Mr. Knotts found the difference of the following expression. Which statement is true about Mr. Knotts’s work?

StartFraction x Over x squared minus 1 EndFraction minus StartFraction 1 Over x minus 1 EndFraction

Step 1: StartFraction x Over (x + 1) (x minus 1) EndFraction minus StartFraction 1 Over x minus 1 EndFraction

Step 2: StartFraction x Over (x + 1) (x minus 1) EndFraction minus StartFraction 1 (x + 1) Over (x + 1) (x minus 1) EndFraction

Step 3: StartFraction x minus x + 1 Over (x + 1) (x minus 1) EndFraction

Step 4: StartFraction 1 Over (x + 1) (x minus 1) EndFraction
In step 1, he did not correctly factor the denominator.
In step 2, he did not use the correct common denominator.
In step 3, he did not distribute the negative sign when he subtracted.
In step 4, he did not correctly subtract the numerator.

Answers

Answer 1

Answer:

He did not distribute the negative sign when he subtracted.

Step-by-step explanation:

x-(x+1) is equal to a -1. He did not distribute the negative.

Answer 2

In third step, he did not distribute the negative sign when he subtracted. Then the correct option is C.

What is Algebra?

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Mr. Knotts found the difference of the following expression.

The expression is given below.

[tex]\rm \rightarrow \dfrac{x}{x^2-1} - \dfrac{1}{x -1}[/tex]

Then the first step of the expression will be

[tex]\rm \rightarrow \dfrac{x}{(x+1)(x-1)} - \dfrac{1}{x -1}[/tex]

The second step of the expression will be

[tex]\rm \rightarrow \dfrac{x}{(x+1)(x-1)} - \dfrac{1(x+1)}{(x+1)(x -1)}[/tex]

The third step of the expression will be

[tex]\rm \rightarrow \dfrac{x - (x +1)}{(x+1)(x-1)}\\\\\rm \rightarrow \dfrac{x - x -1}{(x+1)(x-1)}[/tex]

In third step, he did not distribute the negative sign when he subtracted.

Then the correct option is C.

More about the Algebra link is given below.

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Related Questions

help help!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

The first option, the mayor will lose by a large percentage.

Step-by-step explanation:

If you look at the numbers, You can see that the two best answers which are excellent and satisfactory are low, and in total equal 28.

Being compared to the lower ratings which are needs improvement and unsatisfactory are high, and in total equal 52.

Seeing this, this shows that the mayor will lose the election the with more than half of the people voting for someone else.

All the other options excluding the first one, say that he will win by a close call, a big percent, or a close call again.

which just leaves the first option saying that he will lose by large percent, which is true.

Fond the equation of the line shown

Answers

Answer:

y+-1/2x-1

Step-by-step explanation:

The line is negative

It rises one digit and runs 2

and it crosses though -1 on the y axis

There were 23 students running in a race. How many different arrangements of first, second, and third place are possible?

Answers

Answer:

10626 different arrangements

Step-by-step explanation:

As we have a total of 23 students and we want to form groups of 3, where the order of the 3 students matters, we can solve this problem using a permutation of 23 choose 3.

The formula for a permutation of n choose p is:

P(n,p) = n! / (n-p)!

So, using n = 23 and p = 3, we have:

P(23,3) = 23! / (23-3)! = 23! / 20! = 23 * 22 * 21 = 10626

So we have a total of 10626 different arrangements of first, second and third place.

Help me find the MAD volume please
How many sundaes are there?

Answers

Answer:

2

Step-by-step explanation:

8+12+4+8 = 32

32/4 = 8

8-8 = 0

12-8 = 4

8-4 = 4

8-8 = 0

4+4+0+0 = 8

8/4 = 2

A triangle has a base of x 1/2 m and a height of x 3/4 m. if the area of the triangle is 16 m^2, what are the base and the height of the triangle

Answers

Answer:

base = 6.4m

height = 5m

Step-by-step explanation:

Given area = 16m^2

3/4 -1/2 = 1/4  into something x 0.25 its size then add

We see that 2.5 is 10 multiplied. not relevant unless doing algebra

We also see that 0.5 is 0.25 x 2  not relevant unless doing algebra

We start with 5

16/5 = 3.2

if 5 is the height then 3.2 x 2 must be the base.

