Use triangles ABC and RST to answers the following questions. Is triangle ABC a right triangle? Explain your answer.

The inverse of the given function is y = x³ + 2

Given the radical function below expressed as;

f(x) = ∛x-2

This can be written as;

y = ∛x-2

Replace y with x

x = ∛y-2

Take the cube of both sides

x³ =y - 2

y = x³ + 2

Hence the inverse of the given function is y = x³ + 2

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Answer:

[tex]f^{-1} (x)=x^{3} +2[/tex]

Step-by-step explanation:

from plato

Answer:

The second table

Step-by-step explanation:

A proportional relationship is a relationship in which the ratio of two variables is equivalent.

2:10, 4:20, and 6:30 are all equivalent ratios that can all be simplified and written as 1:5, thus the second table is the correct answer

Answer:

M=(11,−2)

Step-by-step explanation:

Find the midpoint for [tex]P = \left(6, -9\right)P=(6,-9) \text{and} Q = \left(16, 5\right)Q=(16,5).[/tex]

The midpoint for two points P and Q is a point M whose coordinates is the half-sum of the corresponding coordinates of the two points.

Thus, [tex]M = \left(\frac{6 + 16}{2}, \frac{-9 + 5}{2}\right) = \left(11, -2\right)[/tex]

M=(11,−2)

By looking at the graph of the piecewise function, we can see that:

On the graph, we have a piecewise function, which we want to evaluate in some different values.

First we have x  = -0.0001

This value belongs to the interval (-5, 0), and by looking at the graph, you can see that the function on that interval is equal to -9, then:

G(-0.0001) = -9

x = 0

x = 0 belongs to the interval [0, 9). On that interval the function values -1. (x = 0 belongs to that interval because we have a closed dot). Then we conclude

G(0) = -1

x = 0.0001

This value also belongs to the interval  [0, 9)

Then G(0.0001) = -1

Finally, x = 9.

If you look at the domain of the function, you can see that there is an open dot at x = 9.

This means that x = 9 does not belong to that domain, so:

G(9) is not defined.

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The expression that represents the product of negative three-fourths x and –8x is 6x^2

The statement is given as:

the product of negative three-fourths x and –8x

Rewrite properly as:

-3x/4 * -8x

Divide 4 and 8 by 4

-3x * -2x

Multiply -3 and -2

6x * x

Multiply x and x

6x^2

Hence, the expression that represents the product of negative three-fourths x and –8x is 6x^2

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Answer:

answer is 6x2 or D

Step-by-step explanation:

Using it's concept, it is found that the probability that the first three balls are drawn out of the box alternated in colour is of 0.1541 = 15.41%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the situation described, the ways that alternate colored balls can be taken, and their probabilities, are given as follows:

Hence the probability is given by:

[tex]p = \frac{5}{11} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex]

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Answer:

4.96 dollars

Step-by-step explanation:

20-5.12=14.88

14.88/3= 4.96 dollars

so each pair of socks costs 4.96$

Answer:

4cos(θ)

{4cospheta}

Answer:

4cos(θ)

{4cospheta}

Step-by-step explanation:

[note, brainly doesn't allow pheta to be entered as a symbol when writing an equation, so I had to write it out, my apologies]

[tex]\frac{\sin \left(2pheta \right)}{\sin \left(pheta\right)}+\frac{1+\cos \left(2pheta\right)}{\cos \left(pheta\right)}\\[/tex]

[tex]\frac{1+\cos \left(2pheta\right)}{\cos \left(pheta\right)}\ = 2\cos \left(pheta\right)[/tex]

[tex]\frac{\sin \left(2pheta \right)}{\sin \left(pheta\right)}=2\cos \left(pheta\right)[/tex]

2cos(θ) + 2cos(θ) = 4cos(θ)

so, 4cos(θ) is your answer

(4cospheta)

hope this helps!! :)

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Answer:  [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]

Find:  [tex]\textsf{The equation in point-slope form}[/tex]

Solution: We need to take the values that were given to us and plug them into the point-slope form.  It doesn't seem like the problem is asking for anything more than that so we will leave it at that.

Plug in the values

Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).

Answer:

[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

Step-by-step explanation:

[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]

We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).

Then, we substitute these values into the Point-Slope Form to find the equation.

Here are both forms for future reference:

⇒ Slope-Intercept Form: y = mx + b

[ Where: m is the slope, and b is the y-intercept (when x = 0). ]

⇒ Point-Slope Form: y - y₁ = m(x - x₁)

[ Where: m is the slope, and (x₁, y₁) is a given point. ]

Substitute the values into the Point-Slope Form:

[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

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Answer: [tex]k \parallel l[/tex]

Step-by-step explanation:

Lines that are parallel to the same line are parallel.

The value of the expression (82/n – 26) at n = 2 will be 15. Then the correct options are B, D, E, and G.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Tawny wrote an expression to represent “the quotient of 82 and a number, decreased by 26.”

