Three students were given the expression shown and were asked to take a common factor out of two of the terms. Use the drop-down menus to complete the statements about whether each student's answer is an equivalent expression. Then choose an expression that is equivalent.

Three Students Were Given The Expression Shown And Were Asked To Take A Common Factor Out Of Two Of The

Answers

Answer 1

Answer:

Step-by-step explanation:

Given: 4 - 9x +21

Factorizing this expression, we have;

              4 -3(3x - 7)

i. Chang's expression: 4 - 3(3x + 7)

This is not an equivalent expression, because by expansion of the bracket, the expression gives: 4 -9x -21

ii. Benjamin's expression: 4 + 3(3x + 7)

This is not an equivalent expression, because by expansion of the bracket, the expression gives: 4 +9x +21

iii. Habib's expression: 4 + 12x

This is not an equivalent expression, because the expression is not related to the given question

Comparing the three student's answers with the appropriate expression, none of the student's is an equivalent expression.

This expression that is  equivalent to the given question is;

            4 -3(3x - 7) = 4 -9x + 21

Answer 2

Answer:

1,2,4

Step-by-step explanation:

Three Students Were Given The Expression Shown And Were Asked To Take A Common Factor Out Of Two Of The

Related Questions

Given v(x) = g(x) (3/2*x^4 + 4x – 1), find v'(2).​

Answers

Answer:

Step-by-step explanation:

Given that v(x) = g(x)×(3/2*x^4+4x-1)

Let's find V'(2)

V(x) is a product of two functions

● V'(x) = g'(x)×(3/2*x^4+4x-1)+ g(x) ×(3/2*x^4+4x-1)

We are interested in V'(2) so we will replace x by 2 in the expression above.

g'(2) can be deduced from the graph.

● g'(2) is equal to the slope of the tangent line in 2.

● let m be that slope .

● g'(2) = m =>g'(2) = rise /run

● g'(2) = 2/1 =2

We've run 1 square to the right and rised 2 squares up to reach g(2)

g(2) is -1 as shown in the graph.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's derivate the second function.

Let h(x) be that function

● h(x) = 3/2*x^4 +4x-1

● h'(x) = 3/2*4*x^3 + 4

● h'(x) = 6x^3 +4

Let's calculate h'(2)

● h'(2) = 6 × 2^3 + 4

● h'(2) = 52

Let's calculate h(2)

●h(2) = 3/2*2^4 + 4×2 -1

●h(2)= 31

■■■■■■■■■■■■■■■■■■■■■■■■■■

Replace now everything with its value to find V'(2)

● V'(2) = g'(2)×h(2) + g(2)× h'(2)

● V'(2)= 2×31 + (-1)×52

●V'(2) = 61 -52

●V'(2)= 9

if a salesman has a base salary of 35,000 per year makes 5% commission on each sales ,how much must he do in sales to make a total of 75,000 for the year

Answers

The answer will be 3750

He must do a 8,00,000 sales to make total of 75000 for the year.

For salesman base salary = 35000, Salary to be atained is 75000. Having commission of 5% on every sales. Sales to be determine so the salesman attained 75000 for year.

What is arithmetic?

In mathematics it deals with numbers of operations according to the statements.

Here, according to the statement.
Let x be sales,
35,000 + 5%x = 75,000
0.05x = 75000-35000
x = 40000/0.05
x = 8,00,000

Thus, he must do a 8,00,000 sales to make total of 75000 for the year

Learn more about arithmetic here:

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What is the area of the regular polygon shown below?

Answers

Answer:

shown below..I can't see..

Answer:

93.5 for area

Step-by-step explanation:

there is no picture so that's  a simple guess

During the school year, there were 315 total points scored between basketball, soccer, baseball, and football. The baseball team scored 55 points. The soccer team scored twice as much as the baseball team. The football team scored 0.5 more than 1.5 times as much as the baseball team. How many points did the basketball team score?

Answers

Answer:

67.5p.

Step-by-step explanation:

315p in total.

- Baseball has 55p.

- Soccer teams points = 55x2 = 110p.

-  Football team points = 110 x 0.5 = 55 x 1.5 = 82.5p.

So then you just do 315p - 82.5p - 55p - 110p = 67.5p

Combine like terms to simplify the expression: 2/5k - 3/5 +1/10k

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

1/2k - 3/5

▹ Step-by-Step Explanation

2/5k - 3/5 + 1/10k

Collect like terms:

2/5k + 1/10k = 1/2

Final Answer:

1/2k - 3/5

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

1/2k - 3/5

Step-by-step explanation:

Hey there!