As we half base to find area so we change this value and reverse the area 1/2 above. 3.2 x 2 = 6.4m base.  and 5m height stays as it is.

If we did algebra

Then 1/2 = 0.5  = 4.5  

3/4 = 0.75 = 3.75

and we would have to plug in 1 as x

3 as x to find one value as 5.5 (-1) = 4.5

We find 3.75 as 5 (-1 )- 1/4 = 3.75

3.75 x 4.5 = 16.875m^2

and is closest fit using 1/4, 1/2 and -1.

But 3.2 x 5 is a better multiplication as 3 1/5 and finds 16 exact.

Consider the following polynomial.
-2xys + 3x? - 10x°y6 + 8x + 4
Which of the following statements are true? Select all that apply.
-The polynomial has 5 terms.
-The leading coefficient is -2.
.
-The degree of the polynomial is 7.
-The constant term is 4.
-The polynomial is in decreasing degree order.

Answers

Answer:

Step-by-step explanation:

If you write correctly:

[tex]P = -2xys+3x? - 10xy^{6} +8x+4\\[/tex]

I do not know the "?" in the formule de P

-The polynomial has 5 terms.  Yes

-The leading coefficient is -2. No

.

-The degree of the polynomial is 7.  Yes

-The constant term is 4.  Yes

-The polynomial is in decreasing degree order. No

I need help with this please ASAP!!!

Answers

Answer:

B and c

Step-by-step explanation:

I need help. How do you get 12.4 as an answer with using these instruction below.

Answers

Answer:

There are many solutions.

Here is one of them:

1 x 4 / 10 + 14 - 2 = 12.4

Hope this helps!

:)

It took Darcy two days to drive from Orlando to Pittsburgh. She drove 595 miles on the first day and at least 1,020 miles in total. How many miles did she drive on the second day?

Answers

Answer:

Darcy drove 425 miles

Step-by-step explanation:

you find this out by doing the equation 1,020-595

What is the volume of a cube that has a height of 10 inches

Answers

Answer:

1000 inches

Step-by-step explanation:

V= a3=103=1000in³

Answer:1,000in3

Step-by-step explanation:

V=LxWxH

V=10x10x10

V= 1,000

Name the first 10 perfect squares. Why are they perfect squares?"​

Answers

Answer:

why a math problem

Step-by-step explanation:

math is hard

help plz question is in the photo

Answers

Answer:

A. Trinomial

Step-by-step explanation:

It says it's a polynomial and that based on the number of terms. So right then you can cancel out cubic and quadratic because they aren't polynomials. Also:

Cubic is just a variable with the exponent of 3. Examples:

[tex]x^3,y^3,z^3[/tex]

Binomial is a polynomial with 2 terms. Examples:

[tex]5x+3; 6x+2; x+7[/tex]

A quadratic has a division sign.

add or subtract (7x^2-x-2)-(-6x^3+3)

Answers

Answer:

[tex] \tt{}6x ^{3} + {7x}^{2} - x - 5[/tex]

Step-by-step explanation:

[tex] \tt{}(7 {x}^{2} - x - 2) - ( - 6 {x}^{3} + 3)[/tex]

[tex] \tt{}7 {x}^{2} - x - 2 + 6x^{3} - 3[/tex]

[tex] \tt{} {7x}^{2} - x - 5 + 6x ^{3} [/tex]

[tex] \tt{}6x ^{3} + {7x}^{2} - x - 5[/tex]

Answer:

[tex]6 {x}^{3} + 7 {x}^{2} - x - 5[/tex]

Step-by-step explanation:

[tex](7 {x}^{2} - x - 2) - ( - 6 {x}^{3} + 3)[/tex]

➡️ [tex]7 {x}^{2} - 2 - ( - {6}^{3} + 3)[/tex]

➡️ [tex]7 {x}^{2} - x - 2 + 6 {x}^{3} - 3[/tex]

-2 - 3-(2 + 3)-5

➡️ [tex]7 {x}^{2} - x - 5 + 6 {x}^{3} [/tex]

➡️ [tex]6 {x}^{3} + 7 {x}^{2} - x - 5[/tex] ✅

Ms. Sanders put $5,200 in a savings account that pays 4.2% simple interest. Each year she withdraws the interest and treats herself to a visit to a spa. How much can she spend each year?

