If the sides of a polygon are x + 3 units, 2x – 4 units, 5x units, and 7x + 8 units, then find the perimeter of the polygon.

To make sure the flip is in unison after 4  seconds should the flip occur, as given by option C: 4 seconds.

We have given that,

Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience.

Synchronized motion is a motion of two or more system which goes in synchronization with each other.

For this case, the flip will occur such that both gymnasts are synchronized and the flip is in unison (simultaneous).

For that, we need the time(x) and the height (y) same.

Since the motion paths are:

[tex]y=-(x-5)^2+3[/tex]

[tex]y=-3(x-3)^2+x+1[/tex]

Therefore, we need to find the values of x for which the same y comes as output.

Let x =  t be the time for which the height y is the same, then:

[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex] = height achieved by both gymnasts.

Solving it further:

[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex]

t=4,t=1/2

Assuming they planned to do a flip after an integral number of time in seconds, the correct option is t = 4 seconds.

Thus, to make sure the flip is in unison after 4  seconds should the flip occur, as given by the option C: 4 seconds.

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[tex]\Large\Box\underline{\textsf{A. What is Asked}}[/tex]

Evaluate [tex]\bf{\dfrac{1}{12^{-2}}}[/tex]

[tex]\Large\Box\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{9cm} \text{If we have negative exponents in the denominator} \\ \text{we turn over the number,} \\ \text{leaving positive exponents only.} \end{minipage}}[/tex]

Thus,

[tex]\bf{\dfrac{1}{12^{-2}}=\dfrac{12^2}{1}}[/tex]. | see, the negative exponent turned into a positive one as soon as the fraction was turned over.

[tex]\bf{144}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

             [tex]\bf{=144}[/tex]

      [tex]\begin{tabular}{c | 1} Expression & Exponent Rule\\\cline{1-2} \\ x^m*x^n & add the powers \\ x^m\div x^n & subtract the powers \\(x^m)^n & multiply the powers \\ x^{-m} & turn over the number \\ x^0 & this equals one\end{tabular}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

For the given right triangle, we have:

Here we have a right triangle, remember that the sum of the internal angles of a triangle must be 180°, then:

N + M + L = 180°

We can see that:

N = 37°

M = 90°

Then:

L = 180° - N - M = 180° - 37° - 90° = 53°

Also, if we step on N, the adjacent cathetus measures 6 units, then we can use the relations:

tan(37°) = (opposite cathetus)/(adjacent cathetus)

tan(37°) = ML/6

tan(37°)*6 = ML = 4.5

cos(37°) = (adjacent cathetus)/(hypotenuse)

cos(37°) = 6/NL

NL = 6/cos(37°) =  7.5

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The equation of the segments perpendicular bisector is; y = -¹/₂x + 2

i) Since it is a perpendicular bisector, hence point M is the midpoint. Thus;

Midpoint (AB) = [(x₁ + x₂)/2], [(y₁ + y₂)/2] = (x_m, y_m)

Slope AB will be;

m₁ = ((x₁ - x₂)/(y₁ - y₂))

Slope of perpendicular bisector is;

m₂ = -1/m₁

Equation of perpendicular bisector is;

(y - y_m) = m₂(x - x_m)

ii) Midpoint (AB) = [(-2 + 6)/2], [(3 - 1)/2] = (2, 1)

Slope AB will be;

m₁ = ((6 + 2)/(-1 - 3)) = -2

m₂ = -1/-2 = 1/2

Equation of perpendicular bisector is;

(y - 1) = -¹/₂(x - 2)

y - 1 = -¹/₂x + 1

y = -¹/₂x + 2

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The average monthly salary of the female employees is $900.

An equation is a mathematical statement that equates algebraic expression  to other algebraic expressions or constants by an equal sign that helps to determine the value of unknown variables.

It is given that

the average of the monthly salary of female and male employees is $ 2000

Let the average monthly salary of the female employees is $b

It is again given that

The average monthly salary of the male employees is $(b +200)

so , the equation can be formed as

b + b + 200  = 2000

2b + 200 = 2000

2b = 2000 - 200

2b = 1800

b = $900

The average monthly salary of the female employees is $900.

