determine the midpoint of the line segment connecting (6,-5) and (-1,-6)

Option A is the correct answer g(x) = |x+3| by using the relation with the parent function.

Explain absolute value function.

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.

The definition of the absolute value parent function, f(x)=| x |, is as follows:

f(x) = [tex]\left \{ {{x ~, ~ x > 0} \atop {0 ~ , ~x = 0}} \atop {-x ~, ~x < 0} \right.[/tex]

Given parent function is f(x) = |x|

g(x) is obtained by stretching the graph of f(x) by a factor of 3.

Use the function g(x)=f(x−h) to translate the absolute value function f(x)=| x | horizontally.

The graph of f(x) is moved h units to the right to obtain g(x) for h>0

The graph of f(x) is translated h units to the left to obtain g(x) when h>0

Therefore, g(x) = |x+3|

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The completion of the trend analysis for sales with 2010 as the base year is as follows:

                             2013           2012           2011           2010

Sales            $ 620,000   $ 580,000   $ 450,000   $ 600,000

Trend Analysis      103%             97%              75%             100%

Trend analysis is a technical analysis that uses historical data over some periods to predict and monitor future developments in a particular topic.

To undertake a trend analysis for sales, a base year is chosen and the sales account for the base year is set at 100% and used to check how sales have changed during the review periods.

The other years' results are compared to the base year's by dividing each year's result by the base year's.

Percentages are used to depict trend analysis so that the resulting increases and decreases can be easily compared to the base year.

2013 (D) = 103% ($620,000/$600,000 x 100)

2012 (C) 97% ($580,000/$600,000 x 100)

2011 (B) 75% ($450,000/$600,000 x 100)

2010 (A) = 100% ($600,000/$600,000 x 100)

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Answer:

BC = 6

Step-by-step explanation:

since BD = CD then Δ BCD is isosceles.

the line a through D is a perpendicular bisector of BC, then

BX = CX = 3 , so

BC = BX + CX = 3 + 3 = 6

Applying the area of square and triangle, the amount of paper needed is:  180 inches².

The area of a square shape = (side length of the shape)².

The area of a triangular shape = 1/2(base)(height)

The diagram that illustrates the problem given is shown in the image attached below, where the triangular paper to cover the triangular plank and the square paper for the square plank are shown also with their dimensions.

Therefore, the amount of paper that would cover the piece of art = area of the square shape + area of the triangular shape.

Area of the square shape = 12² = 144 inches²

Area of the square shape = 144 inches²

Area of the triangular shape = 1/2(12)(6)

Area of the triangular shape = 36 inches²

Amount of paper needed = 36 + 144

Amount of paper needed = 180 inches²

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Complete Question:

Theresa created a piece of art by attaching a square plank to a triangular plank. The square plank has a perimeter of 48 inches. The triangular plank has a base length of 12 inches and a height of 6 inches. She wants to cover the piece of art with colored paper.

How many square inches of paper are needed to cover Theresa's art piece?

Answer: Read explanation

Step-by-step explanation: Observations of setting: Humanoid beings. Earth-like world. A human base to collect information. Forest like setting. Bird-like transportation creatures.

Theme ideas: Man a part of research group enters an avatar of beings to collect information on this world. Research group makes an invasion on these creatures home land.  

Make any corrections if you want! Make it more comfortable to your style!

The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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Answer:

Answer would be $3.25

Step-by-step explanation:

First you would have to divide 19.5 by 6 to get 3.25 then check your answer by multiplying 3.25 by 6 which would be 19.50 .

Answer:

Step-by-step explanation:

If each day a player of climbing shoes cost 84 it cost 169 to buy six days of climbing one pair of climbing shoes and one harness. The amount that the harness cost is $25.

Cost of climbing = ( $10×6)

Cost of climbing = $60

Harness cost = Total cost  - (Cost of climbing  + Cost of shoes)

Harness cost =$169 - ($60 + $84)

Harness cost =$169 - $144

Harness cost =$25

Therefore $25 is the harness cost.

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A) The speed (in m/s) at which the ball hits the ground is; 23.43 m/s

B) The time (in s) that it takes the ball to remain in the air is; 3.67 s

C) The maximum height attained by the ball is; 16.51 m

A) The motion of the ball on the vertical axis is basically uniformly accelerated motion, with acceleration g = 9.81 m/s² and initial vertical velocity v_y = 18 m/s, so the vertical position of the ball at time t is:

y(t) = v_y*t - ¹/₂gt²

The formula for time when the ball hits the ground is;

t = 2v_y/g

t = (2 * 18)/9.81

t = 3.67 s

Thus, vertical velocity at time t is given by the formula;

v_y(t) = v_y - gt

v_y(t) = 18 - (9.81 * 3.67)

v_y(t) = -18 m/s (which shows it is in the opposite direction because of the negative sign)

Thus, the speed at which the ball hits the ground is the resultant of the vertical and horizontal velocity at time t;

v = √(v_x² + v_yt²)

v = √(15² + 18²)

v = 23.43 m/s

b) From a above, the time that the ball remains in the air is the time it takes to hit the ground which is t = 3.67 s

c) The time to reach maximum height is half the time it takes to reach the ground. Thus;

t = 3.67/2 = 1.835 s

Thus maximum height is given by the formula;

y(t) = v_y*t - ¹/₂gt²

y(1.835) = 18(1.835) - ¹/₂(9.81)(1.835²)

y = 16.51 m

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Answer:

3/12 or 40%

not 10000% sure on this tho

The student pay initial fess of $20 and addition $10 per hour.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Plan 1:

students pay = $15 per hour.

