5=logb(32) what does b equal

Step-by-step explanation:

For a rational function, we cannot values in the domain that will make the denominator 0.

So set the denominator =0

[tex] {x}^{2} - 1 = 0[/tex]

[tex] {x}^{2} = 1[/tex]

[tex]x = 1[/tex]

or

[tex]x = - 1[/tex]

So the answer is (-1,1)

Answer:

1. f(x) is reflected across the x-axis

2. f(x) is translated 1 unit up

3. f(x) is vertically scaled by a factor of 2

4. f(x) is reflected across the x-axis AND is vertically scaled by a factor of 2

5. f(x) is vertically scaled by a factor of 3 AND is translated 1 unit down

6. f(x) is vertically scaled by a factor of 1/6 AND is translated 1 unit up

Solving question:

(1)  [tex]g(x) = -f(x)[/tex]

This graph has been reflected in the x axis. Equation:  [tex]\sf g(x) = -\dfrac{2}{x}[/tex]

(2) [tex]g(x) = f(x) + 1[/tex]

Graph has been translated 1 units up vertically. Equation: [tex]\sf g(x) = \dfrac{2}{x} +1[/tex]

(3) [tex]g(x) = 2f(x)[/tex]

This graph has been stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = \dfrac{4}{x}[/tex]

(4) [tex]g(x) = -2f(x)[/tex]

This graph has been reflected in the x axis and stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = -\dfrac{4}{x}[/tex]

(5)  [tex]g(x) = 3f(x) - 1[/tex]

This graph has been stretched vertically by a factor of 3 and translated 1 units down. Equation: [tex]\sf g(x) = \dfrac{6}{x} -1[/tex]

(6)   [tex]g(x) = \frac{1}{6} f(x) + 1[/tex]

This graph has been stretched vertically by a factor of 1/6 and translated 1 units up. Equation: [tex]\sf g(x) = \dfrac{1}{3x} +1[/tex]

Since there is only one value of x, hence the equation given has only one solution

Equations are expressions separated using mathematical operations. Given the equation below;

2x+5+2x+3x = x

Collect the like terms

2x+2x+3x -x = -2

7x -x = -2

Simplify

6x = -2

x = -2/6

x = -1/3

Since there is only one value of x, hence the equation given has only one solution

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Answer:

-4

Step-by-step explanation:

Given vertex, the axis of symmetry is x = h.

Answer:

Step-by-step explanation:

This linear programming problem is described by an objective function and constraints on the variables. A graphical solution works well.

The goal is to maximize the number of people exposed to the company's ad(s). The number of people reached is the sum of the products of the number of ads and the number reached per ad.

For n newspaper ads, we are told that 6750n people are reached.

For r radio ads, we are told that 7800r people are reached.

The total number of people reached is ...

  P = 6750n +7800r . . . . . . . the function we wish to maximize

We can run at most 19 newpaper ads:

  n ≤ 19

We can run at most 31 radio ads:

  r ≤ 31

The cost of n newspaper ads will be $160n.

The cost of r radio ads will be $620r.

We must stay within a budget for the ads, $8100:

  160n +620r ≤ 8110

The white area in the first quadrant of the attached graph represents the feasible solution space. (We reversed the inequality symbol in each inequality so the solution space would be white, not triple-shaded.) The corners of the solution space represent possible (n, r) pairs where the objective function might be maximized.

The solid red line on the graph shows the maximum value the objective function might have, and the (n, r) pairs that would give that maximum value. The value of the objective function increases the farther the line is from the origin. Drawing the line on the graph lets us readily identify the (n, r) coordinate pair that will place this line as far as possible from the origin, maximizing P. We find that to be (n, r) = (19, 8).

Answer:

76,42,92,50........

Step-by-step explanation:

Each number is series of product of the digit

11*4=44,

13*2=26,

15*4=60,

17*2=34,

19*4=76,

21*2=42,

23*4=92,

25*2=50,

27*4=108,...

May be this çould help you.

Numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.

