Without graphing, what are the vertex , axis of symmetry, and transformations of the parent function? Y - |8x-3| - 3

Answers

Answer 1

Given:

Consider the given function is

[tex]y=|8x-3|-3[/tex]

To find:

The vertex , axis of symmetry, and transformations of the parent function?

Solution:

We have,

[tex]y=|8x-3|-3[/tex]

[tex]y=\left|8\left(x-\dfrac{3}{8}\right)\right|-3[/tex]

[tex]y=8\left|x-\dfrac{3}{8}\right|-3[/tex]      ...(i)

It is an absolute function.

The vertex form of an absolute function is

[tex]y=a|x-h|+k[/tex]       ...(ii)

where, a is a constant, (h,k) is vertex and x=h is axis of symmetry.

From (i) and (ii), we get

[tex]a=8,h=\dfrac{3}{8},k=-3[/tex]

So,

[tex]\text{Vertex}:(h,k)=\left(\dfrac{3}{8},-3\right)[/tex]

[tex]\text{Axis of symmetry}:x=\dfrac{3}{8}[/tex]

Parent function of an absolute function is

[tex]y=|x|[/tex]

Since, a=8 therefore, parent function vertically stretched by factor 8.

[tex]h=\dfrac{3}{8}>0[/tex], so the function shifts [tex]\dfrac{3}{8}[/tex] unit right.

k=-3<0, so the function shifts 3 units down.

Therefore, the vertex is [tex]\left(\dfrac{3}{8},-3\right)[/tex] and Axis of symmetry is [tex]x=\dfrac{3}{8}[/tex]. The parent function vertically stretched by factor 8, shifts [tex]\dfrac{3}{8}[/tex] unit right and  3 units down.


Related Questions

what is 9x minus 7= 65 what is x

Answers

Answer:

8

Step-by-step explanation:

First, you add the 7 to both sides. Then you divide both sides by 9. This gets you left with x by its self on one side. x = 8

Answer:

x=8

Step-by-step explanation:

x=8 because if you add 65 and 7 you get 72 and when you divide it by 9 you get 8.

HELP54465745653475vccbxdsztgfghdcdx

Answers

Answer:

Solution is invalid

Step-by-step explanation:

Let the time when they will have the same water content be x hours

At x hours;

For the first tank, the content will be;

50 + 10x

For the second;

29 + 3x

Equating both, will give us x

29 + 3x = 50 + 10x

We will get x as a negative number here

Since number of hours can not be negative, the solution is invalid

A slow boat to china travels at a constant speed of 17.25 miles per hour for 200 hours. how far was the voyage?​

Answers

Answer:

3450 miles

Step-by-step explanation:

Multiply the number 17.25 by 200 since the boat is traveling for 200 hours and each hour is 17.25 miles to get 3450 miles which is your answer.

Answer:

[tex]\boxed {\boxed {\sf 3,450 \ miles}}[/tex]

Step-by-step explanation:

Distance can be found by multiply the speed by the time.

[tex]d=st[/tex]

Where d is the distance, s is the speed, and t is the time.

1. Define Variables

The speed is 17.25 miles per hour and the time is 200 hours.

[tex]s= 17.25 \ mi/hr[/tex]

[tex]t= 200 \ hr[/tex]

2. Calculate Speed

Substitute the values into the formula.

[tex]d=17.25 \ mi/hr * 200 \ hr[/tex]

Multiply. The hours (hr) will cancel each other out and leave miles as the units.

[tex]d=17.25 \ mi *200\\[/tex]

[tex]d=3450 \ mi[/tex]

The voyage was 3,450 miles


The value of
+40.01 is much less than 1.
Select one:
04
40
4000
Submit Answer

Answers

Answer:

1. The value 40÷40.01 is close to 1.

2. The value 4÷40.01 is much less than 1.

3. The value 4000÷40.01 is greater than 1.

Step by step explanation:

The given numbers are 4, 40 and 4000.

Divide each number 4, 40 and 4000 by 40.01

 The value __40___÷40.01 is close to 1.

The value __4___÷40.01 is much less than 1

The value __4000___÷40.01 is greater than 1.

 

simplify
[tex] \sqrt{ - 3} \sqrt{ - 12} [/tex]
please help me I've been stuck on this for ever​

Answers

Answer:

36

Step-by-step explanation:

the square root of any negative value results in an imaginary number, 'i'

so, [tex]\sqrt{-3}[/tex] = 3i and [tex]\sqrt{-12}[/tex] is 12i

'i' is equal to -1

3(-1) x 12(-1) = 36

What is 1/5 times 24 as a estimate?

Answers

Answer:

1/5 times 24 is 24 1's, so we will divided 24 by 5, but since were estimating it will be 25/5 and we will get 5. That means 1/5 times 24 as an estimate will be 5. Hoped I helped!

