Answer:
Below in bold.
Step-by-step explanation:
sin 60 = √3/2
so √3/2 = h / 12
height h = 12√3/ 2
= 6√3 inches or 10.39 inches to nearest hundredth.
Volume = area of base * height = 10*8*6√3
= 480√3 in^3 or 831.38 in^3 to nearest hundredth.
Let
a--------> original side length side of a cube
we know that
[volume of a original cube]=a³
<span>If the side lengths are decreased to 50% of their original size
then
[volume of a new cube]=(a/2)</span>³----> a³/8
the answer is
the volume of the new cube is a³/8
Answer:
1/20
Step-by-step explanation:
So, he eats 5/8 of 1/3 of the pizza. That would be 5/8*1/3=5/24
Then, he eats 2/5 of what is left. What is left is 3/8*1/3=1/8.
So, 1/8*2/5=1/20
Therefore, Teddy ate 1/20 of the original pizza
a. The value of x is 7
b. The measure of ∠1 is 99°
<h3>Calculating angles </h3>
From the question, we are to solve for x
From the given diagram, we can write that
m∠NMQ + m∠MQN + m∠QNM = 180° (<em>Sum of angles in a triangle</em>)
From the given information,
m∠NMQ = 5x +19
m∠MQN = 8x -11
m∠QNM = 11x + 4
Then,
5x + 19 + 8x -11 + 11x + 4 = 180
Collect like terms
5x + 8x + 11x = 180 - 19 + 11 - 4
24x = 168
∴ x = 168/24
x = 7
Hence, the value of x is 7
b.
Measure of ∠1 + m∠QNM = 180° (<em>Sum of angles on a straight line</em>)
∴ Measure of ∠1 = 180° - m∠QNM
But m∠QNM = 11x + 4
∴ m∠QNM = 11(7) + 4
m∠QNM = 77 + 4
m∠QNM = 81°
Then,
Measure of ∠1 = 180° - 81°
Measure of ∠1 = 99°
Hence, the measure of ∠1 is 99°
Learn more on Calculating angles here: brainly.com/question/25716982
#SPJ1
Answer: They are perpendicular lines, because their slopes are negative reciprocals ()
Step-by-step explanation:
The missing graph is attached.
You need to remember that the slope of a line can be found with the following formula:
First, find the slope of the line AB. The steps are:
- Choose two points on the line. These can be:
You can say that:
Substituting values into the formula and evaluating, you get that the slope of this line is:
Now you must find the slope of the line CD. The steps are shown below:
- Choose two points on the line. These can be:
- You can say that:
- Now you must substitute values into the formula and evaluate, in order to find the slope. This is:
By definition, the slopes of perpendicular lines are negative reciprocals.
Therefore, since the slopes of the lines AB and CD are negative reciprocals, you can conclude that they are perpendicular.