When 2 is subtracted from one-fourth of a number, the result is seventeen. Find the number
2 answers:
<u>Answer: </u>
-60 is the number we got if we subtract 2 from one-fourth of a number and also the result is seventeen.
<u>Solution: </u>
Step 1:
Let the number we need to find be K.
We can write the given data as below
Step 2:
Evaluate the above expression to find the value of k.
So take LCM of L.H.S. Since both the denominators are 4, the L.C.M is also 4
Step 3:
Bring 4 to R.H.S
8 – K = 68
-K = 68 – 8
-K = 60.
K = -60
<u>Result: </u>
Finally we got the value of K as -60 using the given data.
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Answer:
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Step-by-step explanation:
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<h3>Answers:</h3>
- f(-5) = 23
- f(12) = 433
==================================================
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.
-----------------------
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
------------------------
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