help please it’s due soon

If the point P has polar coordinates (r, π/7), then we have:

x = r cos(π/7) and y = r sin(π/7)

(a) To find the polar coordinates of P' = (x, -y), we need to first determine its Cartesian coordinates:

x' = x = r cos(π/7)

y' = -y = -r sin(π/7)

The distance from the origin to P' is:

r' = sqrt(x'^2 + y'^2) = sqrt((r cos(π/7))^2 + (-r sin(π/7))^2) = sqrt(r^2 (cos(π/7))^2 + r^2 (sin(π/7))^2)

   = sqrt(r^2 (cos(π/7))^2 + r^2 (sin(π/7))^2) = sqrt(r^2 (cos^2(π/7) + sin^2(π/7))) = sqrt(r^2) = r

The angle that P' makes with the positive x-axis is:

θ' = atan2(y', x') = atan2(-r sin(π/7), r cos(π/7)) = atan2(-sin(π/7), cos(π/7))

We can simplify this expression using the formula for the tangent of a difference of angles:

tan(π/7 - π/2) = -cot(π/7) = -1/tan(π/7) = -sin(π/7)/cos(π/7)

Therefore, the polar coordinates of P' are (r, θ') = (r, π/2 - π/7) = (r, 5π/14).

Hence, the polar coordinates of P' are (r, θ') = (r, 5π/14).

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Answer:

12 feet

Step-by-step explanation:

Perimeter=l+l+w+w

48.8=12.4+12.4+2w

48.8=24.8+2w

2w=24, w=12 feet

Answer:

$1247.97

Step-by-step explanation:

$42 per month of service

new phone monthly service is $415.99

415.99 x 3 = 1247.97

1)  The midpoint of AB for A(5, 12) and B(-4, 8) is (1/2, 10)

2) The coordinate of G will be at (-2, -20) if P (-5,10) is the midpoint of EG and E has coordinates (-8,6).

The midpoint of a line is the point that divides such a line into two equal parts.

The formula for calculating the midpoint of a line is expressed as:

\(M(X, Y) =(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\)

1) Given the coordinates A(5, 12) and B(-4, 8).

X = (5+(-4))/2

X = (5-4)/2

X = 1/2

Get the coordinate Y

Y = (12+8)/2

Y = 20/2

Y = 10

Hence the coordinate of the midpoint of AB for A(5, 12) and B(-4, 8) is

(1/2, 10)

The formula for calculating the midpoint of a line is expressed as:

\(M(X, Y) =(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\)

1) Given the midpoint P (-5, 10) and the coordinate  (-8, 6)

Get the X coordinate of G

X = (x1+x2)/2

-5 = (x1-8)/2

-10 = x1 - 8

x1 = -10 + 8

x1 = -2

Get the Y coordinate of G

Y = (y1+y2)/2

10 = (y1+8)/2

20 = y1+8

y1 = 20-8

y1 = 12

Hence the coordinate of G will be at (-2, -20)

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Answer:

The second train speed is 356.4 miles per hour

And, the first train speed is  361 miles per hour

Step-by-step explanation:

The computation of the speed of each train is as follows

Given that

The Sum of the speed of two trains is 717.4 miles per hour

Let us suppose the second train speed be x

So for the first train, the speed is x + 4.6

Now the equation is

x + x + 4.6 = 717.4

2x + 4.6 = 717.4

2x = 717.4 - 4.6

2x = 712.8

x= 356.4

Therefore the second train speed is 356.4 miles per hour

And, the first train speed is = 356.4 + 4.6 = 361 miles per hour

Answer:

5.5

Step-by-step explanation:

mean is the synonym for average

to calculate the mean/average , u add all the numbers(the total amount) and then divide it by how many numbers there is.

3+4+5+6+7+8=33

33÷5=5.5

Answer:

Step-by-step explanation:

2.8 × (-11) - 3 × 8 =

-30.8 - 24 =

-54.8 ( in fraction -274/5)

\( = (x^2 \times x^3)^3 \\ = x {}^{6} \times {x}^{9} \\ = (x) {}^{6 + 9} \\ = {x}^{15} \)

Answer:

Yes

Step-by-step explanation:

There are 3 triangles for both 1 and 3 and 12 triangles in total.

The chance of getting 1 is 3/12 and the chance of getting 3 is 3/12

Since 3/12 = 3/12 then the chances are equal.

Answer:

3 because it's a most common number 1 Is rare

Answer:

Kunie is 25

Step-by-step explanation:

Let's make Yemi's age y, and Kunie's age k.

Because Yemi is 5 years older that Kunie, k + 5 = y.

Because the product of their ages is 750, k * y = 750.

With substitution, we can determine that k * (k + 5) = 750.

Then with distributive property we can simplify the equation to get k^2 + 5k = 750.

