Solve the following system of linear equations by substitution:
8x-y=-13
6x-3y=15

Answers

Answer 1

Answer: Rearrange 8x-y=-13 to y=8x+13
Substitute this in so:
6x-3(8x+13)=15
6x-24x-39=15
-18x-39=15
-18x=54
x=-3

Substitute x into 1st equation:
Y=(8*-3)+13
Y=-24+13
Y=-11

Answer 2

Answer: $\begin{cases} 8x-y=-13 \n 6x-3y=15 \end{cases}\n \n \begin{cases} -y=-8x-13 \ \ *(-1) \n 6x-3y=15 \end{cases}\n \n\begin{cases} y= 8x+13 \n 6x-3(8x+13)=15 \end{cases} \n \n\begin{cases} y= 8x+13 \n 6x-24x-39=15 \end{cases}$

$\begin{cases} y= 8x+13 \n 6x-24x =15+39 \end{cases} \n \n\begin{cases} y= 8x+13 \n -18x =54 \ \ / :(-18)\end{cases} \n \n\begin{cases} y= 8*(-3)+13 \n x = -3 \end{cases} \n \n\begin{cases} y= -24+13 \n x = -3 \end{cases} \n \n \begin{cases} y= -11 \n x = -3 \end{cases}$

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Which expression gives the surface area of a sphere with radius r?A. r2
B. 4r3
C. 4r2
D. 4r2

Answers

The surface area of a sphere is the area of four great circles . . . 4 π r² .

Apparently, either 'C' or 'D' was supposed to be the correct choice,
but the π got lost in the pantry on the way to the printer.

Answer:

Area of sphere is given by $4\cdot \pi\cdot r^2$

Step-by-step explanation:

The surface area of sphere is given by:

$\text{Area of sphere}=4\cdot \pi\cdot r^2$

Option C and D are correct but $\pi$ is missing in the options

Option A and B are incorrect.

$\pi=3.14$ to solve the area of sphere when radius is given a constant value.

Find the cube of 12. A.
36

B.
144

C.
1728

D.
20,736
next question
Find the volume of a cube with the given side length.

7 units

A.
49 square units

B.
49 cubic units

C.
343 square units

D.
343 cubic units

next question
What is the volume of a cube with a side of length 14 units?

A.
2744 cubic units

B.
196 cubic units

C.
84 cubic units

D.
42 cubic units
next question
How many 1 by 1 unit cubes would equal the volume of the figure shown?

A.
60

B.
120

C.
250

D.
3500
next question
What is the volume of the figure?

A.
648 cubic units

B.
216 cubic units

C.
108 cubic units

D.
54 cubic units

Answers

The cube of 12 is (12 x 12 x 12) = 1,728 .

The volume of a cube with side-length of 7 units is
(7 units x 7 units x 7 units) = 343 cubic units.

The volume of a cube with side-length of 14 units is
(14 units x 14 units x 14 units) = 2,744 cubic units.

The number of 1 by 1 unit cubes that would equal the volume
of the figure shown can't be determined, because the figure is
not shown.

The volume of the figure can't be determined, because the figure
is not shown.

What is the inverse of y=4x-2

Answers

$y=4x-2\n \nreverse \ the \ x \ and \ y \ to \ get \n \n x=4y-2 \n \n solve \ for \ the \ new \ y \ to \ get \n \n4y =x+2 \ \ / :4 \n \ny=(x)/(4) + (2)/(4) \n \ny=(1)/(4)x + (1)/(2)\n \n The \ answer \ is : \n \n y=(1)/(4)x + (1)/(2)$

y=4x-2

change:

x = 4y - 2
4y = x + 2
y = x/4 + 1/2 <--- inverse

Find the area of ABC if the area of PRT=24 mm^2

Answers

Given:

$\triangle ABC\sim\triangle PRT$

As the triangles are similar, the corresponding sides are proportional

$(AC)/(PT)=(BC)/(RT)$

Given: AC = 15, BC = 12 , PT = 6

$\begin{gathered} (15)/(6)=(12)/(RT) \n \n RT=(6\cdot12)/(15)=4.8 \end{gathered}$

We will find the area of the triangle ABC using the following ratio:

$\frac{Area\triangle\text{ABC}}{Area\triangle\text{PRT}}=(0.5\cdot AC\cdot BC\cdot\sin C)/(0.5\cdot PT\cdot RT\cdot\sin T)$

The angle C is congruent to the angle T

So, substitute with the given values:

$\begin{gathered} (Area\triangle ABC)/(24)=(15\cdot12)/(6\cdot4.8)=(180)/(28.8)=6.25 \n \n Area\triangle\text{ABC}=24\cdot6.25=150 \end{gathered}$

So, the answer will be:

The area of ΔABC = 150 mm²

What number times it self 3 times equals 729

Answers

729 ÷ 3 = 243
so if you do 243 × 3 = 729
so your answer will be 243

Express 3.12 as a fraction in lowest terms.3 10/12

3 5/6

312/1000

3 3/25

Answers

Answer:

3 3/25

Step-by-step explanation:

The number 3.12 has a decimal number of 0.12. We know that numbers after the point is divided by 100. Therefore 0.12 is:

$=12/100$

We can simplify this by dividing by 4. Four goes into twelve 3 times and into a hundred 25 times:

$=12/100=3/25$

Theforet the answer is 3 3/25.

The decimal 3.12 as a fraction in lowest terms is (d) 3 3/25

How to express 3.12 as a fraction in lowest terms.

From the question, we have the following parameters that can be used in our computation:

Number = 3.12

Express 3.12 as the sum of numbers 3 and 0.12

So, we have the following representation

Number = 3 + 0.12

Express 0.12 as a fraction

So, we have the following representation

Number = 3 + 12/100

Simplify

Number = 3 + 3/25

Evaluate the sum

Number = 3 3/25

Hence, the fraction 3.12 as a fraction in lowest terms is (d) 3 3/25

Solve the following system of linear equations by substitution: 8x-y=-13 6x-3y=15

Answers

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How to express 3.12 as a fraction in lowest terms.

Solve the following system of linear equations by substitution:
8x-y=-13
6x-3y=15