The figure shows a circle inscribed into a regular pentagon.Cis the center of the circle and the regular pentagon.G and H are on the edge of both the circle and the regular pentagon.The radius of the circle is 3 inches.GHCPart A. Find the area of the dark shaded region. Show your work.Part B. Find the area of the light shaded region. Show your work.

The factoring of the expression 2x² + 7x + 6 is (2x + 3)(x + 2).

It should be noted that a factor of a number is a number that can be multiplied with another number to get the original number.

In this case, 2x² + 7x - 6 will be factored thus:

= 2x² + 7x + 6

= 2x² + 4x + 3x + 6

= 2x(x + 2) + 3(x + 2)

= (2x + 3)(x + 2)

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Answer and Explanation:

If f(x) = x^2 is transformed to h(x)=2x^2 + 15, the below will be the effect on the its graph;

* The graph will be shifted up 15 units

*The graph will be vertically stretched since the value o

Answer

The 1.45 dollar chocolates will weigh (20 - x) pounds.

Explanation

We are told that the mixture weighed 20 pounds and one of the chocolates in the mixture weighed x pounds.

We are then to cslculate the weight of the other type of chocolate in the mixture.

Total mixture = 20 pounds

0.90 dollar chocolate weighed x pounds

The 1.45 dollar chocolates will weigh (20 - x) pounds.

Hope this Helps!!!

The company should must sell 923 radios to break even.

Fixed cost refer to those costs which do not vary directly with the level of output. For example salary given to staff.

Variable cost that cost which vary directly with the level of output..

The selling price of radio is $59.

Total radios sell are of value $41500. This is the fixed cost.

Let us say that they sell x number of radios,

As we know,

For break even point,

Total revenue = Total cost

Cost of one radio x number of radio = fixed cost plus variable cost of all radios

54x = 41500 + 14x

40x = 41500

x = 922.22~923

So, they should sell 923 radio to break even.

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Answer:

  12.  68%

  13.  50%

  14.  0.15%

  15.  8 students

Step-by-step explanation:

Given a normal distribution with mean 20 and standard deviation 5, you want several probabilities based on the empirical rule.

The empirical rule tells you the percentages of a normal distribution that are within 1, 2, or 3 standard deviations of the mean. They are ...

Wait times between 15 and 25 are within 20±5, so within 1 standard deviation of the mean. The percentage of students waiting 15–25 minutes is 68%.

The mean of the distribution is 20, which is its line of symmetry.

50% of students will wait less than 20 minutes.

35 is 3 standard deviations above the mean, so the fraction in this group is half of the difference between 1 and 99.7%.

0.15% of students will wait more than 35 minutes.

Of 5300, the number waiting more than 35 minutes is ...

  0.15% × 5300 = 7.95 ≈ 8

About 8 students will wait more than 35 minutes.

__

Additional comment

These values are based on the empirical rule, as required by the problem statement. The actual number for P(Z>3) is about 0.0013499 (0.13%), and the number of students is about 7.15 ≈ 7. That is, the result using the empirical rule is slightly different than what you get using a calculator, spreadsheet, or table.

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Explanation

In the question,

The number of tomatoes is described as x

The number of lettuce is described as y

As per the question, the number of vegetables Aneil can plant in the garden is modelled by:

The graph of the above model can be seen above.

From the graph, we have the y-intercept to be 20 and the x-intercept to be 30.

Answer:

Y-intercept = 20 ---- This is the number of lettuce plants Aneil can plant if he plants zero tomatoes

X- intercept =30 ---- This is the number of tomatoes plants Aneil can plant if he plants zero lettuce

ANSWER

EXPLANATION

h. We want to find the volume of the rectangular prism given.

The volume of a rectangular prism is given as:

where L = length

w = width

h = height

Therefore, we have that the volume of the prism is:

so the answer is pi/2, 3pi/2, and pi/3

Perimeter = 18 ft

Area = 20 ft ^2

Perimeter = 2l + 2w

Area = lw

Substitution

18 = 2l + 2w

20 = lw

Solve for l

20/w = l

18 = 2(20/w) + 2w

18 = 40/w + 2w

18w = 40 + 2w^2

2w^2 - 18w + 40 = 0

w^2 - 9w + 20 = 0

(w - 5)(w - 4) = 0

w1 = 5 w2 = 4

Conclusion

width = 4 ft

length = 5 ft

Given the turning points of the graph:

(-1.73, -10.39) and (1.73, 10.39).

Let's determine the range of the graphed function.

The range of a function is the set of all possible values of y.

The y-values are represented on the vertical axis.

From the graph, we can see the function goes up continuously and goes down continuously.

Therefore, we can say the range of the function is real numbers.

