question in screenshot

Applying the side splitter theorem

we have that

PT/TS=PQ/QR

so

substitute the given values

7/21=PQ/27

solve for PQ

PQ=27*7/21

PQ=9

Find the value of PR

PR=PQ+QR

PR=9+27

Answer: 270m

Step-by-step explanation:

The width is the same on both sides of the rectangle: 75m.

The length is also the same on each side of the rectangle: 60m each.

Add these all up for the perimeter: 75+75+60+60 = 270

Answer:

270 m is the answer

Step-by-step explanation:

add 75m + 60m + 75m + 60m

= 270m

Trigonometric functions using the ratio of two sides of a triangle can be used to solve D.right triangles.

To solve for a missing side of a right angle, one can use trigonometric functions that will use the ratio of the other two known sides of the triangle in question.

For instance, using the trigonometric function of Sin can allow for the use of the opposite side and the hypotenuse to find the adjacent side. The Cos and Tan can also be used for the other sides.

This means that either of two sides (including the hypotenuse) can be used to find the other.

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Taking into account the definition of a system of linear equations, the  local hamburger shop sold 199 hamburgers on Thursday.

A system of linear equations is a set of equations in which every equation is linear., in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

h + c= 449

h= c - 51

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

c - 51 + c= 449

c+ c= 449 + 51

2c= 500

c= 500÷2

c= 250

Remembering that h= c - 51, you get:

h= 250 - 51

h= 199

Finally, 199 hamburgers were sold on Thursday.

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Answer:

1/8

Step-by-step explanation:

First Pick P(red card) = 26/52 = 1/2

Second Pick after replacement P(heart) = 13/52 = 1/4

P(red on first pick and heart on second pick

= 1/2 x 1/4 = 1/8

Answer:

The y-value of the point (4, 8) is (obviously) 8. Since the line has a slope of zero, everywhere on the line will have a y-value of 8. So the equation of the line is y = 8. The x-value can be any number, but the y-value will always be 8

The equation that calculates the time taken to get to Springfield is x = 926/57

Rate is used to establish the relationship between two quantities of different units. one of the quantity is usually expressed to unity in order to estimate the change in the other quantity.

If Hillwood and Springfield are 926 mile apart, and the speed taken to get to Springfield is 57miles per hour.

Let the time taken to get to Spring field be x.

Then if 57 miles is covered in an hour and it takes x hours to get to the destination

It means total distance covered is 57 × x

This distance is equal to the distance from Hillwood to Springfield which is 926 miles.

Equating both equations.

57x = 926

In conclusion, 57x = 926 is the equation that can be used to find out the time taken.

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The numbers that are written in scientific notation are:

1.8 x [tex]10^{9}[/tex]

3.2 x [tex]10^{-9}[/tex]

5.99 x [tex]10^{-9}[/tex]

Scientific notation is a method used in mathematics to compress large numbers to smaller numbers.  In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example:  1 x 10² is equivalent to 100

The decimal point in scientific notation, must be between the first non zero digit number and the second non-zero digit number.

When writing numbers that are less than zero in scientific notation, the power would have a negative sign in front of it. For example, 1 x [tex]10^{-2}[/tex] is equal to 0.01.

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Answer:

56

Step-by-step explanation:

[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]

Answer:

D

Step-by-step explanation:

[tex]-3(3+p)<-66 \\ \\ 3+p>22 \\ \\ p>19[/tex]

The ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are NOT the same for the graph of  y = 3x + 4

In this question, we have been given the graphs of lines y = 3x and y = 3x + 4.

Consider the ratios of y/x for the graph y = 3x

6/2 = 3

3/1 = 3

(-6)/(-2) = 3

Consider the ratios of y/x for the graph y = 3x + 4.

7/1 = 7

(1)/(-1) = -1

(-2)/(-2) = 1

We can observe that the ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are different for the graph of  y = 3x + 4.

Therefore, the ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are NOT the same for the graph of  y = 3x + 4

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The function y =|x|+3 has been plotted in the graph and

Domain =  {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Range =  {7,6,5,4,3}

The function y =|x|+3

The some values of x = -4, -3, -2, -1, 0, 1, 2, 3  and 4

Substitute the values in the function

y=|-4|+3 =7

y=|-3|+3 = 6

y=|-2|+3 = 5

y=|-1|+3 = 4

y=|0|+3 = 3

y=|1|+3 = 4

y=|2|+3 =5

y=|3|+3 = 6

y=|4|+3 = 7

Using the values complete the graph

The domain is the set of all possible inputs of the function

Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}

The range is the set of all possible outputs of the function

Range = {7,6,5,4,3}

Hence, the function y =|x|+3 has been plotted in the graph and, the Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Range = {7,6,5,4,3}

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From the given vectors, we have that:

a) The vectorial products are given as follows:

b) The angle between vectors a and c is of 6.84º.