Given a paragraph in which there are blanks:

A _____ is a number whose only factors are 1 and itself. If a number has  factors besides 1 and itself, it is called a _____. You can use divisibility rules or _______ to help you determine whether a number is prime or composite.

We are required to fill the blank with appropriate options.

We have to fill "prime numbers" in the first blank.

We have to fill "composite numbers" in the second blank.

We have to fill "the sieve of Eratosthenes" in the third blank.

Hence numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.

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Check the picture below.

so the composite is really a trapezoid and two triangles, let's get their area and sum them all up.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a = 2\\ b = 5\\ h = 7 \end{cases}\implies A=\cfrac{7(2+5)}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{yellow~trapezoid}{\cfrac{7(2+5)}{2}}~~ + ~~\stackrel{blue~triangle}{\cfrac{1}{2}(\stackrel{b}{3})(\stackrel{h}{5})}~~ + ~~\stackrel{orange~triangle}{\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{2})}} \\\\\\ 24.5~~ + ~~7.5~~ + ~~10\implies \text{\LARGE 42}[/tex]

The value of x in A is 7 and the value of y in B is -15

Functions are represented as a function of variable. Given the following sets of numbers.

A = [3 x 6 1 -8 5] and;

-5A = [-15 35 -30 -5 40 y]

Equate the individual values to have:

-5A= -15

Divide both sides by -5

-5A/-5 = -15/-5
A = 3

Determine the value of y

-5A = y

-5(3) = y

y = -15

Similarly;

5x = 35

x = 35/5

x = 7

Hence the value of x in A is 7 and the value of y in B is -15

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Answer:

The value of x in A is -7

The value of y in B is -25

Step-by-step explanation:

Everything in the first matrix can be multiplied by -5 to equal everything in the second matrix, since we are dealing with x and y, only the first and third rows matter.

In the first row, we know that 3 times -5 equals -15 and x times -5 equals 35

therefore, -5x=35, with basic algebra we find that X = -7

In the third row, we know that 8 times -5 is 40 and 5 times -5 equals y.

This takes just basic multiplication to find that Y = -25

Based on the data presented, it can be concluded out of the 52 females 26 prefer cats.

To read the graph we must take into account that the rows refer to the preference of men, preference of women and those who have no preference.

On the other hand, the columns refer to the number of students of both genders who prefer or do not prefer each animal. Additionally, adding all the students of each gender we have the total of the sample.

According to the above, the total sample of female students would be 52.

According to the above, the fraction that expresses this relationship correctly is:

[tex]\frac{26}{52}[/tex]

Note: This question is incomplete because the graph is missing. Here is  the graph.

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Answer:

1/4

Step-by-step explanation:

Rebecka already chose a retriever, so the puppies left for Aaron to pick are:

2 poodles

2 terriers

1 retriever

Total: 4

Number of retrievers left after Rebecka's pick: 1

p(Aaron picks retriever) = 1/4

Based on the given graph relating to the company's profit f(x), the x-intercepts are (0, 0) and (0, 8) and the maximum value is 270.

The x-intercepts are the points where the graph crosses the x axis. It does so at first at (0,0) and then after going up and coming down, it again intersects at (0, 8).

The maximum value the graph reaches is 270 on the y-axis.

The function is increasing at the interval, (0, 4) and decreasing from (4, 8).

What this shows is that an increase in price between 0 and 4 would lead to an increase in profit but between 4 and 8 results in profits dropping.

In part B, the average rate of change from x=1 to x =4 is:

= (270 - 120) / (4 - 1)

= 50

In part c, the constraints are:

x ≥ 0

f(x) x ≤ 8

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green balls = 83

orange balls = 19

Step-by-step explanation:

green balls = g

orange balls = r

g = 7 + 4r

g + r = 102

7 + 4r + r = 102

5r = 95

r = 19

g + 19 = 102

g = 83

Answer: for number 3, x= 6

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

The company sells all that it produces, the profit function is:-0.5x2+60x-250.

