Given the functions ƒ(x) and g(x), which of the following statements is true?

Answer:

The correct answer is X²/³

Step-by-step explanation:

Points to remember

Identity

Xᵃ/Xᵇ = X⁽ ᵃ⁻ ᵇ ⁾

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

(Xᵃ)ᵇ = Xᵃᵇ

To find the equivalent expression

We have, (X⁴/³ X²/³)¹/³

Using identities we can write,

(X⁴/³ X²/³)¹/³ = (X⁴/³  * X²/³)¹/³

 = (X⁴/³ ⁺ ²/³)¹/³

 = ( X⁽⁴⁺²⁾/³)¹/³

 = (X⁶/³)¹/³

= (X²)¹/³

= X²/³

Therefore the correct answer is X²/³

Answer:

BC = 144 units

Step-by-step explanation:

It is given a line segment BC.

D is the point on the line segment.

To find the length of BC

BC = 8x

CD = 3x + 8  and BD = 4x + 10

BC = CD + BD

8x = 3x + 8 + 4x + 10

8x = 7x + 18

x = 18

BC = 8x = 8 * 18 = 144 units

Therefore the length of segment BC = 144 units

Segment BC is 144 units

I don't know if you still need this but here you go

Answer: Equation for the line of best fit is given by

f(x)=-4.28402x+0.0875

Step-by-step explanation:

Long Course Season       Recorded Best time

2005                          2:33.42

2006                          2:24.81

2007                          2:10.93

2008                          2:03.45

2009                          1:58.67

2010                          1:59.17

2011                          1:55.06

2012                          1:55.82

2013                          1:54.81

2014                          2:00.03

Since we can see from the scatter plot that it has negative correlation.

Equation for the line of best fit is given by

f(x)=-4.28402x+0.0875

Answer:

7x6x2= 84 ft cubed

Step-by-step explanation:

multiply length by width by height

Answer: its the one under the first one i think good luck adriana lol

Step-by-step explanation:

Answer:

18. 36.36%

22. 53.71

Step-by-step explanation:

Answer:

x < - 1

Step-by-step explanation:

Given

5x + 8 < 3(x + 2) ← distribute

5x + 8 < 3x + 6 ( subtract 3x from both sides )

2x + 8 < 6 ( subtract 8 from both sides )

2x < - 2 ( divide both sides by 2 )

x < - 1

The inequality 5x + 8 < 3(x + 2) simplifies to x < -1.

To solve the inequality 5x + 8 < 3(x + 2), we must simplify and isolate the variable x. We start by distributing the 3 on the right side:

5x + 8 < 3x + 6

Next, we'll subtract 3x from both sides to get:

2x + 8 < 6

Now subtract 8 from both sides to isolate the term with x:

2x < -2

Finally, we divide both sides by 2:

x < -1

The solution to the inequality is all x-values that are less than -1.

Check the picture below.

let's notice that the angle at K is an inscribed angle with an intercepted arc

[tex]\bf \stackrel{\textit{using the inscribed angle theorem}}{K=\cfrac{\widehat{LI}+\widehat{IJ}}{2}}\implies 9x+1=\cfrac{(10x-1)+59}{2} \\\\\\ 9x+1=\cfrac{10x+58}{2}\implies 18x+2=10x+58\implies 8x+2=58 \\\\\\ 8x=56\implies x=\cfrac{56}{8}\implies x=7 \\\\[-0.35em] ~\dotfill\\\\ K=9x+1\implies K=9(7)+1\implies \boxed{K=64}[/tex]

now, let's notice something again, the angle at L is also an inscribed angle, intercepting and arc of 97 + 59 = 156, so then, by the inscribed angle theorem,

∡L is half that, or 78°.

now, let's take a look at the picture down below, to the inscribed quadrilateral conjecture, since ∡J and ∡I are both supplementary angles, then

∡I = 180 - 64 = 116°.

∡J = 180 - 78 = 102°.

The measure of all the angle of KLIJ which is inscribed in circle k(O) are, 64, 78, 116, 102 degrees.

Inscribed angle theorem is the theorem, which state that the angle inscribed in a circle will be half of the angle which delimits the same arc on the circle.

