Mathematics High School

If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor of 5, what is the equation of the new function?

A. g(x) = (5x)2
B. g(x) = x2
C. g(x) = 5x2
D. g(x) = (x)2

Answers

Answer 1

Answer:

g(x)= (1/5x) ^2

Step-by-step explanation:

Just did the test got a 100.

Answer 2

The function f(x) = x² after stretching horizontally by a factor of 5 will be g(x) = [(1/5)x]² so none of the given option are correct.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

If we streatch a function f(x) horizontally by factor of c then the value of new function g(x) become f(x/c)

By stretching f(x) by 5 it will  be

g(x) = f(x/5)

So replace x → x/5

Since,f(x) = x²

So,

g(x) = (x/5)²

Hence "The function f(x) = x² after stretching horizontally by a factor of 5 will be g(x) = [(1/5)x]²".

For more about the function,

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Related Questions

What is the remainder when 4x4 − 10x3 + 14x2 + 7x − 19 is divided by 2x − 1

Answers

Using long division, we have


        ___________________
2x-1 | 4x^4-10x³+14x²+7x-19

Next, we divide the first term of 2x-1 by the first term of 4x^4-10x³+14x²+7x-19 to get 4x^4/2x=2x³ (since 4/2=2 and to divide exponents you subtract the denominator from the numerator). Next, we put our 2x³ on the top and multiply (2x-1) by that. With the result of (2x-1) and 2x³, we multiply that by -1 and add it to 4x^4-10x³+14x²+7x-19, looking like


        2x³
        ___________________
2x-1 | 4x^4-10x³+14x²+7x-19

       - (4x^4-2x³)
         ____________________
                  -8x³+14x²+7x-19. Repeating the process, we get


        2x³-4x²+5x+6
        ___________________
2x-1 | 4x^4-10x³+14x²+7x-19

       - (4x^4-2x³)
         ____________________
                  -8x³+14x²+7x-19. 
                  -(-8x³+4x²)
       ______________________
                         10x²+7x-19
                        -(10x²-5x)
                        __________
                                 12x-19
                               -(12x-6)
                              _________
                                       -13 as our remainder


The remainder when [tex]4x^4 - 10x^3 + 14x^2 + 7x - 19[/tex] is divided by 2x − 1 is -13.

The given expressions are [tex]4x^4 - 10x^3 + 14x^2 + 7x - 19[/tex] and 2x-1.

What is the remainder?

The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.

The division of the given expressions are given below:

           2x³-4x²+5x+6

       ___________________

2x-1 | [tex]4x^4 - 10x^3 + 14x^2 + 7x - 19[/tex]

      - ([tex]4x^4-2x^3[/tex])

     ____________________

                 -8x³+14x²+7x-19.

               -(-8x³+4x²)

      ______________________

                        10x²+7x-19

                      -(10x²-5x)

                       __________

                                12x-19

                               -(12x-6)

                             _________

                                      -13

Therefore, the remainder when [tex]4x^4 - 10x^3 + 14x^2 + 7x - 19[/tex] is divided by 2x − 1 is -13.

To learn more about the algebraic expressions visit:

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Find a) the GCM (Greatest Common Multiple) and b) the LCM (lowest common multiple:
x²- 3x + 2; x²- 4x + 4

Answers

I assume you mean to find (a) the GCF (greatest common factor) and (b) the least common multiple LCM.

To do both parts, you need ot factor the polynomials.

x^2 - 3x + 2 = (x - 2)(x - 1)
x^2 - 4x + 4 = (x - 2)(x - 2) = (x - 2)^2

(a) GCF: use only common factors with lower exponent.

The GCF is x - 2

(b) LCM: use common and not common factors with the larger exponent.

The LCM is (x - 2)^2(x - 1)

Please Help Me Anyone !!!
Addison earned a gross income of $42,750 last year. She made $537.56 in IRA contributions, donated $918 to her favorite charity and paid $1,351.35 in home mortgage interest. If Addison claims a standard deduction of $5,700 and her exemption is $3,650, what is her taxable income?
$30,593.09
$36,293.09
$31,511.09
$32,862.44

Answers

subtract all the other numbers from 42,750, you get 30,593.09
so A is the answer

Answer:

The answer is: $ 30,593.09.

