Find the exact value of tan F in simplest radical form

The equations that passes through the points (-4, -16) and (5, 2) are: y – 2 = 2(x – 5), y = 2x – 8, and y + 16 = 2(x + 4).

To determine if an equation passes through a given point, plug in the values of the x and y coordinates of the point into the equation to see if it would make the equation true. If it is true, then the equation passes through the points.

Alternatively, graph the equation on a coordinate plane to see if it passes through the given point.

The graph shows the equations given.

The red line represents y + 4 = 2(x – 16).

The blue line represents y – 2 = 2(x – 5), y = 2x – 8, and y + 16 = 2(x + 4).

Therefore, y – 2 = 2(x – 5), y = 2x – 8, and y + 16 = 2(x + 4) passes through the points (–4, –16) and (5, 2).

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Olivia made $288 last week from her 4 percent commission and an average of $14,976 in 52 weeks

The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100.

In this question, she makes a commission of 4% on her weekly sales.

A) How much did she makes last week?

To find how much she made, we simply have to find 4% of 7200

0.04 * 7200 = 288

She made $288 last week.

B) If she made $288 each week, and we have 52 weeks in a year, we can multiply them and find how much she made in a year.

$288 * 52 = $14,976

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Answer:

Step-by-step explanation:

for plan A,  it's 16.50 per month

she paid 99.00

then the equation is   :

m x 16.50 = 99.00

Now solve for m

m = 99.00 / 16.50

m= 6

so she paid for 6 months

The probability that the random variable has a value less than 2.7 is 0.337

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

in the given question we have;

a random variable has a value of less than 2.7.

So,

Probability of (less than 2.7)

= area of rectangle starting from 0 to 2.7

 = (2.7 - 0) × 0.125

 = 0.3375

Hence,

The probability that the random variable has a value less than 2.7 is 0.337

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1. Two constants of proportionality representing the proportional relationship between distance in kilometers and number of hours are 400 km and 8 hours.

2. The relationship (ratio) between the two values is 50 km per hour or the equation, d = 50t.

3. Another equation that relates distance and time in this context is t = d/50 or 400/50.

The constant of proportionality is the ratio relating two given values in a proportional relationship.

Other names for the constant of proportionality include:

Distance, d = 400 km

Constant speed, t = 8 hours

d = 400/8

d = 50t

Constant of proportionality = 50.

t = d/s

Where d, distance = 400 km and s, speed = 50 km/h

= 400/50

= 8 hours

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The total sum of money shared is $4800

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b

The ratio of mark to Mary to gabrielle is 3:5:8

this means the total ratio is 16 i.e 3+5+8=16

if the total money is y and the money shared to mark is x, then

3/16× y= x

therefore 3y=16x

y= 16x/3 equation 1

Mary receives 600 more than mark,this means Mary share = 600+x

therefore 5/16×y= 600+x

5y= 16(600+x)

5y= 9600+16x equation 2

substitute 16x/3 for y in equation 2

5×16x/3= 9600+16x

80x/3= 9600+16x

multiply both sides by 3

80x= 3(9600+16x)

80x= 28800+48x

collect like terms

80x-48x= 28800

32x=28800

x= 900

substitute 900 for x in equation 1

y=16×900/3

y= 4800

therefore the total money shared is 4800

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Answer:

  94.2 mm

Step-by-step explanation:

You want the circumference of a circle that has a diameter of 30 mm.

The circumference is given by the formula ...

  C = πd . . . . . where d is the diameter

Your circle has a circumference of ...

  C = (3.14)(30 mm) = 94.2 mm

The circumference is 94.2 millimeters.

Answer:

57 half dollars and 169 quarters

Step-by-step explanation:

We will need a system of equations to solve this problem.

Given that the number of quarters is 2 less than three times the number of half dollars, we have Q = 3H - 2

Thus, we have 0.25Q + 0.50H = 70.75 and Q = 3H - 2.

The second equation allows us to use substitution:

[tex]0.25(3H-2)+0.50H=70.75\\0.75H-0.50+0.50H=70.75\\1.25H=71.25\\H=57[/tex]

We can plus this 57 into the second equation to find the number of quarters:

[tex]Q = 3(57)-2\\Q=169[/tex]

The percentage

of the increase in the number of bookmards sold is 40%

To solve this problem, first we have to rewrite the problems into some equations, such:

s = 480 --> represent the last year's sale

s' = 672 --> represent this year's sale

Then, we should define

the increase on the sale

by finding the difference between the last year'ssale and this year's sale.