Well the only fraction needed to combine are,

2/5 and 1/10.

To add them we need to make 2/5 have a denominator of 10.

To do that we multiply 5 by 2.

5*2 = 10

What happens to the denominator happens to the denominator.

2*2 = 4

Fraction - 4/10

4/10 + 1/10 = 5/10

5/10

simplified

1/2

1/2k - 3/5

Hope this helps :)

The points (-6,-4) and (3,5) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
The length of the radius is a
(Round to the nearest hundredth as needed.)

Answers

Answer:

40.5

Step-by-step explanation:

diameter^2 = (3 +6)^2 + (5+4)^2

or, d^2 = 9^2 + 9^2

or, d^2 = 81 +81

or,d^2 =162

or d=√ 162

• d= 81

then radius = d/2

r = 81/2

•r= 40.5 ans

F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23

Answers

Answer:

∠ H ≈ 23°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus

∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )

i will give brainliest and 5 stars if you help ASAP​

Answers

Answer:

[tex] Area = 240 m^2 [/tex]

Step-by-step explanation:

The area of the right triangle above = [tex] \frac{1}{2}*base*height [/tex].

Where,

base = 16 m

height = 30 m

Plug in the above values into the area formula:

[tex] Area = \frac{1}{2}*16*30 [/tex]

[tex] Area = 8*30 [/tex]

[tex] Area = 240 m^2 [/tex]

Refer to the attachment for solution.

Write a rational number in fraction form that is equivalent to -1.\overline{5}

Answers

Answer:

[tex]\dfrac{-14}{9}[/tex].

Step-by-step explanation:

The given number is [tex]-1.\overline{5}[/tex].

We need to find a rational number in fraction form that is equivalent to given number.

Let [tex]x=-1.\overline{5}[/tex]

[tex]x=-1.555...[/tex]     ...(1)

Multiply both sides by 10.

[tex]10x=-15.555...[/tex]  ...(2)

Subtracting (1) from (2), we get

[tex]10x-x=-15.555...-(-1.555...)[/tex]

[tex]9x=-14[/tex]

Divide both sides by 9.

[tex]x=\dfrac{-14}{9}[/tex]

Therefore, the required rational number is [tex]\dfrac{-14}{9}[/tex].

Please tell me the answer ASAP Lynette's average score on five tests is 18. If she scores 24 points on her sixth test, what is her average score on all six tests? Show Your Work

Answers

Answer:

The average score of 6 tests is 19.

Step-by-step explanation:

Given that the average score of 5 tests is 18. So first, we have to find the total number of scores for 5 tests :

[tex]let \: x = total \: no. \: of \: scores[/tex]

[tex] \frac{x}{5} = 18[/tex]

[tex]x = 18 \times 5[/tex]

[tex]x = 90[/tex]

We have found out that the total scores for 5 tests is 90. So we have to find the average of 6 scores :

[tex] \frac{x + 24}{5 + 1} = \frac{90 + 24}{6} = \frac{114}{6} = 19[/tex]

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution : )}}}}[/tex]

Given:Average score in 5 tests = 18He scored 24 points in 6th point

To FinD:Find the average score in all six tests?

How to find?

We need to know how to find the average

☄ For this case, We are gonna find average score...!

[tex] \large{ \boxed{ \sf{Avg. \: score = \frac{Total \: score}{No. \: of \: tests} }}}[/tex]

So, Let's proceed further towards solution....

Solution:

We have,

Avg. score = 18No. of tests = 5

Finding total score in 5 tests,

⇛ Total score = Avg. score × No. of tests

⇛ Total score = 18 × 5

⇛ Total score = 90

According to question,

He scored 24 marks in 6th test

⇛ Total score now = 90 + 24 = 114

No. of tests = 6

Finding the average score of 6 tests,

⇛ Avg. score = 114 / 6

⇛ Avg. score = 19 points

☄ Avg. score of lynette in 6 tests = 19

━━━━━━━━━━━━━━━━━━━━

line and passes through C -2,0 in the 1, -3) Quetion of the line in standard form

Answers

Answer:

[tex]\huge\boxed{x+y=-2}[/tex]

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

where

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (-2, 0) and (1, -3).