Then we bring all the terms to one side of the equation to get k^2 + 5k - 750 = 0.

Then with quadratics, we can factor the equation to get (k + 30)(k - 25)=0.

Thus, either k + 30 must equal 0, or k - 25 must equal 0.  Thus, k must equal 25 or -30, and because someone cannot be -30 years old, k = 25.

Then, because Yemi is 5 years older than Kunie, y = 30.

Hope it helps <3

Kunle's age is marked as k.

Yemi's age is therefore k + 5.

The product of k and k + 5 equals 750.

What is k?

Now that we have tought this through...

Here is the equality:

\(k(k+5)=750\)

Expanding the parentheses and subtracting 750 from both sides gives you

\(k^2+5k-750=0\)

Which is a second degree polynomial (ie. quadratic equation).

That means there are two solutions of what Kunle's age might be.

\(k^2+5k-750=0\)

\(k^2+30k-25k-750=0\)

\(k(k+30)-25(k+30)=0\)

\((k+30) (k-25) =0\implies k_1=-30, k_2=25

\)

So we got two results and since age cannot be negative that leaves us with one result and that is 25.

TL;DR The answer is: Kunle is 25 years old.

Hope this helps.

The value of the definite integral ∫[5 to ³] f(x) dx, if f(x) = = {3 if x < 3 x if x ≥ 3, is 2.

To find the definite integral of the function f(x), we need to split the integral into two parts since the function has a different definition for x less than 3 and x greater than or equal to 3. Let's calculate the integral step by step:

For x < 3:

∫[a to b] f(x) dx = ∫[a to b] 3 dx

Since the function is constant, the integral becomes:

∫[a to b] 3 dx = 3x + C

For x ≥ 3:

∫[c to d] f(x) dx = ∫[c to d] x dx

Integrating x with respect to x, we get:

∫[c to d] x dx = (1/2)x^2 + C

Now, to find the definite integral of f(x) from 5 to ³, we need to evaluate both parts of the integral separately and subtract the result for the lower limit from the result for the upper limit.

∫[5 to ³] f(x) dx = [∫[5 to ³] 3 dx] - [∫[5 to ³] x dx]

Evaluating the integrals individually:

[∫[5 to ³] 3 dx] = 3x | [5 to ³] = 3(³) - 3(5) = 9 - 15 = -6

[∫[5 to ³] x dx] = (1/2)x^2 | [5 to ³] = (1/2)(³)^2 - (1/2)(5)^2 = (1/2)(9) - (1/2)(25) = 4.5 - 12.5 = -8

Finally, we subtract the result for the lower limit from the result for the upper limit:

∫[5 to ³] f(x) dx = -6 - (-8) = -6 + 8 = 2

Therefore, the value of the definite integral ∫[5 to ³] f(x) dx is 2.

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The odds of picking a black jellybean are 14 to 23. This means that for every 14 black jellybeans, there are 23 non-black jellybeans in the jar.

To find the odds of picking a black jellybean, we need to determine the probability of picking a black jellybean and the probability of not picking a black jellybean.

The total number of jellybeans in the jar is 14 + 9 + 11 + 3 = 37.

The probability of picking a black jellybean is the number of black jellybeans divided by the total number of jellybeans:

P(black) = \(\frac{14}{37}\)

The probability of not picking a black jellybean is the complement of picking a black jellybean, which is 1 minus the probability of picking a black jellybean:

P(not black) = 1 - P(black) = \(\begin{equation}1 - \frac{14}{37} = \frac{23}{37}\)

The odds of picking a black jellybean are given by the ratio of the probability of picking a black jellybean to the probability of not picking a black jellybean:

\(\text{Odds}(black) = \frac{P(black)}{P(\text{not black})} = \frac{\frac{14}{37}}{\frac{23}{37}} = \frac{14}{23}\)

Therefore, the odds of picking a black jellybean are 14 to 23.

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Answer:

QR= 16

Step-by-step explanation:

HOPE THIS HELPS

Answer:

$120.67

Step-by-step explanation:

1. 55+29.99+27.79 = 112.78

2. 7% of 112.78 is 7.89

Answer:

A sample is a subset of the population.

The value of each trigonometric identity is:

3/2

5/6

14/3

We have,

We will use the trigonometric formula and substitute the given values.

So,

Cosec θ

This can be written as,

= 1/ sin θ

= 1/(2/3)

= 3/2

And,

Sin θ

This can be written as,

= 1/ cosec θ

= 1/(6/5)

= 5/6

And,

Sec θ

This can be written as,

= 1/cosθ

= 1/(3/14)

= 14/3

Thus,

The value of each trigonometric identity is:

3/2

5/6

14/3

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Answer:

Imani: 13r + 3d = 63

Abhasra: 12r + 12d = 132

Step-by-step explanation:

You just fill in the answers from the word problem. It has the answers.

