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3 years ago

11

Line A passes through the points (3,4) and (-1,2). Line B passes through the points (-12,0) and (-6,-4). At what point do the li

nes intersect?

1 answer:

Helen [10]3 years ago

4 0

Answer: -9 is what im geting sorry if not help

Step-by-step explanation:

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Simplify the expression and write out steps plz :)<br> (4- root3)(root7+ root2)

dybincka [34]

You can do this with foil
F(which is the first term of both factors): 4*sqrt(7)
O(outside terms of both factors first and last) 4*sqrt(2)
I (Inside terms 2nd and 3rd) = - sqrt(3) sqrt(7) = - sqrt(21)
L (Last term in each of the factors) - sqrt(3)*sqrt(2) = - sqrt(6)

Combine terms: 4*sqrt(7) + 4*sqrt(2) - sqrt(21) - sqrt(6) <<<< answer.

7 0

4 years ago

Part 3: Use the information provided to write the vertex formula of each parabola. Please show the work

rodikova [14]

Answer: 1. y = 2(x + 4)² - 3

$\bold{2.\quad y=-\dfrac{1}{3}(x+8)^2-7}$

$\bold{3.\quad y=-\dfrac{1}{2}(x-7)^2+1}$

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

Notes: The vertex form of a parabola is y = a(x - h)² + k

(h, k) is the vertex
p is the distance from the vertex to the focus

$\bullet\quad a=\dfrac{1}{4p}$

1)

$\text{Vertex}=(-4,-3)\qquad \text{Directrix}:y=-\dfrac{25}{8}\\\\\text{Given}:(h, k)=(-4, 3)\\\\p=\dfrac{-24}{8}-\dfrac{-25}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2$

Now input a = 2 and (h, k) = (-4, -3) into the equation y = a(x - h)² + k

y = 2(x + 4)² - 3

******************************************************************************************

2)

$\text{Vertex}=(-8,-7)\qquad \text{Directrix}:y=-\dfrac{-25}{4}\\\\\text{Given}:(h, k)=(-8, -7)\\\\p=\dfrac{-28}{4}-\dfrac{-25}{4}=\dfrac{-3}{4}}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-3}{4})}=\dfrac{1}{-3}=-\dfrac{1}{3}$

Now input a = -1/3 and (h, k) = (-8, -7) into the equation y = a(x - h)² + k

$\bold{y=-\dfrac{1}{3}(x+8)^2-7}$

******************************************************************************************

3)

$\text{Focus}=\bigg(7,\dfrac{1}{2}\bigg)\qquad \text{Directrix}:y=\dfrac{3}{2}$

The midpoint of the focus and directrix is the y-coordinate of the vertex:

$\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1$

The x-coordinate of the vertex is given in the focus as 7

(h, k) = (7, 1)

Now let's find the a-value:

$p=\dfrac{2}{2}-\dfrac{3}{2}=\dfrac{-1}{2}}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}$

Now input a = -1/2 and (h, k) = (7, 1) into the equation y = a(x - h)² + k

$\bold{y=-\dfrac{1}{2}(x-7)^2+1}$

7 0

3 years ago

Find two numbers such that their difference and also the difference of their cubes are given numbers; say, their difference is 6

ANTONII [103]

Answer:

Step-by-step explanation:

We are to find two numbers such that their difference and also the difference of their cubes are given numbers

Let the two numbers be x+3 and x-3

so that the difference between the numbers is 6.

Difference between the cubes

= $(x+3)^3-(x-3)^3\\= (x+3-x+3)[(x+3)^2+(x-3)^2-(x+3)(x-3)] = 504\\3x^2+9=84\\x^2 = 25\\x = 5 or -5$

So the numbers are either 2 and 8 or

(-2 and -8)

4 0

4 years ago

Simplify. 57r−27r this problem

Leno4ka [110]

The answer should be 30r

5 0

3 years ago

Read 2 more answers

F(x)=2x+1and g(x)=3x-2 elevate function f(2)

marysya [2.9K]

Answer:

5

Step-by-step explanation:

f(x)=2x+1

f(x)=2(2)+1

f(x)=4+1

f(x)=5

7 0

3 years ago