Mathematics Middle School

1. Factor this quadratic function:2x2 + 12x +16

Answers

Answer 1

Answer:

4 (3x + 5)

Step-by-step explanation:

Simplify

4 + 12x +16

Simplify

12x + 20

Factor

4 (3x + 5)

Answer 2

Answer:

$2(x+4)(x+2)$

Step-by-step explanation:

We can start with the observation that every coefficent in the quadratic $2x^2 + 12x +16$ is a multiple of 2. Factoring out the 2, our expression becomes $2(x^2+6x+8)$. Let's focus on the second term, $x^2+6x+8$. To factor this, we want to find two numbers that multiply to 8 and add to 6. 4 · 2 = 8 and 4 + 2 = 6, so we can use that fact to split the middle term and factor the quadratic completely:

$x^2+6x+8\\=x^2+2x+4x+8\\=x(x+2)+4(x+2)\\=(x+4)(x+2)$

Putting that back with the 2 we factored out earlier, our fully factored function is

$2(x+4)(x+2)$

Related Questions

Consider the situations in the table below
Situation A: A hang glider descended 33.57 feet, and then ascended 14.98 feet.
Situation B: A football team gained 7 2/5 yards in one play, and then lost 3/5 of a yard in the next play.
Situation C: A hiker walked 3 1/6 miles yesterday and 2 1/2 miles today.
Situation D: A worker earned $23.66 Monday and spent $15.84 Tuesday.

Calculate the sum of each situation. Order the situations from least to greatest based on the numeric value of the sums.

Answers

Answer:

Step-by-step explanation:Situation A: The hang glider descended 33.57 feet and again ascended 14.98. So 33.57 - 14.98 = 18.58. So now the hang glider is at 18.58 feet

Situation B: Initially they gained 7 2/5 yards and then lost 3/5 yards.

7 2/5 yards can be written as 37/5. As they lost 3/5 yards, 37/5 - 3/5 = 34/5. So the remaining yards are 34/5 yards.

Situation C: Hiker walked 3 1/6 miles and then 2 1/2 miles. So the total distance is 3 1/6 + 2 1/2 = 5 4/6 miles.

Situation D: Total amount earned is $23.66 + $15.84 = $39.5.

Answer:

Step-by-step explanation:Situation A: The hang glider descended 33.57 feet and again ascended 14.98. So 33.57 - 14.98 = 18.58. So now the hang glider is at 18.58 feet

Situation B: Initially they gained 7 2/5 yards and then lost 3/5 yards.

7 2/5 yards can be written as 37/5. As they lost 3/5 yards, 37/5 - 3/5 = 34/5. So the remaining yards are 34/5 yards.

Situation C: Hiker walked 3 1/6 miles and then 2 1/2 miles. So the total distance is 3 1/6 + 2 1/2 = 5 4/6 miles.

Situation D: Total amount earned is $23.66 + $15.84 = $39.5.

Step-by-step explanation:

See the picture to solve the question 1Question=10 points

Answers

Answer:

1.5x+2.75y+33

Step-by-step explanation:

Call x: the hour of dogs keeping

y: the hour of wolves keeping

The total charge for dogs keeping: 19+ 1.5x

The total charge for wolves keeping: 14+2.75y

Total cost (19+ 1.5x)+(14+2.75y)= 1.5x+2.75y+33

the answer is 1.5x+2.75y+33

pls help me im confused.. dont answer this just for points answer bc it will halp somebody benifit from it

Answers

Answer: 30/100 a w p

Step-by-step explanation:

the answer is 30/100 a w/p

Liam went out to lunch. He paid his $13.79 bill in cash and received less than $7 in change. How much could Liam have paid the cashier?

Would you write an inequality or an equation?

Answers

Answer:

The answer is he paid with a $20 bill

Step-by-step explanation:

20.00-13.79=6.21

I would write a equation.

After the incorporation of BOOM cards in her lesson plans, Mrs.Ann has seen an increase in student averages from 72% to 75%. Express this change as a percentage.