Plan 2:

From the graph we can see that

slope= Rise/ Run = 10/ 1= 10

and, the graph line starts from 20.

Hence, the student pay initial fess of $20 and addition $10 per hour.

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The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

According to the question,

We have the following information:

[tex]64x^{3} +8[/tex]

The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.

So, we have the following expression:

[tex](4x)^{3} + 2^{3}[/tex]

Now, we can use the following identity to factor the given expression:

[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]

We have a = 8x and b = 2:

(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}

(8x+2) (16[tex]x^{2}[/tex]-16x+4)

Taking 4 as the common factor from the second bracket:

4(8x+2) (4[tex]x^{2}[/tex]-4x+1)

Now, finding the factors of second bracket:

4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)

4(8x+2) {2x(2x-1)-1(2x-1)}

4(8x+2) (2x-1) (2x-1)

4[tex](2x-1)^{2}[/tex] (8x+2)

Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

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Answer:

5q + 5q + 5 is equivalent to 10q + 5

Answer:

A.

Step-by-step explanation:

Answer:

99

Step-by-step explanation: 99

The proof to the above diagram is ∠1 + ∠3 = 180

Supplementary angles are angles whose sum equals 180°

If angle A + angle B = 180°, then both angles are said to be supplementary, meaning angle A is the supplement of Angle B.

∠2 ≅ ∠3. This means ∠2 is approximately equal to ∠3

Also ∠1 + ∠2 = 180°( sum of angles on a straight line)

making ∠2 the subject of the equation

∠2 = 180 - ∠1

But ∠2 ≅ ∠3, which we can say that ∠2 = ∠3

substituting ∠2 for ∠3 in the equation, we have

∠3 = 180 - ∠1

which is further simplified as,

∠1 + ∠3 = 180°

Which  means both angles are also supplementary.

In conclusion,  both angles are supplementary as ∠1 + ∠3 = 180

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The interest eared from the given amount, rate of interest and time period is $426.883.

Given that, amount = $700, rate of interest = 4% and time period = 2 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest is [tex]Amount=Principal(1+\frac{r}{100})^{nt}[/tex]

Let the money deposited be x.

So, [tex]700=x(1+\frac{4}{100} )^{2\times12}[/tex]

⇒ [tex]700=x(1+0.04)^{24}[/tex]

⇒ [tex]700=x(1.04)^{24}[/tex]

⇒ 700 = 2.563x

⇒ x=700/2.563

⇒ x=$273.117

So, interest = 700-273.117

= $426.883

Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.

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Answer:

5736

Step-by-step explanation:

calculator

Answer:          5736

Step-by-step explanation:

Given polynomial with descending degrees of x would be,

x^4z^4 + x^3 - x^2z + z^3

In this question we have been given a polynomial x^3 + z^3 - x^2z + x^4z^4

We need to write given polynomial by descending degrees of x.

The highest degree of x in above polynomial is 4

x^3 + z^3 - x^2z + x^4z^4

then the second term would be x with degree 3.

x^3 + z^3 - x^2z + x^4z^4

the third term would be x with degree 2

x^3 + z^3 - x^2z + x^4z^4

and the last term is the term x with degree 0:

x^3 + z^3 - x^2z + x^4z^4

Therefore, given polynomial with descending degrees of x would be, x^4z^4 + x^3 - x^2z + z^3

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The change in Shamar's bank account after 7 months is

x - 98.

Where x is the amount in the account initially.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount in the account = x

Amount deducted every month = $14

The change in the account after 7 months.

= x - 7 x 14

= x - 98

Thus,

The change in Shamar's bank account after 7 months is

x - 98.

Where x is the amount in the account initially.

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Answer:

S=3/8 miles

T=1/4 hour

V=S/T = 3/8 ÷ 1/4 = (3×4)÷8 = 3/2 miles in an hour

Upon graphing of the function rule h = 8 - 0.4j, we see that the graph is continuous.

We are given the function as; h = 8 - 0.4j

Let h represent the height in inches on the y-axis and let j represent the amount of juice in ounces on the x-axis.

We are told that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j is an independent variable and h is dependent variable.

The function  represents the height of juice after drinking j ounces of juice. Therefore as the juice is being drank, the height of the juice in bottle will change continuously. Therefore, the graph of our given function will be continuous because we can drink fractions of an ounce juice.

The equation of a line in slope-intercept form is given as;

y = mx + b

where;

m is Slope of line

b is y-intercept

If we rewrite our function slope-intercept form of equation, we will get;

h = -0.4j + 8

Thus;

Slope = -0.3

y-intercept = 8.

The graph is as plotted in the attached file

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y = -18(x-7)² + 1 is the vertex form of the given equation.

y = a (x − h) 2 + k, y is the y -coordinate, x is the x -coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (-a).

Given that y = -18x² + 252x - 881, where a = -18, b = 252 and c = -881

h = -b/2a

h = -252/2*(-18) = 7

k = ah² + bh + c = -18*49 + 252*7 - 881 = 1

Therefore, putting the values in y = a (x − h) 2 we get,

y = -18(x-7)² + 1

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Work Shown:

4x + 13 ≥ 27

4x + 13-13 ≥ 27-13

4x ≥ 14

4x/4 ≥ 14/4

x ≥ 7/2

The inequality sign stays the same for each step. The inequality sign only flips if we were to multiply both sides by a negative number (or divide both sides by a negative number).

Note: 7/2 = 3.5