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2 years ago

Write an equation of the line passing through point P(2, 3) that is perpendicular to the line y -4 = -2(x+3)

Mathematics

1 answer:

Mariulka [41]2 years ago

3 0

Perpendicular = opposite sign and reciprocal slope
Slope of -2 turns into 1/2
Y-y1 = m(x-x1)
Solution; y-3 = 1/2(x-2)

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Serhud [2]

Hello how are you today my day is going great I wanted to make a new friend!

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3 years ago

Please help solve this system of equations

stepan [7]

Make a substitution:

$\begin{cases}u=2x+y\\v=2x-y\end{cases}$

Then the system becomes

$\begin{cases}\dfrac{2\sqrt[3]{u}}{u-v}+\dfrac{2\sqrt[3]{u}}{u+v}=\dfrac{81}{182}\\\\\dfrac{2\sqrt[3]{v}}{u-v}-\dfrac{2\sqrt[3]{v}}{u+v}=\dfrac1{182}\end{cases}$

Simplifying the equations gives

$\begin{cases}\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81}{182}\\\\\dfrac{4\sqrt[3]{v^4}}{u^2-v^2}=\dfrac1{182}\end{cases}$

which is to say,

$\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81\times4\sqrt[3]{v^4}}{u^2-v^2}$

$\implies\sqrt[3]{\left(\dfrac uv\right)^4}=81$

$\implies\dfrac uv=\pm27$

$\implies u=\pm27v$

Substituting this into the new system gives

$\dfrac{4\sqrt[3]{v^4}}{(\pm27v)^2-v^2}=\dfrac1{182}\implies\dfrac1{v^2}=1\implies v=\pm1$

$\implies u=\pm27$

Then

$\begin{cases}x=\dfrac{u+v}4\\\\y=\dfrac{u-v}2}\end{cases}\implies x=\pm7,y=\pm13$

(meaning two solutions are (7, 13) and (-7, -13))

8 0

2 years ago

What does the x coordinate of a point tell you?

valentinak56 [21]

Answer:

X is for the height

Step-by-step explanation:

Arcodding to the coordinate table , this chart has x and y. We measure the y first then we measure the x.

the y coordinate show the length and the y measure the height

I hope it'll help you much

Thank you for asking

6 0

3 years ago

Multiply each binomial and find the coefficients.

Bas_tet [7]

Answers:

Row one: 1 and 1

Row two: 1, 2, and 1

Row three: 1, 3, 3, and 1

Row four: 1, 4, 6, 4, and 1

=========================================

Explanation:

Each value can be found in Pascal's triangle. You can also use the nCr combination formula to get each value. The nCr formula is

$_n C _r = \frac{n!}{r!(n-r)!}$

The value of n represents the row number. The r value is the column number, so to speak, for each row.

5 0

2 years ago

Steve and Elizabeth decide to become partners in a children’s cooking school. They need $80,000 for the franchise. They invest i

PilotLPTM [1.2K]

Answer:

The share of Steve is $34,285 .71

The share of Elizabeth is $45,714.28

Step-by-step explanation:

The total investment of Steve and Elizabeth in cooking school = $80, 000

The ratio of investment of Steve and Elizabeth = 3: 4

Let us assume the common factor in the ratio is m.

So, the ratio of Steve = 3 m

and the ratio of Steve = 4 m

So, according to the question:

⇒ 3 m + 4 m = 80,000

or, 7 m = 80,000

⇒ m = 80,000 / 7 = 11,428.57

or, m = 11,428.57

⇒ The share of Steve = 3 m = 3 x (11,428.57) = 34,285 .71

⇒ The share of Elizabeth = 4 m = 4 x (11,428.57) = 45,714.28

4 0

2 years ago