A-4.2% increase
B-96% increase
C-26% increase
D-38% increase

Answers

Answer:96% increase

Step-by-step explanation:

the answer is B (96% increase)

1. 9s + 4t

2. 46rs + 10x

3. 18q + 14x

4. 10x + 14y

5. 17rs + 32x

6. 5x + 7y - 5z

7. 3ab + 70m

8. 3r + 20a + 10m

9. 7k + 16m

10. 7r + 5s

11. 9j + 120m

12. 12k + m

13. 6c + 15h + w

14. 2c - 19d + 12f

15. 3t + 14r - 31j

Answers

Answer:

1. 9, 4

2. 46, 10

3. 18, 14

4. 10, 14

5. 17, 32

6. 5, 7

7. 3, 70

8. 3, 20, 10

9. 7, 16

10. 7, 5

11. 9, 120

12. 12, 1

Step-by-step explanation:

Definition of coefficient. Your welcome :)

the numbers are the coefficients and the letters are variables

If the relationships below are given in the form (input, output), which pairing always describes a function? (a person’s age in years, that same person’s height in inches) (a person’s weight in pounds, that same person’s height in inches) (a person’s height in centimeters, that same person’s height in inches) (a person’s telephone number, that same person’s height in inches)

Answers

Answer:

A function is a mathematical relation in which each input (domain value) is associated with exactly one output (range value). In other words, for a relation to be a function, each input can have only one corresponding output. Let's analyze the given pairings:

(a person’s age in years, that same person’s height in inches) - This can be a function because one person's age in years should correspond to a single height in inches.

(a person’s weight in pounds, that same person’s height in inches) - This can also be a function because one person's weight in pounds should correspond to a single height in inches.

(a person’s height in centimeters, that same person’s height in inches) - This can be a function because one person's height in centimeters should correspond to a single height in inches.

(a person’s telephone number, that same person’s height in inches) - This may not necessarily be a function. It's possible for two different people to have the same height in inches but different telephone numbers.

So, the pairings that always describe a function are:

(a person’s age in years, that same person’s height in inches)

(a person’s weight in pounds, that same person’s height in inches)

(a person’s height in centimeters, that same person’s height in inches)

These three pairings meet the criteria of a function, where each input corresponds to a unique output.

The pairing that always describes a function is option C. (a person’s height in centimeters, that same person’s height in inches)

How did we arrive at this assertion?

A pairing describes a function when each unique input (domain element) is associated with exactly one unique output (range element). In other words, there should be no ambiguity or multiple outputs for a single input. Let's analyze the given pairings:

1. (a person’s age in years, that same person’s height in inches): This pairing may not always describe a function because multiple people can have the same age, but they might have different heights. So, there can be multiple outputs for the same input (age).

2. (a person’s weight in pounds, that same person’s height in inches): Similar to the first pairing, this may not always describe a function because different people can have the same weight but different heights.

3. (a person’s height in centimeters, that same person’s height in inches): This pairing describes a function because for each unique height in centimeters, there is only one corresponding height in inches.

4. (a person’s telephone number, that same person’s height in inches): This pairing may not always describe a function because multiple people can have the same telephone number, but they might have different heights. So, there can be multiple outputs for the same input (telephone number).

So, the pairing that always describes a function is: (a person’s height in centimeters, that same person’s height in inches)

learn more about function describing pairs: https://brainly.com/question/31919824

#SPJ1

Can someone help pls and thank you

Answers

Answer:

0.70

Step-by-step explanation:

you add up the numbers for red green and purple. Then you add all of the numbers together separately. Then you take the number you got after you added red green and purple and divide it by the number you got when you added them all together. Then you round your decimal to the nearest hundredth.

Can someone answer I don't understand?

Answers

Answer:
A or top answer
Step-by-step explanation:
the minimum is the lowest point and that is 42 and maximum is highest point which is 56
The median is the line in the middle at 50
Q1 and a3 are the other lines located at 44 and 54
Hopes this helps please mark brainliest

Answer:

i i i i i i i i i i i i i i i i i i i i i i i i i i i i 56

8x/13 = 64/52

If answer is in a decimal, put in fraction (simplest form)

Answers

x=2
Simplify 64/52
64/52=16/13
To get 16/13, you have to cancel out the common factor which is 4.
8/13x=16/13
8•13=104
13•16=208
208 / 104 = 2
Therefore,
x=2

Answer: 2

Step-by-step explanation: This is incredibly simple first we can match the denominators, 4*13 = 52 and that means we have to do that to numerators to, 8x*4 = 32x so now our equation is 32x/52 = 64/52 and as we know 32*2 = 64 so that means x = 2.