Step-by-step explanation:

If it’s not correct sorry

in an 7th grade class with 80 people, seven tenths of the students wore shorts, how many students wore shorts

Answers

Answer:

56

Step-by-step explanation:

80 x (7 / 10) = 56

80 times 7=560

560/10=56

Answer: 56

Cindy works in a cake shop and earns $42 per day. She earns an extra $4 for each cake she sells. If Cindy wants to earn at least $50 per day, which inequality shows the minimum number of cakes, n, that she should sell?

42 + 4n ≤ 50, so n ≤ 2
42 + 4n ≥ 50, so n ≥ 4
42 + 4n ≥ 50, so n ≥ 2
42 + 4n ≤ 50, so n ≤ 4

Answers

Answer:

Step-by-step explanation:

42+4n<50, so n<4

Answer:

42+4n ≥ 50, so n ≥ 2

If the two factors (below, not the picture tho) 6 and 10,000,000 make 60,000,000 what is the second factor is the equation?

Answers

Answer:

It's 6 to the power of 7

Step-by-step explanation:

60,000,000

There are 7 zeros

Please help ASAP I hate maths and am so confused

Answers

Answer:

90 i think im sorry if its wrong

Step-by-step explanation:

Determine whether the inverse of f(x)=2x2−5
is a function. Then find the inverse.

Answers

Answer:

Not a function. The inverse is

[tex]y = \sqrt{ \frac{x + 5}{2} } [/tex]

and

[tex]y = - \sqrt{ \frac{x + 5}{2} } [/tex]

Step-by-step explanation:

Any even-degree polynomial functions that are inverted will not be a function.

[tex]f(x) = 2 {x}^{2} - 5[/tex]

Let y = f(x)

[tex] y = 2 {x}^{2} - 5[/tex]

To proceed the inverse, swap the x-term and y-term.

[tex]x = 2 {y}^{2} - 5[/tex]

Convert into function form.

[tex]x + 5 = 2 {y}^{2} \\ 2 {y}^{2} = x + 5 \\ {y}^{2} = \frac{x +5 }{2} [/tex]

The reason why inverted even-degree polynomial function cannot be a function because the inverse graph doesn't pass line test.

Thus the answer is

[tex]y = \sqrt{ \frac{x + 5}{2} } \\ y = - \sqrt{ \frac{x + 5}{2} } [/tex]

Kennedy got money for her birthday. She spent half of her money on a blanket, $74 on a jacket, $36 for a pair of shoes, and had $47 left after shopping. How much money did Kennedy get for her birthday?

A. $157
B. $214
C. $304
D. $314

Answers

The correct answer would be C :)
she received $157 , the answer is a

72 equals 83 decreased by a number

Answers

Answer:

83 - x = 72

x= 11 (if you need it)

Step-by-step explanation:

You wanted an expression, correct?

List two numbers that are between the two given numbers:
2 3/5 and 2 7/10

Answers

Answer:

There are many choices, but one answer is 2 3.1/5 and 2 3.2/5.

Step-by-step explanation:

These are equivalent to 2 6.2/10 and 2 6.4/10 which is between both.

(pls mark as brainliest!)

which is greater -12/6 or -9/3​

Answers

Answer:  -9/3

Step-by-step expla

-9/3 is the correct answer

The New England Revolutions are having a charity soccer event for which tickets cost $18 per person. However, the ticket agency adds a fixed fee to every order so a person who orders 5 tickets pays $93.

Answers

Let as consider, we need to find the fixed fee.

Given:

Cost of each ticket = $18

Number of tickets = 5

Total cost = $93

To find:

The fixed fee.

Solution:

Let x be the fixed fee..

Cost of 1 ticket = $18

Cost of 5 ticket = $(5 × 18)

                         = $90

Total cost 5 tickets = Fixed fee + Cost of 5 tickets

[tex]93=x+90[/tex]

[tex]93-90=x[/tex]

[tex]3=x[/tex]

Therefore, the fixed fee is $3.

Find the 13Th term of geometric sequence 1,2,4,

Answers

Answer:

a₁₃ = 4096

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then

a₁₃ = 1 × [tex]2^{12}[/tex] = 4096

Please help me I’m so confused

Answers

Answer:

60

Step-by-step explanation

Okay, uh... this is gonna be confusing to explain.

So a hexagon's angles add up to 720. This means, we can find each angle's supplementary angle by subtracting each value we know away from the total.

So, we know the inside angle of angle 6 is 90.

So: 720-90=630

Now, typically, you would divide by the remaining angles, but we have basically 2 angles of different values since 1, 2, and 3 are equal, and 4 and 5 are equal.

However, we know that 1, 2, and 3 are 10 degrees less than 4 and 5. So if we "add" 10 degrees to each of those angles we get:

10*3=30

630-30=600

Now we made it as though each angle (1-5) is equal. So now we divide by 5.

600/5=120

This means the supplementary of angles 4 and 5 is 120, so we subtract that value from 180 since a straight angle is 180.

180-120=60

Now, to check this we reverse it.

(120*2)+(120*3)+(10*3)+(90)=

240+360+30+90=

600+30+90=

600+120=

720.

