7. Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altog
1 answer:
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<h3>Answers:</h3>
- f(-5) = 23
- f(12) = 433
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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:
x = 1
y = -1
z = 2
Step-by-step explanation:
You have the following system of equations:
First, you can subtract euqation (3) to equation (1):
x + 2y - z = -3
<u>-x +y -z = - 4 </u>
0 3y -2z = -7 (4)
Next, you can multiply equation (3) by 2 and subtract it to equation (2):
2[ x -y + z = 4]
<u> -2x +y -z = -5</u>
0 -y + z= 3 (5)
You multiply equation (5) by 2 and sum (5) with (4):
2[ -y + z = 3]
<u> 3y -2z= -7</u>
y + 0 = -1
Then y = -1
Next, you replace y=-1 in (5) to obtain z:
-(-1) + z = 3
z = 2
Finally, you can replace z and y in the equation (3) to obtain x:
x - (-1) + (2) = 4
x = 1