P(x)= R(x)-C(x)      

=-0.5(x-110)2 +6050-(50x+250)

Let Distribute Negative Sign      

P(x)= -0.5(x-110)2 + 6050 +-1(50x+250)

P(x)= -0.5(x-110)2 + 6050 +-1(50x) + (-1) (250)

P(x)= -0.5(X-110)2 +6050 +-50x + -250

Distribute P(x)= -0.5x2+110x+-6050+6050+-50x+-250

Combine Like Terms

P(x)= -0.5x2 +110x+-6050+6050+-50x+-250

P(x)=(-0.5x2) + (110x+-50x) + (-6050+6050+-250)  

P(x)= -0.5x2+60x-250

Therefore the company sells all that it produces, the profit function is:-0.5x2+60x-250.

The missing requirement is:

Assuming that the company sells all that it produces, what is the profit function?

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Answer:

120

Step-by-step explanation:

The angle below x is 40 degree cause alternate angle. Then you get,

20+x+40=180

60+x=180

x=180-60

x=120

Answer:

30 cm

Step-by-step explanation:

every 5 cm of a belt, 16 more green beads are used.

there are 96 more green beads than silver, so it will take 6 5 cm belts in order to have equal numbers of green and silver beads left

Answer:

Step-by-step explanation:

After Aspen sews 30 cm of the belt, they have equal numbers of green and silver beads left. ANSWER:30

The statement which is false among the answer choices as indicated in the task content is; Choice A; The parallel sides of an isosceles trapezoid are congruent.

It follows from the answer choice A that The parallel sides of an isosceles trapezoid are congruent.

However, it follows from the study of isosceles trapezoids that the base angles of such trapezoids are congruent and their measures are equal, consequently, the isosceles sides have equal length measures.

On this note, the other two sides are parallel but cannot be concluded as congruent.

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The 10the term of the sequence -1/1, -1/2, -1/9, -1/64....is -1/1,000,000,000

-1/1, -1/2, -1/9, -1/64

This can be written as;

-1/1° , -1/2¹, -1/3², -1/4³, -1/5⁴, -1/6^5, -1/7^6, - 1/8^7, -1/9^8, -1/10^9

So,

First term = -1/1,

Second term = -1/2,

Third term = -1/9,

Fourth term = -1/64,

Fifth term = -1/625,

Sixth term = -1/7,776,

Seventh term = -1/117,649,

Eighth term = -1/2,097,152,

Ninth term = -1 / 43,046,721,

Tenth term = -1/1,000,000,000

Therefore, the 10th term is -1/1,000,000,000

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The cost of manufacturing the article bin 2004 will be 1875.

Percentage increase is the ratio of increase to the initial value in percentage.

Given that In 2001 the total cost of manufacturing an article was sh.1250 and this was divided between the cost of materials was doubled, labor cost increased by 30% and transport costs increased by 20%

Given that in 2001, the cost of manufacturing = 1250

If this cost was divided between the Material, labor, and transportation equally, then, cost for each sector will 1250/3 = 416.67

The cost of manufacturing = 833.33 + 541.67 + 500

The cost of manufacturing = 1875

Therefore, the cost of manufacturing the article bin 2004 will be 1875.

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Answer:

-

-

+

+

Step-by-step explanation:

Answer:

Answer is c, 67.

Step-by-step explanation:

So angle L and K are going to be the same, and so its going to be:

46+2n=180, since 180* inside a triangle and n= both L and K.

180-46=134

134/2=67

Both K and L will be 67.

Answer is c, 67.

To check, 46+67+67=180

The measure of angle JLK is 67 degree.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The angle L and K are going to be the same;

46+2n=180,

Since 180 inside a triangle and n= both L and K.

180-46=134

134/2=67

Both K and L will be 67.

The answer is c, 67.

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Answer: 57 cm²

Step-by-step explanation:

We can split this figure into two shapes: the rectangle on the left and the triangle on the right. We can find the area of each separately and add them to get the total area.

The area of a rectangle is [tex]lw[/tex], where l is the length and w is the width. We can just multiply 8 and 6 to get the area of the rectangle.

