(a) Simplify x² − (x − m)(x + m). (b) Using your answer to (a), write down the value of 1023² - 1022 x 1024 without using a calculator.​

Answer:

  a. see the attachment for the table (also reproduced below)

  b. slope = -3; see the attachment for a graph

Step-by-step explanation:

A table of values for the function can be filled a couple of ways. One way is to draw the graph of the equation, and read the point values from it. Another way is to solve for each of the variables, and use those equations to find the missing table values.

__

Solving the equation for y, we get ...

  3x +y = 15

  y = -3x +15 . . . . . . subtract 3x; this is "point-slope form"

For the purpose of evaluating for different values of x, we can rearrange this a bit to ...

  y = 3(5 -x) . . . . factor out 3

The given table has x-values of 0, 2, 3, 6. The corresponding y-values are ...

  y = 3(5 -{0, 2, 3, 6}) = 3{5, 3, 2, -1} = {15, 9, 6, -3} . . . . for x={0, 2, 3, 6}

Solving the equation for x, we get ...

  y/3 = 5 -x . . . . . divide the above equation by 3

  x = 5 -(y/3) . . . . . add x-(y/3)

For y-values {0, 3, 8}, the corresponding x-values are ...

  x = 5 -{0, 3, 8}/3 = 5 -{0, 1, 8/3} = {5, 4, 7/3} . . . . for y={0, 3, 8}

Then our table of values is ...

  [tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-8}x&2&4&6&0&3&5&7/3\\y&9&3&-3&15&6&0&8\\\cline{1-8}\end{array}[/tex]

__

The points in the above table can be plotted, and the line drawn through them. Sometimes using the points that are farthest apart makes this easier: (0, 15) and (6, -3).

slope

When we solved for y, we had the equation in slope-intercept form. The slope is the x-coefficient in that equation:

  y = -3x +15   ⇒   slope = -3

Answer:

a) 7 hours ; b) 2.5 hours ; c) look at explanation

Step-by-step explanation:

a)

The mean of a data set is what we usually refer to as the average. To find the mean, you add up all of the values and divide by the number of values.

So, to find the mean, you need to add all of the values (the "value" is the the number hours each student watched)

11 + 7 + 9 + 3 + 3 + 8 + 10 + 5

= 56

You have 8 seventh-grade students, so your number of values is 8.

Dividing the sum of the values by the number of values would then be:

56 / 8

= 7

So, your mean is 7.

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

b)

(A deviation is how much a value differs from a certain value. If a person was supposed to be 5 feet tall, and they were 6 feet tall, they would deviate 1 foot from the value of 5. If the person was 4 feet tall, they would also have a deviation of 1 foot.)

The mean absolute deviation is complicated. You probably want to set up two columns (or at least this is how I was taught to do it), the first column being the value (represented by x in the mean absolute deviation formula), the second column being the difference between the mean of the data set and the value (the mean is represented as x with a line over it).

∑ is the sum of the values of the second column.

To find the mean (remember, mean = average) of the deviations, you are going to add all of the deviations together, and divide by your number of values.

I'll write out the second column (the difference from mean) below:

| x - [tex]\frac{}{x}[/tex] |

4

0

2

4

4

1

3

2

if you add all of these values up, you will get 20; ∑ = 20

[  | | means absolute value--essentially the distance of the value from 0, so a negative number is written as a positive numbers; |-3| = 3 ; |3| = 3 ]

Now you will find the mean of your deviations. The sum of all deviations (∑) = 20. The number of deviations/the number of values is 8.

So, the equation of 20 / 8 will give us the absolute mean deviation.

20/8 = Mean Absolute Deviation

Mean Absolute Deviation = 2.5

Your Mean Absolute Deviation is 2.5 [hours] .

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

c)

Now you are being asked to interpret what this 2.5 indicates. It means that each student has, on average, a difference of 2.5 hours of TV watched from the mean. The Mean Absolute Deviation gives us a sense of how spread out the values of a data set are. We know that a mean absolute deviation of 0 would indicate that all values of the set are exactly identical. A mean deviation of 100 would indicate that all of the values are drastically different. So, a mean deviation of 2.5 indicates that all of the values (each student's watch hours) are fairly similar.

Answer:

(-10,0)(-5,0)(-10,-10)(-10,-5)

Step-by-step explanation:

If we count each box as one unit then we just count and if you left or down it is negative

Answer:

20

Step-by-step explanation:

because 4 can go into 20 5 times without a remainder

Answer:

1/4 = 1/4 × 5/5 = 5/20

2/5 = 2/5 × 4/4 = 8/20

Therefore, the LCD is 20

Step-by-step explanation:

Answer:

67.69

Step-by-step explanation:

You have your equation, t = -1.63 a + 92.14

a = age

a = 15

if you update your equation to fill in for a you get:

= -1.63 (15) + 92.14

-1.63 x 15 = -24.45

-24.45 + 92.14 = 67.69

67.69

Answer:

67.69

Step-by-step explanation:

You have your equation, t = -1.63 a + 92.14

a = age

a = 15

if you update your equation to fill in for a you get:

= -1.63 (15) + 92.14

-1.63 x 15 = -24.45

-24.45 + 92.14 = 67.69

67.69

Answer:

a = 51
b = 51 (??not so sure)
c = 20 cents

Step-by-step explanation:

a) 25 x 408 = 10200
10200 ÷ 200 = 51 square ft is one one roll.


b) the surface area of an average gift is 51 sq ft (?)


c) 40  ÷  200 = 0.2
each roll costs $40 dollars. each roll can wrap 200 gifts so 40  ÷ 200 = $0.20/ 20 cents

Answer:

Step-by-step explanation:

assuming its repeating as .580808080 etc your answer would be 115/198 :)

Answer:

115/198

Step-by-step explanation:

.580 = .5808080

.5808080 = x

5.808080 = 10x

58.08080 = 100x

580.8080 = 1000x

1000x - 10x = 575

575 = 990x

x = 575/990

Simplify:

575/990 = 115/198

Hope this helps :)

Answer:

No explanation, THIS IS ALL ABOUT SPEED

*speedrunning intensifies*

1.

