6(m + 2 + 7m)

Part A: Write two expressions that are equivalent to the given expression. (3 points)

Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)

There are 120 different ways the people can line up

The number of people that arrived is:

n = 5

Take the factorial to calculate the number of ways they can line up

n! = 5!

Expand

n! = 5* 4 * 3 * 2 * 1

Evaluate

n! = 120

Hence, there are 120 different ways the people can line up

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There are 720 ways that the 3 homes could be chosen if the order of visiting is considered. There are 120 ways that the 3 homes could be chosen if the order of visiting is not important.

A permutation is the arrangement or ordering of a finite set of an element.

From the information given:

If there are  10 homes in the desired price range listed in the area:

Then:

So, the number of ways of choosing 3 out of 10 (without replacement) and arranging is:

[tex]\mathbf{^nP_r= \dfrac{n!}{(n-r)!}}[/tex]

[tex]\mathbf{^nP_r= \dfrac{10!}{(10-3)!}}[/tex]

[tex]\mathbf{^nP_r= \dfrac{10\times 9\times 8 \times 7!}{(7)!}}[/tex]

= 720 ways

Now, the number of ways of choosing 3 out of 10 if the order of visiting is not important is the combination of the elements and it can be computed as:

[tex]\mathbf{^nC_r= \dfrac{n!}{(n-r)!r!}}[/tex]

[tex]\mathbf{^{10}C_3= \dfrac{10!}{(10-3)!3!}}[/tex]

[tex]\mathbf{\implies \dfrac{10\times 8\times 9 \times 7!}{(7)! \times 3\times 2}}[/tex]

[tex]\mathbf{\implies \dfrac{10\times 8\times 9}{6}}[/tex]

= 120 ways

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Using the trigonometric ratios, the measures are:

a. z = 222.5 ft

b. h = 38.6 ft.

c. b = 10.4 ft

d. B = 219.1 ft.

The ratios of trigonometry that can be used to solve a right triangle are:

sin ∅ = opp/hyp

cos ∅ = adj/hyp

tan ∅ = opp/adj.

a. Find h using the sin ∅ = opp/hyp:

sin 75 = opp/hyp = h/40

h = (sin 75)(40) = 38.6

Find z using the sin ∅ = opp/hyp

sin 10 = opp/hyp = 38.6/z

z = 38.6/sin 10

z = 222.5 ft. (length of the zip line)

b. Height of the tree = h = 38.6 ft.

c. Using sin ∅ = opp/hyp, find b (distance between the base of the ladder and the base of the tree):

sin 15 = b/40

b = (sin 15)(40)

b = 10.4 ft

d. Using sin ∅ = opp/hyp, find B as shown in the image:

sin 80 = opp/hyp = B/222.5

B = (sin 80)(222.5)

B = 219.1 ft.

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Answer:

x = 0 or x = 1

Step-by-step explanation:

f(x) = |x| - 4

g(x) = x³ - 4

f(x) = g(x)

|x| - 4 = x³ - 4

Add 4 to both sides.

|x| = x³

x = x³  or  -x = x³

x³ - x = 0   or   x³ + x = 0

x(x² - 1) =   or  x(x² + 1) = 0

x = 0 or x + 1 = 0 or x - 1 = 0

x = 0 or x = -1 or x = 1

x = -1 does not work, so we discard that solution.

Answer: x = 0 or x = 1

Answer:

values of x: x = 1 and x = 0

Step-by-step explanation:

Given:

Want: x - values when f(x) = g(x)

|x| - 4 = x³ - 4, the 4 cancel out on both sides

|x| = x³

|x| - x³ = x³ - x³

|x| - x³ = 0, x ≥ 0

-x - x³ = 0, x < 0

x = 0

x = -1, x ≥ 0

x = 1

x = 0, x < 0

The intersections are x = 0 and x = 1 and no solution

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Answer:

-x-2<y<-x-10

Step-by-step explanation:

Option B. The correct answer to this question is that The mixture has less than the intended volume and has more than the intended percent of butterfat.

From the graph that we have here, the point L is under the blue line of the graph.

x + y = 500

From here we have

0.18x + 0.04y = 500(0.12)

Continuing on trhe graph the solution is given as x = 285.7 and y = 214.3

From the explanation here we can conclude that option B is correct.

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Answer:

The mixture has the intended volume and has more than the intended percent of butterfat.

Step-by-step explanation:

Answer:

2 seconds

Step-by-step explanation:

To find the time it takes for the balloon to reach the ground, you need to set the equation equal to 0. This is because the ground technically has a height of 0.

h(t) = -16² + 128t                         <----- Original expression

0 = -16² + 128t                            <----- Plug 0 in for h(t)

16² = 128t                                    <----- Add 16² to both sides

256 = 128t                                  <----- Solve 16²

2 = t                                            <----- Divide both sides by 128

Therefore, if t = 2, it will take the balloon 2 seconds to reach the ground.

