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3 years ago

What is the vertex form of y = x2 + 8x – 3

Mathematics

1 answer:

9966 [12]3 years ago

6 0

Answer:

(-4,-19)

Step-by-step explanation:

y = x² + 8x - 3

y = x² + 2(x)(4) + 4² - 4² - 3

y = (x + 4)² - 16 - 3

y = (x + 4)² - 19

Vertex: (-4,-19)

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35. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

Montano1993 [528]

Answer:

The linear equation for the line which passes through the points given as (-2,8) and $(4,6), is written in the point-slope form as $y=-\frac{1}{3} x-\frac{26}{3}$ .

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-2,8) and (4,6).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-2,8) and (4,6). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute $6 \& 8$ for $y_{2}$ and $y_{1}$ respectively, and 4&-2 for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows, $m=\frac{6-8}{4-(-2)}$

$\begin{aligned}&m=\frac{-2}{6} \\&m=-\frac{1}{3}\end{aligned}$

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute $-\frac{1}{3}$ for m,-2 for $x_{1}$ , and 8 for $y_{1}$ in the above equation and simplify using the distributive property as follows, $y-8=-\frac{1}{3}(x-(-2))$\\ $y-8=-\frac{1}{3}(x+2)$\\ $y-8=-\frac{1}{3} x-\frac{2}{3}$$

Step 3 of 3

Simplify the equation further.

Add 8 on each side of the equation $y-8=-\frac{1}{3} x-\frac{2}{3}$ , and simplify as follows, $y-8+8=-\frac{1}{3} x-\frac{2}{3}+8$

$y=-\frac{1}{3} x-\frac{2+24}{3}$$\\ $$y=-\frac{1}{3} x-\frac{26}{3}$$

This is the required linear equation.

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1 year ago

A sphere has a volume of Vequals=3600 in cubedin3. Find its surface area.

Mice21 [21]

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad 
\begin{cases}
r=radius\\
------\\
V=3600
\end{cases}\implies 3600=\cfrac{4}{3}\pi r^3
\\\\\\
3600=\cfrac{4\pi r^3}{3}\implies \sqrt[3]{\cfrac{3\cdot 3600}{4\pi }}=\boxed{r}\\\\
-----------------------------\\\\
\textit{surface area of a sphere}\\\\
S=4\pi r^2\implies S=4\pi \left(\boxed{\sqrt[3]{\cfrac{3\cdot 3600}{4\pi }}} \right)^2$

simplify away

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3 years ago

2. Lindsay, who is the youngest member of the softball team at King's Fork High School, is 7

Andrei [34K]

Lindsay’s age = 7 - 1/3n

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3 years ago

A car weighs 4,000 pounds wich comparison is true

Stella [2.4K]

Answer:

Step-by-step explanation:

2000=1 ton so 4000=2tons

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2 years ago

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For what value of the variable will the expression 8b−27 be equal to the following:<br> 5

qaws [65]

Answer:

We need to find the value of b to make 8b - 27 be equal to 5, so:

8b - 27 = 5

We solve the equation:

8b = 5 + 27

8b = 32

We divide both sides by 8:

b = 32/8 = 4

So now, we know that b=4, and we can verify:

8*4 - 27 = 5

32 - 27 = 5 TRUE

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3 years ago

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