Answers

Answer:

$218.40

Step-by-step explanation:

i=prt

i=(5200)(.042)(1)

Which of the points (s, t) is inside the shaded region of the set of inequalities shown below?

s<24 - 0.66t
s>12 - t
s< 30 - t
s>0
t>0

O A. (1,8)
O B. (-9,21)
O C. (9,4)
O D. (30, 10)​

Answers

Answer:

Only point C. (9,4)

Step-by-step explanation:

To check if the points are inside the region of the inequalities, we just need to use the values of the point in each inequation, and if the point satisfy all inequations, the point is inside the region.

point A = (1,8): s = 1 and t = 8

first inequation: s<24 - 0.66t

1 < 24 - 0.66*8

1 < 18.72 (true)

second inequation: s>12 - t

1 > 12 - 8

1 > 4 (false)

So point A is not inside the region.

point B = (-9,21): s = -9 and t = 21

As we can see from the fourth inequation, the s value needs to be greater than 0, and point B has s negative, so point B is not inside the region.

point C = (9,4): s = 9 and t = 4

first inequation: s<24 - 0.66t

9 < 24 - 0.66*4

9 < 21.36 (true)

second inequation: s>12 - t

9 > 12 - 4

9 > 8 (true)

third inequation: s< 30 - t

9 < 30 - 4

9 < 26 (true)

fourth inequation: s>0

9 > 0 (true)

fifth inequation: t>0

4 > 0 (true)

As all conditions are true, point C is inside the region.

point D = (30,10): s = 30 and t = 10

first inequation: s<24 - 0.66t

30 < 24 - 0.66*10

30 < 17.4 (false)

So point D is not inside the region.

Answer:9,4

Step-by-step explanation:

HELP will mark brainliest

Answers

Answer:

x=55 degrees

Step-by-step explanation:

Angle X + 125 degrees is 180 degrees. 180 minus 125 is 55.

Find the area of a trapezoid, base 1 measures 5 inches, base 2 measures 11 inches, height measures 7 inches ​

Answers

Answer:

56

Step-by-step explanation:

Which ratio is not equivalent to the others?

Answers

Answer:

4:7

Step-by-step explanation:

3:5=6:10/2=3:5

9:15=9:15/3=3:5

Answer:

number 13. is d

Step-by-step explanation:

(x+2)(x-3)(x+5) is identical to x^(3)+ax^(2)-11x+b
Find the value of a and the value of b

Answers

Answer:

a = 4 and b = - 30

Step-by-step explanation:

Expand the left side and compare like terms on both sides, that is

(x + 2)(x - 3)(x + 5) ← expand the first pair of factors using FOIL

= (x² - x - 6)(x + 5) ← distribute

= x³ + 5x² - x² - 5x - 6x - 30 ← collect like terms

= x³ + 4x² - 11x - 30

Compare like terms with x³ +ax² - 11x + b

4x² and ax² ⇒ a = 4

+ b and - 30 ⇒ b = - 30

The requried simplified values of a and b are given as 4 and -30 respectively.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
(x+2)(x-3)(x+5) = x³+ax²-11x+b
(x + 2)[x² +2x -15 ] = x³+ax²-11x+b
x³ +4x² -11x - 30 = x³+ax²-11x+b

Comparing both sides,
a = 4 and b = -30

Thus, the requried simplified value of a and b are given as 4 and -30 respectively.

Learn more about simplification here:

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Can someone help with this

Answers

Answer:

the answered is -3 like in the picture

Step-by-step explanation:

Zayne has a bag filled with coins. The bag contains 7 quarters, 8 dimes, 3 nickels, and 9 pennies. He randomly chooses a coins from the bag. What is the probability that Zayne chooses a quarter or a nickel?

Answers

10/27

hope this helps :)

Answer:

Q=7/27 N=1/9 which is 10/27

Step-by-step explanation:

you add all the coins together

then if it is quarter then it is 7/27

if it is a nickel then it is 3/27 = 1/9

When there is no outlier is thebetter measure of center for a set of data


Median
Mode
Range
None of the above

Answers

Answer:

Median

Explanation:

The median is the middle number. This answer fits best with the question asked.

