y=x^2-6x+7 from algebra nation

Final answer:

To organize the results into a two-way frequency table, fill in the known values and calculate the remaining values based on the total number of students.

Explanation:

To organize the results into a two-way frequency table, we can use the information given. First, we know that 6 students play both a musical instrument and a sport. We also know that 3 students play neither a musical instrument nor a sport. Furthermore, we know that a total of 14 students play a sport. From this information, we can fill in the table:

Plays a sport Does not play a sport

Plays a musical instrument 6 To be filled

Does not play a musical instrument To be filled 3

We can calculate the values for the empty cells by subtracting the known values from the total. So, the number of students who play a musical instrument but do not play a sport is 24 - (6 + 3 + 14) = 1. Likewise, the number of students who do not play a musical instrument but play a sport is 24 - (6 + 3 + 14) = 1.

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Answer:

the degree of homogeneity is 20.

Step-by-step explanation:

In a polynomial P (x, y), homogeneous and complete in "x" and "y", the sum of the absolute degrees of all its terms is 420. What is its degree of homogeneity?

A homogeneous polynomial is one in which all monomials have the same degree.

This is an example of a homogeneous polynomial of degree 4 (the degree of all monomials is 4):

x ^ 4 + 3x ^ 3y + 2x ^ 2y ^ 2 + xy ^ 3 + 8y ^ 4.

As you can see, the sum of the exponents of the variables x, y in each monomial is 4.

And the number of terms is 5, that is, it is the degree of homogeneity plus 1.

In relation to the sum of the absolute degrees of all monomials or terms it will be: 4 + 4 + 4 + 4 + 4 = 4 * 5 = 20.

In general, you can say that the sum of the absolute degrees in a homogeneous polynomial will be the degree of each monomial by the number of terms = degree * (degree + 1)

Calling n, the degree of our polynomial, it must be fulfilled:

n (n + 1) = 420

=> n ^ 2 + n = 420

=> n ^ 2 + n - 420 = 0

Factoring:

(n + 21) (n - 20) = 0

=> n = -21 and n = 20.

Only the positive value makes sense, therefore n = 20.

In other words, the polynomial is of the form (excluding the coefficients):

x ^ 20 + x ^ 19 y + x ^ 18 y ^ 2 + x ^ 17 y ^ 3 + .... x ^ 3 y ^ 17 + x ^ 2y ^ 18 + xy ^ 19 + y ^ 20

That polynomial has 21 terms.

So the sum of the degrees will be 20 * 21 = 420, as required in the statement.

Therefore, the degree of homogeneity is 20.

Answer:

32

Step-by-step explanation:

The measure of ∠X is approximately 47.9 degrees to the nearest tenth of a degree.

To find the measure of ∠X in triangle WXY, you can use the trigonometric relationship of the tangent function.

Given that ∠Y is a right angle (90°), and you have the lengths of two sides, WX and XY, you can use the following relationship:

tan(∠X) = opposite/adjacent

In this case:

Opposite side to ∠X = WX

Adjacent side to ∠X = XY

So, you have:

tan(∠X) = WX / XY

tan(∠X) = 7.9 feet / 6.7 feet

Now, you can find ∠X by taking the arctan (inverse tangent) of this value:

∠X = arctan(7.9 / 6.7)

Using a calculator, you can find:  

∠X ≈ 47.9 degrees (rounded to the nearest tenth of a degree)

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Answer:

w = 100 ft

Step-by-step explanation:

A football fields is of rectangular shape, and for that shape, we know the length (300 ft) and one diagonal (316,2 ft). To determine the width we have to understand that diagonal, length and a width form a right triangle, and in a right triangle we can apply Pytagoras theorem. Therefore:

d(diagonal)²  =  l²  +  w²    where l is the length and w the width

d²  =  l² + w²    ⇒    d²  -  l²  = w²

w²  =  ( 316,2)² - (300)²   ⇒   w²  =  99982,44 - 90000

w² = 9982,44

w = √9982,44

w = 99,91 ft

Rounded to the nearest foot

w = 100 ft

Answer:

y = 5

Step-by-step explanation:

25 = y + 20

y = 25 - 20

y = 5

hope it helps!