She then evaluated the expression when n = 2.

Then the expression will be

⇒ 82 / n – 26

If the value of n is 2, then the value of the expression will be

⇒ 82 / 2 – 26

⇒ 41 – 26

⇒ 15

Then the correct options are B, D, E, and G.

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Answer:

T = 15 + 0.75c

T = $19.5

Step-by-step explanation:

Assume that T stands for total cost and c stands for number of single cookies purchased, the equation would be:

T = 15 + 0.75c

Therefore, a dozen cookies plus six single cookies would cost:

T = 15 + 0.75(6)

T = 15 + 4.5

T = $19.5

The description of the correlation in terms of strength (weak or strong) and direction positive or negative) is as explained below.

A correlation coefficient, is expressed as r and it indicates a measure of the direction and strength of a relationship between two variables.

Now, in terms of strength, Correlation strength ranges from -1 to +1. Thus, The closer the correlation is to 0, the weaker it is while the closer it is to ±1, the stronger it is.

Now, in terms of direction;

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Answer:

  a) 182.90 m

  b) 203.85 m

Step-by-step explanation:

The relations between trig functions and measures in a right triangle are summarized in the mnemonic SOH CAH TOA. Here, we are given an angle and the side opposite, and we are asked to find the adjacent side and the hypotenuse.

__

The foot of the cliff to the boat is the adjacent side of the angle in our model. So, we can use the relation ...

  Tan = Opposite/Adjacent

Solving for the adjacent side, we have ...

  BF = (90 m)/tan(26.2°) ≈ 182.90 m

The boat is about 182.90 meters from the foot of the cliff.

__

The top of the cliff to the boat is the hypotenuse of the triangle we're using to model the situation. This means the applicable relation is ...

  Sin = Opposite/Hypotenuse

  BC = (90 m)/sin(26.2°) ≈ 203.85 m

The boat is about 203.85 meters from the top of the cliff.

Answer:

(-4, -3)

(-4,3)

(4,3)

The clock wise rotation of the coordinate will be

(3,4)

(3,-4)

(-3,-4)

(-3,4)

Answer:

(-4,3)

Step-by-step explanation:

starting at  -3 , 4

   rotate clockwise 90°    this will change (x,y ) to   (y ,-x)

   doing this 3 times   results in

      4,3      then     3, -4      then    -4,-3       so the answer is (-4,3)

The secant of circle is SU and RT.

A straight line that intersects a circle in two points is called a secant line.

From the given diagram,

The line which intersects the circle at two points or an extended chord is SU and RT.

Hence, secant is SU and RT.

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m∠ZAB + m∠CAB = 180° by the angle addition postulate

m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem

m∠ZAB = m∠ACB + m∠CBA using the subtraction property

An equation is an expression that shows the relationship between two or more numbers and variables.

m∠ZAB + m∠CAB = 180° by the angle addition postulate

m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem

m∠ZAB = m∠ACB + m∠CBA using the subtraction property

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Answer:

We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.

We know that m∠ZAB + m∠CAB = 180° by the

✔ angle addition postulate

.

We also know m∠CAB + m∠ACB + m∠CBA = 180° because

✔ of the triangle angle sum theorem

.

Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.

Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the

✔ subtraction property

.

Step-by-step explanation:

Answer:

x = 55°

Step-by-step explanation:

Hello!

The sum of angles in a triangle is 180°.

To solve for x, we have to subtract the given angles from 180°.

The value of x is 55°.

Angle sum property of a triangle

∠A + ∠B + ∠C = 180°

We need to find the value of ∠A

According to the angle sum property of a triangle

⇢∠A + ∠B + ∠C = 180°

⇢∠A + 75° + 50° = 180°

⇢∠A + 125° = 180°

⇢∠A = 180° - 125°

⇢∠A = 55°

Answer:

n = -5

Step-by-step explanation:

Given:

  [tex]\dfrac{y^4 \cdot y^n}{y^2}=y^{-3}[/tex]

Multiply both sides by y²:

[tex]\implies \dfrac{y^4 \cdot y^n}{\diagup \!\!\!\!\!y^2} \cdot \diagup \!\!\!\!\!y^2=y^{-3}\cdot y^2[/tex]

[tex]\implies y^4 \cdot y^n=y^{-3} \cdot y^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies y^{4+n}=y^{-3+2}[/tex]

[tex]\implies y^{4+n}=y^{-1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies 4+n=-1[/tex]

Solve for n by subtracting 4 from both sides:

[tex]\implies 4+n-4=-1-4[/tex]

[tex]\implies n=-5[/tex]

Answer:

===========

Given equation:

Solve it for n:

===========

Used properties:

The square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.

It should be noted that square root is factor of a number that when multiplied by itself will give the original number.

In this case, the square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.

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Answer:

The answer is C

Step-by-step explanation:

Just got it.