The quadrilateral KLIJ is inscribed in circle k(O). In this the measure of the angle are given as,

[tex]m\angle K = (9x+1)^o[/tex]

m (arc) LI = (10x−1)°

m (arc) IJ = 59°,

m (arc) KJ =97°

All angles of the quadrilateral KLIJ has to be found out. By the inscribed angle theorem,

[tex]K=\dfrac{LI+IJ}{2}\\9x+1=\dfrac {10x-1+59}{2}\\18x+2=10x+58\\8x=56\\x=7[/tex]

Therefore, the value of the angle k is,

[tex]m\angle K = (9(7)+1)^o\\m\angle K = 64^o[/tex]

Similarly, the measure of the angle L is,

[tex]m\angle L=\dfrac{KJ+IJ}{2}\\m\angle L=\dfrac {97+59}{2}\\m\angle L=\dfrac{156}{2}\\m\angle L=78^o[/tex]

Now the angles I and J are the supplementary angles of the angle K and angle L respectively. Therefore,

[tex]m\angle I=180-m\angle K=180-64=116^o\\ m\angle J=180-m\angle L=180-78=102^o[/tex]

Hence, the measure of all the angle of KLIJ which is inscribed in circle k(O) are, 64, 78, 116, 102 degrees.

Learn more about the inscribed angle theorem here;

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Answer:

step 2

Step-by-step explanation:

Given step 1

324π = π × 12² h

Then second step should read

324π = π × 144h ← 144 not 24 is the error

Answer: Last option.

Step-by-step explanation:

We need to apply the Rule for 90° counterclockwise rotation about the origin. Given a point [tex]P(x,y)[/tex]:

[tex]P(x,y)[/tex] → [tex]P'(-y,x)[/tex]

We can observe in the figure that the coordinates of the points E, F, G and H are:

[tex]E (2,6)[/tex]

[tex]F(7,-4)[/tex]

[tex]G(-2,-7)[/tex]

[tex]H (-5,1)[/tex]

Then, applying the rule, we get the coordinates of the new location of the figure EFGH:

[tex]E (2,6)[/tex] → [tex]E'(- 6,2)[/tex]

[tex]F(7,-4)[/tex] → [tex]F'(4,7)[/tex]

[tex]G(-2,-7)[/tex] → [tex]G'(7,-2)[/tex]

[tex]H (-5,1)[/tex] → [tex]H'(-1,-5)[/tex]

Answer:

78

Step-by-step explanation:

78 is the answer because if you count inwards then you get 78

Answer:

D

Step-by-step explanation:

add them all except 50 divide by 9 because only used 9.

Answer: 6

Step-by-step explanation: -8 x -8 = 64

64 - -58 = 6

Answer:

The answer is 6.

Step-by-step explanation:

Since negative × negative = positive, therefore -8(-8)=64 and 64-58=6.

Answer:C 30

Step-by-step explanation: They all divide evenly when divided by 30.

ANSWER

[tex]y = 5 \sin( \frac{6}{5} x - \pi)-4 [/tex]

EXPLANATION

The given function is

[tex]y = 5 \cos( \frac{3}{5} x - \pi) + 4[/tex]

The period of this function can be determined using the formula:

[tex]T= \frac{2\pi}{ |b| } [/tex]

.

The period is

[tex]T= \frac{2\pi}{ \frac{3}{5} } = \frac{10\pi}{3} [/tex]

Half the period of this function is:

[tex] \frac{ \frac{10\pi}{3} }{2} = \frac{5\pi}{3} [/tex]

The function which has this period is

[tex]y = 5 \sin( \frac{6}{5} x - \pi) -4[/tex]

The first choice is correct.

Answer:

The period is 360° ( in radians, the period is 2π)

Step-by-step explanation:

For a sine/cosine (sinusoidal) function in the form

y = ASin(Bx-C) + D, we can say

A is the amplitude

360/B is the period

C is the phase shift

D is the vertical translation

The function given is y = 2Sinx

To find the period, we need 360/B. Since "B" is just "1", the period is

360/1 = 360

Answer:

The period of the function [tex]y = 2sinx[/tex] is [tex]2\pi[/tex]

Step-by-step explanation:

The sinosuidal functions have the following form

[tex]y = Asin (bx) +k[/tex]

Where A is the amplitude of the function

k is the vertical displacement

[tex]\frac{2\pi}{b}[/tex] is the period.