Answer:

y = 5

Step-by-step explanation:

Let's start!

Our equation for today is 25 = y + 20.

First we need to subtract 20 from each side,

                                        25 = y + 20

                                       -20        -20

We get,  

                                          5 = y

So our answer is 5!

(Or y = 5)

NICE JOB EVERYONE!

Answer:

24 blocks long

Answer:

24 blocks.

Step-by-step explanation:

[tex]\frac{1}{6} +\frac{5}{8} =5[/tex] blocks

[tex]\frac{8}{48} + \frac{30}{48}=\frac{38}{48}\\\\ \frac{48}{48} -\frac{38}{48} =\frac{10}{48}[/tex]

[tex]\frac{10}{48}[/tex] is 5 blocks

You can use ratios to find out how many blocks for each color now. (I'm too lazy)

Blue blocks: 4 blocks

Red blocks: 15 blocks

Yellow blocks: 5 blocks

4+15+5=24 blocks in total.

Answer:

x =118

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees.  Let the unknown angle be x

37+25 +x = 180

Combine like terms

62+x = 180

Subtract 62 from each side

62+x-62 = 180-62

x =118

Answer:

Probability that the card Connor chooses has a number on it that is even or divisible by 5 is (3/5) or 0.6.

Step-by-step explanation:

We are given that Connor randomly chooses a card from a deck of numbered cards. the cards are numbered 1 through 10, and each number appears only one time.

And we have to find the probability that the card Connor chooses has a number on it that is even or divisible by 5.

Let the Probability that card Connor chooses has a number on it that is even = P(A)

Probability that card Connor chooses has a number on it that is divisible by 5 = P(B)

Probability that card Connor chooses has a number on it that is even and divisible by 5 =  [tex]P(A\bigcap B)[/tex]

Probability that card Connor chooses has a number on it that is even or divisible by 5 =  [tex]P(A\bigcup B)[/tex]

Here, Even numbers are = {2, 4, 6, 8, 10} = 5

Numbers divisible by 5 = {5, 10} = 2

Also, Number which is even and also divisible by 5 = {10} = 1

Total numbers = 10

Now, Probability that card Connor chooses has a number on it that is even =  [tex]\frac{5}{10}[/tex]  = 0.5

Probability that card Connor chooses has a number on it that is divisible by 5 =  [tex]\frac{2}{10}[/tex]  = 0.2

Probability that card Connor chooses has a number on it that is even and divisible by 5 =  [tex]\frac{1}{10}[/tex]  = 0.1

Now,     [tex]P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)[/tex]

                             =  0.5 + 0.2 - 0.1

                             =  0.6  =  [tex]\frac{3}{5}[/tex]

Hence, probability that the card Connor chooses has a number on it that is even or divisible by 5 is 0.6.

The graph of g(x) = 2x + 7 is a vertical shift of the graph of f(x) = x by 7 units upward.

The linear parent function, f(x) = x, is transformed to g(x) = 2x + 7. The transformation is a vertical shift of 7 units upward and a horizontal stretch by a factor of 2. To compare the graphs of the functions, we can plot a few points and observe the differences. For example, if we consider x = 0, for the parent function f(x) = x, the output is f(0) = 0. However, for the transformed function g(x) = 2x + 7, the output is g(0) = 7. This shows that all the y-values of the transformed function are 7 units higher than the corresponding y-values of the parent function. Therefore, the statement that correctly compares the graphs of the functions is that the graph of g(x) is a vertical shift of the graph of f(x) by 7 units upward.

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Final answer:

The function g(x) = 2x + 7 has a steeper graph than f(x) = x due to a larger slope and is also shifted upward by 7 units.

Explanation:

The linear parent function f(x) = x is transformed to g(x) = 2x + 7. When comparing the graphs of the two functions, we notice that g(x) is a transformed version of f(x). Specifically, the graph of g(x) has a slope of 2, which is a steeper incline than the parent function f(x), which has a slope of 1. Additionally, g(x) has a vertical shift upwards by 7 units. Therefore, the statement that correctly compares the two graphs would indicate that g(x) is steeper and shifted 7 units up from the graph of f(x).