Substitute:

[tex]x_1=-2;\ y_1=0;\ x_2=1;\ y_2=-3[/tex]

[tex]m=\dfrac{-3-0}{1-(-2)}=\dfrac{-3}{1+2}=\dfrac{-3}{3}=-1\\\\y-0=-1(x-(-2))\\\\y=-(x+2)[/tex]

[tex]y=-x-2[/tex]         add x to both sides

[tex]x+y=-2[/tex]

What are the solution(s) of the quadratic equation 98 - x2 = 0?
x = +27
Ox= +63
x = +7/2
no real solution

Answers

Answer:

±7 sqrt(2) = x

Step-by-step explanation:

98 - x^2 = 0

Add x^2 to each side

98 =x^2

Take the square root of each side

±sqrt(98) = sqrt(x^2)

±sqrt(49*2) = x

±7 sqrt(2) = x

Answer:

[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]

Step-by-step explanation:

[tex]98-x^2 =0[/tex]

[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]

[tex]98=x^2[/tex]

[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]

[tex]\pm \sqrt{98} =x[/tex]

[tex]\sf Simplify \ radical.[/tex]

[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]

[tex]\pm 7\sqrt{2} =x[/tex]

[tex]\sf Switch \ sides.[/tex]

[tex]x= \pm 7\sqrt{2}[/tex]

the length of a triangle is x and its width is 2x. what is the area if the length and width are each increased by 1?
A. 2x^2+ 3x+ 1
B. 2x^2+ 1
C. 2x^2+ 2x+ 1
D. 2x^2+ 3x+ 2

Answers

The answer to the question is B.

Answer:

Hey there!

(2x+1)(x+1)

2x^2+1x+2x+1

2x^2+3x+1

The answer would be A.

Let me know if this helps :)

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2+5/2n

Answers

Answer:  [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

Step-by-step explanation:

[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

A football team starts on the 10 yard line moving toward the 50 yard line so they can score on the other side of the field. In three plays they gain 14 yards, lose 12 yards, and gain 4 more yards. What yard line do they start their fourth play?

Answers

Answer:

16 yard line

Step-by-step explanation:

The football team is starting on the 10 yard line. In the first play, they move up to the 24 yard line. Then in the second play, they go back to the 12 yard line since they lost 12 yards. Then in the third play, they gain 4 yards so you add 4 to 12. They end up at the 16 yard line after the third play. This means that they're going to start their fourth play at the 16 yard line.

Answer:

16 yards.

Step-by-step explanation:

They start at 10 yards. They are moving towards the 50 yard line, so gaining yards will add to the 10 yards instead of subtract from the 10 yards.

In the first play, they gain 14 yards. 10 + 14 = 24 yards.

In the second play, they lose 12 yards. 24 - 12 = 12 yards.

In the third play, they gain 4 yards. 12 + 4 = 16 yards, which is where they start their fourth play.

Hope this helps!

Find the length of a square with a perimeter of 48cmeter

Answers

Answer:

12

Step-by-step explanation:

Perimeter of a square:

4(L)

L = Length

=> 4(L) = 48

=> 4L = 48

=> 4L/4 = 48/4

=> L = 12

The length of the square is 12 cm.

Answer:

12

Step-by-step explanation:

Since the lengths of the sides of a square are equal, divide the perimeter by 4

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5 . If there were 4545 no votes, what was the total number of votes?

Answers

Answer:

The total number of votes= 9999

Step-by-step explanation:

The ratio of vote specifically the ratio of yes to no vote in a city vote is 6 to 5.

There is a total of 4545 no votes.

Yes/no = 6/5

Yes= no(6/5)

Yes= 4545(6/5)

Yes= 5454

The total number of yes votes are 5454.

The total number of votes= yes votes+ no votes

The total number of votes= 5454+4545

The total number of votes= 9999

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b? –15 –9 3 9

Answers

Answer:

b = -9.

Step-by-step explanation:

The line passes through (4, 3) and (7, 12). First, we need to find the slope: the rise over the run.

(12 - 3) / (7 - 4) = 9 / 3 = 3.

Now that we have the slope, we can say that m = 3. So, we have an equation of y = 3x + b. To find b, we can use M(4, 3) and say that y = 3 and x = 4.

3 = 3 * 4 + b

b + 12 = 3

b = -9.

Hope this helps!

The value of b in the equation is -9

How to determine the value of b?

