Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:

Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.

The revenue is maximized for a value p = 100, and the maximum revenue is:

R =  23,500

We know that the number of items sold for a prize p is:

-2.35p + 470

Then the revenue will be:

R = (-2.35p + 470)*p

So we need to find the value of p that maximizes that quadratic equation, we can see that the maximum will be at the vertex, then let's write:

R = -2.35p² + 470p

The vertex is at:

p = -470/(2*2.35)

p = 100

Finally, the maximum revenue is:

R =  -2.35*100² + 470*100

R = 23,500

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The problem can be translated into an equation as follows: 8x = (1/3)(x+2)

the answer that represents this situation is: 8x = (1/3)(x+2)

Simplifying the right side of the equation:

8x = (1/3)x + (2/3)

Multiplying both sides of the equation by 3 to eliminate the fraction:

24x = x + 2

Subtracting x from both sides of the equation:

23x = 2

Dividing both sides of the equation by 23:

x = 2/23

Therefore, the answer that represents this situation is:

8x = (1/3)(x+2)

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Answer:

25/4 quarts of cranberry juice

40/3 quarts of apple juice

25/8 quarts of lemonade

Step-by-step explanation:

just multiply everything by 5

:)

The correct graph is Option D - the bottom left graph.

Given function is f(x)=ceil(x+1)

To plot graph of f(x) in interval of(-3,3) :

ceil(x+1) is ceiling function

The output of ceil(x) is least integer greater than x

for example ceil(5.5)=6

For an interval of (-3,-2):

Take x=(-2.4)

x+1=(-1.4)

y=f(x)=ceil(x+1)=(-1)

Similarly,

For an interval of (-2,-1):

Take x=(-1.4)

x+1=(-0.4)

y=f(x)=ceil(x+1)=(0)

For an interval of (-1,0)

y=f(x)=1

For an interval of (0,1)

y=f(x)=2

For an interval of (1,2)

y=f(x)=3

For an interval of (2,3)

y=f(x)=4

Thus, The correct graph is the bottom left graph.

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The minor arc in the given diagram as required to be determined is; arc TU and it's measure is; 116°.

The major arc in the given diagram as required to be determined is; arc TVU and it's measure is; 244°.

It follows from the task content that the minor and major arcs are to be named and their measures determined as required.

The minor arc in a circle is usually subtended by an angle less than 180° while the major arc is subtended by an angle greater than 180°.

Ultimately, the minor arc is; arc TU and it's measure is; 116° while the major arc is; arc TVU and it's measure is; 244°.

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Answer:

dont understand 14+14=π

Answer:

Step-by-step explanation:

[tex]y=\frac{1}{2} x+2[/tex]

[tex]y=(x-h)^2+k[/tex]

[tex]y=(x+3)^2-2=x^2+6x+7[/tex]

The probability models that represents a probability of winning of 1/6 are given as follows:

A) a fair six-sided number cube.

D) a spinner with 6 equal sections.

E) a bag of 12 black chips and 60 red chips.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

For this problem, we want a probability of 1/6 of winning each trial, hence the events are given as follows:

A) a fair six-sided number cube. -> One out of the six numbers is equivalent to winning.

D) a spinner with 6 equal sections. -> One out of the six regions is equivalent to winning.

E) a bag of 12 black chips and 60 red chips. -> 12/(12 + 60) = 12/72 = 1/6.

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Answer:

25 + 5√29

Step-by-step explanation:

(I added a photo below)

First, let's find BC using the Pythagorean theorem (from ∆BCD):

[tex] {bc}^{2} = {25}^{2} + {10}^{2} = 625 + 100 = 725[/tex]

[tex]725 > 0[/tex]

[tex]bc = \sqrt{725} =5 \sqrt{29} [/tex]

Then we see, that AB = 25 + x

So, now we can find AC:

[tex] {ac}^{2} = ({25 - x})^{2} - ({5 \sqrt{29} })^{2} = 625 - 50x + {x}^{2} - 25 \times 29 = 625 - 50x + {x}^{2} - 725 [/tex]

Now we have a quadratic equation:

[tex] {x}^{2} - 50x - 100 = 0[/tex]

[tex]d = {b}^{2} - 4 \times a \times c = ({ - 50})^{2} - 4 \times 1 \times ( - 100) = 2500 + 400 = 2900 > 0[/tex]

[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{50 - 10 \sqrt{29} }{2} = 25 - 5 \sqrt{29} [/tex]

This is a negative number and we cannot use it, since x has to be a natural number

[tex]x2 = \frac{ - b + \sqrt{d} }{2 a} = \frac{50 + 5 \sqrt{29} }{2} = 25 + 5 \sqrt{29} [/tex]

Answer:

[tex]31+4x > 63[/tex]

To reach her fitness goal, she needs to run for more than 8 days.

Step-by-step explanation:

She has already run 31 miles and runs 4 miles per day:

This means that after x days, the distance she will have run is:

[tex]D(x)=31+4x[/tex]

Tammy must run more than 63 miles total to reach her fitness goals.