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Using a system of equations, it is found that it would take 2 servings of macaroni and 8 servings of broccoli to get the desired amount.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Researching the problem on the internet, each serving of macaroni has 3 grams of protein, while each serving of broccoli has 2 grams. Since 22 grams of protein are needed, we have that:

3M + 2B = 22.

Each serving of macaroni has 16 grams of carbohydrates, while each serving of broccoli has 4 grams. Since 64 grams of carbohydrates are needed, we have that:

16M + 4B = 64

Simplifying by 4:

4M + B = 16 -> B = 16 - 4M

Replacing in the first equation:

3M + 2B = 22

3M + 2(16 - 4M) = 22

5M = 10

M = 10/5

M = 2.

B = 16 - 4M = 16 - 8 = 8

2 servings of macaroni and 8 servings of broccoli are needed.

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Answer:

8 * sqrt2

Step-by-step explanation:

the area of a square can be found by squaring the length of the diagonal and then dividing it by 2. 16^2 / 2 = 128. if the area of a square is 128, each side is sqrt 128 = 8 * sqrt2

The value of the Z-score will be equal to 2.

The z score indicates how many standard deviations your score is from the mean.

At the mean position, the standard deviation is 0 now the z score is the measure of the data which is how far from the mean. So the given data is at two standard deviations to the right of the mean so the Z-Score will be 2.

Therefore the value of the Z-score will be equal to 2.

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The equation for the distance d from Dallas, in terms of h, the number of hours Joe has traveled is d = 320 - 69h. Hence, option B is the right choice.

The total distance that Joe needs to cover to travel to Dallas = 320 miles {As he lives 320 miles away from Dallas}.

The distance that Joe covers after traveling for h hours at an average speed of 69 miles per hour = 69h {as Distance = Speed*Time}

Therefore, the distance left to cover by Joe, that is the distance from Dallas d can be written as the difference between the total distance needed to be covered and the distance Joe already covered.

Thus the equation is d = 320 - 69h.

Thus, the equation for the distance d from Dallas, in terms of h, the number of hours Joe has traveled is d = 320 - 69h. Hence, option B is the right choice.

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Answer:

x = 2; y = -1

Step-by-step explanation:

We can solve (first for y, then for x) using substitution:

[tex]x+y=1\\7x+4y=10\\(x+y=1)-y\\x=1-y\\\\7(1-y)+4y=10\\7-7y+4y=10\\(7-3y=10)-7\\(-3y=3)/-3\\y=-1\\\\(x-1=1)+1\\x=2[/tex]

Answer:

Step-by-step explanation:

10.

[tex]\left \{ {{x-2y=4} \atop {4x+2y+6}} \right.[/tex]

The y values cancel out if you add the equations

5x = 10

x = 2

plug in x

2 - 2y = 4

-2y = 2

y=-1

Answer: C. (2, -1)

11.

[tex]\left \{ {{6x-2y=-4} \atop {-4x+3y=-4}} \right.[/tex]

In order to get terms to cancel out, multiply the top by 3 and bottom by 2

[tex]\left \{ {{18x-6y=-12} \atop {-8x+6y=-8}} \right.[/tex]

The y values cancel out if you add the equations

10x = -20

x = -2

plug in x

6(-2) - 2y = -4

-12 - 2y = -4

-2y = 8

y = -4

Answer: B. (-2, -4)

Answer:

20x^2 + 47x + 24

Step-by-step explanation:

The area of a rectangle is LENGTH * WIDTH. From the diagram, we see that  LENGTH = 4x + 3 and WIDTH = 8 + 5x. Therefore the area is:

A = LENGTH*WIDTH

  = (4x+3)(5x+8)

  = 20x^2 + 32x + 15x + 24

  = 20x^2 + 47x + 24

Answer: C. 20x²+47x+24

Step-by-step explanation: Use the FOIL Method (First, Outer, Inner, Last). Equation: (5x+8) (4x+3). Hope this helps!