In this case we have the function

[tex]y = 2sinx[/tex]

Therefore the amplitude A = 2

The vertical displacement is k = 0

The period is [tex]\frac{2\pi}{1} = 2\pi[/tex] because b=1

Therefore the function completes a cycle every [tex]2\pi[/tex]

The total cost of 1 pair of pants and 1 shirt is $18 . If s represents the cost of 1 shirt, which equation could you use to find .

For this case we propose a system of equations:

p: Variable representing the cost of a pair of pants

s: Variable representing the cost of a shirt

A pair of pants costs twice as much as a shirt, means:

[tex]p = 2s[/tex]

The total cost of 1 pair of pants and 1 shirt is $ 18:

[tex]p + s = 18[/tex]

We substitute the first equation in the second:

[tex]2s + s = 18\\3s = 18\\s = \frac {18} {3}\\s = 6[/tex]

Answer:

The following equation can be used:

[tex]2s + s = 18[/tex]

f(x) = x³ – 2x² – x + 2

 0 = x3 – 2x2 – x + 2

 (x-2)(x-1)(x+1)=0

 x1=-1

 x2=1

 x3=2

For this case we must follow the steps below:

We factor the polynomial, starting by factoring the maximum common denominator of each group:

[tex]x ^ 2 (x-2) - (x-2)[/tex]

We factor the maximum common denominator[tex](x-2):[/tex]

[tex](x-2) (x ^ 2-1)[/tex]

Now, by definition of perfect squares we have:

[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]

Where:

[tex]a = x\\b = 1[/tex]

Now, we can rewrite the polynomial as:

[tex](x-2) (x + 1) (x-1)[/tex]

To find the roots we equate to 0:

[tex](x-2) (x + 1) (x-1) = 0[/tex]

So, the roots are:

[tex]x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]

Answer:

[tex]x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]

Solution:

Given :

So, We have to find the area of Triangle .

Area of triangle = 1/2*b×h, Where represents

Step : Substitute those value in Formula;

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 19 × 11

Area of triangle = 104.5 units Square

Therefore, Option B is correct Answer.

Area of triangle is 104.5 units Square.

One of the most fundamental geometric shapes is the triangle. The simplest and most widely used formula is area = 0.5 * b * h, where b is the triangle's base length and h is the triangle's height or altitude. Almost everyone knows this formula from school.

Given :

Base of triangle = 19

Height of triangle = 11

So, We have to find the area of Triangle .

Area of triangle = 1/2*b×h, Where represents

B represent Base

H represent Height

Step : Substitute those value in Formula;

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 19 × 11

Area of triangle = 104.5 units Square

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Answer:

WRONG THE ANSWER IS ACUALLY C

Step-by-step explanation:

I know this because i decided to take th4e test use his answer and it was wrong telling me the right answer it's (c).

The equation that can be used to find the volume of the cylinder is V = π(4.5)²h (option C).

The equation that can be used to find the volume of the cylinder is V = π(4.5)²h (option C). To find the volume of a cylinder, you need to use the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. In this case, the radius is 4.5 cm and the height is not given, so it is represented as h. By substituting the values into the formula, you get V = π(4.5)²h.

Answer:

A.) 30

Step-by-step explanation:

The entire figure consists of two angles supplementary to each other, which means that ∠YWZ + ∠ZWX = 180°. Since ∠ZWX is 20°, we know that ∠YWZ is 160°.

So now we have an equation to solve:

5x + 10 = 160

     - 10     - 10

5x = 150

÷ 5   ÷ 5

x = 30

Answer:

The rate of sales tax is 6%.

Step-by-step explanation:

First you must subtract 12.50 from 13.25

This brings you to .75

Then, divide .75/12.50 to get 0.06 which is equivalent to 6 percent.

Answer:

see below

Step-by-step explanation:

The function is only defined for x < 1, and is undefined for x=1 or more. Thus the graph stops at x=1, with an open circle indicating the function is not defined there.

Answer:

The required graph is shown in figure 1.

Step-by-step explanation:

Consider the provided function f(x)=x if x<1

Here the sign of inequality is x<1.

That means the value of x can be anything less then 1.

Note the sign "<" indicates that the value x is strictly less than 1 also it is not equal to 1.

For x=1 the function is not defined.

For the inequity "<" and ">" we use an open dot or open circle which shows that the value is not included.

Now draw the table and substitute some value of x as shown.

Substitute x=0 in the provided equation.

f(x)=0

For x=0 the value of f(x) is also 0.

Substitute x=-1

f(x)=-1

For x=-1 the value of f(x) is also -1.