This means that:

[tex]D(x) > 63[/tex]

[tex]31+4x > 63[/tex]

The inequality is:

[tex]31+4x > 63[/tex]

Solution:

[tex]4x > 32[/tex]

[tex]x > \dfrac{32}{4}[/tex]

[tex]x > 8[/tex]

To reach her fitness goal, she needs to run for more than 8 days.

Option B. The length of the hypotenuse of Carter's triangle is 13cm.

Since Carter's triangle is similar to Peyton's triangle, the ratio of corresponding side lengths will be the same. Let's use x to represent the length of the hypotenuse of Carter's triangle.

We know that the ratio of the lengths of the hypotenuse and the shorter leg of Peyton's triangle is 13:5. So, the ratio of the lengths of the hypotenuse and the shorter leg of Carter's triangle must also be 13:5.

Thus, we have x/5 = 13/5, which simplifies to x = 13.

Therefore, the length of the hypotenuse of Carter's triangle is 13cm.

Therefore, the only possible length for Carter's hypotenuse is 13cm, and the correct answer is A.

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Peyton drew a right triangle with sides 5cm, 12cm, and 13cm long. Carter drew a similar triangle to Peyton’s. Which of the following can be the measurements of Carter’s triangle?

A. 15cm

B. 13cm

C. 11cm

D. 10cm

Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P =  2(11v + 5w) cm.

The perimeter of a rectangle is the length measured around the edge of the rectangle. Although a rectangle has two dimensions, its perimeter only has one and is expressed in linear distances like feet or meters.

The perimeter calculation can be used, for instance, to calculate that many ft of brick border are required overall if somehow the rectangle depicts a garden which needs a brick border.

The sum of the lengths of a rectangle's four sides is known as its perimeter.

Rectangle perimeter = 2L + 2W.

Length = (6v+7w)

width = (5v - 2w)

P = 2 (length  + width)

P = 2(6v+7w + 5v - 2w)

On simplifying:

P =  2(11v + 5w)

Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P =  2(11v + 5w) cm.

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Compete question:

The width of a rectangle measures (5v - 2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?​

Answer: 156

Step-by-step explanation:

Annual Salary = $35, 000

Subtract anual salary from 46, 700. ---> 46,700-35,000= 11,700

One sale = $75

To find out how many sales, divide the remaining 11,700 by 75.

11,700/75= 156

156 sales.

a. The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.

What is the statistics

b.the pressure to build to its highest point (75/264).

c. Sample statistic's value is 0.2835.

d. Estimate's standard error is 0.0255.

e. Its highest level, the 95% confidence interval, is (0.2326, 0.3344).

A subfield of mathematics called statistics is concerned with the gathering, examination, interpretation, presentation, and arrangement of data.

Several disciplines, including business, economics, sociology, psychology, epidemiology, and public health, employ it. Statistic uses a variety of techniques to gather and analyse data to better understand.

(A) The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.

(b) The sample statistic, given as p, is the percentage of subjects that allowed the pressure to build to its highest point (75/264).

(c) The sample statistic's value is 0.2835.

(d) The estimate's standard error is 0.0255.

(e) For the percentage of people who would permit the pressure to reach its highest level, the 95% confidence interval is (0.2326, 0.3344).

Therefore, Overall, the findings of this study indicate that a significant majority of high school pupils will tolerate pressures up to 300 mmHg without ever complaining about the discomfort. The range of values inside the 95% confidence.

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The Area οf the shaded pοrtiοn is given by (16 π -32) inch², the cοrrect οptiοn is A.

A circIe is a rοund shaped figure whοse aII pοints Iie in οne pIane and the distance between the center οf the circIe and aII the pοints οn the circIe is cοnstant.

The area οf the shaded pοrtiοn is equaI tο the difference οf the area οf the arc and  Area οf the TriangIe.

Area οf an Arc =(θ /360) × π r²

Area = (90/360) × π × (8)²

Area οf the arc = 16 π in²

Area οf the triangIe = (1/2) × base × height

Area οf the triangIe = (1/2) × 8 × 8 = 32 in²

Area οf the shaded pοrtiοn = (16 π -32) inch²

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Answer:

Step-by-step explanation:

16 × 19 = 304

1/2(19×9)=85.5

304-85.5= 218.5

Answer:

-3x+7 < -5

Step-by-step explanation:

Lets set x as the number of hours since the time it was 7 degrees.

This means that the expression 7-3x would represent the temperature after x hours.

To find the inequality that represents when it would be below -5 degrees, we just set this less than -5:

-5 > 7-3x.

If you want, you can also rearrange this to -3x+7 < -5.

