What is the multiplicative inverse of 156

The graph of the quadratic function y = ax^2 + bx + c is given.<br> Find a + b + c.

andrey2020 [161]

Answer:

$\frac{145}{24}\approx 6$ ***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

$(0,3)$

$(2,8)$

$(6,5)$

Step-by-step explanation:

I see that the graph crosses at $(0,3)$ , $(2,8)$ , and $(6,5)$ .

The equation $y=ax^2+bx+c$ tells us the $y$ -intercept is $c$ since when $x=0$ we have $y=a(0)^2+b(0)+c=0+0+c=c$ .

The $y$ -intercept for our graph is $3$ . Therefore, $c=3$ .

So far we have the equation:

$y=ax^2+bx+3$ .

Let's enter the other points creating a system of linear equations to solve:

$8=a(2)^2+b(2)+3$

$5=a(6)^2+b(6)+3$

Let's simplify:

$8=4a+2b+3$

$5=36a+6b+3$

Let's subtract 3 on both sides:

$5=4a+2b$

$2=36a+6b$

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

$-15=-12a-6b$

$2=36a+6b$

Now adding the equations results in:

$-13=24a$

Divide both sides by 24:

$\frac{-13}{24}=a$

Now using one of the equations we can find $b$ :

$5=4a+2b$ with $a=\frac{-13}{24}$

$5=4\frac{-13}{24}+2b$

$5=\frac{-13}{6}+2b$

Add 13/6 on both sides:

$5+\frac{13}{6}=2b$

$\frac{30+13}{6}=2b$

$\frac{43}{6}=2b$

Divide both sides by 2:

$\frac{43}{2(6)}=b$

$\frac{43}{12}=b$

So we have the equation:

$y=\frac{-13}{24}x^2+\frac{43}{12}+3$

Let's evaluate $a+b+c$ now:

$\frac{-13}{24}+\frac{43}{12}+3$

$\frac{-13+86+72}{24}$

$\frac{73+72}{24}$

$\frac{145}{24}$

4 0

3 years ago

5.8(3)+3(1.1). gjcjggv

timurjin [86]

- Answer -

20.7

- Work -

5.8 * 3 = 17.4

3 * 1.1 = 3.3

3.3 + 17.4 = 20.7

3 0

3 years ago

Read 2 more answers

Please please please

Anna007 [38]

15:7.5:30
This is because 15 is the smallest, which is half of 4(30). And right between 15 and 30 is 7.5.

Hope this helps

8 0

3 years ago

Read 2 more answers

Factor the expression completely.<br><br> 7x - x2

steposvetlana [31]

Answer:

x(7 - x)

Step-by-step explanation:

Given

7x - x² ← factor out x from both terms

= x(7 - x) ← in factored form

4 0

3 years ago

(TEN POINTS)

Rainbow [258]

F(-1)= -3 is (-1,-3) and f(2) = 6 is (2,6) where f(x) = y
y=mx + b is the slope-intercept form whereas m equals the slope (rate of change) and b equals the y-intercept (initial amount/what y is when x is 0.)

First, we need to find the slope between the two points (-1,-3) and (2,6). To find the slope we could use one of it's formulas $\frac{y^2 - y^1}{x^2 - x^1}$ .
1. (-1,-3)
2. (2,6)
$\frac{6 - -3}{2 - -1}$ → $\frac{9}{3}$ → $\frac{3}{1}$

The slope is 3 ( $\frac{3}{1}$ ). Thusly, y = 3x + b

To find out the y-intercept, we can reverse the slope. [Note: This $\frac{3}{1}$ is in $\frac{rise}{run}$ where rise is 'y' and run is 'x'. Reversed would be $\frac{-3}{-1}$ ]. Take the second ordered pair and use our reversed slope on it until we get 0 for x.

(2, 6) ⇒ (2 - 1, 6 -3) ⇒ (1, 3) ⇒ (0,0)

Y-intercept is 0. Therefore, y= 3x + 0 [NOTE: y = f(x), so if you want it in function notation form it's just f(x) = 3x + 0.]

6 0

3 years ago