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4 years ago

Given that f(x) =3x^2 - 6x + 11 ,find the values of a,b and c for which f(x) = a(x - b)^2 + c

1 answer:

6 0

First you have to complete the square. The first step would be 3x^2-6x=-11. Then you divide -6 by 2 and square the number you get. 3x^2-6x+9=-11+9. 3x^2-6x+9=-2. Factor out the three to get 3(x^2-2x+3)=-2. You can't factor what is in the parenthesis. You should then add two to each side. 3(x^2-2x+3)+2.
A=3
B= I have no clue sorry.
C=2

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The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132. Lara wrote the foll

ra1l [238]

It is incorrect because the length of the unknown side is the square root of 7,225.

If you use the pythagorean theorem and plug in the values,

a^2 + 132^2 = 157^2

a^2 + 17424 = 24649
-17424 -17424
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a^2 = 7225

If you square root it, the final answer would be 85.

7 0

3 years ago

Read 2 more answers

Simplify the square root 84/169

morpeh [17]

Answer:

2 times the square root of 21 all over 13

Step-by-step explanation:

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3 years ago

The solution to a system of linear equations is (-3,-3) Which system of linear equations has this point as its solution? x -5y=-

Ann [662]

Answer:

$x-5y=12$ and $3x+2y=-15$

Step-by-step explanation:

The first system is

$x-5y=-12$ and $3x+2y=-15$

We substitute x=-3 and y=-3

$-3-5*-3=12\ne-12$ and $3*-3+2*-3=-15$

Both equations are not satisfied

The next system is

$x-5y=12$ and $3x+2y=-15$

We substitute x=-3 and y=-3

$-3-5*-3=12$ and $3*-3+2*-3=-15\ne15$

Both equations are satisfied

The next system is

$x-5y=-12$ and $3x+2y=15$

We substitute x=-3 and y=-3

$-3-5*-3=12\ne12$ and $3*-3+2*-3=-15$

Both equations are not satisfied

The next system is

$x-5y=12$ and $3x+2y=15$

We substitute x=-3 and y=-3

$-3-5*-3=12\ne-12$ and $3*-3+2*-3=-15$

Both equations are not satisfied

6 0

4 years ago

Identify the values of m and b of the linear function y = mx + b, graphed below.

Varvara68 [4.7K]

<h2>Finding the slope and y-intercept of a line given the graph</h2><h3>Answer:</h3>

$b = 4$

$m = -\frac{1}{3}$

<h3>Step-by-step explanation:</h3>

An equation of a line written in its Slope-intercept Form, $y = mx +b$ , has $b$ as its $y$ -intercept and $m$ as its slope.

$b$ or the $y$ -intercept is the $y$ -coordinate when $x = 0$ . On the given line, we can see that when $x = 0$ , $y = 4$ . It's $y$ -intercept is the point $(0,4)$ so $b = 4$ .

The slope, $m$ , of the line can be calculated by $\frac{y_2 -y_1}{x_2 -x_1}\\$ where $x_n$ and $y_n$ is the $xy$ -coordinates of any point $n$ on the line. In the given line, we can see that $(5,3)$ is on the line so this can be point $1$ . $(0,4)$ is also on the line (yes, you can also use the $y$ -intercept in calculating the slope of the line) so this can be our point $2$ .