Answer:

4 hours

Step-by-step explanation:

Inequality:

[tex]7-3x < -5[/tex]

[tex]7-7-3x < -5-7[/tex]

[tex]-3x < -12[/tex]

[tex]\frac{-3x}{-3} < \frac{-12}{-3}[/tex]

[tex]x > 4[/tex]

Hope this helps

Answer:

-8

Step-by-step explanation:

f(3) = -4(3) + 4 = -12 + 4 = -8

Answer:

Step-by-step explanation:

[tex]\boxed{\sf f(x) = -4x + 4 \;\: when \;\; x=3}[/tex]

For f(x) -4x+4 substitute x with 3:-

[tex]\sf f\left(3\right)\:=\:-4(3)\:+\:4[/tex]

[tex]\sf f\left(3\right)\:=\:-4\times 3\:+\:4[/tex]

[tex]\sf f(3)=-12+4[/tex]

[tex]\sf f(3)=-8[/tex]

Therefore, f(x) = -8.

______________________

Hope this helps!

The height of the building is 160 ft

Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.

Types of  proportion :

Direct Proportion

Inverse Proportion

Continued Proportion

Comparing the heights and shadows using ratio proportions

Sam Height = 8 ft

Sam Shadow = 10 ft

Building Height = x ft

Building Shadow = 200 ft

Sam Height/Sam Shadow = Building Height/Building Shadow

AB/BC = PQ/QR

8/10 = x/200

8*200 = 10*x

1600/10 = x

x = 160 ft

The height of the building is 160 ft

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The projectile will attain a height of 85 feet at approximately 0.775 seconds or 3.225 seconds.

Given that

Velocity = 64 feet per second --- v

Initial height = 45 feet --- h

The height function can be represented as

h(t) = -16t² + vt + h

So, we have

h(t) = -16t² + 64t + 45

where h is the height in feet and t is the time in seconds.

To find when the projectile will attain a height of 85 feet, we need to solve the equation for t

So, we have

-16t² + 64t + 45 = 85

-16t² + 64t - 40 = 0

Using a graphing tool, we have

t = 0.775 and t = 3.225

Therefore, the projectile will attain a height of 85 feet at approximately t = 0.775 seconds or t = 3.225 seconds.

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Answer:

21.5 m^2

Step-by-step explanation:

Area of circle A = πr^2 = 3.14(10/2)^2 = 78.5

Area of square A = 10^2 = 100

Area of shaded area: 100 - 78.5 = 21.5 m^2

(a) f'(7) = 9. The derivative of the function f(x) evaluated at x=7, is 9.

(b) The instantaneous rate of change of y with respect to x at x = 7 is 9.

Given that the tangent line to the graph of y = f(x) at point (7, 56) has the equation y = 9x - 7, we can use the slope-intercept form of the equation of a line to find the slope of the tangent line.

The slope of the tangent line is 9. This is also equal to the derivative of the function f(x) evaluated at x=7, which gives us the answer to part (a).

The instantaneous rate of change of y with respect to x at x = 7 is also given by the derivative of the function at x=7. Therefore, the answer to part (b) is also f'(7) = 9.

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The missing values in the figure are solved to be

angle KLI = 111

angle LIJ = 129 degrees

The missing angles are solved using the inscribed angle theorem and the knowledge of cyclic quadrilateral

arc KLI = 138 degrees = 2 * angle KJI (inscribed angle theorem)

angle KJI = 138 / 2

angle KJI = 69 degrees

angle KLI + angle KJI = 180 degrees (cyclic quadrilateral property)

where angle KJI = 69

angle KLI = 180 - 69

angle KLI = 111 degrees

angle LIJ + angle LKJ = 180 degrees (cyclic quadrilateral property)

angle LKJ = 51 degrees (given)

angle LIJ = 180 - 51

angle LIJ = 129 degrees

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Answer:

Step-by-step explanation:

To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:

16 miles / 18 quarts = 24 miles / 27 quarts

Cross-multiplying, we get:

16 miles * 27 quarts = 18 quarts * 24 miles

432 milesquarts = 432 milesquarts

The equation holds, so the proportion is true.

The proportion is true .

To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:

16 miles / 18 quarts = 24 miles / 27 quarts

Cross-multiplying, we get:

16 miles * 27 quarts = 18 quarts * 24 miles

432 milesquarts = 432 milesquarts

Proportion can be checked by simplifying the ratios given,

16miles/18quarts=24miles/27quarts​

Simplifying further,

8miles/9squarts = 8miles / 9squarts .

The equation holds, so the proportion is true.

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Solution,

CP for rajan=180 rs

Sp for rajan=(20%+1)×180

=216

Cp for niranjan=216

And, Sp=.8×216

=172.8

Cp for niranjan=172.8

For 5% profit,

Sp for Niranjan=(5%+1)×172.8

=181.44

Hence, for Niranjan to gain 5% profit, he must sell it for 181.44 rs

Answer - 181.44

Explanation - For Rajan,

Cost Price = Rs 180

Profit Percent = 20%

Profit Percent = (S.P - C.P/C.P)*100

20 = (S.P - 180/180) *100

S.P = Rs 216

For Sajan,

C.P = Rs 216

Loss Percent= 20%

Loss = (C.P - S.P/C.P)*100

20 = (216-S.P/216)*100

S.P = Rs 172.8

For Niranjan to Sell Book and get 5% profit,

C.P = Rs 172.8

Profit Percent = (S.P - C.P/C.P)*100

5 = (S.P-172.8/172.8)*100

S.P = 181.44