Answer:
x = 136°
Step-by-step explanation:
We can use a theorem to help us.
<em>Theorem: </em>
<em>The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.</em>
For exterior angle x, the remote interior angles are z and <CBD.
From the theorem, we get this equation.
x = z + m<CBD
We know z = 52°.
We need to find m<CBD.
Angles CBD and y are a linear pair. They are supplementary, so the sum of their measures is 180°. We are given y = 96°.
m<CBD + y = 180°
m<CBD + 96° = 180°
m<CBD = 84°
x = z + m<CBD
x = 52° + 84°
x = 136°
There are 37 eight ounce of cheese.
37 times 8 = 296 ounces of cheese.
There are 16 ounces in a pound, so divide.
296/16 = 18.5 pounds on the shelf.
Then he places 24 ounce of cheese on the shelf. Divide that by 16.
24/16 = 1.5 pounds.
Add the pounds together-
18.5 + 1.5 = 20 pounds (lbs)
it would be a ratio5:6
Step-by-step explanation:
Basketball has a mass of 0.1kg
m = 0.1 kg
The basket ball is moving at constant speed, this shows that it is not accelerating. So, acceleration is zero
a = 0m/s²
The constant speed is 6m/s
v = 6m/s
So, force to keep it moving with this constant speed can be calculated using Newton second law of motion
F = ma
F = m × 0
F = 0N
So, since the basket ball is moving at constant speed, then, the force need to keep the ball moving is 0N.
Answer:
![\left[\begin{array}{ccc}9\\10\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D9%5C%5C10%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Evaluate 3a by multiplying each element by 3
3a = 3 ![\left[\begin{array}{ccc}2\\4\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5C%5C4%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}3(2)\\3(4)\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%282%29%5C%5C3%284%29%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}6\\12&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%5C%5C12%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
, then
3a + b
= ![\left[\begin{array}{ccc}6\\12\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%5C%5C12%5C%5C%5Cend%7Barray%7D%5Cright%5D)
+ ![\left[\begin{array}{ccc}3\\-2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C-2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
← sum corresponding elements
= ![\left[\begin{array}{ccc}6+3\\12-2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%2B3%5C%5C12-2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
=
