4) Shown below is a series of steps to solve the equation 4x + 2(x - 4) = 28.
Given: 4x + 2(x - 4) - 28
Step 1 = 4x + 2x - 8 = 28
Step 2 => 6x - 8 = 28
Step 3 => 6x - 8 + 8 = 28 + 8
Step 4 = 6x = 36
6x36
Step 5
6 6
Step 6 => x = 6
Which THREE statements are correct?
A) Step 1 is justified by the distributive property.
B) Step 2 is justified by the subtraction property of equality
C) Step 3 is justified by the addition property of equality
D) Step 4 is justified by the additive Identity property.
E) Step 5 is justified by the division property of equality

A regression can be modeled by linear regression, quadratic regression, quartic regression or exponential regression

The quadratic regression equation that models the data is

[tex]\^y = -0.875\^x^2 -3.596\^x +20.179[/tex]

The table entries are given as:

x: 0,1,2,3,4,5

y: 20,16,10,0,-7,-20

A quadratic regression is represented as:

[tex]\^y = a\^x^2 + b\^x + c[/tex]

Using a graphing calculator to determine the quadratic regression equation, we have the following calculation summary

a = -0.875

b = -3.596

c = 20.179

Hence, the quadratic regression equation is:

[tex]\^y = -0.875\^x^2 -3.596\^x +20.179[/tex]

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Answer:

ITS C

Step-by-step explanation:

Organizing the problem:

Which THREE expressions are equivalent to:

(x + 6) + (x + 6) + (x + 6) + (x + 6)

O 4(x + 6)

0 2 (x + 12)

2 + 12 + 22

12 3a + 6 + 1 = 6

тиб 42 = 24

Out of these selections, i can only tell that number one is correct, number two isn't, and i can't tell for the rest. Please organize the question more clearly.

--Hunter

7:5 mean that to every 7 men there is 5 woman.

There are 54 women working for the company.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The ratio of men to women working for the company is 7:5, which means that for every 7 men, there are 5 women.

We can express this as a fraction by writing 7/7 as 1 and 5/7 as 5/7, so the ratio becomes 1:5/7.

This fraction can be rewritten as 7/7:35/7, and since the two fractions have the same denominator, we can say that the ratio is equal to 7:35.

Since there are 192 total employees, and the ratio of men to women is 7:35, we can set up the following proportion:

7/35 = x/192

We can solve this proportion by cross-multiplying:

7/35 × 192 = x

This simplifies to:

x = 54

Therefore, the company hired 54 female employees.

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Seafloor spreading can be defined as a process that involves the formation of new oceanic crust as a result of volcanic activities and an upwelling of molten magma at mid-ocean ridges, as well as a slowly increasing distance (outward movement) from the ridge.

The theory of seafloor spreading was established by Harry Hammond Hess and it can be used to explain in details the slowly increasing distance between South America and Africa which grows from the center.

A hot spot refers to an area deep within Earth's mantle or under the rocky outermost layer of Earth, from which heat rises through convection and acquired as heat energy by a landform.

In the United States of America, you will see a layered sedimentary rock that is exposed by erosion when you view the Grand Canyon.

Furthermore, Australia is made up of relatively old and thick continental crust. Also, subduction causes the formation of extremely deep ocean Marianas Trench.

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Given, m<7 = 108°

To find, m<3

Since both the given angles are on the same side of transversal, thus there sum is 180°

Thus, m<7 + m<3 = 180°

108° + m<3 = 180°

m<3 = 180° - 108°

m<3 = 72°

Hope this helps :)

Answer: x=-56/3 (the second answer)

Answer: 1716/25 or 16 68/25

Step-by-step explanation:

Formula: 1/2 x height x (a+b)

Answer:

The number is 5

Step-by-step explanation:

Let the number be x,

13 - x = 2x - 2

or, 13 + 2 = 2x + x

or, 3x = 15

so, x = 5

The correct answer is z can take on the values of both -6 and 6, not -5 and 5.

The equation that has both -5 and 5 as possible values of z is:

[tex]z^2 = 36[/tex]

When we solve this equation, taking the square root of both sides, we get:

z = ±6

Therefore, z can take on the values of both -6 and 6, not -5 and 5.