The solution of the given Inequality is; D: x ≤ 6

We want to find the solution to the Inequality;

5x - 9 ≤ 21

Using Addition property of equality, add 9 to both sides to get;

5x ≤ 30

Using division property of equality, divide both sides by 5 to get;

x ≤ 6

All real numbers less than or equal to 6

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The most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equations:

0.02x - 0.05y =  -0.38

0.03x + 0.04y = 1.04

We can write above equations as follows:

2x - 5y = -38

3x + 4y = 104

After solving with the substitution method:

x = 16

y = 14

-20 ≤ x ≤ 20

-15 ≤ x ≤ 15

Thus, the most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.

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Answer:

x=-6

Step-by-step explanation:

-6+4=-2
Give brainliest please

Billy get 5.9% raise after completing first year.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Here, Billy's initial salary = $ 42,500

After raise, salary become $ 45,000

Change in salary = Raised salary - Initial salary

                            = 45000 - 42500

                            = $ 2500

% Change = change / initial salary  X 100

                  = 2500 / 42500 X 100

                  = 0.0589 X 100

                  ≈ 5.9 %

Thus, Billy get 5.9% raise after completing first year.

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The function g(x) is [tex]g(x) = (x + 7)^3[/tex]

The function f(x) is given as:

[tex]f(x) = \sqrt[3]{x} - 7[/tex]

If f(g(x)) = g(f(x)) = x, then the functions are inverse functions.

So, we have:

[tex]f(x) = \sqrt[3]{x} - 7[/tex]

Rewrite as:

[tex]y = \sqrt[3]{x} - 7[/tex]

Swap x and y

[tex]x = \sqrt[3]{y} - 7[/tex]

Add 7 to both sides

[tex]x + 7 = \sqrt[3]{y}[/tex]

Take the cube of both sides

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

This implies that

[tex]g(x) = (x + 7)^3[/tex]

Hence, the function g(x) is [tex]g(x) = (x + 7)^3[/tex]

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Answer:

It should look like a v with the origin at +0.5

Step-by-step explanation:

Answer: Multiple Choice $15 understated. $135 overstated. $135 understated. $150 understated. $150 overstated. 2.The numbering system used in a company's chart of accounts: Typically begins with income statement accounts.

Step-by-step explanation:

The statement that's is likey true about the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.

It should be noted that a dot plot simply gives a pictorial representation of the information given.

In this case, the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.

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Answer: Most likely, about 40% to 60 % of the people in the town join a health club yearly.

Step-by-step explanation:

Answer:

x^2+4x+2

Step-by-step explanation:

√4 = 2

=x^2+2x+2x+2

add the ones that are the same (2x+2x)

x^2+4x+2

The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.

Note that At the point H, there is  found to be an intersection between the distance taken by both people involve so:

Y (a)= 10 + 2x ------ Josiah

Y (0) = 3x   ----- Chana

If  Y (a)= Y (0)

Then:

10 + 2x = 3x

x = 10

F = x = 20

Y (o) = 60

If x = 20

= then Y(0) = 3 x 20

= 60

Therefore, The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.

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The two compositions for the functions are:

[tex](p\°q)(2) = -6\\\\(q\°p)(2) = 6[/tex]

When we have two functions q(x) and p(x), the composition is:

[tex](q\°p)(x) = q(p(x))[/tex]

Here we have:

[tex]p(x) = -x\\\\q(x) = 2x^2 - 2[/tex]

The first composition is:

[tex](q\°p)(2) = q(p(2)) = 2*(p(2))^2 - 2 = 2*(-2)^2 - 2 = 6[/tex]

The other composition is:

[tex](p\°q)(2) = p(q(2)) = -(q(2)) = -(2*2^2 - 2) = -(8 - 2) = -6[/tex]

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The truth values of the propositions are false, true and false

The Boolean variables are given as:

p = false

r = false

q = true

s = true

The truth values of the propositions are as follows:

1. (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s)

As a general rule:

∧ means and

¬ not

∨ or

So, we have:

(true → (false ∧ ¬ false)) ∧ ((false → (false ∨ true)) ∧ true)

¬ false= true.