==========================================================

Explanation:

The balloon is on the ground when the height is zero.

Replace h with 0 and solve for t.

[tex]h(t) = -16t^2 + 128t\\\\0 = -16t^2 + 128t\\\\-16t^2 + 128t = 0\\\\-16t(t - 8) = 0\\\\-16t = 0 \ \text{ or } \ t-8 = 0\\\\t = 0/(-16) \ \text{ or } \ t = 0+8\\\\t = 0 \ \text{ or } \ t = 8\\\\[/tex]

Ignore t = 0 because this is when the balloon is initially on the ground. In other words, the balloon starts on the ground, so it makes sense that t = 0 leads to h = 0.

The other solution t = 8 is what we're after. The balloon touches the ground again at the 8 second mark. This is the length of time the balloon is in the air.

A quick way to determine and confirm the answer is to use graphing software. Check out the diagram below. We have a parabola with x intercepts of 0 and 8.

Answer:

As the bag doesnt conatain any purple token;

purple token = 0

number of total tokens in bag = 24

therefore, the probability of choosing a purple token = 0/24

Hope it helps

The expression 3/16 of 200 expression as a percentage is; 6.25%.

The value of the expression given in the task content can be evaluated as follows;

3/16 × 200 = 12.5

Hence, the value 12.5 expressed as a percentage of 200 is;

(12.5/200) × 100%.

= 6.25%.

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Step-by-step explanation:

substitute different values of x inorder to get values of y. so since the value of y will have 2 units substracted from the original function leaving us with shifting. but the graph would be parabolic or slightly curved than my graph.

Answer:

Positive number are located above 0 and negative numbers are located below 0 on a vertical number line

Answer:

On a horizontal number line, positive numbers are down from ANS= 0 to the left of 0✔ to the right of 0X up from 0.On a vertical number line, negative numbers are ✔ ANS=down from 0 to the left of 0to the right of 0up from 0.The number 0 is a negative numbera positive number✔Ans= neither positive nor negative.

Step-by-step explanation:

yw

Answer:

[tex]q^2+7q+2[/tex]

Step-by-step explanation:

Check the attachment I added, hope it helps!

Answer:  (0, -5) which is choice C

Explanation:

The solution is where the lines cross or intersect. This point is on both lines at the same time to make both equations true.

Answer:

See below

Step-by-step explanation:

Look at it from the front and the side as shown in the diagram and draw what you would  see:

An equation is formed of two equal expressions. Julian should invest $160,000 in CD and $640,000 in Bond.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount invested in CD be represented by x, while the amount invested in bond be represented by y. The total amount that Julian had is,

x + y = 800,000

x = 800,000 - y

The interest that Julian needs in a year is $36,000. Therefore, the total interest should be,

0.025x + 0.05y = 36000

0.025(800,000 - y) + 0.05y = 36000

20,000 - 0.025y + 0.05y =36,000

0.025y = 16,000

y = $640,000

Substitute the value of y

x + y = 800,000

x = $160,000

Hence, Julian should invest $160,000 in CD and $640,000 in Bond.

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Answer:

Vertical shift up 2, horizontal shift left 2 reflection over x-axis then reflection over the y-axis.

Step-by-step explanation:

Answer:

2x² - 12x + 13

Step-by-step explanation:

Given following:

Start solving from right to left across the function.

Steps:

Answer:

2x² - 12x + 13

Step-by-step explanation:

Steps:

k[p(x)]

k[x - 3]

2(x - 3)² - 5

2(x² - 6x + 9) - 5

2x² - 12x + 18 - 5

2x² - 12x + 13             pls brainlest

The slope of the given line according to the table is -8

The slope of a function is also defined as the rate of change of the function.

Using the coordinate points (-3, 8) and (-2, 0) from the table

Slope = 0-8/-2-(-3)

Slope = -8/-2+3
Slope = -8/1

Slope = -8

Hence the slope of the given line according to the table is -8

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Answer:

simple interest

Step-by-step explanation:

this is because r is interest rate, p is principal, and t is time

Answer:

simple interest

Step-by-step explanation:

Simple interest rate is defined as: I = p * r * t. So you're taking the principle amount (initial amount loaned) and multiply it by the interest rate. This gives you the interest rate in a year (usually, depends on time unit of t). Generally speaking, it gives you the interest over a specific amount of time. Now multiply it by the amount of time that's passed. So you're just calculating the total amount of interest. So the I stands for the simple interest.

The answer is Point B.

