IDNLearn.com is designed to help you find the answers you need quickly and easily. Get the information you need quickly and accurately with our reliable and thorough Q&A platform.
Sagot :
Sure, let's break down each part of the problem and solve it step by step:
### Part 4: Finding [tex]\( h(2) \)[/tex]
Given the function [tex]\( h(x) = x^2 - 5x + 7 \)[/tex], we need to find [tex]\( h(2) \)[/tex]:
1. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ h(2) = 2^2 - 5(2) + 7 \][/tex]
2. Calculate the squared term and the product:
[tex]\[ 2^2 = 4 \][/tex]
[tex]\[ 5(2) = 10 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ h(2) = 4 - 10 + 7 \][/tex]
4. Perform the arithmetic:
[tex]\[ 4 - 10 = -6 \][/tex]
[tex]\[ -6 + 7 = 1 \][/tex]
Thus, [tex]\( h(2) = 1 \)[/tex].
### Part 5: Finding [tex]\( h(-5) \)[/tex]
Now, we need to find [tex]\( h(-5) \)[/tex]:
1. Substitute [tex]\( x = -5 \)[/tex] into the function:
[tex]\[ h(-5) = (-5)^2 - 5(-5) + 7 \][/tex]
2. Calculate the squared term and the product:
[tex]\[ (-5)^2 = 25 \][/tex]
[tex]\[ 5(-5) = -25 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ h(-5) = 25 + 25 + 7 \][/tex]
4. Perform the arithmetic:
[tex]\[ 25 + 25 = 50 \][/tex]
[tex]\[ 50 + 7 = 57 \][/tex]
Thus, [tex]\( h(-5) = 57 \)[/tex].
### Part 6: Finding [tex]\(\frac{1}{3} \cdot h(-8)\)[/tex]
We need to find [tex]\( \frac{1}{3} \cdot h(-8) \)[/tex]:
1. Substitute [tex]\( x = -8 \)[/tex] into the function:
[tex]\[ h(-8) = (-8)^2 - 5(-8) + 7 \][/tex]
2. Calculate the squared term and the product:
[tex]\[ (-8)^2 = 64 \][/tex]
[tex]\[ 5(-8) = -40 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ h(-8) = 64 + 40 + 7 \][/tex]
4. Perform the arithmetic:
[tex]\[ 64 + 40 = 104 \][/tex]
[tex]\[ 104 + 7 = 111 \][/tex]
5. Calculate [tex]\(\frac{1}{3} \cdot 111 \)[/tex]:
[tex]\[ \frac{1}{3} \cdot 111 = 37 \][/tex]
Thus, [tex]\( \frac{1}{3} \cdot h(-8) = 37.0 \)[/tex].
### Part 9: Finding [tex]\( -5 \cdot g(4) -1 \)[/tex]
Given the function [tex]\( g(x) = 1 - \frac{3}{4}x \)[/tex], we need to find [tex]\( -5 \cdot g(4) - 1 \)[/tex]:
1. Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[ g(4) = 1 - \frac{3}{4}(4) \][/tex]
2. Calculate the product:
[tex]\[ \frac{3}{4}(4) = 3 \][/tex]
3. Substitute this value back into the equation:
[tex]\[ g(4) = 1 - 3 \][/tex]
4. Perform the arithmetic:
[tex]\[ 1 - 3 = -2 \][/tex]
5. Calculate [tex]\( -5 \cdot g(4) \)[/tex]:
[tex]\[ -5 \cdot (-2) = 10 \][/tex]
6. Subtract 1:
[tex]\[ 10 - 1 = 9 \][/tex]
Thus, [tex]\( -5 \cdot g(4) - 1 = 9.0 \)[/tex].