The points are given as:

M(4, 3) and N(7, 12)

The equation is then calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1} * (x - x_1) + y_1[/tex]

This gives

[tex]y = \frac{12 -3}{7 -4} * (x - 4) + 3[/tex]

Evaluate the quotient

y = 3 * (x - 4) + 3

Open the bracket

y = 3x - 12 + 3

Evaluate the difference

y = 3x - 9

Hence, the value of b is -9

Read more about linear equations at:

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Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 50 p = 0.2

Answers

Answer:

The mean, variance, and standard deviation of the binomial distribution are 10, 8, and 2.83 respectively.

Step-by-step explanation:

We have to find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p, i.e; n = 50 p = 0.2.

Let X = binomial random variable

So, X ~ Binom(n = 50, p = 0.2)

Now, the mean of the binomial distribution is given by;

         Mean of X, E(X) = n [tex]\times[/tex] p

                                    = 50 [tex]\times[/tex] 0.2 = 10

Now, the variance of the binomial distribution is given by;

        Variance of X, V(X) = n [tex]\times[/tex] p [tex]\times[/tex] (1 - p)

                                         = 50 [tex]\times[/tex] 0.2 [tex]\times[/tex] (1 - 0.2)

                                         = 10 [tex]\times[/tex] 0.8 = 8

Also, the standard deviation of the binomial distribution is given by;

        Standard deviation of X, S.D.(X) = [tex]\sqrt{\text{n} \times \text{p} \times (1 - \text{p})}[/tex]

                                                              = [tex]\sqrt{\text{50} \times \text{0.2} \times (1 - \text{0.2})}[/tex]

                                                              = [tex]\sqrt{8}[/tex] = 2.83

In your own words, define Quadratic Equation. How many solutions does a Quadratic Equation have?

Answers

Answer: an equation that has one term which is nameless and squared also no term which gets raised to higher power.

Step-by-step explanation:

arthur walks 5/8 mi to school jonathan rides a bus 8 times that far> How far does Jonathan ride to school

Answers

Answer:

Step-by-step explanation:

Distance walked by Arthur = 5/8 miles

Distance ride  by Jonathan = 8 times that of Arthur

it means that Distance rode on bus by Jonathan is 8 multiplied by Distance walked by Arthur

Distance rode on bus by Jonathan = 8 * Distance walked by Arthur

Distance rode on bus by Jonathan = 8 * 5/8 = 5 Miles Answer

I help! solve 12x^2+54x=-42

Answers

Answer: Hi!

Let's solve your equation step-by-step.

12x^2 + 54x = −42

Step 1: Subtract -42 from both sides.

12x^2 + 54x − (−42) = − 42 − (−42)

12x^2 + 54x + 42 = 0

Step 2: Factor left side of equation.

6(2x + 7)(x + 1) = 0

Step 3: Set factors equal to 0.

2x + 7 = 0 or x + 1 = 0

You have two answers.

x = −7/2 or x = −1

Hope this helps!

logx - logx-1^2=2log(x-1)

Answers

Answer:

x is approximately 2.220744

Step-by-step explanation:

This can be simplified a little using properties of logarithms, and then solve it by graphing:

[tex]log(x)-log(x-1)^2=2\,log(x-1)\\log(x)-2\,log(x-1)=2\,log(x-1)\\log(x)=4\,log(x-1)[/tex]

So we use a graphing tool to find the intersection point of the graph of [tex]log(x)[/tex], and the graph of [tex]4\,log(x-1)[/tex]

Please see attached image for the graph and solution.

The value of x is approximately 2.220744

Answer:

  x = 2.32011574011

Step-by-step explanation:

The problem with your original equation is that it is a long way of saying ...

  log(x) -log(x) -1 = 2log(x-1)

  0 -1 = 2log(x-1)

which has the solution ...

  -1/2 = log(x -1)

  1/√10 = x -1

  x = 1 + 1/√10 ≈ 1.3162278

__

We have asked for clarification, and what we got was ...

  [tex]\log{(x)}-\log{(x-1^2)}=2\log{(x-1)}[/tex]

which, again, is a long way of saying ...

  [tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]

The other reasonable interpretation of your 'clarified' equation is ...

  [tex]\log{(x)}-\log{((x-1)^2)}=2\log{(x-1)}[/tex]

which you already have an answer to. You have declared that a "misconception."

