The teachers’ editions of a statistics textbook sell for $150 each, and students’ editions of the book sell for $50 each. Which function can be used to find the average cost per book if two teachers’ editions and x students’ editions are purchased?

To convert the quadratic polynomial into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation. [tex]\dfrac{b^2}{4a^2}[/tex] can be added to both sides of the equation.

The given equation is  [tex]x^2+\dfrac{b}{a}x+?=\dfrac{-c}{a}+?[/tex]

Now,

To change the quadratic equation into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation.

Therefore,

[tex]x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=\dfrac{-c}{a}+\dfrac{b^2}{4a^2}[/tex]

Thus, [tex]\dfrac{b^2}{4a^2}[/tex] should be added to both sides of the equation to convert the above equation into the quadratic polynomial.

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Answer:

d

Step-by-step explanation:

edge

9x3 - 9x2y + 4x - 4y A) (x + y)(9x2 - 4) B) (x - y)(9x2 + 4) C) (9x + y)(x - 2)(x + 2) D) (x + y)(3x - 2)(3x + 2)

Answer:

69.1

Step-by-step explanation:

Mean height of 14 students = 69.0 inches

Mean = sum of data/number of data

69 = sum of data/14

sum of data = 966

FOR NEW MEAN:

Height of additional student = 70.5

Mean = sum of data/ number of data

Mean = 966+70.5/14+1

Mean = 1036.5/15

Mean = 69.1

Therefore, the mean height of the 15 students in the class is 69.1

Final answer:

To find the new mean height after Danielle joins the class, calculate the total height of all students, add Danielle's height, and divide by the new number of students. The mean height increases to 69.1 inches.

Explanation:

Mr. Zuro finds the mean height of all 14 students in his class to be 69.0 inches. When Danielle, who is 70.5 inches tall, walks in late, we need to calculate the new mean height of all 15 students.

First, we find the total height of the initial 14 students by multiplying the mean height by the number of students: 69.0 inches × 14 = 966 inches. Next, we add Danielle's height to this total: 966 inches + 70.5 inches = 1036.5 inches. Finally, to find the new mean height, we divide this total by the number of students, now 15: 1036.5 inches ÷ 15 = 69.1 inches.

Therefore, the mean height of the 15 students in the class, including Danielle, is now 69.1 inches.

876.405, 887.053, 887.208

887.208

887.053

876.405

Hope this helps

Answer:

Translate

Step-by-step explanation:

To shift a graph vertically and/or horizontally is to  Translate it.

Translation--

A translation is a rigid transformation in which the graph of the original function is shifted some units to the left or to the right( i.e. horizontal shift) or some units up or down ( i.e. vertical shift ).

The horizontal shift of the function f(x) by k units is given by:

   f(x) → f(x+k)

and the vertical shift of the function f(x) by k units is given by:

   f(x) → f(x)+k

Answer:

-18 - 24y.

Step-by-step explanation:

6(-3-4y)

We use the distributive law to give:

6 * -3 + 6* -4y

= -18 - 24y.

Answer:

10 amps

Step-by-step explanation:

Ohm's law states

I = [tex]\frac{V}{R}[/tex]

I is the current, V the voltage and R the resistance, thus

I = [tex]\frac{30}{3}[/tex] = 10

Answer: SECOND OPTION

Step-by-step explanation:

Given the following equation:

[tex]x^2-36=5x[/tex]

You can follow these steps in order to find the values of "x" that makes the equation true:

1. Subtract [tex]5x[/tex] from both sides of the equation:

[tex]x^2-36-5x=5x-5x\\\\x^2-5x-36=0[/tex]

2. Factor the equation. Find two numbers whose sum be -5 and whose product be -36. These are 4 and -9:

[tex](x+4)(x-9)=0[/tex]

Then you get:

[tex]x_1=-4\\\\x_2=9[/tex]

Checking:

[tex](-4)^2-36=5(-4)\\\\-20=-20[/tex]

TRUE

[tex](9)^2-36=5(9)\\\\45=45[/tex]

TRUE

Answer:

Its B. -4 and 9

Step-by-step explanation:

Just took it and got 100%

Answer:

Table C

If the bacteria population triples every hour, it must multiply by three each time.