Answer:

A

Step-by-step explanation:

Answer:A-70

Step-by-step explanation:

180-110=70

Answer:

3+3x+7 or 3x+10

Step-by-step explanation:

Answer:

3x+10

Step-by-step explanation:

3(1 + x) + 7

Distribute

3+3x+7

Combine like terms

3x+3+7

3x+10

Answer:

1 every 2.5 feet

Step-by-step explanation:

20 divided by 8 20 being the plants 8 being the length gives u 2.5

Rounding to the nearest hundredth, the distance between each plant will be approximately 1.26 feet.

To find the distance between each plant when they are evenly spaced around the edge of the circular garden, we can use the formula for the circumference of a circle:

[tex]Circumference (C) = \pi * diameter[/tex]

Rounding to the nearest hundredth, the distance between each plant will be approximately 1.26 feet.

Given that the diameter of the circular garden is 8 feet, we can calculate the circumference:

[tex]C = \pi * 8[/tex]

Now, let's calculate the circumference:

[tex]C = \pi * 8[/tex]

[tex]C = 3.14 * 8[/tex]

[tex]C = 25.12 feet[/tex]

Now, since there are 20 plants evenly spaced around the circumference, we can divide the circumference by 20 to find the distance between each plant:

[tex]Distance between plants = Circumference / Number of plants[/tex]

[tex]Distance between plants =25.12 / 20[/tex]

[tex]Distance between plants = 1.256 feet[/tex]

Complete correct question:

Jared is going to plant 20 small plants around the edge of a circular garden

that is 8 feet in diameter. If he spaces the plants evenly, how much distance

will be between the plants? (Round to the nearest hundredth)

Answer:

629.11

Step-by-step explanation:

Six hundred twenty-nine and eleven hundredths

Hundreds | Tens | Ones | Tenths | Hundredths  

Fill in the above place value chart

Hundreds (100) | Tens (10) | Ones (1) | Tenths (0.1)  | Hundredths  (0.01)

       6                          2               9        .         1                        1

Multiply each value in the chart by their respective number above it.

6 (100) + 2 (10) + 9 (1) + 1 (0.1) + 1(0.01)

600 + 20 + 9 + 0.1 + 0.01

Add

629.11

Hope this helps :)

Answer:

a. y = 4,200 [tex]0.976^{4t}[/tex]

b. 9.2%

Step-by-step explanation:

Given the information:

=> the base number of the exponential function is:

100% - 2.4% = 97.6% = 0.976

Let t is quarter

Let y is the population

=>  the following shows an exponential decay function to find the quarterly decay rate is:

y (t)= 4,200 [tex]0.976^{4t}[/tex]

b. The population is decreasing by how much percent per quarter?

Let t = 0 we have: y(0) = 4,200 [tex]0.976^{4*0} = 4200[/tex]

Let t = 1 we have:  y(1) = 4,200 [tex]0.976^{4*1} = 3811[/tex]

=> the decreasing percentage is:

= (y(0) - y(1)) / y(0)*100%

= (4200 - 3811) / 4200 *100%

= 389/4200*100%

= 9.2%

The expoenetial function that represents the quarterly decay is y = 4200(0.994)^4t.

The  population is decreasing by 0.4% every quarter.

The formula that can be used to determine the rate of decrease every quarter is:

FV = P(1 - r/m)^tm

y = 4200( 1 - 0.024/4)^4t

y = 4200(1 - 0.006)^4t

y = 4200(0.994)^4t

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Answer:

9.2 seconds

Step-by-step explanation:

got it right on edg 2020

Answer:

The probability of an eighth grader winning is 1/3

Step-by-step explanation:

Total no. of students = 42

Number of students in 7th grade = 21

Number of students in 8th grade = 14

Number of students in 9th grade = 7

Probability of event = [tex]\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

So,the probability of an eighth grader winning= [tex]\frac{14}{42}=\frac{2}{6}=\frac{1}{3}[/tex]

Hence The probability of an eighth grader winning is 1/3

The answer is conditional. I had this question and got it right have a great day

Answer:

The answer would be C.) x = 6

Step-by-step explanation:

7+5 (4-3) = 12

7+5 (5 -3) = 17

7+5 (6-3) = 22

7+5 (7-3) = 27

The total profit from July through September is -$1 if Milk & Cookies is an ice cream sandwich stand.