B,  8x + 12

2.

G, she subtracted before adding

3.

C, 3x + 6

4.

F, Student 1 and 4

Answer:

1. B

2. G

3. C

4. F

Step-by-step explanation:

1. Soln:

4(2x+3)

=4*2x+4*3

=8x+12 ans.

2. Soln:

14-8/2+3*4

=14-4+3*4

=14-4+12

=26-4

=22 ans.

3. Soln:

=x+x+x+1+1+1+1+1+1+1+1-1-1

=3x+8-2

=3x+6 ans.

Answer:

-16n - 41

Step-by-step explanation:

To simplify the equation, you need to get rid of the parentheses by multiplying the numbers outside the parentheses to the numbers inside. Then, you can combine the similar terms.

2(-n - 3) - 7(5 + 2n)                         <---- Original equation

-2n - 6 - 7(5 + 2n)                           <---- Expand first parentheses by mult.

-2n - 6 - 35 - 14n                            <---- Expand second parentheses by mult.

-16n - 6 - 35                                    <---- Combine terms with "n"

-16n - 41                                          <---- Combine whole numbers

Answer:-2n-29

Step-by-step explanation:2*-n=-2n

2*-3=-6

-7*5=35

-7*2n=-4n

2n-6-35-44n

2n-4n=-2n

6-35=-29

2n-29

Answer:

Part A :

The scale factor of the dilation that transforms triangle PQR to triangle P'Q'R' is divided by 3.

Part B :

P"(-1,2), Q"(0,3), R"(1,0)

Part C :

Triangle PQR and P"Q"R" are not congruent because congruent means equal and similar but triangle PQR and P"Q"R" are proportional because they are rational to each other but do not have the same measures of sides but the angles are congruent.

This is the graphing of the triangle.

Answer:

155 acres

Step-by-step explanation:

corn = 215

wheat = 215 - 60 = 155

Let

Eq1 : x - 2y = 12

Eq2 : 4x + 2y = 16

For substitution, we need to rearrange on of the equations so that we can substitute it in the other. Let's pick eq2 and rewrite it as 2y = 16 - 4x. We see that eq1 also has 2y in it, so we can plug this new version of eq2 in there.

3x - (16-4x) = 12

Now solve for x.

7x=28, so x=4

Plug that into either equation to solve for y. You get y=0.

So your answer is x=4, y=0

Answer:

i think its X squared=y squared +4

Step-by-step explanation:

thats what i got

Answer:

133

Step-by-step explanation:

Answer:

the answer is 28 in

hope this helps

Answer:

.643

Step-by-step explanation:

just put it in the calc and round

Answer:

0.6429

Step-by-step explanation:

[tex]9\sqrt{14} = 0.64285\\round up to nearest thousandth = 0.6429[/tex]

Answer:

Unit fraction cubes is 8

Blue cube = 1/2

Step-by-step explanation:

1/2 in × 1/2 in × 1/2 in = 1/8 in³

unit fraction cubes × 1/8 in³ = 1 in³

then the unit fraction cubes is equal to 8

8 × 1/8 in³ = 1 in³

Answer:1/8 cubic inches is the volume of the cube

Step-by-step explanation:

Answer:

The digit that makes the statement true is 2...hope this helps:)

Answer:

The digit is two.

Step-by-step explanation:

It is very simple, to find if a number is divisible by 3 specifically, you need to add all the digits together. All the digits together added up to 37, which is not divisible by 3. But if you make the missing digit 2 then the digits add up to 39 which is divisible by 3.

Answer: 8√2

Step-by-step explanation:

Plug in with the Pythagorean theorem: a^2 + b^2 = c^2

So we have 18^2=14^2 + x^2

Solve for X

X is 8√2

Answer:8 hours

Step-by-step explanation: There are 250 samples, but there are only actually 200, since 50 need to be on display. That means that they will last 200/25=8 hours.

Answer:

b

Step-by-step explanation:

because its a reasonal answer if you do the math

Answer:

[tex]m\angle MNI = 135^{\circ}[/tex]

Step by step explanation:

[tex]\text{The exterior angle of a triangle = sum of two opposite interior angles.}[/tex]

[tex]~~~~~~\angle MNI = \angle LMN + \angle MLN\\\\\implies 19x+2=(15x-12)+6x\\\\\implies 19x +2 = 21x-12\\\\\implies 21x -19x = 12+2\\\\\implies 2x = 14\\\\\implies x=\dfrac {14}2\\\\\implies x = 7\\\\\text{So,}~ m\angle MNI = 19(7)+2=135^{\circ}[/tex]

Answer: divide by 6?

Step-by-step explanation:

What is the least positive integer by which 24 should be divided so that the resulting integer is a perfect square?

If we actually guess and check by dividing by 1, then 2, then 3, then etc. we will get the answer. I tried and divided by 6, which is 4, which is a perfect square. Do not trust me completely on this, for I am not quite sure.

Answer:

The answer is 8

Please mark me as brainliest

Answer:

8

Step-by-step explanation:

Pythagoras theorem

A^2 +b^2 = C^2

please mark as brainliest