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Answers:</h3>
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Explanation:
The given piecewise function is

At first piecewise functions may be strange confusing things, but they aren't so bad. I like to think of it like this: f(x) is a function that changes its identity based on what the input x is. We have three situations
- f(x) = -4x+3 when x < 3
- f(x) = -x^3 when

- f(x) = 3x^2+1 when x > 8
In a sense, we have three different functions but they are combined somehow.
If x is smaller than 3, then we go for the first definition. Or if x is between 3 and 8, then we go for the second definition. Or if x is larger than 8, then we go for the third definition.
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f(-5) means f(x) when x = -5. We see that -5 is smaller than 3, so x = -5 makes x < 3 true. We'll use the first definition
f(x) = -4x+3
f(-5) = -4(-5)+3
f(-5) = 20+3
f(-5) = 23
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Now the input is x = 12. This is larger than 8. In other words, x = 12 makes x > 8 true. We'll use the third definition
f(x) = 3x^2+1
f(12) = 3(12)^2+1
f(12) = 3(144)+1
f(12) = 432+1
f(12) = 433
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Side notes:
- We won't use the second definition since we don't have any x inputs between 3 and 8
- To say "less than or equal to" on a keyboard, you can write "<=" without quotes. For example,
is the same as x<=5
Answer:
25 units
Step-by-step explanation:
use the distance formula to get the square root of 24² + 7²
this will give you the square root of 625, which is 25
Answer:
D) x = 4, y = -2, z = 3
Step-by-step explanation:
x = 3z − 5
2x + 2z = y + 16
2(3z - 5) + 2z = y + 16
6z - 10 + 2z = y + 16
8z = y + 26 ---> (A)
7x − 5z = 3y + 19
7(3z - 5) - 5z = 3y + 19
21z - 35 - 5z = 3y + 19
16z = 3y + 54 ---> (B)
8z = y + 26
16z = 3y + 54
2(y + 26) = 3y + 54
2y + 52 = 3y + 54
y = -2
8z = -2 + 26
8z = 24
z = 3
x = 3(3) - 5
x = 4
Answer: 50653
37³ = (40 - 3)³ = 40³ - 3.40².3 + 3.40.3² - 3³
= 64000 - 14400 + 1080 - 27
= 50653
Step-by-step explanation:
Answer:
y-7=1/4(x+5)
Step-by-step explanation:
y-3=-4(x+2)
y=-4x-8+3
y=-4x-5
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y-y1=m(x-x1)
y-7=m(x-(-5))
y-7=m(x+5)
perpendicular means negative reciprocal of the slope,
so the slope will be 1/4
y-7=1/4(x+5)