The functions f(x) and g(x) are shown on the graph.



Using f(x), what is the equation that represents g(x)?

g(x) = log3(x) – 4
g(x) = log3(x) + 4
g(x) = log3(x – 4)
g(x) = log3(x + 4)

The given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.

The given function is f(z)=3z-8.

We need to find the value of f(-4), f(2), f(z-7).

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Now to find f(-4), replace z from -4.

f(-4)=3(-4)-8=-12-8=-20

Now to find f(2), replace z from 2.

f(2)=3(2)-8=6-8=-2

Now to find f(z-7), replace z from z-7.

f(z-7)=3(z-7)-8=3z-21-8=3z-29.

Therefore, the given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.

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~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

[tex]\textsc{heya!}[/tex]

[tex]\square\!\!\!\!\checkmark[/tex]what we need to do:

[tex]\square\!\!\!\!\!\checkmark[/tex] what we are provided with:

[tex]\textsc{solution:}[/tex]

[tex]\textsc{explanation:}[/tex]

divide both sides by 9; after performing this operation, we obtain:

[tex]\bold{x=\frac{6}{9}}[/tex]

divide top & bottom by 3; we obtain the solution

[tex]\bold{x=\frac{2}{3}}[/tex]

[tex]\textsc{hopefully\;helpful!}[/tex]

by: [tex]^da_n^cIn_g}[/tex]

have a great rest of your day ahead ~ = )

~

Answer:

X= -3

Step-by-step explanation:

(4+5)-1/3(40-4)=X

X=9- 1/3(36)

X=9-12

The perimeter and area of the basketball court is 18x + 6 and 8x² + 24x respectively.

Perimeter of basketball court = 2(length + width)

= 2(8x + x + 3)

= 2(9x + 3)

= 18x + 6

Perimeter of basketball court = 18x + 6

Area of basketball court = length × width

= 8x × (x + 3)

= 8x² + 24x

Area of basketball court = 8x² + 24x

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Answer:

[tex]\mathsf {SA = 112 in.^{2} }[/tex]

Step-by-step explanation:

[tex]\textsf {Formula used :}\\\implies \textsf {SA = 2(length * width + width * height + length * height) }[/tex]

[tex]\textsf {Given :}\\\textsf {Length = 5 in.}\\\textsf {Width = 4 in.}\\\textsf {Height = 4 in.}[/tex]

[tex]\textsf {Solving :}[/tex]

[tex]\implies \mathsf {SA = 2 (5 * 4 + 4 * 4 + 5 * 4)}[/tex]

[tex]\implies \mathsf {SA = 2 (20 + 16 + 20)}[/tex]

[tex]\implies \mathsf {SA = 2 (56)}[/tex]

[tex]\implies \mathsf {SA = 112 in.^{2} }[/tex]

Answer:

In order for each child to receive a book, first distribute one book to each.

This can be done in [math] 5\times 4\times 3 = 60 [/math] ways.

The remaining two books can be distributed in [math] 3^2 [/math] ways.

Total number of ways[math] = 60 \ times 9 = 540 [/ math]

In order to determine your take home pay, multiply your gross income by the percent of taxes then subtract the amount to find your net pay.

Gross pay is the total income earned before any deductions. Net pay is the  gross income less any deductions.

Assume your net pay is $10000 and tax is 10%, net pay is:

$10,000 - (0.1 x 10,000) = $9,000

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Answer:

the answer is $24.3

Step-by-step explanation:

==================================================

Explanation:

Replace f(x) with 0 and solve for x.

f(x) = 3x-12

0 = 3x-12

3x-12 = 0

3x = 12

x = 12/3

x = 4 is a zero, aka root, of the function

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

Check:

f(x) = 3x-12

f(4) = 3(4)-12

f(4) = 12-12

f(4) = 0

The answer is confirmed.

Answer: 60 degrees

Step-by-step explanation:

1. Make a right triangle where the right angle is and label the hypotenuse r.

2. Since the chord is equal to r and a 90-degree angle is formed at the intersection, the chord is bisected. Therefore, the chord segment is 1/2 r.

3. Since we have to solve for the intercepted arc, we must find the central angle ( the angle of the right triangle closest to the dot/center) of the arc, which in this case is the sin, or 0.5r/r.

4. We must get rid of the fraction in the numerator, so multiply both the numerator and denominator by 2 which gets you 1r/2r.

5. The r's cancel out, leaving you with 1/2.

6. Since we have to find the angle measure, you must take the negative sin of 1/2 which is 30 degrees.

7. Finally multiply by 2 since you only solved one bisected portion to get 60 degrees.

Answer:

Step-by-step explanation:

60

Answer:

D. 60

Step-by-step explanation:

60 is the only number that 3 and 4 and 5 all go into.



4 does not go into 15, so not answer A.



5 does not go into 12, so not answer B

3 does not go into 20, so not answer C

D is correct. 4 and 5 and 3 all go into 60.

The student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.

We are told that the author of the article is making a claim that a playground will benefit a particular community.

