Answer:
The average rate of change of <em>g</em> from <em>x</em> = <em>a</em> to<em> x</em> = <em>a</em> + <em>h</em> is -3.
Step-by-step explanation:
We are given the function:
![g(x) = -3x + 4](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-3x%20%2B%204)
And we want to determine its average rate of change of the function for <em>x</em> = <em>a</em> and <em>x</em> = <em>a</em> + <em>h</em>.
To determine the average rate of change, we find the slope of the function between the two points. In other words:
![\displaystyle \text{Avg} = \frac{g(a + h) - g(a) }{(a + h ) - a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctext%7BAvg%7D%20%3D%20%5Cfrac%7Bg%28a%20%2B%20h%29%20-%20g%28a%29%20%7D%7B%28a%20%2B%20h%20%29%20-%20a%7D)
Simplify:
![\displaystyle \begin{aligned} \text{Avg} &= \frac{g(a + h) - g(a) }{(a + h ) - a} \\ \\ &=\frac{(-3(a+h) + 4) - (-3a+4)}{h} \\ \\ &= \frac{(-3a -3h + 4) + (3a - 4) }{h} \\ \\ &= \frac{-3h}{h} \\ \\ &= -3\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20%20%5Ctext%7BAvg%7D%20%26%3D%20%5Cfrac%7Bg%28a%20%2B%20h%29%20-%20g%28a%29%20%7D%7B%28a%20%2B%20h%20%29%20-%20a%7D%20%5C%5C%20%5C%5C%20%26%3D%5Cfrac%7B%28-3%28a%2Bh%29%20%2B%204%29%20-%20%28-3a%2B4%29%7D%7Bh%7D%20%5C%5C%20%5C%5C%20%26%3D%20%5Cfrac%7B%28-3a%20-3h%20%2B%204%29%20%2B%20%283a%20-%204%29%20%7D%7Bh%7D%20%5C%5C%20%5C%5C%20%26%3D%20%5Cfrac%7B-3h%7D%7Bh%7D%20%5C%5C%20%5C%5C%20%26%3D%20-3%5Cend%7Baligned%7D)
In conclusion, the average rate of change of <em>g</em> from <em>x</em> = <em>a</em> to <em>x</em> = <em>a</em> + <em>h</em> is -3.
This is the expected result, as function <em>g</em> is linear, so its rate of change would be constant.
Answer:
26/3 as a mixed number is 8 2/3
Step-by-step explanation:
hope this helped you if it did plz mark brainiest
Answer:
(3, -6)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
- Coordinates (x, y)
- Terms/Coefficients
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = 4x - 18
y = -5x + 9
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em> [2nd Equation]: 4x - 18 = -5x + 9
- [Addition Property of Equality] Add 5x on both sides: 9x - 18 = 9
- [Addition Property of Equality] Add 18 on both sides: 9x = 27
- [Division Property of Equality] Divide 9 on both sides: x = 3
<u>Step 3: Solve for </u><em><u>y</u></em>
- Substitute in <em>x</em> [1st Equation]: y = 4(3) - 18
- Multiply: y = 12 - 18
- Subtract: y = -6
Let <span>simplify the equations
![a^7xy-a^6y-a^5x=a^4(b^4-1)](https://tex.z-dn.net/?f=a%5E7xy-a%5E6y-a%5E5x%3Da%5E4%28b%5E4-1%29)
and
![(a^mx-a^n)(a^py-a^2)=a^4b^4](https://tex.z-dn.net/?f=%28a%5Emx-a%5En%29%28a%5Epy-a%5E2%29%3Da%5E4b%5E4)
:
</span>
<span>1)
</span>
<span>and
</span>
<span>2)
![a^{m+p}xy-a^{n+p}y-a^{m+2}x+a^{n+2}=a^4b^4](https://tex.z-dn.net/?f=a%5E%7Bm%2Bp%7Dxy-a%5E%7Bn%2Bp%7Dy-a%5E%7Bm%2B2%7Dx%2Ba%5E%7Bn%2B2%7D%3Da%5E4b%5E4)
.
</span>
<span>Equate the coefficients:
</span><span>
</span><span>
![xy: m+p=7 \\ y: n+p=6 \\ x: m+2=5 \\ 1: n+2=4](https://tex.z-dn.net/?f=%20xy%3A%20m%2Bp%3D7%20%20%5C%5C%20y%3A%20n%2Bp%3D6%20%5C%5C%20x%3A%20%20m%2B2%3D5%20%5C%5C%201%3A%20n%2B2%3D4%20)
.</span>
Then
![n=2 \\ p=4 \\ m=3](https://tex.z-dn.net/?f=n%3D2%20%5C%5C%20p%3D4%20%5C%5C%20m%3D3)
and mnp=24.
<span />
Answer:
1. 50 m
2. 80 cm
Step-by-step explanation:
1. There are 2 triangles, subtract the area of 1 of them from the other.
The triangle that needs to be subtracted: b = 20 m, h = 10 m
A = 1/2b * h = 1/2(20) * 10 = 10*10 = 100 m
The big triangle, the one that needs to be subtracted plus the one you need to find the area of: b = 20 cm, h = 15 cm, 1/2(20) * 15 = 10 * 15 = 150
150 - 100 = 50 c
2. Divide it into 3 parts:
1- 3*4 = 12
2. 7*(4 + 4) = 7*8 = 56
3. [(4 + 4) * (13 - 7 - 3)]/2 = (8*3)/2 = 24/2 = 12
12 + 56 + 12 = 80 cm