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3 years ago

Rewrite without absolute value for the given conditions, y=|x−5|+|x+5|, if x>5

Mathematics

1 answer:

34kurt3 years ago

3 0

Answer:

y=2x when x>5

Step-by-step explanation:

y=|x−5|+|x+5|

If x > 5 then x-5 is greater than 0 so we can remove the absolute value bars from the first term

x>5 then x+5 >0 so we do not need the absolute value bars on the second term

y = x-5 + x+5

Combine like terms

y = x+x-5+5

y = 2x

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Find the solution set of the following equations: 2y=2x+7 X=y+2

kirill115 [55]

Answer:

The system of equations has no solution.

Step-by-step explanation:

Given the system of equations

2y = 2x+7

x = y+2

solving the system of equations

$\begin{bmatrix}2y=2x+7\\ x=y+2\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}2y-2x=7\\ -y+x=2\end{bmatrix}$

Multiply -y+x=2 by 2: -2y+2x=4

$\begin{bmatrix}2y-2x=7\\ -2y+2x=4\end{bmatrix}$

so adding

$-2y+2x=4$

$+$

$\underline{2y-2x=7}$

$0=11$

so the system of equations becomes

$\begin{bmatrix}2y-2x=7\\ 0=11\end{bmatrix}$

0 = 11 is false, therefore the system of equations has no solution.

Thus,

No Solution!

3 0

3 years ago

X -1 3 5 y 7 3 1 find the average rate of change from x=-1 to x=5

zloy xaker [14]

X -1 3 5
y 7 3 1 

avgroc = ( 1 -7) / (5 - -1) = -6/6 = -1

7 0

4 years ago

Can someone solve these please using the formula AB | a - b | And can you show work

Lana71 [14]

Answer: 1) AC = 13

The formua does not actually apply to all of the problems.

Step-by-step explanation:

1) The absolute value of -8 is added to the absolute value of 5. 8+5=13

2) Subtract the length of the EF from EG to get the length of FG 21 -6 = 15

3) Take what's given and create an equation to solve. 4x + 15 +39 =110. 4x = 110 - (15+39).

4x =110-54. 4x =56. x=56/4. x=14

4) Create another equation. You have two segments that add up to the length of EG, given =23

EF+FG=EG

(2x-12)+(3x-15)=23

5x - 27 = 23

5x= 23+27 5x =50. x = 10

Substitute 10 for x

EF=2(10) -12 EF=8

FG=3(10)-15. FG=15

EF+FG =EG.

8 + 15 = 23

5) 2/5 of 25 is 10 So EF is 10. Subtract from 25 to get FG

FG = 15

I hope this helps you.

4 0

3 years ago

What is the surface area of the figure shown? Plz answer asap

Luba_88 [7]

Answer:

$264\ cm^{2}$

Step-by-step explanation:

we know that

The surface area of the figure is equal to the lateral face of the triangular pyramid plus the lateral face of the rectangular prism plus the area of the base of the rectangular prism

step 1

Find the lateral face of the triangular prism

The lateral area is equal to the area of its four lateral triangular faces

$LA=4(\frac{1}{2}(6)(7))=84\ cm^{2}$

step 2

Find the lateral area of the rectangular prism

The lateral area is equal to the perimeter of the base multiplied by the height

$LA=(4)(6)(6)=144\ cm^{2}$

step 3

Find the area of the base of the rectangular prism

$B=(6)(6)=36\ cm^{2}$

step 4

Find the surface area

$84\ cm^{2}+144\ cm^{2}+36\ cm^{2}=264\ cm^{2}$

3 0

3 years ago

Is 42.9 a rational number

Elan Coil [88]

Answer:

Yes.

Step-by-step explanation:

What is a rational number?

A whole number, fraction, terminating or recurring decimal.

42.9 = 429/10 which is a fraction.

So it's rational.

3 0

4 years ago