Hence, none of the given equations have both -5 and 5 as possible values of z.For the equation z^2 = 36, we need to find the values of z that satisfy the equation. Taking the square root of both sides, we get:

z = ±√36

Simplifying the square root of 36, we have:

z = ±6

This means that z can take on the values of both -6 and 6. However, the values -5 and 5 are not solutions to this equation.

Similarly, for the equation z^3 = 125, there are no values of z that satisfy the equation for z equal to -5 or 5.

Therefore, none of the given equations, z^2 = 36 and z^3 = 125, have both -5 and 5 as possible values of z.

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Answer:

[tex]\frac{3}{7}[/tex]

Step-by-step explanation:

Start by finding how many integers there are from 10-30...

30-10+1=20+1=21

Note we have to add 1 since it is inclusive.

Now, let's find how many multiples of 4 or 5 there are from 10-30...

4*3=12

4*4=16

4*5=20

4*6=24

4*7=28

5*2=10

5*3=15

5*4=20

5*5=25

5*6=30

5+5-1=9

Note we have to subtract 1 since 20 is counted twice.

The probability would be...

[tex]\frac{Multiples\ of\ four\ and\ five\ from\ 10-30}{Amount\ of\ integers\ between\ 10-30}=\frac{9}{21}=\frac{3}{7}[/tex]

Answer:

andrew can drive 20 miles for every 1 gallon of gas

Step-by-step explanation:

Answer:

42 inches

Step-by-step explanation:

Let x represent the length of the shorter piece then...

2x=28

Divide both sides by 2

x=14

The shorter one is 14 inches long and the longer one is 28 inches long. Now, we add these two numbers to find the original length of the lumber.

14in+28in=42 inches

Answer:

0.171 m

Step-by-step explanation:

First, let's determine how many mm of track he has in total...

74mm+97mm=171 mm

Now, we can set up a unit converter to convert mm to m (note that 1 mm is [tex]10^{-3{[/tex] m)...

[tex]171mm(\frac{10^{-3}m}{1mm})[/tex]

The "mm" cancels out...

[tex]171*10^{-3}m=0.171m[/tex]

Answer:

Step-by-step explanation:

74 +  97 = 171 mm

Length of the train track = 171 mm = 171÷ 1000 = 0.171 m

Answer:

Cube root of 27 in radical form: ∛27???

Step-by-step explanation:

hope this helps

Answer:

6

Step-by-step explanation:

slope is rise/run

to get from -1 to 5 is 6 points

y axis to 1 is 1 point

6/1=6

Answer:

geotheral

Step-by-step explanation:

A- 9B- 87C- -2D -9

Step-by-step explanation:

Answer:

  All apply

Step-by-step explanation:

Complementary angles are ones that total 90°. Here, we have two pairs of congruent angles such that each pair totals 90°. We can mix and match to find pairs of complementary angles.

  less than 45°: BGC and EGF

  more than 45°: AGB and DGE

A complementary pair will consist of one angle from the first list and one angle from the second list. There are 4 possible pairings, and all are shown as answer choices.

All of the choices apply.

Answer:

Cos of B = 36 / 38.884

Step-by-step explanation:

To find the cos of b you need the hypotenuse

(a)^2 + (b)^2 = (c)2

(36)^2 + (15)^2 = 1521

1521 squared is 38.884

Hypotenuse side goes on bottom and adjacent side on top

Cos of B = 36 / 38.884

Answer:

I believe your answer is 9

Step-by-step explanation:

The way I found this answer was by assuming that triangle CDE was expanded to get triangle FGH. So I divided 18/4 and got the answer 4.5, which means that the triangle was expanded by a factor of 4.5. So I then multiplied the similar side to HG by 4.5 which was side ED. This got me with 4.5 x 2 and I got the answer 9.