A vectorial product between two vectors A and B is found from the determinant of a matrix, in which:

Then for the vectorial product b x a, the matrix is:

[tex]\left[\begin{array}{ccc}i&j&k\\3&-1&2\\-2&2&1\end{array}\right][/tex]

Using a calculator, the determinant, which is the vectorial product, is given by:

b x a  = -3i - j + 4z.

For the vectorial product a x c, the matrix is:

[tex]\left[\begin{array}{ccc}i&j&k\\-2&2&-1\\-2&3&-1\end{array}\right][/tex]

a x c  = 1i - 2z.

The angle is found as follows:

sin(θ) = |a x c|/(|a| x |c|)

The norms are given as follows:

Hence:

[tex]\sin{\theta} = \frac{\sqrt{5}}{3\sqrt{14}}[/tex]

[tex]\theta = \sin^{-1}{\left(\frac{\sqrt{5}}{3\sqrt{14}}\right)}[/tex]

θ = 6.84º.

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[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+3} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(1)}~~~~ ,~~~~ 3-\cfrac{ (6)^2}{4(1)}\right) \implies \left( - \cfrac{ 6 }{ 2 }~~,~~3 - \cfrac{ 36 }{ 4 } \right)\implies (\stackrel{x}{-3}~~,~~-6)[/tex]

Answer: 3

Step-by-step explanation: We know that Felipe has driven 1/4 of the way, so 12 divided by 4 is 3.

The answer to your question is =

0.583333333

I believe the answer is 0.58333333333. I think it would be 0.583 if you rounded it up. Hope this helps:)

1.Consider a 5-degree-of-freedom t distribution. P (t≤1.05)=0.829.

2. Think about a t distribution with 26 possible degree. P(t>c)=0.05 and c=1.7056

Given that,

We have 2 question

1. Consider a 5-degree-of-freedom t distribution.

We have to find P (t≤1.05) at least three decimal places, round your response.

From t- value cumulative distribution function

Given a t-value and the degrees of freedom, locate the area under the t-distribution from -t to t.

P(t≤1.05)=0.829.

Therefore, P(t≤1.05) is 0.829.

2. Think about a t distribution with 26 possible degree. P(t>c)=0.05.

We have to find c at least three decimal places.

From inverse t-value distribution function

t=invT(0.95,26)=1.7056

Therefore, c is 1.7056

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The factor that is the least important thing for Lelia to consider right now is D. Average cost of Uber, Lyft, or taxi fare.

It should be noted that Leila just graduated from college and is comparing a few different cities to move to.

It's important for her to consider the average rent for an apartment, food and grocery store options in the area, and employment opportunities.

In this case, the. oat of Uber isn't necessary. The correct option is D.

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Leila just graduated from college and is comparing a few different cities to move to. Which of these factors is the LEAST important thing for her to consider right now?

Average rent for an apartment

Food and grocery store options in the area

Employment opportunities

Average cost of Uber, Lyft, or taxi fare

Answer:Explanation:

(3)=5

In a graph, te value of f(x) is the cy-value for the given x-value.

Consider the graph below:

• When the x-value = 3

• The corresponding y-value = 5.

Therefore, the value of f(3) is 5.

Answer:

ur answer is 8 1/5

Step-by-step explanation:

AAS congruency is used to show the required proportion.

Angle-Angle-Side is referred to as AAS. The triangles are said to be congruent if two of a triangle's angles and one of its non-included sides are equal to the equivalent angles and sides of another triangle.

In the given question ΔPQT ≅ ΔRSU

because ∠QPR= ∠RUS [ each 90°]

∠PQR= ∠URS [ since QP is parallel to UR so these two angles are corresponding angles]

PT= US

thus from AAS congruency  ΔPQT ≅ ΔRSU

Thus QT = US from cpct

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The dividends per share on each class of stock for each of the four years are as follows:

                       Cumulative Preferred       Common Stock

First-year,             $0.50                                  $0

Second year,       $0.70                                   $0.08

Third year,           $0.60                                   $0.13

Fourth year,         $0.60                                  $0.21

The dividends per share for each class can be determined by dividing the allocated dividend by the number of shares in the issue.

