Geometry question..can anyone help?

In order to solve the following system of equations by addition, which of the

Pavlova-9 [17]

Answer:

Multiply the top equation by -3 and the bottom equation by 2

Step-by-step explanation:

Given system of equations:

$\begin{cases}4x-2y=7\\3x-3y=15 \end{cases}$

To solve the given system of equations by addition, make one of the variables in both equations sum to zero. To do this, the chosen variable must have the same coefficient, but it should be negative in one equation and positive in the other, so that when the two equations are added together, the variable is eliminated.

To eliminate the variable y:

Multiply the top equation by -3 to make the coefficient of the y variable 6:

$\implies -3(4x-2y=7) \implies -12x+6y=-21$

Multiply the bottom equation by 2 to make the coefficient of the y variable -6:

$\implies 2(3x-3y=15) \implies 6x-6y=30$

Add the two equations together to eliminate y:

$\begin{array}{l r r}& -12x+6y= &-21\\+ & 6x-6y= & 30\\\cline{1-3}& -6x\phantom{))))))} = & 9\end{array}$

Solve for x:

$\implies -6x=9$

$\implies x=-\dfrac{9}{6}=-\dfrac{3}{2}$

Substitute the found value of x into one of the equations and solve for y:

$\implies 3\left(-\dfrac{3}{2}\right)-3y=15$

$\implies -\dfrac{9}{2}-3y=15$

$\implies -3y=\dfrac{39}{2}$

$\implies y=-\dfrac{39}{2 \cdot 3}$

$\implies y=-\dfrac{13}{2}$

Learn more about systems of equations here:

brainly.com/question/27868564

brainly.com/question/27520807

3 0

2 years ago

Read 2 more answers

The coordinates of the vertices for rectangle ABCD are A (2,4), B (6,10), C (9,8) and D (5,2). What

sweet [91]

Answer:

D. $\sqrt{65}$

Step-by-step explanation:

The computation of the length of a diagonal (AC or BD) of the rectangle is shown below:

As we know that

The Diagonal length of AC is

$= (x_2 - x_1)^2 + (y_2 - y_1)^2\\\\= (9 -2)^2 + (8 - 4)^2\\\\= (7)^2 + (4)^2$

$= \sqrt{49 + 16}\\\\= \sqrt{65}$

Therefore correct option is D.

3 0

2 years ago

Which of the following rational functions is graphed below?

Nimfa-mama [501]

Answer:

F(x) = 1/x^2

Step-by-step explanation:

F(x) = 1/x^2 is

y = 1/x^2

graph goes up to 10 each side

plug in 1,2,3,4,5,6,7,8,9,10 for x and see what y looks like

when x is 1,2,3,4,5,6,7,8,9,10

y is 1,1/4,1/9,etc

5 0

2 years ago

(2.3 x 105)(1.5 x 104) in scientific notation plssss ASAP

zhenek [66]

By using scientific notation we calculated (2.3 $\times$ 10⁵)(1.5 $\times$ 10⁴) we got 345 $\times$ 10⁷.

Given that,

(2.3 $\times$ 10⁵)(1.5 $\times$ 10⁴)

By using scientific notation

The scientific notation allows us to express extremely large or extremely small numbers by multiplying them by single-digit integers and by 10 raised to the power of the corresponding exponent. The exponent is either positive or negative depending on how big or little the number is.

Now, we calculate

(2.3 $\times$ 10⁵)=2.5 $\times$ 100000=230000

(1.5 $\times$ 10⁴)=1.5 $\times$ 10000=15000

Now,

=230000 $\times$ 15000

=3450000000

=345 $\times$ 10⁷

Therefore, By using scientific notation we calculated (2.3 $\times$ 10⁵)(1.5 $\times$ 10⁴) we got 345 $\times$ 10⁷.

To learn more about scientific notation visit: brainly.com/question/18073768

#SPJ1

3 0

1 year ago

A company sells fruit smoothies in two sizes: 6 ounces and 12 ounces. You know that a 6-ounce bottle contains 96 milligrams of s

galina1969 [7]

Answer:

I believe it would be 192 milligrams.

Step-by-step explanation:

They said the amount of sodium is equal to the amount of ounces meaning it would be 6ounce:96milligrams. In this case, doubling 6 would be 12, resulting in doubling 96 as well. I'm not 100% sure, this problem contains an unnecessary amount of information for a simple concept.

3 0

3 years ago