Um... I think this is it?? Your school is scary :o

A car travels about 25 miles on 1 gallon of gas. About how far can the car travel on 8 gallons of gas?

Answers

The answer is
8x25 = 200 miles

3(x+5/3) ...........................

Answers

Answer: if your asking to simplify then the answer is

3x+5

Step-by-step explanation:

expand 3a(2b+c) .............​

Answers

Answer:

We know that the distributive property says this:

a(b+c) = ab + ac

If we apply this to our case, we can put

3a(2b+c) = 3a * 2b + 3a * c

When we multiply numbers and letters, we should multiply both of them:

3a * 2b + 3a * c = 3*2*a*b + 3*a*c = 6ab +3ac

We can use this when we find a number multiplied by a parenthesis..

Answer:

6ab + 3ac

Step-by-step explanation:

3a(2b) + 3a(c)

6ab + 3ac

Mai owes the bank $60. She gets $85 for her birthday and deposits it into her account. How much does she now have in the bank?
a
$25
b
-$25
c
$145
d
-$145

Answers

Mai now has $25 in the bank
The answer is A. Mai has $25 in her bank account.

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=−16x^{2} + 157x+104

Answers

Can you send a picture of it? Then maybe I can help you answer it.

I WILL MARK BRAINEST!!! Someone please help me please!!! I rly need help with question 4, my friend and I both don’t understand it and is it okay if you could explain? Thanks!

Answers

Answer:

The original number is (i)

The whole amount is (ii)

Step-by-step explanation:

So when finding a number in a percent you wanna see how much that percent will go into that number. So like if I said how many times does 60% go into 200 you would have to see how many times the number 200 would go into 60%. does this make sense? If so this is how you can find your answer.

Sorry if I'm wrong I hope you get this right!! Stay beautiful ❤️

Will give Brainliest!! This graph models the number of teachers assigned to a school, as determined by the number of students. What is the constant of proportionality? Number of Teachers A line graph titled Number of Teachers has number of students on the x-axis, and number of teachers on the y-axis. For every 60 students, there are 4 teachers; 120, 8. StartFraction 1 over 25 EndFraction StartFraction 1 over 20 EndFraction StartFraction 1 over 15 EndFraction StartFraction 1 over 10

Answers

Answer:

b

Step-by-step explanation:

rude people delete meh answers

rude the answer is b

thank u very much now i must b on my way

Answer:

Its B

Step-by-step explanation:

Because the first one is correct give the credit to her.

20 points for simple math

Answers

Answer:

128

Step-by-step explanation:

Answer:

Verticle     x=128°

Step-by-step explanation:

A vertical angle is each of the pairs of opposite angles made by two intersecting lines.

And vertical angles are congruent so x = 128° as well!

Hope this helps!

3x + 7y = 2 6x-5y=4 solve this by elimination method

Answers

Answer:

x=2/3, y=0

Step-by-step explanation:

3x + 7y = 2,

6x - 5y = 4

Make the x coefficient the same in both equations.

3x + 7y = 2

(whole thing multiplied by 2)

6x + 14y = 4

Now subtract the equations to eliminate the x variable.

 6x + 14y = 4

-(6x - 5y   = 4)

        19y  = 0

           y = 0

Substitute 0 for y in one of the equations.

3x + 7(0) = 2

         3x = 2

           x = 2/3

Answer:

well your equation has 2 equal signs in it but imma take a guess and say the first one is supposed to be a plus sign so

Step-by-step explanation:

here's ur answer

x= −2 /29y+4/29

a movie is advertised to last 2 1/3 hours. Of this time, 1/4 is used for showing previews. How long long is the actual movie?

Answers

Answer:

The movie is actually 3/28 hours.

Step-by-step explanation:

1

4

÷

2 1

3

=

1

4

÷

7

3

=

1

4

×

3

7

=

1 × 3

4 × 7

=

3

28

Write the expression as a single natural logarithm. 3 In m + 4 Inn​

Answers

Answer:

[tex] ln( {m}^{3} {n}^{4} )[/tex]

Step-by-step explanation:

[tex] \alpha ln(x) = ln( {x}^{ \alpha } ) [/tex]

[tex] ln( {m}^{3} ) + ln( {n}^{4} ) [/tex]

[tex] ln(a) + ln(b) = ln(ab) [/tex]

[tex] ln( {m}^{3} {n}^{4} ) [/tex]

Answer:

Step-by-step explanation:

ln(m^3*n^4)

We should check this out to see if it works.

Givens

m = 2

n = 3

3 ln(2) = 3*0.6931 = 2.0794

4*ln(3) = 4*1.0986 = 4.3944

Add                          6.4738

Check Answer

ln(2^3*3^4)

ln(8*81)

ln(648)

6.4738                  Just as it should be

Write the following algebraically, using x as your
Own.
"I think of a number, take away 1 and multiply the result by 3.".

Answers

Answer:

(X - 1)3

Step-by-step explanation:

I’m not so sure but this is the best I can do. If this helps, pls give brainliest.

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