A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.

Which is a possible turning point for the continuous function f(x)?


(–2, 0)

(0, –2)

(2, –1)

(4, 0)



On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).


On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).

The average change in the temperature of the city is 0.87°C.

The average quantity is the sum of all quantities divided by the number of quantities.

In the question, we are informed that a newspaper reports the changes in the temperature of the city over 4 days to be 3.24°C, - 3/8 °C, - 0.15 °C, and 7/9 °C.

We are asked to write an expression to show the daily average change in the temperature of the city.

As we know, the average quantity is the sum of all quantities divided by the number of quantities.

Thus, average = {(3.24 - 3/8 -0.15 +7/9)/4} °C,

or, average = {{324/100 - 3/8 - 15/100 + 7/9}/4} °C,

or, average = [{(23328 - 2700 - 1080 + 5600)/7200}/4] °C,

or, average = 25148/28800 °C,

or, average = 6287/7200 °C = 0.8732 °C ≈ 0.87 °C.

Thus, the average change in the temperature of the city is 0.87°C.

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The value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06

The expression is given as:

[tex]x \sim B (10, 0.75)[/tex]

This means that:

n = 10

p = 0.75

The probability is then calculated as

[tex]P(x)= ^nC_x * p^x *(1 - p)^{n-x[/tex]

This gives

[tex]P(5)= ^{10}C_5 * 0.75^5 *(1 - 0.75)^5[/tex]

Evaluate the combination expression

[tex]P(5)= 252 * 0.75^5 *0.25^5[/tex]

Evaluate

P(5)= 0.06

Hence, the value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06

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The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.

Given :

Expression - 8 + (n - 4)

To simplify the given expression following steps can be used:

Step 1 - Rewrite the given expression.

= (n - 4) + 8

Step 2 - Now, remove the parenthesis in the given expression.

= n - 4 + 8

Step 3 - Now, write 8 as the addition of 4 and 4.

= n - 4 + 4 + 4

Step 4 - Subtract 4 by 4.

= n + 4

Therefore, the correct answer is (12+n).

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Answer:

-36 and 36

Step-by-step explanation:

moving the 9x to the left it changes to -9x and that plus -27x is -36x

-27-9 = -36

moving -27x to the right it changes to 27x so that plus 9x is 36x

27+9 = 36

Answer:

A. -36

F. 36

Step-by-step explanation:

The unknown sides and angles of the triangle are 18 cm and 39 degrees respectively.

The side and angle of a triangle can be found as follows:

using sine law,

Angle A = 180 - 68 - 59 = 53 degrees

19.5 / sin 59 = a / sin 53

19.5 sin 53 = a sin 59

a = 19.5 sin 53 / sin 59

a = 15.5733924459 / 0.8571673007

a = 18.1680280047

a = 18 cm

15 / sin ∅ = 20 / sin 57

15 sin 57 = 20 sin ∅

sin ∅ = 12.5800585192 / 20

sin ∅= 0.62900292595

∅ = sin ⁻¹ 0.62900292595

∅ = 38.9763828249

∅ = 39 degrees.

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Answer:

x = 21.013155617496

Step-by-step explanation:

we have a right triangle then ,

[tex]\cos \left( 36\right) =\frac{17}{x}[/tex]

Then

[tex]x=\frac{17}{\cos \left( 36\right) } = 21.013155617496[/tex]

Then

x ≈ 21

Step-by-step explanation:

imagine this right-angled triangle is the sine and cosine scenario in a circle. just turn it in your mind or on the paper until it looks like this.

the point with the 36° angle is the center of this circle.

x is the radius of the circle, that is under 36° connecting the center of the circle with the arc of the circle.

17 is the cosine of the angle multiplied by the radius (as the standard cosine function is normed for the standard circle with radius 1).

and the other leg is the sine of the angle multiplied by the radius (this is FYI, we don't need that for the solution here).

so,

17 = cos(36) × x

x = 17/cos(36) = 21.01315562...

The triangle ABC was reflected over the x axis to form triangle A'B'C, hence the measures of the corresponding angles are congruent.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The triangle ABC was reflected over the x axis to form triangle A'B'C, hence the measures of the corresponding angles are congruent.

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The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours. Option A

c(h) = 250 + 200h

s(h) = 300 + 180h

Where,

To have equal tuition in both schools,

equate both function

250 + 200h = 300 + 180h

200h - 180h = 300 - 250

20h = 50

h = 50/20

h = 2.5 hours.

The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours.

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Answer:

Step-by-step explanation:

B: 1, 16, 81

WHY?