The allocated dividend to each class depends on the amount of dividend declared.  For cumulative preferred stock, when their fixed dividend cannot be sufficiently settled, the arrears are carried forward.

                               3% Cumulative Preferred       Common Stock

Par value                              $20                                         $25

Issued shares                      60,000                             405,000

Stock Value                        $1,200,000                     $10,125,000

Preferred Fixed Dividend =  $36,000 ($1,200,000 x 3%)

Distributed Dividends:     Cumulative Preferred       Common Stock

First-year,       $30,000     $30,000         $0.50         $0              $0

Second year,  $75,000    $42,000          $0.70       $33,000     $0.08

Third year,     $90,000     $36,000         $0.60       $54,000     $0.13

Fourth year, $120,000     $36,000         $0.60       $84,000     $0.21

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The zeroes of the function k(x)=15x³-48x²-48x are 0, 4 and -4/5.

The function provided is a cubic polynomial.

There will be three zeroes in total for the function k(x).

K(x) = 15x³-48x²-48x

If we put x = 0,

We can see that k(x) becomes zero,

So we can say that 0 is a solutions for this function,

Now,

K(x) = x(15x²-48x-48)

Solving 15x²-48x-48 seperately using quadratic formula,

a = 15

b = -48

c = -48

x = (-b+√D)/D and (-b-√D)/D

D = b²-4ac.

D = (-48)²-4(15)(-48)

D= 5184.

√D = 72

putting all the values to find x,

x = (-(-48)+72)/30 and (-(-48)+72)/30

x = 4 and -4/5.

our function becomes,

k(x) = x(x-4)(x+4/5)

so the zeroes are 0, 4, -4/5.

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The members and non-members who pay the equal cost after 5 visits for the local zoo.

For the given question;

The cost of membership of local zoo is $135 for members.

The parking cost is $3 for members.

Non-member admission cost is $25 for the zoo and $5 for the parking.

Let the number of number of visits paid the same amount be 'x'.

Then, the equation becomes.

Members: m = 135 + 3x

Non-Members: n = 25x + 5x

As, members and non-members are equal.

m = n

Put the values;

135 + 3x =  25x + 5x

135 + 3x = 30x

27x = 135

x = 5

Thus, members and non-members who pay the equal cost after 5 visits.

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Answer:

1/6th chance

Step-by-step explanation:

Since there are 6 possible outcomes that will be the denominator, now count the number you want to roll, in this case 1 since you only want to find the probably of getting a 3. So the probably is 1/6

The total cost of the metal needed to cover the tank shaped like a metal is $5,099.36.

In order to determine the total metal cost, we are to first calculate the total surface area of the tank. Since the tank is a closed cylinder, we are to determine the total surface area of a cylinder.

The total surface area of a closed cylinder can be determined by adding the area of all its faces.

Total surface area of the closed cylinder = 2πr(r + h)

Where:

r = radius = diameter / 2 = 8/2 = 4ft

h = height

π = pi = 3.14

(2 x 3.14 x 4)(4 + 3)

25.12 x 7 = 175.84 ft²

Total cost of the metal = $29 x 175.84 = $5,099.36

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Answer:

1 × 10^-4

Step-by-step explanation:

This is because after the decimal point there are 4 numbers so u have to put -4, and the 1 is there because of the last number

Answer:

1 × 10^-4

Step-by-step explanation:

Point (C) C closely approximates the given mathematical operation that is the difference between B and A (B - A).

So, when we add up 2 numbers let's say A and B, the result is always a 3rd number which is C.

Similarly, when we subtract a number from another number (B - A), the result is always a third number C.

So, (C) C closely approximates the difference between B and A (B - A).

Therefore, point (C) C closely approximates the given mathematical operation that is the difference between B and A (B - A).

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The required inequality is k > -8.48. Option A is correct.

Given that,

To determine the equivalent expression to the k / -1.6 > -5.3

What is inequality?

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

As per the given condition, we have to simplify the given expression to get the equivalent expression,

k / -1.6 > -5.3

k > -1.6 (-5.3)

k >- 8.48.

Thus, the required inequality is k > -8.48. Option A is correct.