Answer:

x = 31°

Step-by-step explanation:

The rightmost corner of the triangle is where we start.

We know that a line has 180° in it, therefore to find that angle, simply do:

180° - 153° = 27°

We also know that there are 180° in a triangle, write an equation for the triangle:

(2x-7)° + (3x+5)° + 27° = 180°

Combine like terms:

5x° + 25° = 180°

Subtract 25° from both sides:

5x° = 155°

Divide both sides by 5°:

x = 31°

The solutions using laws of exponents are:

a) \((4x)^{\frac{3}{2} }\)= \(8 \sqrt[]{x^{3} }\)

b) \(x^{\frac{-2}{3}}\)\(= \sqrt[3]{x^{2} }\)

d) \(\frac{\sqrt[3]{x} }{\sqrt{x} }\)\(=\)  \(\sqrt[3]{x^{2} }\)

e) \(\frac{\sqrt{x} * x^{2} }{{x^{\frac{5}{2} } } }\)= 1

Some of the laws of exponents are:

- When multiplying by like bases, keep the same bases and add exponents.

- When raising a base to a power of another, keep the same base and multiply by the exponent.

- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.  

The expression we want to solve is given as:

a) \((4x)^{\frac{3}{2} }\)

Using laws of exponents, the bracket is simplified to get:

\(4^{\frac{3}{2}} * x^{\frac{3}{2}}\)

= \(8 \sqrt[]{x^{3} }\)

b) The expression we want to solve is given as:

\(x^{\frac{-2}{3}}\)

This simplifies to get:

\(\sqrt[3]{x^{2} }\)

d) The expression we want to solve is given as:

\(\frac{\sqrt[3]{x} }{\sqrt{x} }\)

This simplifies to get:

\(x^{\frac{-2}{3}}\) = \(\sqrt[3]{x^{2} }\)

e) The expression we want to solve is given as:

\(\frac{\sqrt{x} * x^{2} }{{x^{\frac{5}{2} } } }\)

This simplifies to get:

\(\frac{{x^{\frac{5}{2} } } }{{x^{\frac{5}{2} } } }\)

= 1

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The probability of spinning a 1 is the same for both spinners: False​

The spinners that complete the question are added as an attachment

From the attached figures, we  have

Spinner 1

Number of 1 = 1

Sections = 4

Spinner 2

Number of 1 = 2

Sections = 6

The probability of obtaining 1 is calculated as

P(1) = Number of 1/Sections

So, we  have

Spinner 1

Number of 1 = 1

Sections = 4

P(1) = 1/4

Spinner 2

Number of 1 = 2

Sections = 6

P(1) = 2/6

By comparison

1/4 and 2/6 do not have the same value

Hence. it is false that the probability of spinning a 1 is the same for both spinners

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Answer:

77

Step-by-step explanation:

c + 103 = 180

180- 103 = 77

c and b = 77

Amount of money earned per number of hours of work =  \(f(g(x)) = 6x^{3} + 4\)

To evaluate a composite function f(g(x)) at some x = a, first compute g(a) by substituting x = a in the function g(x). Then substitute g(a) into the function f(x) by substituting x = g(a). In the same way, we can calculate g(f(a)) as well.

Required calculation -

Amount of money (the earning) per unit x = \(f(x) = 2x^{2} + 4\)

Number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works = \(g(x) = \sqrt{3x^{3}}\)

we are to find the composite function \(f(g(x))\)

Substituting g(x) into the x of f(x), we find:

\(f(g(x)) = 2(\sqrt{3x^{3} } )^{2} + 4\\\\= 2(3x^{3} ) + 4\\= 6 x^{3} + 4\)

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Answer:

f(g(x)) = 6x3 + 4 dollars over hour

Step-by-step explanation:

Answer:

Hey! Ok so the answers are A.50% B.100% C.80%

Step-by-step explanation:

Just predict the number to what they're next to.

Hoped this helped Im Eve btw. Hope you have a great day and consider marking this brainliest Thank you so much if you do! ✨

Answer: 636,000

Step-by-step explanation:

1. 8% of 300,000 is 24,000

2. Multiply 24,000 by 14 to get 336,000

3. Add 300,000 to 336,000

If this is incorrect, I think I know what I could have done wrong so just lmk

Answer:

24a²-73ab+24b²

Step-by-step explanation:

(8a - 3b) (3a - 8b) =

24a²-64ab-9ab+24b²

= 24a²-73ab+24b²

Answer:

7 . time os on axis X. total vector lenght is 7.

Answer: 60/61

Step-by-step explanation:

Answer:

-69q+74

Step-by-step explanation:

Distribute:

80-48q-21q-6

Simplify:

74-69q