Answer: About 3.06
Step-by-step explanation:
We can use trigonometry functions to solve for AC. Let the ?, representing AC, be "x" in our mathematical work.
Since we have the hypotenuse and x is adjacent to the angle given, I am going to use cosine.
cos(θ) = 
cos(40) = 
0.766 ≈ 
3.06 ≈ x
x ≈ 3.06
Answer: 3.14285714.....
<u>Step-by-step explanation:</u>
pi is 

Thiis is a non-terminating and non-repeating decimal.
Answer:
TU = 18
Step-by-step explanation:
TV = 21
TU + VU = 21
-31 - 7z + (-39 - 6z) = 21
-31 - 7z - 39 - 6z = 21
-7z - 6z - 31 - 39 = 21 {Combine like terms}
-13z - 70 = 21 {Add 70 to both sides}
-13z = 21 + 70
-13z = 91 {divide both side by (-13)}
z = 91/-13
z = -7
TU = -31 - 7z
= -31 - 7*(-7)
= - 31 + 49
= 18
1.5 quarts of 20% fruit juice and 4.5 quarts of 100% fruit juice.
Step-by-step explanation:
Let x be the number of quarts of 100% fruit juice
Let y be the number of quarts of 20% fruit juice
The equation for amount of quarts is ;
x+y=6
x=6-y-------------------equation 1
The equation for the amount of quarts of fruit juice to get 80% fruit juice will be;
x(100%)+y(20%)=80%------however you need to make 6 quarts so divide first portion of equation by 6
{x(100%)+y(20%) }/6=80%
Multiply both parts of the equations by 6
x(100%)+y(20%)=480% --------------equation 2
Use equation 1 in 2
(6-y)(100%)+y(20%)=480%
600-100y+20y=480
600-80y=480
600-480=80y
120=80y
120/80 =y
1.5=y
Use the value of y in equation 1
x=6-y , x= 6-1.5=4.5
So you have,
1.5 quarts of 20% fruit juice and 4.5 quarts of 100% fruit juice.
Learn More
Mixtures equations;brainly.com/question/11898822
Keywords : quarts,party,bottles,punch
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First find the x and y values because where the lines will intersect, they share the point of the intersection so they will share the x and y coordinates.
Rearrange equations


To cancel y, we must do equation 1 minus equation 2. Similarly:




So the x coordinate is 3.
The y coordinate can be found with substitution of x into one of the equations:

So where the two lines intersect is at the point (3, 7), which is the solution to the equations.