Set A is perfect squares from A to 100:

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

10^2 = 100

Set A = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Set C is perfect fourths

1^4 = 1

2^4 = 16

3^4 = 81

4^4 = 254 (This is greater than 100)

Set C = 1, 16, 81

Hope this helps :)

Answer:

20

Step-by-step explanation:

so we need to see that

3/4 x ? = 15

so we say

3 x ? = 15x4

? =60/3

?= 20

Using the proportionality theorem, the length of the missing segment is 25 units.

According to the proportionality theorem, the middle segment in the diagram given divides the two sides it intersects proportionally.

Therefore, we would have:

x = missing segment

36/21 = (35 + x)/35

Cross multiply

35(36) = 21(35 + x)

1,260 = 735 + 21x

1,260 - 735 = 21x

525 = 21x

525/21 = x

x = 25

The missing segment is: 25 units.

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Job order costing also gives managers the advantage of being able to keep track of individuals' and teams' performance in terms of cost control, efficiency, and productivity. A disadvantage of job order costing is that employees are required to track all materials and labor used during the job.

With the standardization of products, managers track performance, productivity, and costs over time. Process costing allows for greater flexibility when making changes in the production process. Managers can target specific departments' processes or materials to lower production costs.

With process costing, companies track the flow of costs from department to department, rather than tracking costs for each individual item. Each department adds direct labor and manufacturing overhead costs, plus the cost of any raw materials it uses.

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John get money $630 and bill get money $270.

Given that John and bill shared $900 in the ratio 7:3 respectively.

The ratio is defined as the comparison of two quantities of equal units, indicating the quantity of one quantity contained in the other quantity.

The total ratio is 7+3=10

For john:

John has money seven out of 10 for the $900, we get

J=900×(7/10)

J=90×7

J=630

For bill:

Bill is three out of ten for $900, we get

B=900×(3/10)

B=90×3

B=270

Hence, john get money $630 and bill get $270 when they both shared $900 in the ratio 7:3 respectively.

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The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.

Option A) is the correct answer.

Given the expression;  1/5 (-16-9) + 4² ÷ 8

First we remove the parentheses and perform the operations using the guidelines of BODMAS

1/5 (-16-9) + 4² ÷ 8

1/5 × -25 + 4² ÷ 8

1/5 × -25 + 16 ÷ 8

-25/5 + 16/8

-5 + 2

-3

The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.

Option A) is the correct answer.

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Postulate: AA

Similarity statement: [tex]\triangle CBA \sim \triangle FED[/tex]

To solve a triangle means to obtain al the missing parts of the triangle.

To solve a triangle means to obtain al the missing parts of the triangle. Now we have the following information;

<ABC = 51°

c = 8

a = 11

Then;

b^2 = a^2 + c^2 - 2acCos B

b^2 = (11)^2 + (8)^2 - [2 * 11 * 8 * cos 51]

b^2 = 121 + 64 - 55.38

b = 11.39

Now;

a/sinA = b/sinB

asinB = bsinA

sinA = asinB/b

sinA = 11 * sin 51/11.39

A = 48.6 or 49°

C = 180 - (49 + 51)

C = 80°

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The two methods which can be used to solve the quadratic equation are; The completing the square method and the factor method.

Although, not limited to the aforementioned methods of solving quadratic equations, the two methods are major methods of solving quadratic equations.

The completing the square method (also used in expressing quadratic equations in vertex form) and the factor method are very efficient method of solving quadratic equations.

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Answer:

9w+1402

Step-by-step explanation:

Completing the squares, we have that:

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For the parabola of standard form y = x² - 6x + 17, we have that it can be written as follows, completing the squares:

y = x² - 6x + 17 = (x - 3)² + 8, hence the extreme value is (3,8).

For the parabola of standard form y = x² + 8x + 21, we have that it can be written as follows, completing the squares:

y = x² + 8x + 21 = (x + 4)² + 5, hence the extreme value is (-4,5).

For the parabola of standard form y = x² - 16x + 60, we have that it can be written as follows, completing the squares:

y = x² - 16x + 60 = (x - 8)² - 4, hence the extreme value is (8,-4).

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The pig pen is 14 sq. meters larger than the chicken pen built by the former.

Consider a rectangle with length 'L' and width 'W'.

So, its perimeter = 2(L + W) units and area = L × W sq. units.

It is given that a farmer built a rectangular pen for chickens.

The chicken pen's perimeter is 12 meters, and she used only one side of the barn as one length of the rectangular pen.

