Solution

**Part A**: The area of the dark shaded region = **S1**,

where

The radius of the circle is 3 inches.

[tex]\begin{gathered} S_1=\frac{4}{5}\pi r^2 \\ =\frac{4}{5}\pi.3^2 \\ S_1=\frac{36}{5}\pi in^2 \end{gathered}[/tex]**Part B**: The area of the light shaded region = **S,**

if A(-3,4) is on BC and divides it in the ratio of BA:AC = 1:2 find C if B is (-9,8)

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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Given that bisects use the diagram above to complete the following statement.m∠AOB= m∠…

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:**

Find the value of x. The diagram is not to scale. Lines fand g are parallel. f g

5x

9x+26

A. 10

B. 11

C. 12

D. -11

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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Hola!, me ayudan porfa!!

En la cerrada economía Chalupa, el consumo familiar triplica el de las unidades productivas y este supera en $2,500 al del gobierno, que tiene un equilibrio presupuestario y sus ingresos fueron $6,700. Si el consumo de capital fijo es 25% del PNB pm y el monto de impuestos netos de subsidios $1750 encuentre el ingreso nacional.

**Answer:**

hola comasa due when 123 dfosb971 24

can you please solve this practice problem for me I really need assistance. the original slope is blue and the parallel slope is green

**Answer:**

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

What is the effect on the graph of f(x)=x^2 when it is transformed to h(x)=2x^2 + 15

**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

Find the dimensions of a rectangular Persian rug whose perimeter is 18 ft and whose area is 20ft^2. *Answer fill in*The Persian rug has a length (longerside) of [___]ft and a width (shorter) of [__]ft

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**

The quadratic function -2x ^ 2 + 4x + 6 is shown below. What are the solutions of this function? *

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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PartA)What are the transformations are needed in in order to obtain the graph of G(x) from the graph of f(x) Select all that applyPartB) Graph g(x)

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:

[tex]f(x+m)+n\text{.}[/tex]2) The function represented by the graph of the function f(x) reflected over the x-axis is:

[tex]-f(x)\text{.}[/tex]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:**

Least squares regression line is y=4x-8 what is the best predicted value for y given x =7?

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

The equation of this regression line is:

[tex]y=4x-8[/tex]We then can calculate y for x = 7 as:

[tex]y(7)=4(7)-8=28-8=20[/tex]**Answer: the predicted value of y when x = 7 is y(7) = 20**

which graph represents the equation x - 4y = -16

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**

Triangles DEF and HJK are similar. DEF has side lengths DE=4, EF=6, FD=8. Which of the following could be the side lengths of HJK?• 2, 6, 7• 2, 5, 7• 8, 12, 16• 5, 7, 9

**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:

desired ratio: 4 : 6 : 8 = 2 : 3 : 42 : 6 : 7 — reduced, not equivalent2 : 5 : 7 — reduced, not equivalent8 : 12 : 16 = 2 : 3 : 4 . . . . . same as the desired ratios5 : 7 : 9 — reduced, not equivalent**Side lengths 8, 12, 16 will form a triangle similar to ∆DEF**.

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Solve by factoring: f(x) = 2x² + 7x+6

Write the final answers in the two blanks. Do NOT write x =, just the number. If there is a fraction in your answer, write as #/#.

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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The turning points of the graph are (-1.73, -10.39) and (1.73, 10.39). What is the range of the Polynomial function f?

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: (-∞, ∞)**

There are multiple choices. but they didn’t fit in the picture

**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:

[tex]2x+3y=60[/tex]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**

A map is drawn using the scale 2cm: 100miles. On the map, Town B, is 3.5 cm from Town A and Town C is 2 cm past Town B. How many miles apart are Town A and Town C

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**

A ball is thrown in the air from a platform that is 96 feet above ground level with an initial vertical velocity of 32 feet per second. The height of the ball, in feet, can be represented by the function shown where t is the time, in seconds, since the ball was thrown. Rewrite the function in the form that would be best used to identify the maximum height of the ball and find Approximately when the object lands on the ground when rounded to the nearest tenth.

**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

[tex]y=ax^2+bx+c[/tex]then the x-coordinate of the vertex is

[tex]h=-\frac{b}{2a}[/tex]Now in our case b = 32 and a = -16; therefore,

[tex]h=\frac{-32}{2(16)}=1[/tex]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

[tex]k=-16(1)+32(1)+96=112[/tex]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.