Hope this helps! :)

[tex]\\ \tt\hookrightarrow Perimeter [/tex]

[tex]\\ \tt\hookrightarrow 15+4+7+10[/tex]

[tex]\\ \tt\hookrightarrow 19+17[/tex]

[tex]\\ \tt\hookrightarrow 36km[/tex]

There is only one value for x that makes [tex](x+4)^2=0[/tex]

Given the vertex form of the function expressed as:

[tex]f(x) = -(x+4)^2+5[/tex]

If the function f(x) = 5

[tex]5 = -(x+4)^2+5[/tex]

Subtract 5 from both sides

[tex]5 = -(x+4)^2+5\\-(x+4)^2= 5-5\\-(x+4)^2=0\\[/tex]

Hence there is only one value for x that makes [tex](x+4)^2=0[/tex]

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We are given –

We are asked to find volume of the given cylinder.

Let the radius be "r".Then according to the question,it’s given –

[tex]\qquad[/tex] [tex]\pink{\twoheadrightarrow\bf Curved\: surface\: area _{(Cylinder)}= 2\pi r h }[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 2\pi r h = 24 \pi[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 2\cancel{\pi} rh = 24 \cancel{\pi}[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r =\dfrac{24}{2h}[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \dfrac{24}{2\times 4}[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \dfrac{24}{8}[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \cancel{\dfrac{24}{8}}[/tex]

[tex]\qquad[/tex] [tex]\pink{\twoheadrightarrow\bf r = 3 \: cm}[/tex]

Now, Let's find volume of cylinder

[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf V_{(Cylinder)} = \pi {r}^{2}h}[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 3^2\times 4 [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 9 \times 4[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 36[/tex]

[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf V_{(Cylinder)} = 36 \pi \: cm^3}[/tex]

Step-by-step explanation:

Given :-

to find :-

Solution :-

Lateral surface area of cylinder = 2πrh

24π cm = 2πrh

Cancelling π on both the sides ,

24/2h = r

putting the value of h i.e, 4 cm

24/2×4 cm = r

3 cm = radius

Now volume of Cylinder = πr²h

putting all the values ,

Volume = 3.14 × 3² × 4 cm³

Volume = 113.04 cm³

Answer:

y=3x-10

Step-by-step explanation:

A line parallel to another line has the same slope.

Therefore, we can create the equation y=3x+b.

Substituting (4,2) into y=3x+b,

2=3(4)+b

2=12+b

-10=b

y=3x-10

Therefore, the equation of the line parallel to y=3x-8 which passes through the point (4,2) is y=3x-10

Answer:

y = 3x - 10

Step-by-step explanation:

Equation: y = 3x + b

Point: (4, 2)

y = 3x + b

2 = 3 (4) + b

2 = 12 + b

b = -10

y = 3x - 10

Answer: Most of the time, we're going to have to look at the graph of the function to determine its range. Examples. • Example 1 g(x) = 6x − 2. 3x − 4. (4).

5 pages

Step-by-step explanation:

hope this helps

The given graph is  a one-to-one function

A relation is a function if it has only One y-value for each x-value.

A function is said to be one-one if corresponding to each x we get a distinct y-value.

i.e. No two x have the same y-value.

Also it can be seen from the graph when any horizontal line is drawn parallel to the x-axis then the line intersect the curve atmost once.

it passes the horizontal line test.

Many-to-one function is a function is many to one when many x-values are mapped to same y-value.

Clearly from the graph we see that the graph is a one-to-one function.

Hence, the given graph is  a one-to-one function

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Answer:

  x = 4

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the remote interior angles.

  18x +5 = (46) +(-1 +8x)

  10x = 40 . . . . . . . . . . . . . subtract (5+8x) from both sides, simplify

  x = 4 . . . . . . divide by 10

__

Additional comment

The exterior angle is (18)(4) +5 = 77°. The marked unknown interior angle is -1+(8)(4) = 31°. The sum of the two remote interior angles is 46°+31° = 77°. The unmarked interior angle is 180°-77° = 103°.

Answer:

  (b)  x^15/y^5

Step-by-step explanation:

The exponent outside parentheses multiplies all of the exponents inside parentheses.

  (x^3/y)^5 = x^(3·5)/y^(1·5) = x^15/y^5

______

Additional comment

When it comes to exponents, I find it useful to remember that an exponent signifies repeated multiplication: x·x·x = x³. The exponent outside parentheses has the same meaning:

  (x³)² = (x·x·x)·(x·x·x) = x⁶

The rule is summarized by ...

  (a^b)^c = a^(bc)