Two students are asked to come to the board to work a math problem. Each student could work an easy question (E) or a hard question (H). Drag and drop the letters to show all the possible outcomes for the students' choices. List the first student's choice followed by the second student's choice.

Answer:

Slope is 1/4     y-intercept is 0

Step-by-step explanation:

I uploaded the graph below

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The system of equation is:

x + y = 20

x - y = 4

She has 12 dimes and 8 nickels

Step-by-step explanation:

The given is:

We need to write a system of equations that represents the problem and how

many of each coin she has

Assume that she has now x dimes and y nickels

∵ She has x dimes and y nickels

∵ She has a total of 20 coins

- Add x and y, then equate the sum by 20

∴ x + y = 20 ⇒ (1)

∵ One dime = 10 cents

∵ One nickels = 5 cents

- Multiply x by 10 and y by 5 to find how many cents she has now

∵ She has now (10x + 5y) cents

∵ The dimes were nickels and the nickels were dimes

- Multiply x by 5 and y by 10 to find how many cents she has

   after the change

∴ She had after the change (5x + 10y) cents

∵ The value after the change is less than the value now by

   20 cents

- Subtract (5x + 10y) from (10x + 5y) and equate the difference

   by 20

∴ (10x + 5y) - (5x + 10y) = 20

- Add the like terms in the left hand side

∴ (10x - 5x) + (5y - 10y) = 20

∴ 5x - 5y = 20

- Divide both sides by 5

∴ x - y = 4 ⇒ (2)

The system of equation is:

x + y = 20

x - y = 4

Now we have a system of equations to solve it

Add equations (1) and (2) to eliminate y

∴ 2x = 24

- Divide both sides by 2

∴ x = 12

- Substitute the value of x in equation (1) to find y

∵ 12 + y = 20

- Subtract 12 from both sides

∴ y = 8

She has 12 dimes and 8 nickels

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By calculating the shipping fees for regular and rush delivery for a 26.5 pound computer, we find that regular shipping saves approximately 14.90 dollars.

We must first calculate the fee for each method and then subtract the regular "shipping fee" from the rush delivery fee to find the savings.

Using the given expression, the regular shipping fee for a 26.5 pound computer is: 0.5*26.5 + 4.49 = 17.74 dollars. Meanwhile, the rush delivery fee for the same computer, using the other given expression, would be: 0.99*26.5 + 6.49 = 32.635 dollars.

Subtracting the regular fee from the rush fee, we find: 32.635 - 17.74 = 14.895 dollars. Therefore, you save about 14.90 dollars by choosing regular shipping over rush delivery.

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Answer:

Total: 40

Mean: 8

Step-by-step explanation:

To find the total, we add the numbers together and get 40. Then, to find the mean, we take the total and divide by the number of numbers, which is 5, to get our answer: 8

-AXZ

Answer:

C. The men simply keep chasing Nicki, and their motivations are not

revealed

The store initially bought 82 half gallons of milk.

To solve the problem, we need to find out how many half gallons of milk the store initially bought. We can set up an equation to represent the situation where the cost of milk is subtracted from the sales to find the profit.

Let's assume the store bought x half gallons of milk. Then, the cost of the x half gallons is x multiplied by $2.70:

Cost = 2.70x dollars

The store ruined 12 half gallons, so they can only sell x - 12 half gallons. The revenue from selling each half gallon is $4.02, so the total revenue from selling x - 12 half gallons is:

Revenue = 4.02(x - 12) dollars

We are told the store made a profit of $60, so the revenue minus the cost equals the profit:

4.02(x - 12) - 2.70x = 60

Now we solve for x:

4.02x - 48.24 - 2.70x = 60

1.32x - 48.24 = 60

1.32x = 108.24

x = 82 half gallons

Therefore, the store initially bought 82 half gallons of milk.

The depth of sun after 5 minutes is 809.82 feet

Solution:

A submarine dives at an angle of 13 degrees to the surface of the water

The submarine travels at a speed of 720 feet per minute

The figure is attached below

ACB is a right angled triangle

AB is the distance between surafce of water and submarine

BC is the depth of submarine

Let "x" be the depth of sun after 5 minutes

Therefore, distance between submarine and surface of water is:

[tex]AB = 720 \frac{feet}{minute} \times 5 \text{minute} = 3600 feet[/tex]

Submarine dives at an angle of 13 degrees to the surface of the water

Therefore, angle A = 13 degrees

Now we have to find BC

By definition of sine,

[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]

Here, opposite = BC = x

hypotenuse = AB = 3600 feet

Thus, we get,

[tex]sin \theta = \frac{BC}{AB}\\\\sin \theta = \frac{x}{3600}\\\\sin 13 = \frac{x}{3600}\\\\0.2249 = \frac{x}{3600}\\\\x = 3600 \times 0.2249\\\\x = 809.82[/tex]

Thus the depth of sun after 5 minutes is 809.82 feet

Answer:

270

Step-by-step explanation:

Answer:

Step-by-step explanation:

(7,2) , (0,0)

slope = (y2 - y1) / (x2 - x1) = (0 - 2) / (0 - 7) = -2/-7 = 2/7

y = mx + b

slope(m) = 2/7

(0,0)...x = 0 and y = 0

now sub

0 = 2/7(0) + b

0 = b

ur equation is : y = 2/7x + 0.....same as y = 2/7x <====

The equation of the line is y = ( 2/7 )x where the slope is m = 2/7

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 7 , 2 )

Let the second point be Q ( 0 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 0 ) / ( 7 - 0 )

m = 2/7

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 0 = ( 2/7 ) ( x - 0 )

y = ( 2/7 )x

Hence , the equation of line is y = ( 2/7 )x

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Answer:

6

Step-by-step explanation:

Given

2x - 2y ← factor out 2 from each term

= 2(x - y) ← substitute x - y = 3 into the expression

= 2(3)

= 6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

x - y = 3

2x - 2y

The value of 2x - 2y is 6.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x - y = 3  _____(1)

The value of 2x-2y.