It is defined as the depiction of numerical data in a graph using a bar with space.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we can see in the bar graph,

Milk & Cookies is an ice cream sandwich stand.

Total profit from July through September = (+2) + (+2) + (-5)

= -$1

Thus, the total profit from July through September is -$1 if Milk & Cookies is an ice cream sandwich stand.

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Without the bar chart data, the exact total profit for Milk & Cookies' from July through September cannot be calculated. Normally, you would add the monthly profits to find the total profit for the quarter.

To determine Milk & Cookies' total profit from July through September, we would need to examine the provided bar chart that lists profits for each month. However, since the actual bar chart data is not included in the question, we cannot calculate the exact total profit.

In a typical situation, you would add the profit of each month: Profit in July + Profit in August + Profit in September to find the total profit for that quarter.

If the total profits for July, August, and September are positive when added together, then Milk & Cookies has made a profit over these months.

If the sum is zero, the business broke even, and if the sum is negative, the business incurred a loss during that period. The profits from the bar chart are essential to conduct this analysis.

Answer:

23n=11112

n=11112÷23

...n=483.13

The value of n in the equation ( 23n = 11112 ) rounded to the nearest tenth is 483.1.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the data in the question;

We simply divide both sides by 23

23n = 11112

23n/23 = 11112/23

n = 11112/23

n = 483.1

Therefore, the value of n in the equation ( 23n = 11112 ) rounded to the nearest tenth is 483.1.

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Answer:

The answer is 225,000.

Step-by-step explanation:

Hope this Helps!!!

Answer:

225000

Step-by-step explanation:

Answer:

D. 80 mL

Step-by-step explanation:

Given:

- 10.0 mL of HCL

- 2.0 M HCl

- .25 M HCl

1) Convert mL to L

10 mL/1000 mL = .01 L

2) Find # of moles of HCl

2.0 M HCl = (x/.01 L)

x = .02 mol HCl

3) Find volume needed to make .25 M HCl

.25 M = .02 mol HCl/ y

y = .08 Liters

4) Convert Liters to mL

.08 L * 1000 mL = 80 mL

Answer: 80 mL (D)

Answer:

100 boxes are needed to fulfill the order

Step-by-step explanation:

In this question, we are concerned with calculating the number of boxes that are needed to fulfill an order.

Each of the boxes contain 16 bags of flour and each of these bags weigh 5 pounds. What this means is that each of the boxes will have a net weight of 5 * 16 = 80 pounds

Mathematically, 1 ton is the equivalent of 2,000 pounds. Hence, 4 tons is the equivalent of 4 * 2000 = 8,000 pounds

Thus, the number of boxes needed will be 8,000/80 = 100 boxes

Simplify the expression.

Exact Form:

189/2

Decimal Form:

94.5

Mixed Number Form:

94 1/2

Answer: 189 or 94.5

Step-by-step explanation:

divide 3/2 because he fashion is division so 3/2 is 1.5 then multiply 1.5 by 63    and you get 94.5

Answer:

2 3/4 divided by 11/8 would be 2.

Factor the numerator and denominator and cancel the common factors.

I hope that this was helpful :3

STAY SAFE!! :)

Answer:

C. 17

Step-by-step explanation:

f(x)= 3x+2

f(5)= 3(5) + 2

f(5)= 15+2

f(5) = 17

Answer:

2 (x-4) (x-2)

Step-by-step explanation:

2x^2-12x+16

Factor out a 2

2( x^2 -6x +8)

Now we factor the inside term

What multiplies to 8 and add to -6

-4*-2 =8

-4+-2 = -6

2 (x-4) (x-2)

The school has collected $1050.

Answer:

w=10.25

P=900

Step-by-step explanation:

You need to substitute those original numbers and see they dont work