Now, when trying to verify a claim by someone it is very important to try to get facts and figures about that fact to start with before asking for opinions.

Thus, what the student do is that he should look for opinions, the student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.

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Try: Re-reading the question.

Answer: The student should check if the author's article provides more facts or evidence than opinions.

What is the difference between facts and opinions? Facts provide real statements that have been proved with solid evidence by experts. Meanwhile, on the other hand, opinions are what people think. It is more like thinking than something with evidence. It hasn't or can't be proved. If it includes more facts then the author's claims are strong with solid evidence. If it includes more opinions then the author's claims are not strong, they are weak. Since it's only the author's point of view.

Two supplementary angles when addd together equal 180.

let one angle = x

The second angle is 5 times that so would be 5x

x + 5x = 180

Simplify:

6x = 180

Divide both sides by 6:

X = 30

One angle is 30, the second angle would be 150

The answer is 150

Answer:

372

Step-by-step explanation:

We know that a ratio of 3 : 2 has 5 people, so figuring out how many times that ratio goes into our total number helps us find the value of the total number of adults.

930 / 5 = 186

This means that there are 186 groups of 3 children to 2 adults

So, in each of the 186 groups, there are 2 adults.

Therefore, we can multiply (186)(2)

to find the total number of adults: 372

The number of the children and adult will be 558 and 372.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

At a swimming pool, the ratio of children to adults was 3 : 2.

C / A = 3 / 2

Then solve the equation for C, then the equation will be

C = (3/2)A

The total number of the people is 930. Then the equation will be

C + A = 930

Substitute the value of C in the above equation. Then the equation will be

(3/2)A + A = 930

     (5/2)A = 930

            A = 930 x (2/5)

            A = 372

The number of the adult will be 372.

Then the number of the children will be

C + 372 = 930

         C = 930 – 372

         C = 558

The number of the children will be 558.

Thus, the number of the children and adult will be 558 and 372.

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Answer:

315

Step-by-step explanation:

The number is divisible by 3,5,7 and 9. Since 3 is a factor of 9, this number is divisible by 5,7, and 9.

5x7x9= 315.

Answer:

So basically you solve for y

so its gonna be -4y = 12-2x, then divide everything by -4 to solve for y which will be equal to -3 + 1/2x

just write it as 1/2x -3 cause its better

Hope that answers your question

Step-by-step explanation:

Answer:

y = -3 +1x/2

Step-by-step explanation:

2x - 4y = 12

-4y = 12 -2x

y = 12/-4 - 2x/-4

y = -3 +x/2

  ▶︎◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◀︎

[tex]Hello[/tex] [tex]There![/tex]

We need to find what number, if 6 is divided by it, gives us 12.

This isn't hard, I promise! I am going to take you through a few steps, and we'll find the answer.

Are you ready? Then let's begin...:)

[tex]Procedure:[/tex]

  ✦ We can think about it as: 6 divided by what number gives us 12?

(let the number be z)

[tex]^6/_z=12[/tex]

Multiply both sides by z

[tex]6=12z[/tex]

Divide both sides by z

[tex]z=^6/_{12}[/tex]

Which is the same as

[tex]z=^1/_2[/tex]

[tex]Greetings![/tex]

--

The triangle △ABC and △DEC are similar to each other. Then the correct option is A, B, and D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Right triangle ABC is reflected over AC.

Then dilated by a scale factor of Two-thirds to form triangle DEC.

The triangle △ABC and △DEC are similar to each other.

△ABC ≅ △DEC

The dilation is 2/3. Then we have

DE / AB = 2 / 3

     3AB = 2DE

∠B ≅ ∠E = 90

There is no effect of dilation on angle.

Then the correct option is A, B, and D.

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Answer:

A. △ABC ~ △DEC

B. ∠B ≅ ∠E

D. 3DE = 2AB

Step-by-step explanation:

got it right on edge 23

Answer: Common Core Performance Assessment.

The Name Game

Pairs of students in Mr. Kuan's class are playing the

Name Game. One team member is given a list of attributes

and has to draw a shape to match the description. The other

team member must then name the shape. The first pair to

complete the task wins.

Wilfredo was given a list with the information at the right.

He drew a shape and his partner, Olivia, named it. What shape

did Wilfredo draw? Answer Exercises 4-7 to solve the problem.

.

•

4. MP.1 Make Sense and Persevere What are you asked to do?

What can you do to persevere when solving the problem?

5. MP.6 Be Precise What math terms and numbers can help you

solve the problem?

6. MP.7 Use Structure What do you know about a quadrilateral?

Use what you know to draw and name a shape that matches

the information in the list.

. MP.3 Construct Arguments Is there more than one possible

way for Wilfredo to draw the shape? Explain.

A quadrilateral

2 sides are parallel

2 sides are equal

2 right angles

Attend to precision by

identifying words and

numbers that can help you

solve the problem.

Step-by-step explanation:

Answer:

  (c)  5.00×10^-5 kg

Step-by-step explanation:

The mass and energy are related by Einstein's formula E = mc².