Step-by-step explanation:

To the gross income of $ 42,750 of Addison, the amounts of the payments made must be deducted, that is, $ 537.56, $ 918, $ 1,351.35, plus the exemption of $ 3,650, and also if they grant him the standard deduction of $ 5,700; Your taxable income would be: $ 42,750 - ($ 537.56 + $ 918 + $ 1,351.35 + $ 3,650 + $ 5,700) = $ 30,593.09

The answer is: $ 30,593.09.

You can use a minus sign to make a negative number like -2. what happens if you put a plus sign before a number? what about 2++2?

Answers

Final answer:

A plus sign before a number does not change its value. In the expression 2++2, the two plus signs next to each other are interpreted as a positive number followed by another positive number.

Explanation:

When you put a plus sign before a number, it doesn't change the value of the number.

The plus sign is just a symbol to indicate that the number is positive.

In the expression 2++2, the two plus signs next to each other are not a valid mathematical operation.

Instead, it is interpreted as a positive number followed by another positive number.

So, 2++2 is equal to 2+2, which is 4.

How many sides of a polygon have if the sum of the measures of its angle is 2880?

Answers

Using the sum of interior angles formula; 

(n-2)×180=sum
(n-2)×180=2880 
n-2=2880/180 
n-2=16 
n=16+2 
n=18 

Therefore, this polygon would have 18 sides. 

Hope I helped :) 

3 different problems, sorry these type confuse me

f(x) = 5x - 1 and g(x) = 6x, find f(g(x))

f(x) = 5x - 1 and g(x) = 6x, find g(f(x))

f(x) = 5x - 1 and g(x) = 6x, find g(f(2))

Answers

f [g(x)]
= 5(6x) - 1
= 30x - 1

g [f(x)]
= 6(5x - 1)
= 30x - 6

g [f (2)]
= 6 [5(2) - 1]
= 6 (10 - 1)
= 60 - 6
=54

The price of an item has been reduced by 55% . The original price was $80 . What is the price of the item now?

Answers

80×(1-55%)
=$36
the price of the item is $36 now

Mentally estimate the total cost of items that have the following prices 1.85 $ .98 $3.49 $9.78 and $6.18 round off your answer to the nearest half dollar

Answers

The total cost is $22.28, rounded to the nearest half dollar is $22.50.

Final answer:

To estimate the total cost, each item's price is rounded to the nearest half dollar: $1.85 to $2.00, $0.98 to $1.00, $3.49 to $3.50, $9.78 to $10.00, $6.18 to $6.00. Summing the rounded figures, the estimated total is $22.50.

Explanation:

To mentally estimate the total cost of the items, we round each item's price to the nearest half dollar and then add them up.

Item 1: $1.85 rounds to $2.00Item 2: $0.98 rounds to $1.00Item 3: $3.49 rounds to $3.50Item 4: $9.78 rounds to $10.00Item 5: $6.18 rounds to $6.00

Adding up the rounded figures gives us: $2.00 + $1.00 + $3.50 + $10.00 + $6.00, which equals $22.50. Thus, the estimated total cost of the items is $22.50, rounded to the nearest half dollar.

The cost of a pair of jeans was changed from $78 to $68.64. What was the percent change?

Answers

Answer:

-12.00%

Step-by-step explanation:

;)

Answer:

12% decrease

Step-by-step explanation:

The base of a cube is parallel to the horizon. If the cube is cut by a plane to form a cross section, under what circumstance would it be possible for the cross section be a non-rectangular parallelogram?

Answers

The cross-section of a cube can be a non-rectangular parallelogram when the cutting plane is not perpendicular to the cube's base.

The scenario where a cube's cross-section can be a non-rectangular parallelogram occurs when the cutting plane is at an angle other than a right angle to the cube's base. This results in a parallelogram that is not a rectangle, as the cutting plane affects the shape of the cross-section.

When the cutting plane deviates from being perpendicular to the base of the cube, it creates a cross-section that is not a rectangle but can be a parallelogram with unequal angles and sides.

Understanding the geometric implications of the cutting plane's orientation is crucial in visualizing how the cube's cross-section can vary from a rectangular shape to a non-rectangular parallelogram.