[tex]h(t)=a(t-1)^2+112[/tex]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,

[tex]h(0)=-16(0)^2+32(0)+96=96[/tex]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

[tex]96=a(0-1)^2+112[/tex][tex]96=a+112[/tex]subtracting 112 from both sides gives

[tex]a=-16[/tex]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.

[tex]h(t)=0.[/tex]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,

[tex]-16\left(t-1\right)^2+112=0[/tex]Now subtracting 112 from both sides gives

[tex]-16(t-1)^2=-112[/tex]Dividing both sides by -16 gives

[tex](t-1)^2=\frac{-112}{-16}[/tex][tex](t-1)^2=7[/tex]taking the square root of both sides gives

[tex]t-1=\pm\sqrt{7}[/tex]adding 1 to both sides gives

[tex]t=\pm\sqrt{7}+1[/tex]Hence, the two solutions we get are

[tex]t=\sqrt{7}+1=3.6[/tex][tex]t=-\sqrt{7}+1=-1.6[/tex]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. **

What term must go in the space to complete the statement?

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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Which is true?A. 2680 > 2806B. 2860 > 2806C. 2680 < 2086D. 2806 < 2680

from the options;

**The correct is B**

**because 2860 is greater than 2806**

**Other options are false**

Find the equation of the line with slope −3/5 and y-intercept (0,−3).

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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To indirectly measure the distance across a lake, Ethan makes use of a couple

landmarks at points B and C. He measures AE, EC, and DE as marked. Find the

distance across the lake (BC), rounding your answer to the nearest hundredth of a

meter.

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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Evaluate r(x) = 3x - 10 when x= -4. r(-4)=_

**Answer:**

The answer is: r is equal to -22.

Answer this please I really need you to do this

**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).

Transit Technologies plans to produce 2-way radios that will sell for $59 per radio. They estimate fixed costs

in manufacturing the radios to be $41,500. The variable costs of producing each radio will be $14. How many

radios must the company sell to break even?

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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Questions 12-15. Data from Ivy Tech’s advising center shows that their wait times follow a normal distribution. Use theEmpirical Rule to answer the following questions. 5 10 15 20 25 30 3512. What percent of students will wait between 15 and 25 minutes? (round to the nearest whole number)13. What percent of students will wait less than 20 minutes? (round to the nearest whole number)14. What percent of students will wait more than 35 minutes? (round to the hundredths place)15. If 5,300 students come to the advising center, how many students would wait more than 35 minutes? (round to thenearest student)

**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 ...

within 1: 68%within 2: 95%within 3: 99.7%12. Between 15 and 25Wait 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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6. Solve for x. **THINK! a) what type of angles do you have? b) what is theirrelationship (add up to 90, add up to 180, or congruent)? c) set up an equationand solve *

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 mixture of 20 pounds of candy sells for $1.15. The mixture consists of chocolates worth $1.45 a pound and chocolatesworth $0.90 a pound. If x represents the pounds of $0.90 chocolates used, then which of the following represents thepounds of $1.45 chocolates used?20 - x20 xOX-20

**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!!!**

what is 3 1/2 x 4 1/2 x 5 ft * 5 1/6 x 5 1/4 x 3 1/3 x 4 1/2 in 5 ft x 5 1/3 * 2/3

**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:**

a. pi/3 b. pi/2c. 2pi/3d. 3pi/2 These are 4 options but there can be more than 2 or 3 correct answers.Find the solution of each equation the interval

[tex]\sin x\cdot\cos x-\frac{\sqrt[]{3}}{2}\cos x=0[/tex][tex]\cos x(\sin x-\frac{\sqrt[]{3}}{2})=0[/tex][tex]\begin{gathered} \cos x=0 \\ x=\frac{\pi}{2},\frac{3\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \sin x-\frac{\sqrt[]{3}}{2}=0 \\ \sin x=\frac{\sqrt[]{3}}{2} \\ x=\frac{\pi}{3} \end{gathered}[/tex]

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

uncle grandpa once said, “400 reduced by twice my age is 262.” what is his age? Show work

**Answer:**

69

**Step-by-step explanation:**

400-262=138

138÷2=69

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