Answer:
y = 148°
Step-by-step explanation:
4x - 18 = 2x + 12 (alternate exterior angles are congruent)
Collect like terms
4x - 18 = 2x + 12
4x - 2x = 18 + 12
2x = 20
Divide both sides by 2
x = 10
y = 180 - (2x + 12) (linear pair theorem)
Plug in the value of x
y = 180 - (2(10) + 12)
y = 180 - (20 + 12)
y = 148°
Answer: b.14
Step-by-step explanation:
We have two shelves, the top shelf
and the bottom shelf
.
Now, firstly we are told the top shelf has 10 more than 1/3 the number of books on the bottom shelf. This can be expressed as:
(1)
Then, we are told there are 12 books on the bottom shelf:
(2)
Substituting (2) in (1):
(3)
(4)
(5) This is the number of books on the top shelf
Hence, the correct option is b.
For the two lines to be parallel, the angles labeled 1 and 2 must be equal.
m 1 and m 2 have to be equal.
(5 - 3x) = (5x - 11)
Solve for x:
16=8x
2=x
X has to be 2.
Answer:
![\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-%5Cfrac%7B8%7D%7B%5Csqrt%7B117%7D%20%7D%20%5C%5C%5Cfrac%7B7%7D%7B%5Csqrt%7B117%7D%20%7D%5C%5C%5Cfrac%7B2%7D%7B%5Csqrt%7B117%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We are required to find a unit vector in the direction of:
![\left[\begin{array}{c}-8\\7\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-8%5C%5C7%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Unit Vector, ![\hat{a}=\dfrac{\overrightarrow{a}}{|\overrightarrow{a}|}](https://tex.z-dn.net/?f=%5Chat%7Ba%7D%3D%5Cdfrac%7B%5Coverrightarrow%7Ba%7D%7D%7B%7C%5Coverrightarrow%7Ba%7D%7C%7D)
The Modulus of
=![\sqrt{(-8)^2+7^2+(-2)^2}=\sqrt{117}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-8%29%5E2%2B7%5E2%2B%28-2%29%5E2%7D%3D%5Csqrt%7B117%7D)
Therefore, the unit vector of the matrix is given as:
![\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-%5Cfrac%7B8%7D%7B%5Csqrt%7B117%7D%20%7D%20%5C%5C%5Cfrac%7B7%7D%7B%5Csqrt%7B117%7D%20%7D%5C%5C%5Cfrac%7B2%7D%7B%5Csqrt%7B117%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Answer:
![- 4.67](https://tex.z-dn.net/?f=%20-%204.67)
Step-by-step explanation:
![\frac{p}{2 - 5} = \frac{14}{2 - 5} = \frac{14}{ - 3} = - 4.67](https://tex.z-dn.net/?f=%20%5Cfrac%7Bp%7D%7B2%20-%205%7D%20%3D%20%20%5Cfrac%7B14%7D%7B2%20-%205%7D%20%3D%20%20%5Cfrac%7B14%7D%7B%20-%203%7D%20%3D%20%20-%204.67)