MATHEMATICS MIDDLE SCHOOL

A rectangular prism has side lengths of 4 inches, 6 inches, and 7 inches. If all side lengths are multiplied by 5, what happens to the surface area.A) It remains the same.
B) It is multiplied by 5.
C) It is multiplied by 25.
D) It is multiplied by 125.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

The surface are of the prism will be the area of a each side added together. The work would look like this:

SA = 2[(l×h)+(l×b)+(b×h)]

SA = 2(lh+lb+bh)

But if you multiply each dimension by 5, the area becomes

SA = 2[(5l×5h)+(5l×5b)+(5b×5h)]

SA = 2(5²lh+5²lb+5²bh)

SA = 5²×2(lh+lb+bh)

SA = 5²area

Since 5² = 25, then the the surface area is multiplied in size by 25.

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Solve 2x2 + 12x − 14 = 0 by completing the square.

Answers

add 14 both sides
2x^2+12x=14
make term in front of x^2 1

divide both sid s by 2
x^2+6x=7
take 1/2 of 6 and square it and add to both sides (6/2=3 3^2=9)
x^2+6x+9=7+9
factor pefect square
(x+3)^2=16
sqrt both sides
x+3=+/-4
minus 3
x=+/-4-3
x=4-3 or -4-3
x=1 or -7

A study involving teenage golfers was conducted to determine the imapact practice time has on golf scores in a tournament. What is the dependent variable?A. golf scores in the tournament
B. practice time
C. age of golfers
D. difficulty of the golf course

Answers

Remember that the dependent variables'(often referred to as y) value is based off of the independent variable, which can change around on its own and directly change the dependent variable.

With that being said, the answer is A:

Golf scores in the tournament. This is because it depends on

practice time(the independent variable).

Good luck!

-RxL

A. Golf score in the tournament
Hope this helps :)

The volume of a sphere is 288π ft3. What is the radius of the sphere? Use the formula V = 4 3 πr3 to find your answer.

Answers

The volume formula of a sphere is:
V = $(4)/(3)$ $\pi$ r³

Given:
V = 288 $\pi$ ft³
Find: Radius

Plug them in!

288 $\pi$ = $(4)/(3)$ $\pi$ r³
Divide by $\pi$ on either sides to cancel them out

$(288 \pi )/( \pi )$ = $(4)/(3)$ r³
288 = $(4)/(3)$ r³
Multiply by 3
228 × 3 = $(4)/(3)$ × 3 × r³
3 and 3 cancels out

864 = 4r³
Divide by 4
$(864)/(4)$ = $(4r^3)/(4)$
4 and 4 cancels out

216 = r³
Take the cube root
$\sqrt[3]{216}$ = $\sqrt[3]{r^3}$

6 ft is the length of the radius

Answer:

6 cm is the length of the radius

Step-by-step explanation:

The volume formula of a sphere is:

V = r³

Given:

V = 288 ft³

Find: Radius

Plug them in!

288 = r³

Divide by on either sides to cancel them out

= r³

288 = r³

Multiply by 3

228 × 3 = × 3 × r³

3 and 3 cancels out

864 = 4r³

Divide by 4

4 and 4 cancels out

216 = r³

Take the cube root

6 cm is the length of the radius

What is the sum of the arithmetic sequence 8, 14, 20 ..., if there are 22 terms?

Answers

Answer:

The sum of 22 terms of given AP = 1562

Step-by-step explanation:

Formula:-

Sum of n terms of AP,

Sₙ= (n/2)[2a + (n - 1)d]

To find the sum of 22 terms

Here. a = 8, d = 6 and n = 22

Sₙ= (n/2)[2a + (n - 1)d]

S₂₂ = (22/2)[2*8 + (22 - 1)*6]

= 11[16 + 126] = 11 * 142 = 1562

Answer: I'm pretty sure its 1562

Which system of equations is represented by the graph? A. y = x2 − 5x − 3
6x − y = −27

B.y = x2 − 5x + 3
6x − y = 27

C. y = x2 + 5x + 3
6x + y = −27

D. y = x2 + 5x − 3
6x + y = 27

Answers

Answer:

The correct option is C.

Step-by-step explanation:

The vertex form of a parabola is

$y=a(x-h)^2+k$ .... (1)

Where, (h,k) is vertex.

From the given figure it is clear that the vertex of the parabola is at (-2.5, -3.25) and the y-intercept is (0,3).

Substitute h=-2.5, k=-3.25, x=0 and y=3 in equation (1) to find the value of a.

$3=a(0+2.5)^2-3.25$

$3+3.25=6.25a$

$6.25=6.25a$

Divide both sides by 6.25.

$1=a$

Substitute h=-2.5, k=-3.25 and a=1 in equation (1), to find the equation of parabola.

$y=1(x+2.5)^2-3.25$

$y=x^2+5x+6.25-3.25$

$y=x^2+5x+3$

The equation of parabola is $y=x^2+5x+3$ .

If a line passes through two points then the equation of line is

$y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)$

The line passes through two points (-6,9) and (-5,3).

$y-9=(3-9)/(-5+6)(x+6)$

$y-9=(-6)/(1)(x+6)$

$y-9=-6(x+6)$

$y-9=-6x-36$

Add 9 on both the sides.

$y=-6x-36+9$

$y=-6x-27$

The equation of line is y=-6x-27.

Therefore the correct option is C.

C. y = x2 + 5x + 3
6x + y = −27

The length of a ribbon is 3/4 meter.Sun Yi needs pieces measuring 1/3 meter for an art project.what is the greatest number of pieces measuring 1/3 meter that can be cut from the ribbon? How much ribbon will be left after Sun Yi cuts the ribbon? Explain your reasoning