from the above two solutions is x less than -4 and
.
The solution set in terms of interval is
.