The region bounded by the given curve is rotated about the specified axis. Find the volume V of the resulting solid by any method. x2 + (y − 4)2 = 16;    about the y-axis

Answers

[tex]\bf x^2+(y-4)^2=16\implies x^2=16-(y-4)^2 \\\\\\ x=\sqrt{16-(y-4)^2}\implies x=\sqrt{16-(y^2-8y+16)} \\\\\\ x=\sqrt{8y-y^2}\\\\ -------------------------------\\\\ 0=\sqrt{8y-y^2}\implies 0=8y-y^2\implies 0=y(8-y) \implies y= \begin{cases} 0\\ 8 \end{cases}\\\\ -------------------------------\\\\ \displaystyle \stackrel{\textit{disk method}}{\int\limits_{0}^8~\pi (\sqrt{8y-y^2})^2\cdot dy}\implies \pi \int\limits_{0}^8~ 8y-y^2\cdot dy[/tex]

[tex]\bf \displaystyle \pi \int\limits_{0}^8~8y\cdot dy - \pi \int\limits_{0}^8~y^2\cdot dy\implies \pi \left[ 4y^2~-~\cfrac{y^3}{3} \right]_{0}^8 \\\\\\ \pi \left[ \left[ 256-\cfrac{51}{3} \right]~-~[0] \right]\implies \pi \cdot \cfrac{256}{3}\implies \cfrac{256\pi }{3}\implies 85\frac{\pi }{3}[/tex]

Sandy had 161 dollars to spend on 9 books. After buying them she had 17 dollars. How much did each book cost

Answers

Each book costs $16.00.

What is the area of the figure. Show your work.

Answers

This is a 45-45-90 triangle.
The ratio of the sides is
1: 1: sqrt(2)

The legs have length (24 ft)/(sqrt(2)

The legs are the base and height.

A = bh/2 = [(24 ft)/(sqrt(2)) * (24 ft)/(sqrt(2))]/2 = [(576 ft^2)/2]/2

A = 144 ft^2

A total of 697 tickets were sold for the school play. They were either adult tickets or student tickets. There were 53 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

Let x = number of adult tickets sold
Let x-53 = number of student tickets sold

x + x -53 = 697
2x - 53 = 697. 

Add 53 to both sides to get:

2x = 750

Divide both sides by 2 to get:

x = 375

375 adult tickets were sold. 

The ages of the members of a family are 46, 48, 21, 12, 15, and 8. what is the mean age?

Answers

mean means to average. in order to average, add all the numbers then divide by how many numbers you have.

All these ages add up to 150. because there are 7 ages, divide by 7. this is 21.4 which can be rounded to about 21

46 + 48 + 21 + 12 + 15 + 8 = 150
150 ÷ 7= 21.4285 = 21

The mean age of the family members (46, 48, 21, 12, 15, and 8) is calculated by adding all the ages to get a sum of 150, and then dividing by the number of family members, which is 6, resulting in a mean age of 25 years old.

To calculate the mean age of the family members, you add up all of the ages and then divide by the number of family members. The ages given are 46, 48, 21, 12, 15, and 8. Let's find their sum:

Add the ages together: 46 + 48 + 21 + 12 + 15 + 8 = 150.

Count the number of family members, which is 6.

Divide the total sum of ages by the number of family members: 150 \/ 6 = 25.

Therefore, the mean age of the family members is 25 years old.

Which is correct regarding the statement: “If x is an odd integer, then the median of x, x + 2, x + 6, and x + 10 is an odd number”

Answers

any odd number can be represened as 2n+1 where n is a whole number

the median is the  number in the middle when the numbers are arranged in increasing order
if there are an even number of numbers in the set, take the average of the middle 2


we have x,x+2,x+6,x+10
there are 4 numbers, so the median will be the avergage between x+2 and x+6 which is [tex]\frac{x+2+x+6}{2}=\frac{2x+8}{2}=x+4[/tex]
now, if x is odd, then replace x with 2n+1

(2n+1)+4=
2n+1+4=
2n+5=
2n+2(1)+1
even+even+odd=odd
the statement is true
x is odd
x+2 is also odd (eg: x = 3, so x+2 = 3+2 = 5)
x+6 is also odd for similar reasons above
x+10 is also odd