Table C fits this pattern

y | 1 | 3 | 9 | 27 | 81 | 243 | 729

1×3=3, 3×3=9, 9×3=27 etc.

José needs approximately 2 more hours to complete his job.

We should calculate the total time required for 100% completion and then subtract the time he has already worked.

He needs approximately 2 more hours to complete the job.

Complete Question:

Jose sets up computers. He has been working on the job today for 6 hours. He told his boss the job was about 75% complete. Approximately how many more hours does he need to complete the job.

Answer:

B

Step-by-step explanation:

simply by dividing time and miles by number 2 until 6 miles comes to 1 mile

7766 rounded ot the nearest thousands would be 8000, since the hundreds place value, 7, is going to be rounded up to 8000.

Hope this helped!

Nate

Answer:

8000

Step-by-step explanation:

|Thousands||Hundreds||Tens||Ones|

|       7          ||        7       ||   6  ||    6   |

5 or more, raise the score (turn the 7 into an 8 and make the three other numbers 0)

4 or less, let it rest (leave the 7 as a 7 and make the other 3 numbers 0).

The number that we are looking at changing will be bold. The number that determines if we change that number will be underlined.

7766

The 5 or more, raise the score rule applies to 7.

So, we will make the 7 thousand (7000) 8 thousand (8000)

We will make the seven hundred sixty six (766) zero (0).

Our final answer is 8000.

Answer:

NO Pick none :) Step-by-step explanation:

Answer:

6 packs of sugar cookies and 10 packs of chocolate chip cookies.

Step-by-step explanation:

Let the quantity of sugar cookies be x packs and the quantity of chocolate chip cookies be y packs. Total packs are 16. Therefore: x + y = 16. This implies y = 16 - x (Equation 1).

It is given that a pack of sugar cookies is priced at $2.5 and a pack of chocolate chip cookies is priced at $3.5. It is also given that the student spends a total of $50 on the cookies. Since x packs of sugar cookies and y packs of chocolate chip cookies are to be bought, therefore:

2.5x + 3.5y = 50 (Equation 2).

Put equation 1 in equation 2.

2.5x + 3.5(16 - x) = 50.

2.5x + 56- 3.5x = 50.

-x = -6.

x = 6.

Put x = 6 in equation 1.

y = 16 - 6.

y = 10.

Therefore, Angelina will buy 6 packs of sugar cookies and 10 packs of chocolate chip cookies!!!

Hey!

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

Solution:

Divide to get the decimal.

79 / 100 = 0.79

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

Answer:

0.79

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

Hope This Helped! Good Luck!

Answer: 0.79

Step-by-step explanation:

divide to get the decimal.

remeber, if n is two digits, n/100 = 0.n

Answer:5

Step-by-step explanation:

Answer:

x = - 8, x = 6

Step-by-step explanation:

Given

(x - 6)(x + 8) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 8 = 0 ⇒ x = - 8

Answer:

x =  -8, 6.

Step-by-step explanation:

(x– 6)(x + 8) = 0

Either factor can be zero:

x - 6 = 0 gives x = 6 and

x + 8 = 0 gives x = -8.

[tex]X \geq -2[/tex]

3 > √10 > 4

the answer would be 3 & 4

Answer: 3 & 4

Step-by-step explanation:

Final answer:

To find 15% of 75% of 80, calculate 75% of 80 first (0.75  imes 80 = 60), then find 15% of 60 (0.15  imes 60 = 9), resulting in an answer of 9.

Explanation:

The student has asked: What is 15% of 75% of 80?

To solve this problem, we'll need to follow these steps:

First, find 75% of 80.

Then, find 15% of the result from step 1.

Let's start with the first step:

75% of 80 is equivalent to 0.75  imes 80, which equals 60.

Now, for the second step:

15% of 60 is equivalent to 0.15  imes 60, which equals 9.