Therefore, the range of the function in interval notation is:

(-∞, ∞)

ANSWER:

rRange: (-∞, ∞)

a) The types of angles present are:

- 1 right angle

- 1 angles of 50 degrees and 1 angle of 4x degrees

b) their relationship is add up to 90°

c) 50° + 4*x° = 90°

4*x° = 90 - 450

x° = 40/4 = 10

x = 10°

A line is said to bisect an angle if it divides it in two equal parts.

Since the segment OB bisects the angle AOC, then the angles AOB and BOC have the same measure.

Therefore, the complete statement is:

Answer:

The answer is: r is equal to -22.

Answer:

  (c)  8, 12, 16

Step-by-step explanation:

You want to identify the side lengths that are proportional to lengths 4, 6, and 8.

Reducing the ratios to lowest terms, we can compare them:

Side lengths 8, 12, 16 will form a triangle similar to ∆DEF.

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Answer:

hola comasa due when 123 dfosb971 24

SOLUTION

From the question, town B is 3.5cm from town A and town C is 2cm from town B. Therefore C is 5.5 cm from town A.

The scale is 2cm for every 100miles. This means 1cm for every 50 miles.

You get this by dividing 100 by 2.

Now 5.5 cm becomes 5.5 x 50 miles = 275miles.

So town A and town C are 275 miles apart

X has a value of 11

What is an angle?

The vertex of an angle is the common point of contact where two straight lines or rays come together to produce an angle.

As far as we are aware, this question is answered utilizing a quadrilateral's unique property that the sum of its adjacent angles is 180 degrees.

By quadrilateral, what do you mean?

A closed polygon with four sides, four vertices, and four angles is known as a quadrilateral.

thus, A.T.Q:-

We possess 5x+9x+26=180

14x +26=180

14x=154

x = 11 degrees

Consequently, x = 11 degrees.

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Answer:

y = -16 (x - 1)^2 + 112

The object lands on the ground in approximately 3.6s

Explanation:

The equation given is that of a parabola.

Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.

The vertex form of a parabola is

where (h, k) is the vertex.

The only question is, what is the vertex for our function h(t)?

Remember that if we have an equation of the form

then the x-coordinate of the vertex is

Now in our case b = 32 and a = -16; therefore,

We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get

Hence, the y-coordindate is k = 112.

Therefore, the vertex of the parabola is (1, 112).

With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.

The only problem is that we don't know what the value of a is. How do we find a?

Note that the point (0, 96) lies on the parabola. In other words,

Therefore, the vertex form of the parabola must also contain the point (0, 96).

Putting in t = 0, h = 96 into the vertex form gives

subtracting 112 from both sides gives

With the value of a in hand, we can finally write the equation of the parabola on vertex form.

Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.

We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.

Thus we solve,

Now subtracting 112 from both sides gives

Dividing both sides by -16 gives

taking the square root of both sides gives

adding 1 to both sides gives

Hence, the two solutions we get are

Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.

Therefore, it takes about 3.6 seconds for the object to hit the ground.

The coordinate of the point C on the line segment is (9, -4)

On the segment, we have the following endpoints

A = (-3, 4)

B = (-9, 8)

The ratio of point A on the line is given as

Ratio, B : C = 1 : 2

Rewrite as

m : n = 1 : 2

The coordinate of point A is calculated using

A = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Where x and y are the coordinates defined above

So, we have

(-3, 4) = 1/(1+2) * (1 * x + 2 * -9, 1 * y + 2 * 8)

Evaluate

(-3, 4) = 1/3 * (x - 18, y + 16)

So, we have

(x - 18, y + 16) = (-9, 12)

This means that

x - 18 = -9

y + 16 = 12

Solve

x = 9

y = -4

Hence, the location of the point C is (9, -4)

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Answer:

The original slope is 1, so the slope of the parallel line will also be 1.

The equation of the line will be  [tex]y = -\frac{3}{5}x -3[/tex]

In the question given, It is stated that the slope of the line is m = -3/5, and the y-intercept of the line is (0, -3). We have to find out the slope-intercept form of the line. To find out the equation of line first the standard equation for slope intercept form is y = mx + b, where m is the slope, and b is the y-intercept.

Now, we have slope m = -3/5 and y-intercept is -3. Putting these values in the slope intercept form we get:

=> y = mx + b

=> [tex]y = -\frac{3}{5}x -3[/tex]

Hence, we get equation of line [tex]y = -\frac{3}{5}x -3[/tex]

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The term that should go in the space to complete the statement is 5.

The complete statement is 5c + 15 = 5(c + 3).

The given statement is 5c + 15 = __(c + 3).

Now, we will combine the like term from the left side of the expression which is 5, and place it on the right side space to make the expression equivalent.

Hence, the complete statement is 5c + 15 = 5(c + 3).

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We have a regression model to predict y from the value of x.