[tex]A=8*6\\A=48[/tex]

The area of the triangle is [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle and h is the height. Here' the base would be 6 cm as opposite sides of a rectangle have the same measure, and the height is 3.

[tex]A=\frac{1}{2}(6*3)\\A=\frac{1}{2}(18)\\A=9[/tex]

The total area would just be the sum of the two separate areas.

[tex]48+9=57[/tex]

Hence, the area of the figure is 57 cm².

Answer: 57 cm^2

Step-by-step explanation:

To find the entire area of the figure, we have to find the area of the rectangle and the triangle and sum it up

The area of the rectangle is 6 * 8 = 48 cm^2

The area of the triangle is 1/2 * 3 * 6(Opposite sides of a rectangle have equal lengths) = 9 cm^2

So the area of the figure is 48 + 9 = 57 cm^2

Answer:

f(-5) = 30

f(0) = 5

f(3) = 14

Step-by-step explanation:

=> f(x) = x²+5

for , f(-5) = (-5)² +5

=> 25 +5

=> 30

for , f(0) = (0)² +5

=> 5

for , f(3) = (3)² + 5

=> 9 + 5

=> 14

Answer:

$1137.87

Step-by-step explanation:

Frist, we will find the hourly rate.

Given 15 hours = $502,

1 hour = [tex]\frac{502}{15} \\[/tex] = [tex]33\frac{7}{15}[/tex]

Note: Will leave the rate as a fraction as to maintain maximum accuracy.

34 hours = [tex]33\frac{7}{15}*34[/tex] = $1137.87 (nearest cent)

The letter for the graphed function is y = √(x) - 5

The parent function is given as:

y = √x

From the graph, we can see that the function is shifted downwards by 5 unts

This is represented as:

y = √(x) - h

Where h = 5

Substitute the known values in the above equation

y = √(x) - 5

This means that the letter for the graphed function is y = √(x) - 5

Hence, the letter for the graphed function is y = √(x) - 5

So, the complete functions are

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The value of g(x) is (x^3+5) and g(64) = 262149.

According to the statement

we have given that the

f(x)=√x^3 and (fog)(x)=√(x^3+5) and we have to find the value of the g(64).

So, For find the value of g(64), Firstly we have to find the g(x).

So,

We given that

f(x)=√x^3 and (fog)(x)=√(x^3+5)

And here the formula used is

(f o g)(x) = f (g(x))

here (fog)(x)=√(x^3+5) and f(x)=√x^3

From this we get g(x) is (x^3+5)

So,

g(x) = (x^3+5) and

g(64) = ((64)^3+5)

g(64) = 262149.

So, The value of g(x) is (x^3+5) and g(64) = 262149.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

If f(x)=√x^3 and (fog)(x)=√(x^3+5). Then find the value of g(64).

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I take this to mean [tex]f(x) = \sqrt{x^3}[/tex] and [tex](f\circ g)(x) = \sqrt x[/tex].

Let's first find the inverse of [tex]f[/tex].

[tex]f\left(f^{-1}(x)\right) = \sqrt{\left(f^{-1}(x)\right)^3} = x \\\\ \implies \left(f^{-1}(x)\right)^3 = x^2 \\\\ \implies f^{-1}(x) = x^{2/3}[/tex]

(Note that [tex]f[/tex] is defined only if [tex]x^3\ge0[/tex], or [tex]x\ge0[/tex].)

Apply the inverse of [tex]f[/tex] to [tex]f\circ g[/tex].

[tex](f\circ g)(x) = f(g(x)) = \sqrt x \\\\ \implies f^{-1}\left(f(g(x))\right) = f^{-1}(\sqrt x) \\\\ \implies g(x) = \left(\sqrt x\right)^{2/3} = \left(x^{1/2}\right)^{2/3} = x^{1/3} = \sqrt[3]{x}[/tex]

Then

[tex]g(64) = \sqrt[3]{64} = \sqrt[3]{4^3} = \boxed{4}[/tex]