In summary:
- [tex]\( h(2) = 1 \)[/tex]
- [tex]\( h(-5) = 57 \)[/tex]
- [tex]\( \frac{1}{3} \cdot h(-8) = 37.0 \)[/tex]
- [tex]\( -5 \cdot g(4) -1 = 9.0 \)[/tex]
### Part 4: Finding [tex]\( h(2) \)[/tex]
Given the function [tex]\( h(x) = x^2 - 5x + 7 \)[/tex], we need to find [tex]\( h(2) \)[/tex]:
1. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ h(2) = 2^2 - 5(2) + 7 \][/tex]
2. Calculate the squared term and the product:
[tex]\[ 2^2 = 4 \][/tex]
[tex]\[ 5(2) = 10 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ h(2) = 4 - 10 + 7 \][/tex]
4. Perform the arithmetic:
[tex]\[ 4 - 10 = -6 \][/tex]
[tex]\[ -6 + 7 = 1 \][/tex]
Thus, [tex]\( h(2) = 1 \)[/tex].
### Part 5: Finding [tex]\( h(-5) \)[/tex]
Now, we need to find [tex]\( h(-5) \)[/tex]:
1. Substitute [tex]\( x = -5 \)[/tex] into the function:
[tex]\[ h(-5) = (-5)^2 - 5(-5) + 7 \][/tex]
2. Calculate the squared term and the product:
[tex]\[ (-5)^2 = 25 \][/tex]
[tex]\[ 5(-5) = -25 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ h(-5) = 25 + 25 + 7 \][/tex]
4. Perform the arithmetic:
[tex]\[ 25 + 25 = 50 \][/tex]
[tex]\[ 50 + 7 = 57 \][/tex]
Thus, [tex]\( h(-5) = 57 \)[/tex].
### Part 6: Finding [tex]\(\frac{1}{3} \cdot h(-8)\)[/tex]
We need to find [tex]\( \frac{1}{3} \cdot h(-8) \)[/tex]:
1. Substitute [tex]\( x = -8 \)[/tex] into the function:
[tex]\[ h(-8) = (-8)^2 - 5(-8) + 7 \][/tex]
2. Calculate the squared term and the product:
[tex]\[ (-8)^2 = 64 \][/tex]
[tex]\[ 5(-8) = -40 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ h(-8) = 64 + 40 + 7 \][/tex]
4. Perform the arithmetic:
[tex]\[ 64 + 40 = 104 \][/tex]
[tex]\[ 104 + 7 = 111 \][/tex]
5. Calculate [tex]\(\frac{1}{3} \cdot 111 \)[/tex]:
[tex]\[ \frac{1}{3} \cdot 111 = 37 \][/tex]
Thus, [tex]\( \frac{1}{3} \cdot h(-8) = 37.0 \)[/tex].
### Part 9: Finding [tex]\( -5 \cdot g(4) -1 \)[/tex]
Given the function [tex]\( g(x) = 1 - \frac{3}{4}x \)[/tex], we need to find [tex]\( -5 \cdot g(4) - 1 \)[/tex]:
1. Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[ g(4) = 1 - \frac{3}{4}(4) \][/tex]
2. Calculate the product:
[tex]\[ \frac{3}{4}(4) = 3 \][/tex]
3. Substitute this value back into the equation:
[tex]\[ g(4) = 1 - 3 \][/tex]
4. Perform the arithmetic:
[tex]\[ 1 - 3 = -2 \][/tex]
5. Calculate [tex]\( -5 \cdot g(4) \)[/tex]:
[tex]\[ -5 \cdot (-2) = 10 \][/tex]
6. Subtract 1:
[tex]\[ 10 - 1 = 9 \][/tex]
Thus, [tex]\( -5 \cdot g(4) - 1 = 9.0 \)[/tex].
In summary:
- [tex]\( h(2) = 1 \)[/tex]
- [tex]\( h(-5) = 57 \)[/tex]
- [tex]\( \frac{1}{3} \cdot h(-8) = 37.0 \)[/tex]
- [tex]\( -5 \cdot g(4) -1 = 9.0 \)[/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.