Answer:

c = 37 mi

Step-by-step explanation:

   To find 'c' use Pythagorean theorem.

 [tex]\sf \boxed{\bf hypotenuse^2 = base^2 + altitude^2}[/tex]

                     c² = 35² + 12²

                         =1225 + 144

                        = 1369

                    [tex]\sf c = \sqrt{1369}\\\\ c = \sqrt{37*37}\\\\ \boxed{\bf c = 37 \ mi}[/tex]

#A

New side

Area

#2

Now it has turned rectangle

Sides

x+12 and x-7

Area

Answer:

A)  (x + 8)² cm² = (x² + 16x + 64)  cm²

B)  (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²

Step-by-step explanation:

Formula

Area of a square = s²  (where s is the side length)

Given side length of square field:

⇒ Area of field = x² cm²

Part A

If the side length of the square field is increased by 8 cm then:

⇒ new side length = (x + 8) cm

Substitute the new side length into the formula for the area of a square:

⇒ Area of field = (x + 8)² cm²

Expand and simplify:

⇒ Area = (x + 8)²

⇒ Area = (x + 8)(x + 8)

⇒ Area = x(x + 8) + 8(x + 8)

⇒ Area = x² + 8x + 8x + 64

⇒ Area = (x² + 16x + 64)  cm²

Part B

If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:

⇒ new side length a = (x + 12) cm

⇒ new side length b = (x - 7) cm

Substitute the side lengths into the formula for area of a square:

⇒ Area of a square = s × s

⇒ Area of a square = a × b

⇒ Area of the field = (x + 12)(x + 7) cm²

Expand and simplify:

⇒ Area = (x + 12)(x + 7)

⇒ Area = x(x + 7) + 12(x + 7)

⇒ Area = x² + 7x + 12x + 84

⇒ Area = (x² + 19x + 84) cm²

Answer:

C

Step-by-step explanation:

I guess it is the answer because the manager separates the customers into 3 ange groups and randomly selects a sample from each group

Answer:

B. Stratified random sampling

Step-by-step explanation:

The correct answer is option D which is the volume of the square pyramid will be  [tex]V = \dfrac{1}{2}x^2y\ cm^3[/tex].

A solid made up of a square base and four triangles connected side by side and meet at the same edge is called a square pyramid.

Given that:-

The volume of the pyramid will be calculated as:-

Volume = [tex]\dfrac{1}{2}[/tex] x Length of square pyramid x Height

Volume = [tex]\dfrac{1}{2}[/tex]  x (x)² x y

Volume = [tex]\dfrac{1}{2}[/tex] x²y

Therefore the correct answer is option D which is the volume of the square pyramid will be  [tex]V = \dfrac{1}{2}x^2y\ cm^3[/tex].

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Answer:

the answer is -1/8

Step-by-step explanation:

The complete sentence is as follows:

The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.

The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.

Given, An amusement park prices tickets at $55 and sells an average of 500 tickets daily. The management finds, over multiple increases in ticket pricing that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.

Management uses the combined function P to model the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.

[tex]P(x) = -40x^2- 100x + 27,500[/tex].

In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

We need to use the given information to complete the sentences.

The complete sentence is as follows:

The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.

The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.

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The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

An amusement park prices tickets at $55 and sells an average if 500 tickets daily.

The function P(x) represents the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.

Plug x = 0

P(0) = 27500

The above value is the constant of the polynomial function.

The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increases in the price of a ticket.

As the x is the number of $2 increases in the price of a ticket.

Then,

= (500 - 20x) is the binomial that represents the number of tickets sold after x increases by $2

Thus, the constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.

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Answer:

A)  144 feet

[tex]\textsf{B)} \quad h(t)=16t(6-t)[/tex]

Step-by-step explanation:

Part A

Given polynomial:

   [tex]h(t)=96t-16t^2[/tex]

where:

To find the height of the debris 3 seconds after the explosion, substitute t = 3 into the polynomial and solve:

[tex]\begin{aligned}\implies h(3)& = 96(3)-16(3)^2\\ & = 288 - 16(9)\\ & =288-144\\ & =144 \sf \:\: ft\end{aligned}[/tex]

Part B

To factor the polynomial, rewrite 96 as 6 × 16:

[tex]\implies h(t)=6 \cdot 16t-16t^2[/tex]

Rewrite t² as t × t:

[tex]\implies h(t)=6 \cdot 16t-16t \cdot t[/tex]

Factor out the common term 16t:

[tex]\implies h(t)=16t(6-t)[/tex]

Check

Substitute t = 3 into the factored expression:

[tex]\begin{aligned}h(3) & = 16(3)(6-3)\\& = 16(3)(3)\\& = 48(3)\\& = 144\:\: \sf ft \end{aligned}[/tex]

As the height is 144 ft when t = 3 is substituted into the original polynomial and the factored polynomial, this confirms that the factorization is correct.