Δs = s'-s

Δs = 672 - 480

Δs = 192

Then we could get the percentage of increase in sales by dividing the increase in sale with the last year's sales. Hence we could find that:

Δs% = (Δs/s) x 100%

Δs% = [tex]\frac{192}{480}*100%\\[/tex]%

Δs% = 40%

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Answer: x - 5 is less than or equal to -25

Step-by-step explanation:

The cost that the manager will pay for turkey and cheese is $127.182.

From the information, the manager wants to find the total cost of 24.8 pounds of sliced turkey at $1.89 a pound and 38.2 pounds of provolone cheese at $2.05 a pound.

The total cost will be:

=> Cost for turkey + Cost for cheese

= (24.8 × $1.89) + (38.2 × $2.05)

= $48.872 + $78.31

= 127.182

The cost is $127.182

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Step-by-step explanation:

2/3 x 12/17 x 1/4" simplify the expression

"2/3 x 12/17 x 1/4" = 12/102

Answer:

Step-by-step explanation:

look at your bases! do you see how the bases are 3, 17 and 4? All you need to do is find the least common multiple for the numbers, and you will have a base.

If you do that, you get a base of 207.

First, multiply all the fractions top and bottom by 207:

then multiply the top numbers, and leave the bottom the same, to get an answer. Now, simplify.

You should get 2/17 hopefully :)

The point S of line segment RT such that RS / ST = 2 / 5 is equal to (- 3, 0).

Herein we find a line segment whose endpoints are known (R(x, y) = (- 5, - 2), T(x, y) = (2, 5)) and in which we must determine the coordinates of a point S within line segment RT such that the partition ratio is observed:

RS / ST = 2 / 5

[tex]\overrightarrow{RS} = \frac{2}{5} \cdot \overrightarrow {ST}[/tex]

S(x, y) - R(x, y) = (2 / 5) · [T(x, y) - S(x, y)]

(7 / 5) · S(x, y) = (2 / 5) · T(x, y) + R(x, y)

S(x, y) = (2 / 7) · T(x, y) + (5 / 7) · R(x, y)

Now we determine the location of point S:

S(x, y) = (2 / 7) · (2, 5) + (5 / 7) · (- 5, - 2)

S(x, y) = (4 / 7, 10 / 7) + (- 25 / 7, - 10 / 7)

S(x, y) = (- 21 / 7, 0)

S(x, y) = (- 3, 0)

The location of point S is (- 3, 0). A representation of the geometric system is shown in the image attached below.

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The maximum tangential speed that the ball can have is 3.89 m/s. Centripetal acceleration is 0.06561 and tangential speed of ball will be 0.243 m/s

The centripetal force is the force needed to keep a body moving in circular motion. It exists for circular motion. Example - rotation of earth around sun.

We have an athlete swings a 7.9 kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.9 m at an angular speed of 0.27 rev/s.

[A] -

Tangential speed of ball = v = rω = 0.9 x 0.27 = 0.243 m/s

[B] -

Centripetal acceleration = a[c] = rω² = 0.9 x 0.27 x  0.27 = 0.06561

[C] -

Maximum tension = Maximum centripetal force = mrω² = 132.3

ω² = 132.3/mr

ω² = 18.60

v² = 18.60r²

v = 3.89 m/s

Therefore, the maximum tangential speed that the ball can have is 3.89 m/s. Centripetal acceleration is 0.06561 and tangential speed of ball will be 0.243 m/s

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The function notation that represents the value of the television after x years is V(x) = 2100 - 235x

You have just bought a new Sony 55'' 3D television set for $2100. The TV value decreases at a rate of 235 dollars per year.  

The linear function to represent the value of the television after x years can be calculated as follows:

Linear equation in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, using function notation, the linear function of the situation is as follows:

V(x) = 2100 - 235x

where

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We get the next term as -15 when the series are 30,27,21,9,_.

Given that,

The terms are 30,27,21,9,_

We have to find the next term.

An arithmetic sequence is a group of words where the common difference between any two subsequent words remains constant. Reviewing what a sequence is will help. A sequence is a group of integers that exhibit a pattern.

Take the terms,

30,27,21,9,_

Take the 1st 2 terms

30-27=3

Next,

27-21=6

Next,

21-9=12

Here, We have 3,6,12

That mean 3+3=6 and 6+6=12

Next is 12+12=24

So,

9-24=-15

Therefore, We get the next term as -15 when the series are 30,27,21,9,_.

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Answer: the one on the top left corner

Answer: the third one (bottom left) but also the second one (top right)

Step-by-step explanation: 2. there are 8 total parts to the figure and four of those parts are shaded. 4/8

3. There are four total parts to the figure but only 2 are shaded. 2/4

2/4 and 4/8 are both EQUIVALENT to 1/2. Therefore, that is the correct answer.

Answer: The second one is correct.