Therefore, 15% of 75% of 80 is 9.

Answer: -1>n

Step-by-step explanation:1) combine like terms (-5n+2n=-3n) so you have 3<-3n then you divide -3 on both sides and because it’s a negative you flip the sign so you end up with -1>n

Answer:

Step-by-step explanation:

Product of -4 and a number x   is  -4 * x = - 4x

-4x  + 2  < 20

Answer:

Step-by-step explanation:

Turning the word problem into equations:

[tex]-4x+2 = 20[/tex]

Subtracting 2 on both sides

[tex]-4x+2 -2= 20 -2[/tex]

[tex]-4x = 18[/tex]

Dividing by -4

[tex] -4x/(-4) = 18/(-4)[/tex]

Considering that -4x/(-4) = x

Then the answer is x = -18/4 = - 9/2 = - 4 1/2

Answer:

y = - 6x - 19

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 6x - 4 ← is in slope- intercept form

with slope m = - 6

• Parallel lines have equal slopes, thus

y = - 6x + c ← is the partial equation

To find c substitute (- 3, - 1) into the partial equation

- 1 = 18 + c ⇒ c = - 1 - 18 = - 19

y = - 6x - 19 ← in slope- intercept form

Step-by-step explanation:

[tex] \red {\frak{Given}} \begin{cases} & \sf{Two\ consecutive\ natural\ numbers.} \\ & \sf{The\ sum\ of\ the\ numbers\ is\ {\pmb{\sf{475}}}.} \end{cases}[/tex]

We know that,

Therefore,

[tex] \sf \dashrightarrow {x\ +\ x\ +\ 1\ =\ 475} \\ \\ \\ \sf \dashrightarrow {2x\ +\ 1\ =\ 475} \\ \\ \\ \sf \dashrightarrow {2x\ =\ 475\ -\ 1} \\ \\ \\ \sf \dashrightarrow {2x\ =\ 474} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{474}}{\cancel{2}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 237.}}}}_{\sf \blue {\tiny{First\ number}}}} [/tex]

∴ Hence, the first number is 237. Now, let us find out the second number.

[tex]\rule{200}{3}[/tex]

Second NumbeR :

∴ Hence, the second number is 238.

The two consecutive numbers whose sum is 475 are 237 and 238.

Let assume the two consecutive natural numbers as x and x+1.

According to the given information,

the sum of the two consecutive numbers is 475.

So, the equation can be set up as:

x + (x+1) = 475

Combining like terms, we get:

2x + 1 = 475

Subtracting 1 from both sides, we have:

2x + 1 - 1  = 475 - 1

2x = 474

Dividing both sides by 2, we find:

x = 237

Thus, the two consecutive numbers are 237 and 238.

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Sandra made it to the next level in the matching game.

Sandra needs to score at least 10 points to advance to the next level. She scores 18 points for correct matches and -6 points for incorrect matches. To determine if Sandra made it to the next level, we can add up her scores.

18 - 6 = 12 points

Sandra scored 12 points, which is greater than the required 10 points, so she made it to the next level.

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Answer:

(n+3)/7

Step-by-step explanation:

Let

n -----> the unknown number

we know that

The algebraic expression of the phrase " the sum of a number and three" is equal to

(n+3) -----> number n plus number 3

so

The algebraic expression of the phrase " the sum of a number and three divided by seven" is equal to

(n+3)/7 ----> divide (n+3) by the number 7

therefore

The expression is

(n+3)/7

The correct expression is 3a + 17.

The correct expression that represents 'Three times a number, increased by seventeen' is 3a + 17. Option B is the correct answer.

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Answer:

r = 7

Step-by-step explanation:

Use the distributive property by multipling the -8 to the 2r and the -8, do the same thing on the other side with the -3.

Afterwards, combine like terms by adding 64 and 6.

Next, add 3r to the left side, I usually choose the number with the variable (the letter) that looks like it will be easier to subtract. This leaves only 21 on the right side.

Next subtract 70 from both sides

Divide -13 by both sides

You should get the answer of r=7