The equation of this regression line is:

We then can calculate y for x = 7 as:

Answer: the predicted value of y when x = 7 is y(7) = 20

The solution for this function will be x = -1 and x = 3

Quadratic polynomials are those with at least one variable and a variable with a maximum exponent of two. Since the second-degree term is the highest degree term in a quadratic function, it is sometimes referred to as the polynomial of degree 2. In a quadratic function, at least one term must be of the second degree. It has qualities in algebra.

The given function is -2x² + 4x + 6

So, we'll employ the middle term splitting strategy.

-2x² + 4x + 6 = 0

- 2x² + 6x - 2x + 6 = 0

-2x ( x-3) -2 (x-3) = 0

(-2x-2) (x-3) = 0

So, the solution will be

-2x - 2 = 0

-2x = 2

x = 2/-2

x = -1

And, x-3 =0

x = 3

So, the solution of the quadratic function will be

x =-1 and x = 3

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Answer:

69

Step-by-step explanation:

400-262=138

138÷2=69

Part A)

Recall that:

1) The function represented by the graph of the function f(x) translated vertically n units up and horizontally m units left is:

2) The function represented by the graph of the function f(x) reflected over the x-axis is:

Now, notice that g(x) is the function f(x) reflected over the x-axis and then translated vertically 6 units up and horizontally 4 units left.

Answer Part A:

Options B, C, and D.

Part B) To graph g(x) we will reflect the graph of f(x) over the x-axis and then we will translate it vertically 6 units up and horizontally 4 units left.

We know that the graph of f(x)=|x| is:

The above graph reflected over the x-axis is:

Finally, the above graph translated vertically 6 units up and horizontally 4 units left is:

Answer part B:

To the nearest tenth, the distance across the lake is DE = 207.68 m.

The corresponding side lengths of two triangles that are similar are always proportional to each other.

ΔCDE  and ΔCFG are similar to each other

FG = 142.1 m

FC = 130 m

DF = 60 m

DC = 130 + 60 = 190 m

Therefore,

DE/FG = DC/FC

Substitute

DE/142.1 = 190/130

Cross multiply nearest hundredth

Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is DE = 207.68 m

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Answer:

x ≥ 2

Step-by-step explanation:

Given inequality:

[tex]-\dfrac{4(x+3)}{5} \leq 4x-12[/tex]

Values of x less than 2

Substitute two values where x < 2 into the inequality:

[tex]\begin{aligned}x=1 \implies -\dfrac{4(1+3)}{5} & \leq 4(1)-12\\\\ -\dfrac{4(4)}{5} & \leq 4-12\\\\ -\dfrac{16}{5} & \leq -8 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies -\dfrac{4(0+3)}{5} & \leq 4(0)-12\\\\ -\dfrac{4(3)}{5} & \leq 0-12\\\\ -\dfrac{12}{5} & \leq -12 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]

The values of x < 2 are not solutions to the inequality.

--------------------------------------------------------------------------------

Substitute the value of x = 2 into the inequality:

[tex]\begin{aligned}x=0 \implies -\dfrac{4(2+3)}{5} & \leq 4(2)-12\\\\ -\dfrac{4(5)}{5} & \leq 8-12\\\\ -\dfrac{20}{5} & \leq -4\\\\ -4 & \leq -4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

The value of x = 2 is a solution to the inequality.

--------------------------------------------------------------------------------

Values of x more than 2

Substitute two values where x > 2 into the inequality:

[tex]\begin{aligned}x=3 \implies -\dfrac{4(3+3)}{5} & \leq 4(3)-12\\\\ -\dfrac{4(6)}{5} & \leq 12-12\\\\ -\dfrac{24}{5} & \leq 0 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies -\dfrac{4(4+3)}{5} & \leq 4(4)-12\\\\ -\dfrac{4(7)}{5} & \leq 16-12\\\\ -\dfrac{28}{5} & \leq 4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

The values of x > 2 are solutions to the inequality.

--------------------------------------------------------------------------------

Therefore, the solution to the inequality appears to be x ≥ 2.  

To check, solve the inequality:

[tex]\begin{aligned} \implies -\dfrac{4(x+3)}{5} &\leq 4x-12\\-4(x+3) &\leq 5(4x-12)\\-4x-12 &\leq 20x-60\\ -24x & \leq-48\\x & \geq 2\end{aligned}[/tex]

When graphing inequalities on a number line:

To graph the solution to the inequality on number line, place a closed circle at x = 2 and shade to the right.  (See attachment).

from the options;

The correct is B

because 2860 is greater than 2806

Other options are false

the given equation is

x - 4y = -16

put x = 0

0 - 4y = -16

y = 4

so at x = 0 ,, y is 4

put x = 4

4 - 4y = -16

-4y = -16- 4

y = 20/4

y = 5

so, at x = 4 the value of y is 5

thus, the correct graph is option B