The loan's future value will be $6925 when Lynne pays a simple interest rate of 5.4%.

According to the question,

We have the following information:

Lynne needs to borrow $6250 for cosmetic surgery. She obtains a loan from her grandmother for 24 months at a simple interest rate of 5.4%.

We know that the following formula is used to find the simple interest:

Principal*rate*time/100

Principal = $6250

Rate = 5.4%

Time = 2 years

Simple interest = (6250*5.4*2)/100

Simple interest = 67500/100

Simple interest = $675

Now, the total amount of loan will be:

Interest + principal

675+6250

$6925

Hence, the loan's future value will be $6925 when Lynne pays a simple interest rate of 5.4%.

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Answer:

below

Step-by-step explanation:

f(x) = x(x+3)(x+4)     would be one

     = x^3 + 7x^2 + 12x

Set V is a subset of set Y

A set V is a subset of another set Y if all elements of the set V are elements of the set Y. In other words, the set V is contained inside the set Y. The subset relationship is denoted as V⊂Y.

Set V contain the following numbers {4,2,111,6}

It discovered that all the numbers in set V are there in set Y

set Y contains {44,7,90,42,1,111,6}

Therefore since the element of set V are in set Y , then set V is a subset of of set Y.

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Any of the four terms of a discrete geometric proportion is called a proportional fourth.

[tex]\bold{5, 2 \: and \: 10.5}[/tex]

A geometric proportion is formed as follows:

[tex]\bold{5 : 2 :: 10 : x}[/tex]

Since the unknown term is an extreme and as we have seen before, one extreme is equal to the means divided by the other extreme, we will have:

[tex]\boxed{\bold{ \: x = \frac{2 \:∗ \: 10}{5} = 4} }[/tex]

Therefore, the geometric proportion is:

[tex]\bold{5 : 2 :: \: :: 10 :4}[/tex]

Answer:  the answer is 38

Step-by-step explanation:

all you have to do is subtract 51-13 and the answer of that is the asnswer. :)

The pair of polygons that are similar to each other are all the pairs of polygons except the pair of rectangles.

Similar polygons are polygons that have corresponding side lengths that are proportional to each other, thus, they have the same shape by different sizes.

To determine if he given pairs of polygons are similar, check if their corresponding side lengths have the same ratio, that is, if they are proportional to each other.

For the trapezoids:

27/15 = 18/10 = 7.2/4 = 10.8/6 = 1.8

This means the trapezoids are similar.

For the rectangles:

18/10 ≠ 14/7

This means the rectangles are not similar.

For the right triangles:

32/24 = 24/18 = 40/30 = 1.33

This means the right triangles are similar polygons.

So also is the last pair of polygons similar to each other. Therefore, the only polygon that is not similar is the pair of rectangles.

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LJ = 46 is the value when  LK  congruent MK .

What do you mean by congruent?

By given figure ,

        MK = MN - KN

               = 9x - 11 - ( x + 3 )

               = 8x - 14

now given LK ≅ MK

           LK = MK

8x - 14 = 7x - 10

8x - 7x = 14 - 10

 x = 4

length of LJ = LK + KJ

                    = 7x - 10 + 28

                    = 7(4) + 18

                    = 28 + 18  ⇒ 46

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The equation to represent the function P is y=4x as per the given points in the table.

It is easier to see the slope (m) and y-intercept (c) of a line in the slope-intercept form of a linear equation (y=mx+c).

18th-century Switzerland. The first person to present a line's equation in slope intercept format might have been Jakob Hermann.

Y = mx + c is the true slope intercept form. It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

You can see the line's slope and y-intercept in Slope-Intercept form. One point the line travels through and the slope of the line are both clearly displayed in point-slope form.

We know that, the equation of the line is y=mx+c

If this line passes through (0,0) then,

0=m(0)+c

then, c=0

Now, substituting the point (1,4) in the above equation and c=0 then we get,

4=m(1)+0

m=4

Now substitute the point (2,8) then,

8=m(2)+0

m=4

Similarly, by substituting the points  (3,12), (4,16), (5,20), (6,24) we get,

m=4

Now, by substituting c=0 and m=4 in the above equation we get,

y=4x+0

y=4x

Therefore, the equation to represent the function P is y=4x

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Using system of equation, we can determine that Kadeesha played 10 games and went on 5 rides.

System of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Let;

2.50x + 4.75y = 48.75 ...eq(i)

x = 2y ...eq(ii)

Solving equation (i) and (ii)

x = 10, y = 5

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Answer:

I = $ 1,937.50

Step-by-step explanation:

i=prt

18/100=0.18

I=700(0.18)(14)

1,937.50

Answer:

True/Prove

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