Answer:
See below. <u><em>I assume that (x) = 8x2 - 7x + 3 is really (x) = 8x^2 - 7x + 3</em></u>
Step-by-step explanation:
Substitute the value of x given in f(x) into the equation f(x) = 8x^2 - 7x + 3
For example, f(0) would be f(0) = 8(0)^2 - 7(0) + 3. f(0) = 3
f(-2) would be f(-2) = 8(-2)^2 - 7(-2) + 3.
= 8*4 + 14 +3
= 32 + 17 therefore f(-2) = 49
<u>x</u> <u>f(x)</u>
-2 49
-1 18
0 3
1 4
2 21
Answer:
-317 feet
Step-by-step explanation:
Initial point = zero
1. Drop 294 feet
2. Climbing
3. Drop
Overall: -317 feet
Answer: Jim had $28 , Kirk had $16
Step-by-step explanation:
Let's represent the amount of money they had initially as k and j respectively.
From the first statement, Kirk has 12 dollars less than Jim. Mathematically, this could be expressed as :
K + 12 = J or K = J - 12
From the second sentence, we can deduce the following : If Jim's initial amount is halved, Kirk would be 2 dollars richer. This could he expressed mathematically as ;
J/2 = K - 2
NOW , let's solve both equations simultaneously.
K = J - 12 ..........(i)
J/2 = K - 2 ........(ii)
Let's substitute for k in equation ii using equation I
J/2 = J - 12 - 2
J/2 = J - 14
J = 2J - 28
Rearranging yields
2J - J = 28
J = 28
Since K = J - 12, that means k = 28 - 12 = 16
Hence initially, Jim had $28 while Kirk had $16
Answer:
![\large\boxed{b\geq3\to b\in[3,\ \infty)}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bb%5Cgeq3%5Cto%20b%5Cin%5B3%2C%5C%20%5Cinfty%29%7D)
Step-by-step explanation:
![2(b-3)\geq3(3-b)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(2)(b)+(2)(-3)\geq(3)(3)+(3)(-b)\\\\2b-6\geq9-3b\qquad\text{add 6 to both sides}\\\\2b-6+6\geq9+6-3b\\\\2b\geq15-3b\qquad\text{add}\ 3b\ \text{to both sides}\\\\2b+3b\geq15-3b+3b\\\\5b\geq15\qquad\text{divide both sides by 5}\\\\\dfrac{5b}{5}\geq\dfrac{15}{5}\\\\b\geq3](https://tex.z-dn.net/?f=2%28b-3%29%5Cgeq3%283-b%29%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%3A%7D%5C%20a%28b%2Bc%29%3Dab%2Bac%5C%5C%5C%5C%282%29%28b%29%2B%282%29%28-3%29%5Cgeq%283%29%283%29%2B%283%29%28-b%29%5C%5C%5C%5C2b-6%5Cgeq9-3b%5Cqquad%5Ctext%7Badd%206%20to%20both%20sides%7D%5C%5C%5C%5C2b-6%2B6%5Cgeq9%2B6-3b%5C%5C%5C%5C2b%5Cgeq15-3b%5Cqquad%5Ctext%7Badd%7D%5C%203b%5C%20%5Ctext%7Bto%20both%20sides%7D%5C%5C%5C%5C2b%2B3b%5Cgeq15-3b%2B3b%5C%5C%5C%5C5b%5Cgeq15%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%205%7D%5C%5C%5C%5C%5Cdfrac%7B5b%7D%7B5%7D%5Cgeq%5Cdfrac%7B15%7D%7B5%7D%5C%5C%5C%5Cb%5Cgeq3)
![,\ \geq-\text{line to the right}\\-\text{o}\text{pen circle}\\\leq,\ \geq-\text{closed circle}](https://tex.z-dn.net/?f=%3C%2C%5C%20%5Cleq-%5Ctext%7Bline%20to%20the%20left%7D%5C%5C%3E%2C%5C%20%5Cgeq-%5Ctext%7Bline%20to%20the%20right%7D%5C%5C%3C%2C%5C%20%3E-%5Ctext%7Bo%7D%5Ctext%7Bpen%20circle%7D%5C%5C%5Cleq%2C%5C%20%5Cgeq-%5Ctext%7Bclosed%20circle%7D)
Answer: (f)
Step-by-step explanation:
Given
Line that passes through
and ![(0,0)](https://tex.z-dn.net/?f=%280%2C0%29)
Using two point form, equation of a line is given by
![\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7By-y_1%7D%7Bx-x_1%7D%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Insert the values
![\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7By-0%7D%7Bx-0%7D%3D%5Cdfrac%7B3-0%7D%7B-%5Cfrac%7B1%7D%7B2%7D-0%7D%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7By%7D%7Bx%7D%3D-6%5C%5C%5C%5C%5CRightarrow%20y%3D-6x)
Thus, option (f) is correct