Determine the solution, if any, to the system of equations below
8x - 2y = 1
-4x + y=3
Show your work.

Answer:

Step-by-step explanation:

Answer:

1)  True, True, False

Rewritten statement:  46,013.86 cm³ of water was used to fill 40 balloons

2) False, True, True

Rewritten statement:   The formula [tex]\sf V= \sf \dfrac43 \pi (2.4)^3[/tex] can be used to find the volume of the model of Earth.

3) True, False, True

Rewritten statement:  The volume of all the basketballs is 13,467.62 in³

Step-by-step explanation:

[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]

Given:

Substituting the given radius into the formula:

[tex]\begin{aligned}\implies \sf V & = \sf \dfrac43 \pi (6.5)^3\\\\& =\sf \dfrac{2197}{6} \pi \\\\& = \sf 1150.35\: cm^3 \:(nearest\:hundredth)\end{aligned}[/tex]

[tex]\textsf{Volume of 40 balloons}=\sf 40 \times \dfrac{2197}{6} \pi=46013.86\:cm^3\:(nearest\:hundredth)[/tex]

Rewritten statement:  46,013.86 cm³ of water was used to fill 40 balloons

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[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]

Earth

Given:

Substituting the given radius into the formula:

[tex]\implies \sf V= \sf \dfrac43 \pi (2.4)^3[/tex]

[tex]\implies \sf V=57.91\:cm^3\:(nearest\:hundredth)[/tex]

Rewritten statement:  

The formula [tex]\sf V= \sf \dfrac43 \pi (2.4)^3[/tex] can be used to find the volume of the model of Earth.

Saturn

Given:

Substituting the given radius into the formula:

[tex]\implies \sf V= \sf \dfrac43 \pi (22.8)^3[/tex]

[tex]\implies \sf V=49647.02\:cm^3\:(nearest\:hundredth)[/tex]

Difference between models= 49,647.02 - 57.91 = 49,589.11 cm³

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[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substituting the given values into the formula:

[tex]\implies \sf V=\pi (21)^2(54)[/tex]

[tex]\implies \sf V=23814\pi[/tex]

[tex]\implies \sf V=74813.89\:in^3\:(nearest\:hundredth)[/tex]

[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]

Given:

[tex]\begin{aligned}\textsf{Volume of all 30 basketballs} &=\sf 30 \times \dfrac{4}{3}\pi (4.75)^3\\ & =\sf 13467.62\:in^3\:(nearest\:hundredth)\end{aligned}[/tex]

Rewritten statement:  The volume of all the basketballs is 13,467.62 in³

Empty space in the container = volume of container - volume of basketballs

⇒ 74813.89 - 13467.62 = 61,346.27 in³

Answer:

y<7

Step-by-step explanation:

3y-10 < 11     add 10 to both sides of the equation

3y < 21      divide by 3

y < 7

Answer:

282.3 gallons

Step-by-step explanation:

if needed you can round to 282

Answer:

180 units^2

Step-by-step explanation:

The formula to find the area of a sphere is:

A=4(pi)(r)^2

A sphere with radius 2r has an area = 4π(2r)² = 4π.4r² = 16πr²

The ratio of the larger sphere to the smaller = 16πr² : 4πr² = 4 : 1

If the area of the smaller sphere is 45 units then the area of the larger sphere is 45 x 4 = 180 units^2.

hope this helps :)

Answer:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.

Step-by-step explanation:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.

Answer:

7.1 cm^2

Step-by-step explanation:

Area  = pie * radius^2

Area = pie * 1.5^2

= 7.0685

Answer: 7.1 cm ^2

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Substitute v = 15 into 14 + v

14 + 15 = 29

Hope this helps :)

Answer:

Step-by-step explanation:

Use distributive property: a*(b+c) =a*b +a*c

1) 785 * 105 = 785 * (100 + 5)

                  = 785*100 + 785*5

                  = 78500 + 3925

                  = 82425

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2) 1006 * 95 = (1000 + 6) *95

                     = 1000*95 + 6*95

                      = 95000 + 570

                     = 95570

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3) 3096*91  = 3096 * (100 - 9)

                    = 3096*100 - 3096*9

                    = 309600 - 27864

                    = 281736

Answer:

1

Step-by-step explanation:

Factors of 21: 1, 3, 7, and 21

Factors of 64: 1, 2, 4, 8, 16, 32, and 64

These numbers do not share any other factors other than 1

Answer:

Step-by-step explanation:

We know that first 150 postive even Integers are 2,4,6,8,10... 300.

Here,

[tex]\\[/tex]

Substituting values in the formula:

[tex] \\ :\implies \sf \: \: S_{n} = \dfrac{n}{2} (a + a_{n}) \\ \\[/tex]

[tex] :\implies \sf \: \: S_{n} = \dfrac{150}{2} (2 + 300) \\ \\ [/tex]

[tex] :\implies \sf \: \: S_{n} = 75(302) \\ \\ [/tex]

[tex] :\implies \: \:{ \underline{ \boxed{ \pmb{ \pink { \rm{S_{n} = 22650 }}}}}} \\ \\[/tex]

Answer:

Formula for finding sum of nth terms =

n/2 × (a + an)

putting the known values ,

Sum = 150/2 × ( 2+300)

Sum = 75 × 302

Sum of first 150 positive even integers = 22650

Answer:

-1/2

Step-by-step explanation:

pemdas rules

1. 18 x 2 - 30 = 6

2. 3-6= -3

3. 36/-3 = -12

4. 96/-12 = -8

5.  (31-16+1) = 16

6. -8/16 = -1/2

Answer:

f(3) = -37

Step-by-step explanation:

f (x) = -6x - 19

Let x = 3

f (3) = -6*3 - 19

      = -18-19

      = -37

Answer:

108m

Step-by-step explanation:

2 sides are 30m long and 2 sides are 24m long.

