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3 years ago

How do I graph (x−4)(x+2)

Mathematics

1 answer:

Anastasy [175]3 years ago

6 0

(x - 4)(x + 2)

x^2 + 2x - 4x - 8

x^2 - 2x - 8

Let y = x^2 - 2x - 8

It is a parabola.

Take it from here.

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How to solve this one

Stells [14]

Answer:

(-5,1)

Step-by-step explanation:

Add it together

3x - 2x = x

y - y = 0

9 - 14 = -5

x = -5

Choose a random equation, doesn't matter.

3x + y = -14

3(-5) + y = -14

-15 + y = -14

y = -14 + 15

y = 1

7 0

3 years ago

Read 2 more answers

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

3 years ago

Write an equation for a parabola with a focus of (1,-2) and a directrix of y=6

FinnZ [79.3K]

Answer:

y = - $\frac{1}{16}$ (x - 1)² + 2

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and the directrix.

Using the distance formula

$\sqrt{(x-1)^2+(y+2)^2^}$ = | y - 6 |

Square both sides

(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )

(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )

(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )

(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )

16y = - (x - 1)² + 32 ( divide all terms by 16 )

y = - $\frac{1}{16}$ (x - 1)² + 2

8 0

3 years ago

Find the polar equation of the conic with the focus at the pole, directrix x = 4, and eccentricity 1.

BabaBlast [244]

Answer:

Choice D is correct

Step-by-step explanation:

The eccentricity of the conic section is 1, implying we are looking at a parabola. Parabolas are the only conic sections with an eccentricity of 1.

Next, the directrix of this parabola is located at x = 4. This implies that the parabola opens towards the left and thus the denominator of its polar equation contains a positive cosine function.

Finally, the value of k in the numerator is simply the product of the eccentricity and the absolute value of the directrix;

k = 1*4 = 4

This polar equation is given by alternative D

6 0

3 years ago

Question in pic! help asapp! will give brainliest!

Yuliya22 [10]

Answer:

4/x^7

Step-by-step explanation:

4x^-7 = 4* x^-7 = 4* 1/x^7 = 4/x^7

3 0

3 years ago

Read 2 more answers