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3 years ago

What is the equation of the line with a slope of 1/2, and which passes through the point (-2, 4)?

Mathematics

1 answer:

irina1246 [14]3 years ago

7 0

Step-by-step explanation:

How I figured this out is kind of plug in play with a bit of algebra, you want to get it to y = mx + b so to do that, you first need to set up your equation like (y - y1) = m(x - x1)

Plug in what you know:

(y - 4) = 1/2(x + 2) (notice I changed the x- x1 to x + x1 because x1 in this is a negative and subtracting a negative is the same as adding)

Then figure out what you don't know:

Distribute 1/2 to x and -2

(y - 4) = 1/2x -1

add 4 on both sides to leave y by itself

y = 4.5x + 3

Therefore your answer should be y = 4.5x + 3

Let me know if I got it wrong please

Hope this helps! <3

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You invest AED 5000 in a saving account that earns 4% interest each year. If you do not use the account for a year, how much mon

Viktor [21]

Answer:

5200 AED or 1404 USD

Step-by-step explanation:

You have 5000 in your account. If your money grows 4% each year, it's basically like multiplying by 1.04.

5000 * 1.04 = 5200

If the question is asking in USD, the conversion rate from AED to USD is

AED * 0.27 = USD

We can substitute

5200 AED* 0.27 = 1404 USD.

6 0

3 years ago

Solving a Two-Step Matrix Equation Solve the equation:

Cloud [144]

Answer:

$\boxed {x_{1} = 3}$

$\boxed {x_{2} = -4}$

Step-by-step explanation:

Solve the following equation:

$\left[\begin{array}{ccc}3&2\\5&5\\\end{array}\right] \left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right] + \left[\begin{array}{ccc}1\\2\\\end{array}\right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right]$

-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:

-First equation:

$3x_{1} + 2x_{2} + 1 = 2$

-Second equation:

$5x_{1} + 5x_{2} + 2 = -3$

-Choose one of the two following equations, which I choose the first one, then you solve for $x_{1}$ by isolating

$3x_{1} + 2x_{2} + 1 = 2$

-Subtract $1$ to both sides:

$3x_{1} + 2x_{2} + 1 - 1 = 2 - 1$

$3x_{1} + 2x_{2} = 1$

-Subtract $2x_{2}$ to both sides:

$3x_{1} + 2x_{2} - 2x_{2} = -2x_{2} + 1$

$3x_{1} = -2x_{2} + 1$

-Divide both sides by $3$ :

$3x_{1} = -2x_{2} + 1$

$x_{1} = \frac{1}{3} (-2x_{2} + 1)$

-Multiply $-2x_{2} + 1$ by $\frac{1}{3}$ :

$x_{1} = \frac{1}{3} (-2x_{2} + 1)$

$x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}$

-Substitute $-\frac{2x_{2} + 1}{3}$ for $x_{1}$ in the second equation, which is $5x_{1} + 5x_{2} + 2 = -3$ :

$5x_{1} + 5x_{2} + 2 = -3$

$5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3$

Multiply $-\frac{2x_{2} + 1}{3}$ by $5$ :

$5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3$

$-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3$

-Combine like terms:

$-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3$

$\frac{5}{3}x_{2} + \frac{11}{3} = -3$

-Subtract $\frac{11}{3}$ to both sides:

$\frac{5}{3}x_{2} + \frac{11}{3} - \frac{11}{3} = -3 - \frac{11}{3}$

$\frac{5}{3}x_{2} = -\frac{20}{3}$

-Multiply both sides by $\frac{5}{3}$ :

$\frac{\frac{5}{3}x_{2}}{\frac{5}{3}} = \frac{-\frac{20}{3}}{\frac{5}{3}}$

$\boxed {x_{2} = -4}$

-After you have the value of $x_2$ , substitute for $x_{2}$ onto this equation, which is $x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}$ :

$x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}$

$x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}$

-Multiply $-\frac{2}{3}$ and $-4$ :

$x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}$

$x_{1} = \frac{8 + 1}{3}$

-Since both $\frac{1}{3}$ and $\frac{8}{3}$ have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:

$x_{1} = \frac{8 + 1}{3}$

$x_{1} = \frac{9}{3}$

$\boxed {x_{1} = 3}$

5 0

3 years ago

Write an equivalent expression by distributing the

melamori03 [73]

Answer:

-8m + (-7.7n - 6)

Step-by-step explanation:

You distribute the negative in front of the parentheses, to everything inside of the parentheses, and change the sign to addition.

7 0

3 years ago

!!!HELP ME HELP PLSSSSSSS!!!!!!!!!! What is the measure of angle x?

sergiy2304 [10]

Answer:

Step-by-step explanation:

Im to lazy to do the math

4 0

3 years ago

I NEED THIS FOR MY TEST ASAP!

Reptile [31]

Answer:

-1

Step-by-step explanation:

2(.5n-3)=n-0.25(12-12n)

first you distribute whatever is on the outside of the parenthesis to the inside of the parenthesis

1n-6=n-3+3n

then you combine like terms and end up with

1n-6=-3+4n

add 6 to each side to get

n=3+4n

subtract 4n from each side to get

-3n=3

divide -3 from each side to get

n=-1

4 0

2 years ago