We have four values. The median is found in the middle, so exactly halfway between x+2 and x+6

Add up x+2 and x+6 to get
(x+2)+(x+6) = 2x+8

Then divide that result by 2. In other words, divide everything by 2
2x/2+8/2 = x+4

The result x+4 is odd since adding any even number to an odd number is going to result in an odd value

So the claim is true

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

Alternative method:
x is odd so x = 2k+1 where k is any integer
x+2 = 2k+1+2 = 2k+3
x+6 = 2k+1+6 = 2k+7
x+10 = 2k+1+10 = 2k+11

Add up the two middle terms
(x+2)+(x+6) = (2k+3)+(2k+7) = 4k+10

Divide that result in half
4k+10 ---> 4k/2 + 10/2 = 2k+5 = 2k+4+1 = 2(k+2)+1

The expression 2(k+2)+1 fits the form 2m+1 where m = k+2 is an integer

So 2(k+2)+1 is odd making the median to be odd. 

This further helps support why the claim is true

What is the simplified form of the following expression square root 1/121
A 2/121
B 1/242
C 11
D 1/11

Answers

When you multiply a fraction, you do the top and the bottom separately, right?

Since a square root is like the opposite of multiplying, you can think of the top and the bottom separately for this too!

First, let's start with the top. The square root of 1 is 1, so the numerator is 1.

Now, let's do the bottom. The square root of 121 is 11, so the denominator is 11.

So, the answer is D, 1/11. You can check your answer by squaring it, and getting 1/121.

Hope this helps!

If their food and beverages cost $25.30 and there is an 8% meals tax

Answers

Hey there,
Tax = 8% x $23.50 
       = $18.80
End cost = $25.30 + $18.30
               = $44.10

Hope this helps :))

~Top

Answer:

Then they'll pay $27.32

Step-by-step explanation:

In order to determine this, start by multiplying the cost of the meal by the tax amount.

25.30 * 8% = 2.02

Now add the tax to the meal cost

25.30 + 2.02 = 27.32

A newspaper carrier can deliver 49 papers in one hour at this rate how many newspaper can the carrier deliver in 3 hours

Answers

The newspaper carrier can deliver 147 newspapers in 3 hours
You would multiply the time by how many newspapers he can deliver. He can deliver 147 in 3 hours. Hope this helps

Have a nice day.

Find an equation of the line l that contains the points left parenthesis 0 comma 0 right parenthesis(0,0) and left parenthesis 3 comma 2 right parenthesis .

Answers

10 out of 10 need ponits please

HOW CAN I SOLVE IT u=2x-2 for x

Answers

u = 2x - 2

We simply need to isolate x :) That just means that we need to get x onto it's own side of the equal sign.

So, add 2 to both sides.

2 + u = 2x

Then, divide both sides by 2.

2 + u ÷ 2 = 2x ÷ 2

Simplify.

1 + u/2 = x 

So, x = 1/2u + 1

~Hope I helped!~ :)
First, you have to isolate 2x in the first step to solving for x, so you would add 2 to both sides. This would look like this: u+2=2x.
Then, divide both sides by 2 to fully isolate x. This would give you an answer of u+2/2 = x. 

What is the sum of the solution of 2lx-1l-4=-2

Answers

The sum of the two solutions is 4+0 or 4.

Point M and N are midpoints of AB and DA respectively.
Complete the following table to prove triangle CDN ≅ triangle CBM
For the last reason choose from: SSS, SAS, or ASA.
*image attached below*

|
Statement | Reason
line DC ≅ _____ | The sides of a square are congruent.
line BM ≅ _____ | They are both half the length of a side of the square.
angle _____ ≅ angle B | All the angles of a square are congruent.
triangle CDN ≅ CBM | ____________________________________
|

Answers

triangle CDN ≅ triangle CBM

Statement | Reason
line DC ≅ __BC___ | The sides of a square are congruent.
line BM ≅ __DN___ | They are both half the length of a side of the square.
angle __D___ ≅ angle B | All the angles of a square are congruent.
triangle CDN ≅ CBM | 
by
SAS

Answer:

triangle CDN ≅ triangle CBM

Statement | Reason

line DC ≅ __BC___ | The sides of a square are congruent.

line BM ≅ __DN___ | They are both half the length of a side of the square.

angle __D___ ≅ angle B | All the angles of a square are congruent.

triangle CDN ≅ CBM |  

by

SAS

Step-by-step explanation:

Your Turn: In the diagram, AB = 12, BX = 2.5, and DX = 5. Find CD. Show all work. *

Answers

CD = 24 Triangles ABX and CDX are similar triangles. So the ratio of lengths between corresponding legs of the triangles will have the same value. You know that they're similar triangles because both of them are right triangles (so you know that one angle is the same in both) and that arc draw on both angles AXB and CXD indicate that those angles match as well. That tells you there's a second angle that's matching in both triangles, and because two of the angles match, you also know that the unmarked angle matches as well since all the angles in a triangle have to add up to 180 degrees. So you know that AB/CD = BX/DX. Substitute known values and you get AB/CD = BX/DX 12/CD = 2.5/5 Now solve for CD 12/CD = 2.5/5 12/CD = 1/2 24/CD = 1 24 = 1 * CD 24 = CD So the value of CD is 24.

The table gives the numbers of teachers and students in grades 6 to 8 at Earhart Middle School. Grade Teachers Students 6 1 25 7 2 50 8 3 75 Which teacher-to-student ratio maintains the proportional relationship described in the table?

Answers

Rewriting the table:

Grade          Teachers           Students
    6                     1                        25
    7                     2                       50
    8                     3                       75

Grade 6 to 8 all maintained the same proportional relationship because for every one teacher, there's 25 students 

Which shape has congruent diagonals? Question options:
a rectangle
a parallelogram
a trapezoid

Answers

A rectangle has congruent diagonals.

Because some angles are more out than others in Parallelograms and trapezoids, their diagonals aren't congruent.

An equilateral triangle has a perimeter of 102 in. What is the length of each side of the triangle?

Answers

I think its 34.Since its equilateral, all sides have the same length. So if you divide 102 by 3 you should have your answer.

The homegrown Turkey farm is preparing their Thanksgiving shipment. In one container they can put 8 big turkey boxes or 10 small turkey boxes. They send 96 turkey boxes using more big boxes than small boxes. How many containers did they use?

Answers

They used 11 containers. 7 containers contained 56 big turkey boxes while 4 containers contained 40 small turkey boxes. 56 is the largest number which is divisible by 8 when deducting 96 by 10. This method ensured that all the containers are shipped at full capacity.

The correct answer is:

11 containers.

Explanation:

We want 96 boxes total. Each container can hold either 10 small boxes or 8 large boxes. To solve this, we want to subtract multiples of 10 from 96 until we have a number that is divisible by 8. This is because we cannot have a fraction of a container full of either big or small boxes.

96-10(1) = 96 - 10 = 86; this is not divisible by 8.

96-10(2) = 96 - 20 = 76; not divisible by 8.

96-10(3) = 96 - 30 = 66; not divisible by 8.

96-10(4) = 96 - 40 = 56; this is divisible by 8.

This means there are 4 containers of small boxes, for 4(10) = 40 boxes, and 56/8 = 7 containers of large boxes, for 56 boxes. This is a total of 4+7 = 11 boxes for our 40+56 = 96 boxes.

What is slope and how is it determine from a graph?

Answers

Pick two points on the line and determine their coordinates.Determine the difference in y-coordinates of these two points (rise).Determine the difference in x-coordinates for these two points (run).Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
Slope is Y= mx + b
rise over runexample y= 3x+2 
the three

Tia cuts a 4-meter 8-centimeter wire into 10 equal pieces.Marta cut a 540-centimeter wire into 9equal pieces. How much longer is one of Marta's wires than one of Tia's

Answers

 Tia's wire is 4 meter and 8 centimeter long which is  that is  408 centimeter long and it is divided in 10 pieces.
tia = 408/10 = 40.8 cm
 Tia's wire pieces are 40.8 cm long

 Marta's wire, it is 540 centimeter long and is divided into 9 pieces
marta = 540/9 = 60 cm
 Marta's wires are longer than Tia's
Marta's wire is 19.2 cm longer than tias  

60cm - 40.8cm= 19.2 cm 
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