The spinner is divided into 8 congruent sections.

After 96 spins, how many times would Tiffany expect the spinner to land on a color section beginning with the letter "B"?

Answers

Ummmm four over ninty-six

Answer:

Step-by-step explanation:

96/8=12*4=48

Manny drank 100 milliliters of orange juice at breakfast. For lunch, his mom packed him a box of apple juice. He drank all 125 milliliters of apple juice at lunch.
How much juice did Manny drink in all?

Answers

Answer:

Many drank a total of 225 millilitres

100+125=225
Manny drank 225 milliliters of juice

Pls help, 20 points! A number cube is rolled d360 times, and the results are recorded as follows: 96 ones, 31 twos, 49 threes, 76 fours, 45 fives, and 63 sixes. What is the experimental probability of rolling a 2 or a 3?

It would help if you could put the answer in decimal form but you don't have to :D

Answers

Answer:

The experimental probability of rolling a 2 or a 3 is 2/9 or 0.222222 (go as long as you like :D)

Step-by-step explanation:

Total number of times cube roller = T = 360,

we have 96 ones, 31 twos, 49 threes, 76 fours, 45 fives, and 63 sixes

The probability of rolling a 2 is,

since we get 31 twos out of 360 rolls,

P(2) = 31/360

The probability of rolling a 3 is,

since we get 49 threes out of 360 rolls,

P(3) = 49/360

the experimental probability of rolling a 2 or a 3 is the sum of these two,

so,

P(2 or 3) = P(2) + P(3) = 31/360 + 49/360 = 80/360 = 2/9

P(2 or 3) = 2/9

In decimal form, P(2 or 3) = 0.2222222

The experimental probability of rolling a 2 or a 3 is 2/9 or (0.2222) .

The number of times a 2 or a 3 was rolled is the sum of the occurrences of twos and threes,

P(2) = 31

P(3) = 49

P(2) + P(3) = 31 + 49 = 80.

The total number of rolls is given as 360.

Now, calculate the experimental probability:

Experimental probability of rolling a 2 or a 3 = Number of times a 2 or a 3 was rolled / Total number of rolls

P(2 or 3) = 80 / 360

After simplifying the fraction:

Experimental probability of rolling a 2 or a 3 = 2/9

Therefore, the experimental probability of rolling a 2 or a 3 is 2/9.

Learn more about Experimental Probability:

https://brainly.com/question/8652467

i need help with this question please help me

Answers

Answer:

The answer is D.

Step-by-step explanation:

y = mx + b

C = 5/9 (F - 32)

C = 5/9F - 5/9 (32)

Option (D) is correct.

Which inequalities would have an open circle when graphed? Check all that apply.
t Less-than-or-equal-to 25
-2.5 Less-than-or-equal-to m
x > 5.4
One-half less-than x
x > 0

Answers

An open circle is used to graph strict inequalities, which means the inequality does not include the value at the boundary. The inequalities that would have an open circle when graphed are:

x > 5.4

One-half less-than x

x > 0

All of the options that are just LESS THAN are open circled

if an inequality states less than OR equal to that means the circle will be closed when graphed

HELPP :(
The football team at Weston College is having a bigger stadium built to accommodate its growing fan base. The old stadium had enough seats for 59,400 people. The new stadium will have enough seats for 113,454 people. What is the percent of increase in the seating capacity of the stadium?

Answers

Answer: 90%

Step-by-step explanation:

The increase in percentage is 76%

Find the area of the shaded region

Answers

Answer:

104ft

Step-by-step explanation:

104 > 13ft x 16ft divided by 2 :)

Which expression is equivalent to -1/3 ( 6x + 15 ) - 3?
a) -2x + 12
b) -2x + 2
c) -2x - 2
d) -2x - 8

Answers

The correct answer is (D) -2x - 8.

