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wlad13 [49]
3 years ago
14

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

Mathematics
1 answer:
kirill115 [55]3 years ago
3 0

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!

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3 years ago
The sphere is _____ cubic centimeters bigger than the cube. (Round to the nearest cubic centimeter.)
Misha Larkins [42]

ANSWER

The sphere is 10762 cubic centimeters bigger than the cube.

EXPLANATION

We want to find the difference in the volumes of the sphere and the cube.

To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.

The volume of a sphere is given as:

V=\frac{4}{3}\pi r^3

where r = radius

The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:

\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot15^3 \\ V\approx14137\operatorname{cm}^3 \end{gathered}

The volume of a cube is given as:

V=s^3

where s = length of the side

The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:

\begin{gathered} V=15^3 \\ V=3375\operatorname{cm}^3 \end{gathered}

Therefore, the difference in the volumes of the sphere and cube is:

\begin{gathered} V_d=V_s-V_c \\ V_d=14137-3375 \\ V_d=10762\operatorname{cm}^3 \end{gathered}

Therefore, the sphere is 10762 cubic centimeters bigger than the cube.

6 0
1 year ago
What is the value of x?<br> 10<br> 2x
Viktor [21]

Answer:

The only way of getting to 10 using 2x it should mean that x = 5

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4 0
3 years ago
After the tour, Tyler’s mom bought a pretzel and a bottle of water for each family member. The bottles of water cost $1.50 each.
Delicious77 [7]
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Read 2 more answers
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gogolik [260]

Answer:

Step-by-step explanation:

first, we find the slope

slope = (y2 - y1) / (x2 - x1)

(8,2)....x1 = 8 and y1 = 2

(7,1)....x2 = 7 and y2 = 1

now we sub

slope = (1 - 2) / (7 - 8) = -1/-1 = 1

y = mx + b

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now we sub and find b, the y intercept

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so ur equation is : y = 1x - 6....or just y = x - 6 <===

8 0
3 years ago
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