Answer:
Step-by-step explanation:
- Use ratios to solve for x. Corresponding sides have same ratio.
Q1
- (x + 5)/30 = (36 - 20)/20
- (x + 5)/30 = 16/20 = 4/5
- 5(x + 5) = 4(30)
- 5x + 25 = 120
- 5x = 95
- x = 19
Q2
- (5x - 2)/(3x + 1) = 39/26
- (5x - 2)/(3x + 1) = 3/2
- 2(5x - 2) = 3(3x + 1)
- 10x - 4 = 9x + 3
- 10x - 9x = 3 + 4
- x = 7
TS = 3x + 1 = 3(7) + 1 = 22
Answer:
The plane PRS passes through the points P, R and S. So it contains the line RS. Also the plane QRS passes through the points Q, R and S. So it contains the line RS as well. Since both the planes contain the line RS, the line RS must be the intersection of plane PRS and QRS
Step-by-step explanation:
W=x
L=2x+17
Double everything since we need to lengths and two widths to find the perimeter
2x+17+2x+17+x+x = 76
Combine like terms
6x+34=76
Solve for x
First step is subtract 34 from both sides
6x=42
Next you divide both sides by 6 in order to get x by itself
X=7
Now you plug in 7 into the x’s in length and width
W=7 cm
L=31 cm
THE WIDTH IS 31 CM
Check:
7+7+31+31 = 76 cm
It equals 76 cm just like the problem said so therefore it is right.
Answer:
![BA = 6.0](https://tex.z-dn.net/?f=BA%20%3D%206.0)
![BC = 13.4](https://tex.z-dn.net/?f=BC%20%3D%2013.4)
Step-by-step explanation:
Given
The attached triangle
Solving (a) BA
Considering the tangent of angle C, we have:
![tan\ C = \frac{BA}{AC}\\](https://tex.z-dn.net/?f=tan%5C%20C%20%3D%20%5Cfrac%7BBA%7D%7BAC%7D%5C%5C)
This gives:
![tan\ 25 = \frac{BA}{12}](https://tex.z-dn.net/?f=tan%5C%2025%20%3D%20%5Cfrac%7BBA%7D%7B12%7D)
Make BA the subject
![BA = 12 * tan\ 25](https://tex.z-dn.net/?f=BA%20%3D%2012%20%2A%20tan%5C%2025)
![BA = 12 * 0.4663](https://tex.z-dn.net/?f=BA%20%3D%2012%20%2A%200.4663)
--- approximated
Solving (a) BC
Using Pythagoras theorem
![BC^2 = BA^2 + AC^2](https://tex.z-dn.net/?f=BC%5E2%20%3D%20BA%5E2%20%2B%20AC%5E2)
![BC^2 = 6.0^2 + 12^2](https://tex.z-dn.net/?f=BC%5E2%20%3D%206.0%5E2%20%2B%2012%5E2)
![BC^2 = 180](https://tex.z-dn.net/?f=BC%5E2%20%3D%20180)
Square root of both sides
![BC = \sqrt{180](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B180)
![BC = 13.4](https://tex.z-dn.net/?f=BC%20%3D%2013.4)