Answer:
See Below
Step-by-step explanation:
We are given 3 equations.
3x + 8
5x - 20
and
5x + 4y
First lets solve for x using the first two
3x + 8 = 5x -20
Move the variables to one side
3x + 8 = 5x -20
-3x -3x
8 = 2x -20
+20 +20
28 =2x
28/2 =2x /2
14 = x
Now we have x = 14
Lets plug this into the second equation to solve for the angle
3(14) + 8
42 + 8 = 50
5(14) - 20
70 - 20 =50
Now, lets plug the x and the angle into the third equation to find y
5 (14) +4y = 50
70 + 4y = 50
-70 -70
4y = -20
4y/4 = -20/4
y = -5
So now we have:
x = 14
y = -5
and the angle = 50
Hope this helps!
Answer:
=6√3 the third option.
Step-by-step explanation:
We can use the Pythagoras theorem to find the value of y. We need two equations that include y.
a²+b²=c²
c=9+3=12
x²+y²=12²
x²=144 - y².........i (This is the first equation)
We can also express it in another way but let us find the perpendicular dropped to c.
perpendicular²= x²-3²=x²-9 according to the Pythagoras theorem.
y²=(x²-9)+9²
y²=x²+72
x²=y²-72....ii( this is the second equation
Let us equate the two.
y²-72=144-y²
2y²=144+72
2y²=216
y²=108
y=√108
In Surd form √108=√(36×3)=6√3
y=6√3
Answer:
2 1/7 pieces
Step-by-step explanation:
A factory makes rectangular sheets of cardboard, each with an area 2 1/2 square feet. Each sheet of cardboard can be cut into smaller pieces of cardboard measuring 1 1/6 square feet. How many smaller pieces of cardboard does each sheet of cardboard provide?
Each sheet of cardboard = 2 1/2 square feet
Each smaller pieces of cardboard = 1 1/6 square feet
Number of smaller pieces of cardboard per sheet of cardboard = Each sheet of cardboard ÷
Each smaller pieces of cardboard
= 2 1/2 square feet ÷ 1 1/6 square feet
= 5/2 ÷ 7/6
= 5/2 × 6/7
= (5*6) / (2*7)
= 30/14
= 15/7
= 2 1/7 pieces
Number of smaller pieces of cardboard per sheet of cardboard = 2 1/7 pieces
The frequency table, stem and leaf plot, and histogram are attached.
The histogram looks similar to the stem and leaf plot, except turned on its side. It is different from the frequency table in shape, but the numbers in the table are the same as the size of the bars.
The height of the bars in the histogram is the same as the number of leaves in the stem and leaf plot, and it is also the same as the numbers in the frequency table. Using larger intervals will result in larger bars on the histogram and larger numbers in the frequency table; smaller intervals will result in smaller bars and smaller numbers in the table.
Answer: 7
Work: So, the goal is to get z alone, so we are going to add 85 on both sides, cancelling on the side it's currently on. So, the new equation is going to be 25z = 175. Then, to get z even more lonely, we are going to divide 25 on both sides, and again cancelling it on the side it's currently on. So, the answer is z = 7. I hope this helps, and Happy Holidays! :)
