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3 years ago

Use the elimination method to solve the system of equations. Choose the correct ordered pair.

Mathematics

1 answer:

Phoenix [80]3 years ago

7 0

For this problem I would change:

2x + 3y = 25 into

-2x - 3y = -25

Then, I would add up both equations by lining them up top of another.

5x + 3y = 31
+ -2x - 3y = -25

3x = 6
x = 2

Now that you have x, solve for y.

5x + 3y = 31

5(2) + 3y = 31

10 + 3y = 31

3y = 21

y = 7

So, x is 2 and y is 7.

Check to see if the values are correct by plugging them into the other equation.

2x + 3y = 25

2(2) + 3(7) = 25

4 + 21 = 25

25 = 25

Since the values are correct, the solution to this problem is A (2, 7).

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What is the distance between the points (21 , 13) and (3 , 13) in the coordinate plane?

Oxana [17]

Answer:

$\displaystyle d = 18$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Identify

Point (21, 13)

Point (3, 13)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(3-21)^2+(13-13)^2}$
[√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{(-18)^2+(0)^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{324+0}$
[√Radical] Add: $\displaystyle d = \sqrt{324}$
[√Radical] Evaluate: $\displaystyle d = 18$

5 0

3 years ago

George bought 7.5 cases of pancake mix for his diner. A case contains 12 1.3-pound boxes. How many pounds of pancake mix did Geo

Ilya [14]

In order to get the answer to this problem, first we have to find out how many pounds does one case of pancake mix have. We know that one box has 1.3 pounds of pancake mix. We also know that one case has 12 boxes. So first, we multiply 1.3 to 12. The answer we will get is 15.6. One case of pancake mix has a total of 15.6 pounds of pancake mix. Now we also know there are 7.5 cases that George bought. So in order to get the total pounds George bought, we multiply 15.6 to 7.5. So all in all, George bought 117 pounds of Pancake Mix.

8 0

3 years ago

Read 2 more answers

Please helpppppppp -2p-4=2

OlgaM077 [116]

p = -3

Step-by-step explanation:

-2p-4=2

add 4 both sides

-2p-4+4=2+4

-2p=6

divide -2 both sides

-2p/-2=6/-2

p = -3

hope it's helpful ❤❤❤

THANK YOU.

5 0

3 years ago

Work out 12+8÷(9-5) 0.018÷0.06 Express as single fraction 5/7÷2/5

Anettt [7]

Step-by-step explanation:

I don't know if the first set of numbers is all in one set, but I'll do my best to give you an answer.

Really all you need to do is use PEMDAS for the first question.

(Parentheses, exponents, multiply, divide, add, subtract. In that order)

$1 2 + 8 \div (9 - 5) \\ 12 + 8 \div 4 \\ 12 + 2 \\ 14$

Then to simplify that fraction next to it, notice that 0.018 is 3x 0.06.

that's a 3:1 ratio, so it ends up simplifying to this:

$\frac{3}{1}$

Lastly, to solve the division of that fraction. If you divide by a fraction, you multiply whatever it's dividing by its inverse.

So...

$\frac{5}{7} \div \frac{2}{5} \\ \frac{5}{7} \times \frac{5}{2} \\ \frac{25}{14}$

7 0

3 years ago

Given: BC bisects DBE. Prove: ABD is congruent to ABE

Arada [10]

Answer:

See below

Step-by-step explanation:

BC bisects <DBE and if AC is a straight line then you have that:

<ABD + <DBC = 180 (straight angle because of line AC)

<ABE + <CBE = 180 ( straight angle because of line AC)

Because BC bisects <DBE => < DBC = <CBE

So <ABD and <ABE must be the same to both sum 180 when added < DBC

7 0

3 years ago