The mode is the number that occurs the most. This number doesn't really have a correlation to the middle of this data.

The range is just how many numbers the data spans across. It has no relation to the middle of the data.

im pretty sure its median :)


Martha used 2/3
tablespoons of pepper to make 1/6
liters of gravy. If Martha's recipe is for 1 liter of gravy, how much pepper will she need to make double the recipe?
A) 2 tablespoons of pepper
B) 4 tablespoons of pepper
C) 8 tablespoons of pepper
D) 12 tablespoons of pepper
plz helppp

Answers

Answer:

8 tablespoons of pepper

Step-by-step explanation:

Therefore, double the recipe: 4 × 2 = 8 tablespoons of pepper

A monkey is swinging from a tree. On each swing, she travels along an arc that is
75%, percent as long as the previous swing's arc. The total length of the arcs from her first 4 swings is 175m.How long was the monkey's 1st swing?
Round your final answer to the nearest meter.

Answers

Answer:

Total length of the first swing=64 m

Step-by-step explanation:

The total length of all four swings can be expressed as; Total length of all 4 swings=Length of first swing+length of second swing+length of third swing+length of fourth swing

where;

Total length of all 4 swings=175 m

Length of first swing=x

Length of second swing=75% of length of first swing=(75/100)×x=0.75 x

Length of third swing=75% of length of second swing

Length of third swing=(75/100)×0.75 x=0.5625 x

Length of fourth swing=75% of length of third swing

Length of fourth swing=(75/100)×0.5625 x=0.421875 x

replacing;

Total length of all 4 swings

175=x+0.75 x+0.5625 x+0.421875 x

2.734375 x=175

x=175/2.734375

x=64

Total length of the first swing=x=64 m

Find the volume of a pyramid with a square base, where the area of the base is 19.6\text{ cm}^219.6 cm 2 and the height of the pyramid is 12.7\text{ cm}12.7 cm. Round your answer to the nearest tenth of a cubic centimeter.

Answers

Answer:

V = 83.0 cm^3

Step-by-step explanation:

To find the volume of the squared pyramid you use the following formula:

[tex]V=\frac{1}{3}Bh[/tex]   ( 1 )

B: base of the pyramid = 19.6 cm^2

h: height of the pyramid = 12.7 cm

you replace the values of B and h in the equation ( 1 ):

[tex]V=\frac{1}{3}Bh=\frac{1}{3}(19.6cm^2)(12.7cm)\\\\V=82.97cm^3\approx 83.0cm^3[/tex]

hence, the volume of the pyramid is 83.0 cm^3

Which property is illustrated by the
equation below?
7 + (-7) = 0
A. Additive Inverse Property
B. Distributive Property
C. Associative Property of Addition
D. Additive Identity Property

Answers

Answer:

additive inverse

Step-by-step explanation:

-7 is the inverse of 7 so adding it would cancel it out making it 0

the question is on the image

Answers

Answer:

1/6

Step-by-step explanation:

The slope of a line in y=mx+b form is always the number before the x value.

Hope this helps!

Solve this equation 2/3x+ 5= 1

Answers

Answer:

x=-6

Step-by-step explanation:

2/3x+5=1

Subtract 5 from both sides:

2/3x=-4

Multiply both sides by 3:

2x=-12

Divide both sides by 2:

x=-6

Hope this helps!

Answer:

-6

Step-by-step explanation:

2/3x +5 = 1

        -5    -5

2/3x = -4

2/3x/2/3 = -4/2/3

= -6

:3 if I helped, please mark as brainliest!

Answer this there is a pic

Answers

Answer:

A

Step-by-step explanation:

1:2.5 because 2/2=1 and 5/2=2.5

Help please will give brainly! Clara’s friend Brian decides to find his median as well. Find the median and type it in the answer box. What does the median show us?

Answers

Answer:

The median is 88. The median shows that Brian gets on average 88% on his tests.

Step-by-step explanation:

If you put the numbers in order and get the average of the two middle number, it is 88.

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