Answer:

it's ax+b form answer is Q(x-2)=4x-6

Step-by-step explanation:

ax+b=Q(x),Q(x-2)=a(x-2)+2

Q(3x)=a(3x)+b=12x+2, 3a=12 =>a=4,b=2

the original q of x is 4x+2

Q of x-2 =4(x-2)+2=4x-8+2=4x-6

An example of contextualization in teaching is when writing skills are taught with reference to topics.

It should be noted that the contextualization of basic skills is the instructional approach that gives connections in teaching.

In this case, an example of contextualization in teaching is when writing skills are taught with reference to topics.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming the formula:}[/tex]

[tex]\mathbf{a^2 + b^2 = c^2}[/tex]

[tex]\huge\textbf{If so:}[/tex]

[tex]\mathbf{x^2 + y^2 = c^2}[/tex]

[tex]\mathbf{8^2 + 5^2 = c^2}[/tex]

[tex]\mathbf{8\times 8 + 5 \times 5 = c^2}[/tex]

[tex]\mathbf{64 + 25 = c^2}[/tex]

[tex]\mathbf{89 = c^2}[/tex]

[tex]\huge\textbf{Subtract \boxed{\rm{\bf c^2}} to both sides:}[/tex]

[tex]\mathbf{89 - c^2 = c^2 - c^2}[/tex]

[tex]\huge\textbf{Simplify it: }[/tex]

[tex]\mathbf{-c^2 + 89 = 0}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf 89} to both sides:}[/tex]

[tex]\mathbf{-c^2 + 89 - 89 = 0 - 89}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{-c^2 = -89}[/tex]

[tex]\huge\textbf{Divide \boxed{\bf{-1}} to both sides:}[/tex]

[tex]\mathbf{\dfrac{-c^2}{-1} = \dfrac{-89}{-1}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{-c^2 = -89}[/tex]

[tex]\huge\textbf{Take the square root of the number:}[/tex]

[tex]\mathbf{c = \pm \sqrt{89}}[/tex]

[tex]\huge\textbf{Thus, this possibly means:}[/tex]

[tex]\mathbf{c = \sqrt{89} \ or\ c = -\sqrt{89}}[/tex]

[tex]\huge\textbf{Thus, your answer possibly is:}[/tex]

[tex]\huge\boxed{\mathsf{c = \sqrt{89} \ or\ c = -\sqrt{89}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The solution to this is 6.62607e-34.

We have the value is raised to the power of -34

We have to solve this using a calculator

This is similar to

[tex]6.62607004081818181818181*\frac{1}{10000000000000000000000000000000000}[/tex]

The number of zeros are 34

We would have  6.62607e-34 as the final solution.

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Based on the perimeter of the rectangle, and the adjustments to make the plot a square, the sides are 13m and 19m.

The perimeter is:

2(L + W) = 64

L + W = 32

The adjustment to make the plot a square would mean that both sides can be equal:

L + 3 = W - 3

L = W - 6

Substituting in the original formula gives:

L + W = 32

W - 6 + W = 32

2W = 38

W = 19 m

L would be:

L + W = 32

L + 19 = 32

L = 13m

The rest of the question is:

No obstante, para que los terrenos puedan ser cuadrados, se tendría que aumentar el ancho en 3 m y disminuir 3 m de largo. Entonces, ¿cuánto mediría el ancho y el largo del terreno rectangular?

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Answer:

25

Step-by-step explanation:

its both numbers squared and added, then square root the result

Triangle RST was transformed by using the rule (x,y) → (-x,-y) and the transformation is described by the transformation of 180° rotation about the origin.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Here we have transformed the triangle using the rotation method.

Rotation is the geometric transformation that revolves each point in a shape a predetermined number of degrees around that point. When the number of degrees is positive, the shape spins counterclockwise; when the number of degrees is negative, it rotates clockwise. The following is a broad description of how rotation about the origin can be transformed.

Here the points change to R'(-1,-1) , S'(-3,-1) and T'(-1,-6).

A 180° rotation about the origin will be the transformation.

The triangles RST and R'S'T' are first plotted on a graph. The graph is provided for your reference below.

The original triangle RST, which was in quadrant 1, has changed to triangle R'S'T', which is in quadrant 3, as shown in the graph. The rotation around the origin is 180° from quadrant 1 to quadrant 3.

Your question was incomplete. Please check below for full content.

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.

R (1, 1)

S (3, 1)

T (1, 6) R' (–1, –1)

S' (–3, –1)

T' (–1, –6)

Which describes the transformation?

The transformation was a 90° rotation about origin.

The transformation was a 180° rotation about origin.

The transformation was a 270° rotation about origin.

The transformation was a 360° rotation about origin.

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Answer:

a = -1

Step-by-step explanation:

The slope, m from point   -2,7     to    a,2     has to be   -5

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

-5  = ( 7-2)/(-2 -a)     solve for 'a'......cross multiply

10+ 5a = 5

5a = -5

a = -1