__

Solving for mass in kg, we find it to be ...

  m = E/c² . . . . . . . . where E is in joules, and c is in meters/second

  m = (4.50×10^12 J)/(3×10^8 m/s)² = 5.00×10^-5 kg

The lost mass was about 5.00×10^-5 kg.

Answer:

5.00×10^−5 kg

Step-by-step explanation:

I took the test and it was correct! PLEASE LIKE  and have a wonderful day!

Answer:

it is b

Step-by-step explanation:

The solution is Option A.

The coordinates of the vertex A before the reflection across the line y = x is given by A = A ( 10 , -2 )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the coordinates of the point A be A ( x , y )

Now , the vertex A is reflected over the line y = x

When you reflect a point across the y = x , the y-coordinate gets interchanged with x-coordinate. The reflection of point (x, y) across the line y = xis ( y , x )

So , the coordinates of the point A' ( -2 , 10 )

Now , the coordinates of the point A will be

A ( x , y ) = A ( 10 , -2 )

Therefore , the value of A is A ( 10 , -2 )

Hence , the coordinates of the point before reflection is A ( 10 , -2 )

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Answer:

Mr. Garcia had 5 kilograms of blueberries at first

Step-by-step explanation:

to make this easiest, we can imagine that we're undoing mr. garcia's actions.

So, we can start by 'unpacking' mr garcia's bags

we know that each of the nine bags had 1/4 kilograms, so we can multiply 1/4 by 9 to find the collective mass packed into bags

(remember, multiplication is repeated addition. we could also add 1/4 + 1/4 + 1/4... nine times, but this would take a while)

so,

1/4  x 9 = 9/4

(9 = 9/1 [if that is how you're used to multiplying a fraction])

Then, he also sold 2 3/4 kilograms

so, we can add 2 3/4 + 9/4 to find the total mass of the blueberries at first

2 3/4 + 9/4 =  2 + 12/4

(12/4 = 3)

2 + 3 = 5

So, Mr. Garcia had 5 kilograms of blueberries at first

Based on the filing status and the taxable income, the tax for the following people are:

Based on the tax table, a single in the $80,600 - $80,650 bracket should pay $15,950.

A head of household in the $83,550 to $83,600 bracket would pay $15,216 and a married flling jointly in the $77,750 to $77,800 would pay $11,031.

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The half life of the substance is 6.92 days.

Half life can be defined as the time required to reduce the concentration to half of its initial value.

Here the equation given is

[tex]\rm N = N_o e^{-kt}[/tex]

The concentration will reduce to half therefore

[tex]\rm N= \dfrac{N_o}{2}[/tex]

so,

[tex]\rm 39/2 = 39 e^{- 0.1001 * t_{1/2}}[/tex]

ln 0.5 = - 0.1001 * t(1/2)

-0.693 = -.1001 * t(1/2)

t(1/2) = 6.92 days.

Therefore the half life of the substance is 6.92 days.

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Answer:

The minivan must keep a thrust of 496.79 pounds from rolling down the hill while the perpendicular force to the hill would be 5678.31 pounds. The picture illustrates the solutions to the problem.

The magnitude of the force parallel and perpendicular to the hill will be 496.79 pounds and 5678.31 pounds, respectively.

The quantity which has magnitude, direction, and follows the law of vector addition is called a vector.

A minivan with a gross load of 5700 pounds is stopped on a road with a slant of 5°.

Balance the force along the hill. Then the value of the force is given as,

F = W sin θ

F = 5700 x sin 5°

F = 5700 x 0.087

F = 496.79 pounds

The magnitude of the force perpendicular to the hill will be given as,

N = W cos θ

N = 5700 x cos 5°

N = 5700 x 0.9962

N = 5678.31 pounds

The magnitude of the force parallel and perpendicular to the hill will be 496.79 pounds and 5678.31 pounds, respectively.

The diagram is given below.

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Answer :

Step-by-step explanation :

We have been provided with the volume of water tank , it's length and breadth. We are asked to calculate the depth of tank (height), so we all know that water tank is always is in the shape of cuboid.

We would be using the formula of calculating the volume of cuboid and substitute the values in it.

Here,

We have :

Substituting the values :

>> 396 = 7.2 × 5.5 × h

>> 396 = (72 / 10) × (55 / 10) × h

>> 396 = 72 × 55 × h / 100

>> 396 = 3960 × h / 100

>> 396 × 100 = 3960 × h

>> 39600 = 3960h

>> h = 39600 / 3960

>> h = 3960 / 396

>> h = 10

__________________________

If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set

[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]

and as a type II region,

[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]

where we solve y = √(x + 1) for x to get x as a function of y.

A. The area of the type I region is

[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]

B. The area of the type II region is of course also

[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]

I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).

Answer:

the solution is (7,-1)

Step-by-step explanation:

if you dont trust your boy look below

4x + 8(-2x+13)=20

4x -16x + 104 = 20

-12x + 104 *-104* = 20 -104

-12x/-12 = -84/-12

x = 7

y = -2(7) + 13

y = -14 + 13

y = -1