To simplify the expression -1/3 ( 6x + 15 ) - 3, we can first apply the distributive property to the term in parentheses:

-1/3 ( 6x + 15 ) - 3 = -1/3 * 6x - 1/3 * 15 - 3

Then we can simplify using the properties of multiplication and division:

-1/3 * 6x - 1/3 * 15 - 3 = -2x - 5 - 3

Finally, we can combine like terms:

-2x - 5 - 3 = -2x - 8

The correct answer is therefore (D) -2x - 8.✅

The correct answer B

The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.

Mountain View School Seaside School
0 5, 8
9, 8, 2, 0 1 0, 1, 2, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 5, 5, 7, 7, 8
0 3 0, 6
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Seaside

Part A: Calculate the measures of center. Show all work. (2 points)

Part B: Calculate the measures of variability. Show all work. (1 point)

Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)

Answers

To calculate the measures of center, we need to find the mean and median for each school.

For Mountain View School:
Data: 0, 0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 9
Mean: (0 + 0 + 0 + 0 + 1 + 2 + 3 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 7 + 8 + 8 + 8 + 9) / 19
= 100 / 19
≈ 5.26

To find the median, we need to arrange the data in ascending order: 0, 0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 9.
The median is the middle value, which is the 10th value in this case.
Median: 5

For Seaside School:
Data: 0, 0, 0, 1, 1, 2, 2, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9
Mean: (0 + 0 + 0 + 1 + 1 + 2 + 2 + 4 + 5 + 5 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9) / 19
= 80 / 19
≈ 4.21

To find the median, we need to arrange the data in ascending order: 0, 0, 0, 1, 1, 2, 2, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9.
The median is the middle value, which is the 10th value in this case.
Median: 5

Now let's calculate the measures of variability, specifically the range and interquartile range (IQR).

Range: The range is the difference between the largest and smallest values in the dataset.

For Mountain View School:
Range: 9 - 0 = 9

For Seaside School:
Range: 9 - 0 = 9

Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) and measures the spread of the middle 50% of the data.

For Mountain View School:
Q1 = 3
Q3 = 7
IQR = Q3 - Q1 = 7 - 3 = 4

For Seaside School:
Q1 = 2
Q3 = 7
IQR = Q3 - Q1 = 7 - 2 = 5

To determine which school is a better choice for a smaller class size, we can consider both the mean and the median.

Both the mean and median for Mountain View School are higher than those for Seaside School. This suggests that, on average, the class sizes at Mountain View School are larger than those at Seaside School. Therefore, if you are interested in a smaller class size, Seaside School would be a better choice

Part A:

For Mountain View School:
- Median: The median class size is the middle value, which is 25.
- Mean: The mean class size is the sum of all the class sizes divided by the total number of classes, which is (29 + 28 + 28 + 27 + 25 + 24 + 24 + 23 + 21 + 20 + 19 + 18 + 15 + 13 + 10) / 15 = 21.27.

For Seaside School:
- Median: The median class size is the middle value, which is 20.
- Mean: The mean class size is the sum of all the class sizes divided by the total number of classes, which is (25 + 25 + 27 + 27 + 28 + 28 + 28 + 30 + 31 + 35 + 36 + 38 + 40 + 43 + 45) / 15 = 31.13.

Part B:

For Mountain View School:
- Range: The range is the difference between the largest and smallest values, which is 29 - 10 = 19.
- Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). From the stem-and-leaf plot, we can see that Q1 is 20 and Q3 is 28. Therefore, the IQR is 28 - 20 = 8.

For Seaside School:
- Range: The range is the difference between the largest and smallest values, which is 45 - 25 = 20.
- Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). From the stem-and-leaf plot, we can see that Q1 is 27 and Q3 is 38. Therefore, the IQR is 38 - 27 = 11.

Part C:

If you are interested in a smaller class size, Mountain View School is a better choice for you because it has a lower mean and median class size than Seaside School.

Figure ABCD is shown on the coordinate plane. Suppose a graphic designer wants to dilate the figure so that the resulting image has a smaller area than figure ABCD. Describe a way the designer can achieve this type of dilation.

Answers

Answer:

Step-by-step explanation:

If the dilated image is smaller than the original, then 0<k<1.