So, we are left with the interpretation that the equation you want a solution to is ...

  [tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]

_____

When solving these graphically, I like to write the equation as a function whose zero(s) we're trying to find. For this, when we subtract the right side, we get ...

  [tex]f(x)=\log{(x)}-3\log{(x-1)}[/tex]

A graphing calculator shows that f(x) = 0 when ...

  x ≈ 2.32011574011

__

If you don't like my interpretation, check out the second attachment. It has your x-1² as the argument of the middle term. You can see that the calculator interpreted that the same way I did (as required by the order of operations).

A diameter that is perpendicular to a chord bisects the chord. True False

Answers

Answer:

[tex]\Large \boxed{\sf True}[/tex]

Step-by-step explanation:

[tex]\sf A \ diameter \ that \ is \ perpendicular \ to \ a \ chord \ bisects \ the \ chord.[/tex]

Answer:

True!!

I just did the assignment and got it right

Diana paints 150 fence posts and chuck paints 130 fence posts. Diana paints 10 more fence posts than chuck. How many fence posts does chuck paint per hour?

Answers

Complete Question

The  complete question is shown on the first uploaded image

Answer:

Step-by-step explanation:

From the question we are told that

  The  relationship is  [tex]\frac{150 }{d} = \frac{130}{c}[/tex]

   The number of fence post painted by chuck is  [tex]l = 130[/tex]

    The number of fence post painted by Diana  is [tex]k = 150[/tex]

    can paint 10 fences more than chuck  so let say the  of fence painted in an hour by chuck is [tex]g[/tex]

     Then  the number of fence post painted by Diana in one hour is

          [tex]f = g+ 10[/tex]

 So

       [tex]\frac{150 }{ g + 10 } = \frac{130}{g}[/tex]

       [tex]130 g + 1300 = 150g[/tex]

        [tex]g = 65 \ m[/tex]

Please answer this correctly without making mistakes

Answers

Answer:

5/12

Step-by-step explanation:

3/4-1/3=

9/12-4/12=

5/12

What value does the 2 in the number 0.826?

Answers

Answer:

.02

Step-by-step explanation:

2 is in "Hundredths' place in .826

So, the number is multiplied with 1/100 or .01

=> 2 x 1/100

=> 2/100

=> .02

=> 2 x .01

=> .02

The value of 2 in .826 is .02

what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10

Answers

Answer=16. Hope this helps

Answer:18.5

Step-by-step explanation:

10+8=18

18*5=90

90/4

22.5-4=18.5

There are $400$ pages in Sheila's favorite book. The average number of words per page in the book is $300$. If she types at an average rate of $40$ words per minute, how many hours will it take to type the $400$ pages of the book?

Answers

Answer:

50hours

Step-by-step explanation:

Given that there are 400 pages in Sheila's favorite book.

The average number of words per page in the book is 300

She types an average rate of 40words per minute.

So to type 400pages of the book

Total number of words in the pages = 400×300 = 120000 words

Typing rate : 40words ------- 1minute

120000 words ----------- x minutes

Hence we have 40 × X mins = 120000 × 1min

Make X the subject

40X = 120000minutes

X = 120000/40

X = 3000minutes

Since 60minutes = 1hour

3000minutes = 3000minutes/60

= 50hours

Hence it took her 50hours to type 400pages

Solution:

The total number of words in the book is 400 x 300. Sheila types at a rate of 40 words per minute, or 40 x 60 words per hour. The number of hours it takes her is equal to the number of words divided by her rate of typing, or 400x300/40x60 = 50 hours.

Un taxímetro inicia con 50 unidades y el banderazo o arranque es de $4500, las unidades comienzan a cambiar p0r cada kilometros recorrido. La función lineal que representa esta situación es y = 50x +4500 donde y representa el precio que cuesta la carrera y x la distancia recorrida en kilómetros. a) ¿ Cuanto cuesta una carrera si la distancia recorrida fue de 23 kilómetros?

Answers

Answer: $5650

Step-by-step explanation:

El precio de la carrera es:

y = ($50/km)*x + $4500.

Donde x representa la cantidad recorrida en Km.

Ahora se nos pregunta:

¿ Cuanto cuesta una carrera si la distancia recorrida fue de 23 kilómetros?

Para esto, debemos reemplazar la variable en la equacion por 23km:

x = 23km

y = ($50/km)*23km + $4500 = $5650

Other Questions
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