The function f(x) = mx + b is a linear function, and the values of m and b are -1/3 and 7/3, respectively
<h3>How to determine the values of m and b?</h3>
The function is given as:
f(x) = mx + b
The solutions are (1,2) and (-20,9)
The above points mean that:
1 * m + b = 2
-20 * m + b = 9
This gives
m + b = 2
-20m + b = 9
Subtract both equations
m + 20m = 2 - 9
Evaluate the difference and sum
21m = -7
Divide both sides by 21
m = -1/3
Substitute m = -1/3 in m + b = 2
-1/3 + b = 2
Add 1/3 to both sides
b = 2 + 1/3
Evaluate
b = 7/3
Hence, the values of m and b are -1/3 and 7/3, respectively
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Answer:
Y is 90 degrees.
Step-by-step explanation:
This is an equalterial triangle which means all of the angles are the same. The angle for the upper part of the triangle is 60 as well. We can do 2x=60 because they add up to the angle which is 60. This gives us x=30. If x=30 and the other angle is 60, then the other angle has to be 90 because all triangle has an angle sum of 180. So 30 +60 + 90= 180. Hope this helps!
Answer:
It depends on the equation.
If the bases are equal and the variables are only in the exponents, set the exponents equal.
If there are variables in the exponents, but you cannot set the bases equal, then use logarithms.
Example 1:
Here you have the same base on both sides. The variables are in the exponents. Set the exponents equal and solve for x.
2x + 5 = 9
2x = 4
x = 2
Example 2:
The bases are different, but you can make the bases equal using laws of exponents. Remember that 9 = 3^2.
Now you have equal bases, so the exponents must be equal.
2x = 12
x = 6
Example 3:
Here you can't make the bases equal, so you take the log of both sides and use laws of logs.
Recall that:
F(n) = 5n
You are being told n is the number of tables, and there are 15 tables:
f(15) = 5(15)
F(n) = 75
You need 75 candles.
Answer:
Step-by-step explanation:
<u>Triangular Prism</u>
Given a triangular prism of base area A and height H, its volume is obtained with the formula:
V = AH
The area of the base is calculated as follows:
Where W is the width and L is the length. Both dimensions must be perpendicular.
The triangle of the base has a hypotenuse equal to 10 in and the width is 6 in, the length is calculated by:
L = 8 in
The area is:
Finally, the volume is: