Mathematics High School

y = (x2 - 2x + 1)
y = (x - 1)(x - 1)
Prove that the following functions are equivalent through algebraic and numerical proof

Answers

Answer 1

Answer:

see below

Step-by-step explanation:

y = (x² - 2x + 1)

y = (x - 1)(x - 1)

First, recognize that the first equation is fully simplified/expanded already.

Now, we should solve for the second equation.

FOIL the expressions: first–outer–inner–last

(x - 1)(x - 1)

F: x²

O: -x

I: -x

L: 1

Combine these terms.

x² - x - x + 1

x² - 2x + 1

Notice that this equation is identical to our first equation. Therefore, the functions are equivalent.

Hope this helps!

Answer 2

y = (x^2 - 2x + 1)

y = (x - 1)(x - 1)

Algebraic Proof

FOIL y = (x - 1)(x - 1)

y = (x - 1) (x -1 ) = x^2 -2x + 1

Done.

Numeric Proof

Let x = 1

y = x^2 - 2x + 1

y = (1)^2 - 2(1) + 1

y = 1 - 2 + 1

y = 2 + 2

y = 0

Let x be 1 again.

y = (x - 1)(x - 1)

y = (1 - 1)(1 - 1)

y = 0

There you have it. Both equations are the same.

Related Questions

- 2x+2y = -4
3х + Зу = -18
х =
y =

Answers

Answer: x= -2  y= -4

substitute the given values of x into the equation 3x+3y=-18

y substitute the given value of y into the equation x=2y

since all the equalities are true the ordered pair is the solution of the system

Element X is a radioactive isotope such that every 25 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 50 grams, how much of the element would remain after 23 years, to the nearest whole number?

Answers

50*(.5)^(23/25)=26.43

Answer: 26

Step-by-step explanation:

The correct answer is 26

Cora uses 6.2 pints of white paint and blue paint to paint her bedroom walls. 2 5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?

Answers

Answer:She used 3.72 pints of blue paints for the wall

Step-by-step explanation:

Total Quantity of Blue and white paint =6.2 pints

Quantity  of White paint =2/ 5 x 6.2 pints = 2.48 pints

Quantity of blue paint =Total Quantity -Quantity  of White paint

=6.2 pints-2.48 pints

=3.72 pints

Which of the following is the reciprocal of 7?

Answers

Answer:

1/7

Step-by-step explanation:

Answer:

Reciprocal of 7 is 7/1.

Graph f(x)=-(4)^x see the images I have attached. Those are the graphs I can choose from!
If you could provide an explanation that would be great. Thank you

Answers

Answer: it is the one your cursor is on

Step-by-step explanation:

I just put it in a calculator and it showed me

3. Seven teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. Now there are 77 players on the field. Write and solve an equation whose solution is the number of players on each team.

Answers

Answer: equation: 7(x-2) = 77

answer: x=9

Step-by-step explanation:

PLEASE HELP ASAP PLEASE​

Answers

Answer:

rectangular pyramid

Step-by-step explanation:

there's a rectangle at the bottom & the triangle is a pyramid

It’s a Triangular Pyramid

Simplify the expression.
2 + (​g​ + 5)

Answers

Answer is

7 +g

Step-by-step explanation:

2+5+g

=7+g

Answer:

g+7

Step-by-step explanation:

Have an amazing day!

In the right triangle below, the length of AC is 30. What is the length of AB?

Answers

Answer:

No image

Step-by-step explanation:

first to get it correct will get brainleist! :) ASAP

Answers

The answer to this question is B. U’(0,-1)
are the ones on the side the answers ??

1.) Ian needs to save at least $85.00 for a new pair of basketball shoes. He has $25.00 in his
piggy bank, and can save $12.00 from his allowance each week. How many weeks will
Ian need to save to earn at least $85.00?

Variable: _____________________
Inequality: ____________________
Solution: ______________________

Answers

Answer:

ian will need 5 weeks simply multiply 12×5 =60 then add the 25 bucks he has in his piggy bacnk

Solve for x. Round your answer to the nearest tenth. (one decimal place)

X=?? degrees

Answers

Answer:

Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15x = arctan (8/15)x = 28.1° (rounded)

Please help! I’ll mark you brainlist
Question: a relation is not a function when
A: an output is paired with input of zero
B: an input is paired with more than one output
C: an input is paired with an output of zero
D: an output is paired with more than one input

Answers

Answer:

B

Step-by-step explanation:

a relation is not a function when input value leads to two or more outputs

What is the mixed number of 2 1/5 and 5/9

Answers

Answer:

2 1/5 is the mixed number

Hope it helps!

:D

Which graph shows a dilation?

Answers

answer:

now correct me if i am wrong but i think that graph number one is the graph showing a dilation

now i totally forgot now to explain dilations in graphs but if you need anymore help, feel free to ask me!

hope this helps :)

The graph that shows a dilation is the graph on the left which is the 2nd option in the given figure.

A dilation is a transformation that changes the size of an object, but not its shape. The scale factor is a number that tells you how much the object is being enlarged or shrunk. A scale factor of 2 means that the object is being enlarged twice as large, while a scale factor of 0.5 means that the object is being shrunk to half its size.

The graph that shows a dilation is the graph on the left. The scale factor of the dilation is 2, so the object is being enlarged twice as large. The other two graphs do not show a dilation because the objects are being changed in shape.

The graph on the right shows a rotation of the square by 90 degrees. The graph in the middle shows a stretching of the square horizontally. Neither of these transformations are dilations because they change the shape of the object.

To learn more about graph here:

https://brainly.com/question/17267403

#SPJ2


Andre's phone is 11.5 cm long. How many millimeters is this?

Answers

Answer:

about 115 millimeters

Step-by-step explanation:

There will be 45 adults going to a museum. There will be twice as many students as adults. Adult tickets cost $25 each. Student tickets cost $12 each.

Part A: What is the total cost for students and adults?

Question 2
Part B: 10 more adults and 15 more students decide to attend the trip at the last minute. How much will cost increase?
Question 3
Part C: What is the total cost of the trip with the additional adults and students?

Answers

Answer:

=P

Step-by-step explanation:

Find the discounted price.
Light:$18:00 Discount:25%

Answers

The discounted price is $13.5. You do $18 and times it by 0.25. You will get 4.5. You then subtract the 4.5 from the $18 and you get $13.5

please help me i will give point and things? please help me i will give point and things?

Answers

it’s 49:36 if you multiply the dimensions by 6 and divide by the ratio

PLEASE HELPP Find the value of x. Assume that segments that appear to be tangent are tangent. Round your answer to the nearest tenth.

Answers

Answer:

5

Step-by-step explanation:

help me plssssssssssssssssss

Answers

Answer:

78.5

Step-by-step explanation:

Radius: 12.5

Circumference: 2 π r

Circumference: 2 π 12.5 = 78.54

Hope this helps!

Answer:  C ≈78.54

Step-by-step explanation:

C=2πr

C=2 π (12.5)

C=25π

C≈78.54

The diameter of a circle is 8 yards. What is the circle's circumference? Use 3.14 ​

Answers

[tex]\frac{3.14*8^2}{4} =\frac{200.96}{4} =50.24[/tex]

Answer:

25.13274 Yards

Step-by-step explanation:

C = 2pi times r

Circumference = 2pi times radius  

Find m
i’ll give brainlest

Answers

Answer:

its just a black picture

Step-by-step explanation:

Answer:

its in math

Step-by-step explanation:

Find 5 rational numbers between 3/5 and2/3​

Answers

Answer:

The 5 rational are 91/150 , 92/150 , 93/150 , 94/150 , 95/150

Step-by-step explanation:

We have to fine 5 rational numbers between

3/5 and 2/3

First we have to make the denominator same

3/5= 3/5 ×3/3 = 9/15 =9/15×10/10 =90/150

2/3 = 2/3×5/5 = 10/15 = 10/15×10/10 = 100/150

The 5 rational numbers are

91/150 , 92/150 , 93/150 , 94/150 , 95/150

hope this helps :)

Evaluate: six squared. Write the numerical answer only.

Answers

Answer:

36

Step-by-step explanation:

6 squared is basically 6 x 6

6x6 is 36

Answer:

36

Step-by-step explanation:

[tex]6^{2}[/tex]    broken down is 6x6

Please I need Help!!!!!

Answers

the height of the cylinder is 11.8

Answer:11.8

Step-by-step explanation:

A:29
B:38
C:43
D:81
help with this??​

Answers

I’m pretty sure it 81

What is the slope and y intercept of 3x = 9y-9

Answers

Answer:

y = 1/ 3 x − 1

Step-by-step explanation:

y intercept is -1 and slope is 1/3x

The slope and y-intercept will be [tex]\rm m=\frac{1}{3} \ and \ c=-1[/tex]. The slope and the intercept are found with the help of the standard equation;

What is the slope?

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The given linear equation in the problem is;

[tex]\rm 3x = 9y-9[/tex]

On dividing the whole equation  by 3 we will get;

[tex]\frac{1}{3} x=y-1 \\\\ y= \frac{1}{3} x+1[/tex]

Compare the equation with the standard equation;

[tex]\rm y = mx+c[/tex]

Where m is the slope and c is the intercept. After comparing we will get;

[tex]\rm m=\frac{1}{3} \\\\ c=-1[/tex]

Hence the slope and y-intercept will be [tex]\rm m=\frac{1}{3} \ and \ c=-1[/tex].

To learn more about the slope refer to the link;

https://brainly.com/question/3605446

The Rutgers University and Princeton University soccer teams scored goals in a
8:5 ratio. If Rutgers scored 24 goals this season, how many did Princeton University’s
soccer team score? Show ALL of your work and answer in a complete sentence.

Answers

I know the answer is that Princeton scores 15 goals but I don’t know how the work is supposed to be shown. I did it in my head. I multiplied both 8 and 5 by 3 so 8 would become 24(the goals Rutgers scored) and then you would find the number of goals Princeton scored. Sorry I couldn’t show the work but the answer is 15 goals.

Can someone help me with this. Will Mark brainliest. (Need work and explanation)

Answers

Answer:

GUESS: 55ft

Step-by-step explanation:

55 ft is my guess, not 100 percent sure but the math i did was 50% of 110

Answer:

84 ft

Step-by-step explanation:

The ground and the two ropes form a right triangle.

For the 50-deg angle, the height, h, is the opposite leg. The hypotenuse is the 110-ft side.

sin A = opp/hyp

sin 50° = h/110

h = 110 sin 50°

h = 84

Answer: 84 ft

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