So, we have:

(true → (false ∧ true)) ∧ ((false → (false ∨ true)) ∧ true)

false ∧ true = false and false ∨ true = true

So, we have:

(true → false) ∧ ((false → true) ∧ true)

false → true = true and true → false = false

So, we have:

(false) ∧ (true ∧ true)

true ∧ true = true

So, we have:

false ∧ true

Lastly

false ∧ true = false

Hence, the truth value of (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s) is false

2. ((p ∧ ¬ q) → (q ∧  r)) → (s ∨ ¬q)

This means

((false ∧ ¬ true) → (true ∧  false)) → (true ∨ ¬true)

Using the established rules in (1), we have:

((false ∧ false) → (true ∧  false)) → (true ∨ false)

This gives

((false → false)) → true

This gives

true → true

Lastly, we have:

true

Hence, the truth value of ((false ∧ ¬ true) → (true ∧  false)) → (true ∨ ¬true) is true

3. (p → q) ∧ (q → r)

This gives

(false → true) ∧ (true → false)

Using the established rules in (1), we have:

true ∧ false

This gives

false

Hence, the truth value of (p → q) ∧ (q → r) is false

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The effective tax rate based on the assumed information is 2.5%.

Let's assume that the figures are:

Income tax expense = $50

Income before tax = $2000

It should be noted that tax rate is calculated as:

= Income tax expense / Income before tax

= 50/2000

= 0.025

= 2.5%

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The 87th percentile is the value [tex]x_{0.87}[/tex] such that 87% of the distribution lies below [tex]X=x_{0.87}[/tex], i.e.

[tex]P(X \le x_{0.87}) = 0.87[/tex]

Transform [tex]X[/tex] to the standard normal random variable [tex]Z[/tex], then solve for [tex]x_{0.87}[/tex] using the inverse CDF of [tex]Z[/tex].

[tex]P(X\le x_{0.87}) = P\left(\dfrac{X-60}{12} \le \dfrac{x_{0.87}-60}{12}\right) = P\left(Z \le \dfrac{x_{0.87}-60}{12}\right) = 0.87[/tex]

[tex]\implies \dfrac{x_{0.87}-60}{12} = F_Z^{-1}(0.87) \approx 1.12369[/tex]

[tex]\implies \boxed{x_{0.87} \approx 73.5167}[/tex]

Answer:

Her balance at the beginning of November=$973.76

Step-by-step explanation:

What is Natasha's credit balance at the beginning of November?(i.e. at the end of October)

The balance at the end of each month is the beginning balance plus the current month's purchases minus the minimum payment for the month.

Sept =$922.93+$33.70+9.89%/12*($922.93+$33.70)

Sept=$964.51

payment= 964.51*3.08%

balance at the end of Sept=$964.51-($964.51*3.08%)

balance at the end of Sept=$934.80

Oct=$934.80+$61.70+9.89%/12*($934.80+$61.70)

Oct=$ 1,004.71

payment=$1,004.71*3.08%

balance at the end of Oct(at beginning of Nov)=$ 1,004.71-($1,004.71*3.08%)

balance at the end of Oct(at beginning of Nov)=$973.76

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Answer:

The answer is C.$1,000.93 just did it om edge

Step-by-step explanation:

The measure of <2 is 60.

The tangent is defined as a line touching circles or an ellipse at only one point.

given:

VU = 80° and ST = 40°

By using theorem,

The measure of the internal angle is the semi- sum of the arcs comprising it and its opposite.

<2= 1/2 (80+ 40)

<2= 60

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Answer:

the MEAN for class a is 72.6

the MEAN for class b is 84.0

if you take these means and compare them, you can see that on average, class B performed better.

the MEDIAN for class a is 72

the MEDIAN for class b is 85

Step-by-step explanation:

The Distance  between the midpoints of segments OA and AB is 4.5cm

A line is defined as the shortest distance between two points.

Given the following parameters

OA = 12cm

OB = 9cm

AB = OA - OB

AB = 12 - 9 = 3cm

midpoint of OA = 12/2 = 6cm

midpoint of AB = 3/2 = 1.5cm

Distance  between the midpoints of segments OA and AB in each case will be the difference between the midpoints

Difference = 6cm - 1.5

Difference = 4.5cm

Hence the Distance  between the midpoints of segments OA and AB is 4.5cm

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