Meaning the scale factor is less than one, but greater than zero.

You would mulitply each coordinate by this scale factor - to obtain the coordinates of the dilated figure.

Let's choose $\frac{1}2}$.

In the original figure Point A = (-4,3) dilating by $\frac{1}{2}$ results in A' being (-2, 1.5). When you multiply each cooordinate (-4,3) by one half.

Applying the scale factor of one half to the other coordinates - yields these results.

Point B (4,3) becomes Point B' (2, 1.5)

Point C (-4,-4) becomes Point C' (-2,-2).

Point D (4, -4) becomes Point D' (2,-2)

Answer:

K will equal something more than 0 and less than 1.

Explanation:

Multiply each side length by the same factor, a number between 0 and 1.

Multiply the pairs of numbers and match them with their products. Tiles (-5)(4.2) (-7)(-3) (4) (5) (2.5)(-9) Pairs 22.5 21 -22.5 -21 111

Answers

Here are the pairs matched with their products:

- (-5)(4.2) matches with -21

- (-7)(-3) matches with 21

- (2.5)(-9) matches with -22.5

Pairs (4) and (5) do not have corresponding products in the given options.

The products of the given pairs of numbers are:

(-5)(4.2) = -21

(-7)(-3) = 21

(4)(5) = 20

(2.5)(-9) = -22.5

So, the pairs of numbers and their products are as follows:

(-5)(4.2) = -21 matches with -21.

(-7)(-3) = 21 matches with 21.

(4)(5) = 20 matches with 20.

(2.5)(-9) = -22.5 matches with -22.5.

I hope this helps!

Calculate each numbered angle measure.

Answers

Answer:

m1 = 90°

m2 = 68°

m3 = 112°

m4 = 112°

m5 = 68°

m6 = 44°

m7 = 112°

m8 = 112°

Concept used:

- The sum of the internal angles of a triangle is 180

- With two parallel line and one oblique, the angles internal and opposite are congruent (ex: m3 and m4)

- An isosceles triangle has the base angles congruent

Step-by-step explanation:

m1 is a rectangle angle

m2 is 180-m1-22

m3 is 180-m2

m5 is 180-m4

m6 is 180-m5-m5

m3 = m4 = m7 = m8

Solve the equation to get the value y

Answers

Answer:

y=11

x=-4

Step-by-step explanation:

y =-x+7

2x-5y=-7

insert the first equation into the second like so...

2x+5x-35=-7

Now rearrange...

2x+5x=-7+35

Now solve...

7x=-28

x=-4

Now incert x in any equation...

y=4+7

y=11

Y=11
X=-4
Did this exact question

Find the commission.

Answers

Answer:

63.9

Step-by-step explanation:

Convert 9% to a decimal: 0.09

710×.09=63.9

Please give me brainliest

what is 46 divided by 107

Answers

Answer:

0.42990654205

Step-by-step explanation:

Answer: 46/107 or 0.429907 in decimal form

Step-by-step explanation:

Please help, I will give brainliest if possible!

solve for x
x - 3/5 = x + 5/3
(3/5 and 5/3 are fractions)

Answers

2.26666666667 here you go

X= - 9/10 (9/10 is a fraction)

Help pls!! it's urgent.

Answers

Answer:

Step-by-step explanation:

Write the sentence as an equation.
276 increased by z is equal to the sum of 86 and n

Type a slash ( / ) if you want to use a division sign.

Answers

Answer:276+z= 87+n

Step-by-step explanation:

276+z=86+N I hope this helps

???????????????????????????

Answers

Answer:

12 and 78 are complementary.

80 and 100 are supplementary.

50 and 50 are neither.

Step-by-step explanation:

Hope it helps! =D

Using the dot plot, describe the members of the math
club
x
Ages of Math Club Members
+
9
+
10
+
11
12
13
I need help

Answers

There are 9 members in the math club

From the dot plots, we have the following frequency distribution

Age 9 = 2Age 10 = 0Age 11 = 1Age 12 = 2Age 13 = 4

So, the total member of the math club is:

$Total = 2 + 0 + 1 + 2 + 4$

Add all terms, in the above equation

$Total = 9$

Hence, there are 9 members in the math club