Add all 4 sides of the playground to find the perimeter.

30m + 24m + 30m + 24m = 108 m

Using the z-distribution, as we are working with a proportion, it is found that the p-value of the test is of 0.

At the null hypothesis, it is tested if the proportion is of 71%, that is:

[tex]H_0: p = 0.71[/tex]

At the alternative hypothesis, it is tested if the proportion has decreased, that is:

[tex]H_1: p < 0.71[/tex].

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, we have that the parameters are:

[tex]n = 300, \overline{p} = \frac{165}{300} = 0.55[/tex]

Hence, the value of the test statistic is found as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.55 - 0.71}{\sqrt{\frac{0.71(0.29)}{300}}}[/tex]

z = -6.11

Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -6.11, it is found that the p-value is of 0.

More can be learned about the z-distribution at https://brainly.com/question/26454209

Many out there got different opinions on this especially with the influence of religion and science.

LIFE is about learning the best in you and others. Its about loving, being kind and to be someone of great worth who at the the end of the day makes a mark of positivity in every life encountered. Its about living a life of meaning and that's all that matters. Every religion holds it's own perspectives and it's most important that you choose to believe in a religion that helps better Express your faith.

remember that there'll be a day you sit back and look at the life you "lived"

make sure that the choices you make now don't bring ANY regrets.

Answer:

the answer is -85 good luck on your test or honework :)

Answer:

here

Step-by-step explanation:

The distance between the earth and the moon is approximately 384000 km. To Do: Express the distance in meters in exponential notation. Therefore the answer is 3.84 × 10 8 m.

Answer:

Step-by-step explanation:

In the question we have given volume of Sphere that is 562.5 π in³ and we have asked to find the radius of given sphere. We know that the volume of sphere ,

[tex] \blue{ \boxed{ \rm{Volume \: of \: Sphere = \frac{4}{3} \pi r {}^{3} }}}[/tex]

So equating it with given volume for finding the radius of sphere :

[tex] \longmapsto \: \frac{4}{3} \pi r{}^{3} = 562.5\pi[/tex]

Step 1 : Cancelling π as it was present in both side :

[tex]\longmapsto\:\frac{4}{3} \cancel{\pi }r{}^{3} = 562.5 \cancel{\pi}[/tex]

Step 2 : Transposing 4/3 to right hand side :

[tex]\longmapsto \: r {}^{3} = 562.5 \times \frac{3}{4} [/tex]

Step 3 : Multiplying 562.5 with 3 :

[tex]\longmapsto \:r {}^{3} = \frac{1687.5}{4} [/tex]

Step 4 : Dividing 1687.5 by 4 :

[tex]\longmapsto \:r {}^{3} = 421.875[/tex]

Step 5 : Finding cube root of 421.875

[tex]\longmapsto \:r = \sqrt[3]{421.875} [/tex]

Step 6 : We get :

[tex]\longmapsto \: \red{ \boxed{r = 7.5}}[/tex]

Answer:

5i√5

Step-by-step explanation:

Remark

125 factors

It is factored into 5*5*5

The rule for √5*5*5  is that two can be taken outside the square root sign. I is placed in front of the root sign like 5√ and the other 5 is thrown away.

The remaining 5 is left under the root sign

As usual

√-1 is i is taken outside the root sign

Solution

5i √5 is what you get.

Answer:

(7x+9)(x-5)

Hope this helps!

Step-by-step explanation:

The centroid O cuts every median in the ratio 2:1. The distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.

Therefore: |OD| = 2|OCI

3x-2=2(5x)

3x-2=10x

7x=-2

x=(-2/7)

Answer:

0

Step-by-step explanation:

tan(x + [tex]\frac{\pi }{2}[/tex] ) ← substitute x = [tex]\frac{\pi }{2}[/tex]

tan([tex]\frac{\pi }{2}[/tex] + [tex]\frac{\pi }{2}[/tex] )

= tanπ

= 0

Answer:

c po

because that is the answer in the bakc of my module hope its help

Answer: it’s simply a

Step-by-step explanation: X =bsquare

Answer:

7.

4.7 * 10^14 , 9.99 * 10^14 , 2.9 * 10^15 , 4.5 * 10^15

8.

9.99 * 10^-8 , 4.8 * 10^-8 , 9.99 * 10^-4 , 6.5 * 10^-4

To find the slope between two points:

 ⇒ must know the slope's formula

            [tex]\frac{y2-y1}{x2-x1}[/tex]

Let's consider the information given

  ⇒ given two points ⇒ (4, -6) and (-3,1)

          (x1, y) --> (4, -6)

          (x2, y2) --> (-3, 1)          

Let's calculate the slope:

  [tex]slope = \frac{1--6}{-3-4} =\frac{7}{-7} =-1[/tex]

Thus the slope is -1

Hope that helps!