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MatroZZZ [7]
3 years ago
11

The following proof shows an equivalent system of equations created from another system of equations. 2x + 2y = 14 −x + y = 5 Gi

ven 2x + 2y = 14 y = x + 5 Fill in the missing reason in the proof. Statements Reasons 2x + 2y = 14 −x + y = 5 Given 2x + 2y = 14 y = x + 5 ? Multiplication Property of Equality Addition Property of Equality Division Property of Equality Subtraction Property of Equality
Mathematics
1 answer:
anzhelika [568]3 years ago
6 0

Addition Property of Equality

Step-by-step explanation:

The equations are given as;

2x+2y=14----(i)

y-x=5 ?-------apply addition property of equality

y-x+x=5+x

y=5+x -------use this expression in equation (i)

2x +2(5+x)=14 ----------open brackets on the left side

2x+10+2x=14 -------collect like terms

4x+10=14

4x=14-10

4x=4

4x/4=4/4

x=1

y-1=5

y=6

Learn More

Addition property of Equality :brainly.com/question/3474035

Keywords: proof,shows, equivalent,system of equations

#LearnwithBrainly

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Write the equation (use any form you choose) of the line that passes through the points (4, 3) and (-2, 6)
777dan777 [17]
Gradient
m =  \frac{y - y}{x - x}  \\ m =  \frac{6 - 3}{ - 2 - 4}  \\ m =  \frac{ - 1}{2}
equation \\ y = mx + c \\   3 = \frac{ - 1}{2}  \times(4) + c \\ 3 =  - 2 + c \\ c =5


THE ANSWER IS :-
y = mx + c \\ y =  - \frac{1}{2} x + 5



5 0
4 years ago
Margo wants new carpet and a new wallpaper border for her bedroom. The room is 5.7 yards long and 6 7 8 yards wide. About how ma
Lelu [443]

Answer:

39.19 yards^2

25.15 yards

Step-by-step explanation:

To determine the squares square yards of carpet needed, we have to determine the area of the room

The room is shaped like a rectangle

area of a rectangle = length x breadth

5.7 x 6 7/8

To multiply, convert 6 7/8 to a  decimal

to do this, divide 7 by 8. Add the value gotten to 6

5.7 x 6.875 =39.19 yards^2

To determine the yards needed for the border, calculate the perimeter of the room

Perimeter = 2 x (length + breadth)

2 x(5.7 + 6.875) = 25.15 yards

4 0
3 years ago
A baseball diamond is a square whose sides are 9090 feet long. Suppose a player running from second base to third base has a spe
Arada [10]
<h2>Answer:</h2>

<em><u>Rate of change of distance at that instant = 0.066 ft/sec </u></em>

<h2>Step-by-step explanation:</h2>

In the question,

The baseball field is in the square diamond shape.

Side length of square = 9090 ft.

Now,

The player runs from the 2nd base to the 3rd base.

Speed of running of player, v = 30 ft/ sec.

Distance of the player from third base = 20 ft.

Now,

Let us say the distance of the player from the Home base is = l

So,

In the triangle using the Pythagoras theorem, we get,

l^{2}=x^{2}+s^{2}

where, 'x' is the distance of the player from the third base and 's' is the side of the square field base.

So,

l^{2}=x^{2}+s^{2}\\On\,differentiating\,we\,get,\\2l\frac{dl}{dt}=2x\frac{dx}{dt}\\l\frac{dl}{dt}=x\frac{dx}{dt}\\

Now,

Also, at the moment when, x = 20,

Length from the Home base is,

l^{2}=20^{2}+9090^{2}\\l=9090.022\,ft.

Now,

On putting we get,

l\frac{dl}{dt}=x\frac{dx}{dt}\\(9090.022)\frac{dl}{dt}=20(30)\\\frac{dl}{dt}=0.066\,ft./sec.

<em><u>Therefore, the rate of change of distance from the home plate is 0.066 ft/s</u></em>

6 0
4 years ago
triangle J'K'L' shown on the grid below a dilation of triangle JKL using the origin as the center of dilation:​
-BARSIC- [3]

Answer:  b) 3

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

From K to L the y-length is 2 and the x-length is 1

From K' to L' the y-length is 6 and the x-length is 3

Therefore, J'K'L' is 3 times as large as JKL so the dilation is 3.

6 0
4 years ago
11. The length of a tennis court is 78 feet. This is 51 feet more than the width. What is the width?
IRINA_888 [86]
Length - 51 = width
78 - 51 = 27

width = 27
5 0
3 years ago
Read 2 more answers
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