Substitute x=-2

f(x)=-2

For x=-2 the value of f(x) is also -2.

The required table is shown below:

x   0  -1  -2

f(x) 0  -1  -2

Now plot the above points and join them.

The required graph is shown in figure 1.

Answer:

4

Step-by-step explanation:

Answer:

5; you add the two legs for the hypotenuse

Step-by-step explanation:

The length of the hypotenuse is 5 feet.

The hypotenuse is the opposite side of the right angle in the triangle. It’s also the longest side of the triangle.

The Pythagorean Theorem helps us calculate the hypotenuse of a right triangle if we know the sides of the triangle.

Here, a = 3 feet.

         b = 2 feet.

    Then hypotenuse will be = (√3 + √2) feet

                        = 5 feet.

The answer is 5 feet.

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The formula for finding the circumference of the circle is 2 pi r or pi d. R stand for radius and D stand for diameter. The problem gave you the length of the diameter so can either put it in form of pi as in 30pi or multiply it by pi (3.14) which will give you the result of 94.2

Answer:

- 30pi

- 94.2

Answer: 376.99 is the answer

ANSWER

The approximate circumference is 377 inches

EXPLANATION

The circumference of a circle is calculated using the formula

[tex]C=2 \pi \: r[/tex]

Where r=60 inches is the radius of the circle.

We substitute π=3.4 and the radius into the formula to obtain:

[tex]C=2 (3.14)(60) \: inch[/tex]

[tex]C = 376.8inches[/tex]

The approximate circumference of the circle is 377 inches.

Answer:

4.55 meters

Step-by-step explanation:

Answer:

Step-by-step explanation:

your answer is 4.55 :)

Answer:

The value of x is -3

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of a line that passes through points (x1 , y1) and (x2 , y2) is

  [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

* Lets solve the problem

∵ The points (4 , 1) and (x , -6) lie on the same line

∵ The slope of the line is 1

- Let the point (4 , 1) is (x1 , y1) and the point (x , -6) ix (x2 , y2)

∵ x1 = 4 , x2 = x and y1 = 1 , y2 = -6

∴ [tex]m=\frac{x-4}{-6-1}[/tex]

∴ [tex]m=\frac{x-4}{-7}[/tex]

∵ The slope of the line is m = 1

∴ [tex]\frac{x-4}{-7}=1[/tex]

- By using cross multiplication

∴ x - 4 = -7 ⇒ add 4 to both sides

∴ x = -3

* The value of x is -3

the value of x for the point on the line is -3.

The student is asking how to find the value of x for a point on a line with a given slope. Since the slope of the line is 1, we can use the slope formula, which is (y2 - y1) / (x2 - x1) = slope, to find the value of x. Here, we have two points, (4, 1) and (x, -6), and a slope of 1.

Using the formula, we get (-6 - 1) / (x - 4) = 1. Simplifying, we get -7 / (x - 4) = 1. To find the value of x, we solve the equation -7 = x - 4, which gives us x = -3. So, the value of x for the point on the line is -3.

The answer is logarithmic

Answer:

Logarithmic .

Step-by-step explanation:

When we evaluate the logarithmic expression then we prepared to work

with logarithmic function

If , I want to solve the logarithmic expression then first we should  know about the logarithmic theorem rules .

If ,I don't know about the logarithmic rules then we can't evaluate the logarithmic expression.

So , first we should do practice with logarithmic function and we should know  how to use of logarithmic rules during evaluating the logarithmic expression .

Logarithmic rules :

[tex]Log \frac{m}{n}= log m - log n[/tex]

[tex]log m\times n= log m+ log n[/tex]

[tex]log a^b= bloga[/tex]

For example ; we have [tex]log\frac{3}{4}[/tex]

Therefore, by using logarithmic rule then we get

[tex]log\frac{3}{4} = log 3- log 4[/tex]

Therefore, if i want to evaluate the logarithmic expresssion then  i will be prepared to work with logarithmic function .

Answer:

6 inches

Step-by-step explanation:

area of triangle = 1/2 b* h

24 = 1/2 * 8* h

4h = 24

divide both sides by 4

h = 6 inches

Area is 1/2 x base x height.

24 = 1/2 x 8 x H

Multiply both sides by 2:

48 = 8 x Height

Divide both sides by 8:

Height = 48 / 8

Height = 6 inches.