So,

L + 2W = 12

⇒ L = 12 - 2W

Then its area is calculated as below:

Area = L × W

        = (12 - 2W) W

        = 12W - 2W²

Consider A' = 0 for finding the larger area.

So, differentiating the area w.r.t W,

dA/dW = 12 - 4W

0 = 12 - 4W

⇒ 4W = 12

∴W = 3 meters

Then,

L = 12 - 2W = 12 - 2(3) = 6 meters

So, the area of the chicken pen = 6m × 3m = 18 m²

It is given that,

The length of the pig pen was 2 meters more than the length of the chicken pen. I.e., L' = L + 2

The width of the pig pen was 1 meter more than the width of the chicken pen. I.e., W' = W + 1

On substituting L and W values to find the dimensions of the pig pen,

L' = 6 + 2 = 8m

W' = 3 + 1 = 4m

Then,

Area = L' × W'

        = 8m × 4m

        = 32 m²

Finding how much larger is the pig pen than the chicken pen:

Area of the pig pen - Area of the chicken pen

⇒ 32 m² - 18 m² = 14 m²

Therefore, the pig pen is 14 m² larger than the chicken pen.

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The angle of the given ray is of x = 150º.

The angle of the ray is given by the sum of the angles that compose the ray.

In this problem, the angles are of 65º, 40º and 45º, hence:

x = 65 + 40 + 45 = 150º

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See below for the interpretation of the graph

From the graph, the initial values of x and y are 0

As x increases, y decreases.

This means that the first statement is

Slope is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

Using the graph values at the interval x =0 to x = 3, we have:

[tex]m = \frac{-3 - 0}{3 - 0}[/tex]

m = -1

This means that the second statement is

From the graph, y = -3, when x = 3

As x increases at this point, y increases.

This means that the third statement is

Using the graph values at the interval x = 3 to x = 5, we have:

[tex]m = \frac{3 + 3}{5 - 3}[/tex]

m = 3

This means that the fourth statement is

All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0

So, the last two statements are

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Answer:

Step-by-step explanation:

velocity = distance divided by time

velocity of the snail = 1cm / 3min

v of snail = 0.333 cm per minute

to calculate the time of 1 meter displacement, we use the formula t = d/V

time = distance divided by velocity

time = 1meter / 0.333cm/min

time = 100cm / 0.333cm/min

time = 300 minutes

hope it helped!

The table that describes the behavior of the graph of f(x) = 2x3 – 26x – 24 is known to be table B.

To be able to tell the function one need to use a graphing tool and see the attached figure to better tell and know the problem.

The Relation of graph to the x-axis are shown below

Note also that in the image attached, the vertical line is the y-axis and the horizontal line is the x- axis.

Hence, the table that describes the behavior of the graph of f(x) = 2x3 – 26x– 24 is known to be table B.

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Answer:

B

Step-by-step explanation:

It takes 15 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.

The relation between distance 'd', time 't', and speed 's' is given by the formula,

s = d/t or

d = st or

t = d/s

It is given that,

The distance to uncle's house = 444 miles

The time taken to drive to uncle's house = 12 hours

So,

speed = (444)/12 = 37 miles/hour

Then the time to drive 555 miles(to Atlanta) is calculated by,

time t = (555)/37 = 15 hours

Therefore, it takes 15 hours to drive to Atlanta at 555 miles of distance.

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Answer:

slope: undefined

equation: x = p

y-intercept: there is none

slope of perpendicular: 0

Step-by-step explanation:

points: (p, a), (p, -a)

slope = (-a - a)/(p - p) = -2a/0

The slope is undefined since the line is vertical.

equation: x = p

Since p ≠ 0, the vertical crosses the x-axis at a point that is not x = 0 and never intersects the y-axis, so the is no y-intercept.

A line perpendicular to he given line is a horizontal line.

slope = 0

Considering that it is a triangle, the range of the possible lengths, x, of the third side of the tile is: (1, 17).

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

Hence, if 9 is the greater side:

8 + x > 9

x > 1.

If 8 and 9 are the smaller sides:

x < 8 + 9

x < 17.

Hence the range of possible lengths is:

(1, 17).

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Answer:

(D) 30

Step-by-step explanation:

number of green marbles = x

number of red marbles = 5

total number of marbles = x + 5

p(red) = (number of red marbles)/(total number of marbles)

p(red) = 5/(x + 5)

p(red) = 1/7

5/(x + 5) = 1/7

(x + 5) × 1 = 5 × 7

x + 5 = 35

x = 30

Answer: (D) 30