= 2x - 2y

Taking 2 as common.

= 2 (x - y)

From (1) we get,

= 2 x 3

= 6

Thus,

The value of 2x - 2y is 6.

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Answer:

Step-by-step explanation:

The given equations are x = 4 - 2y.......(1) and 3x - 2y = 4......(2).

Putting the value of the first equation in the second, we get

3x - 2y = 4

or, 3(4 - 2y) - 2y = 4

or, 12 - 6y - 2y = 4

or, 8y = 8

or, y = 1.

Putting the value of y in the first equation, we get x = 4 - 2 = 2.

Answer:

The answer is [tex]x=2[/tex] and [tex]y=1.[/tex]

Step-by-step explanation:

Given:

X=4-2y

3x-2y=4

Now, to solve it by substitution.

[tex]x=4-2y[/tex]  .....(1)

[tex]3x-2y=4[/tex]  ......(2)

Now, solving the equation (2) by substitution:

[tex]3x-2y=4[/tex]

Substituting the value of [tex]x[/tex] from equation (1):

[tex]3(4-2y)-2y=4[/tex]

[tex]12-6y-2y=4[/tex]

[tex]12-8y=4[/tex]

Subtracting both sides by 12 we get:

[tex]-8y=-8[/tex]

Dividing both sides by -8 we get:

[tex]y=1.[/tex]

Now, substituting the value of [tex]y[/tex] in equation (1):

[tex]x=4-2y[/tex]

[tex]x=4-2(1)[/tex]

[tex]x=4-2\times1[/tex]

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

[tex]x=2.[/tex]

Therefore, the answer is [tex]x=2[/tex] and [tex]y=1.[/tex]

Answer:

No, (4•6)^3 is not  equivalent to 4•6^3

Step-by-step explanation:

(4•6)^3

4•6^3

Let's solve each one at a time, starting with (4•6)^3

(4•6)^3

Multiply inside the parenthesis first

24^3

Multiply 24 by itself 3 times (Exponents)

24 * 24 * 24

13,824

Now let's solve  4•6^3

4•6^3

Exponents come before multiplication in the order of operations, so multiply 6 by itself 3 times.

4 * (6x6x6)

4 * 216

864

Now we can compare the solutions

13,824 > 864

No, 13,824 is not equivalent to 864.

Hope this helps :)

Answer:

1989xsquared y + 585xsquared+ 2618xy + 770x - 8075y - 2375

Step-by-step explanation:

(9x + 25) x (13x - 19) x (17y + 5)

(117x squared - 171x + 325x - 475) x (17y + 5)

(117x squared + 154x - 475) x (17y + 5)

[tex](9x + 25) (13x - 19) (17y + 5)=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]

We have to simplify the expression:

(9x + 25)(13x - 19)(17y + 5)

Multiply the first two expressions as

[tex][9x(13x - 19)+25(13x - 19)](17y + 5)[/tex]

[tex]=(117x^2 - 171x + 325x - 475)(17y + 5)[/tex]

[tex]=(117x^2 + 154x - 475)(17y + 5)[/tex]

[tex]=17y(117x^2 + 154x - 475) + 5(117x^2 + 154x - 475)\\=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]

Therefore after simplifying , we get

[tex](9x + 25) (13x - 19) (17y + 5)=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]

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Answer:

[tex]\large\boxed{p<\dfrac{30}{11}\to p\in\left(-\infty,\ \dfrac{30}{11}\right)}[/tex]

Step-by-step explanation:

[tex]-7p-4>26p-94\qquad\text{add}\ 7p\ \text{to both sides}\\\\-7p+7p-4>26p+7p-94\\\\-4>33p-94\qquad\text{add 94 to both sides}\\\\-4+94>33p-94+94\\\\90>33p\qquad\text{divide both sides by 33}\\\\\dfrac{90}{33}>\dfrac{33p}{33}\\\\\dfrac{30}{11}>p\to p<\dfrac{30}{11}[/tex]

Answer:

1.536

Step-by-step explanation:

Final answer:

The independent variable in the scenario is the time spent baking, and the dependent variable is the number of cookies baked. The size of the oven might be another independent variable if comparing productivity between different bakeries.

Explanation:

In the context of the question where a baker bakes 40 cookies in an hour, we are being asked to identify the dependent and independent variables in this scenario. First, let's define these terms:

In this particular case, the independent variable could be the time spent baking, because it is what the baker controls. The dependent variable is the number of cookies baked, which depends on the amount of time the baker spends baking. If, for example, the baker decides to bake for two hours instead of one, we would expect the number of cookies baked to potentially double, assuming productivity remains constant.

In a different scenario, where comparing the productivity of bakers with different oven sizes – such as a Canadian worker with an industrial-size oven versus a U.S. worker with a smaller oven – the size of the oven could be seen as the independent variable affecting the dependent variable of productivity measured by the output of loaves of bread in an hour.

Through algebra, we found that Xavier's current age is 61, which makes Yolanda 65. Subtracting the 40 years of marriage from their current ages, we determined that Yolanda was 25 years old when they got married.

The question given by the student is a problem that can be solved with simple algebra. To find out how old Yolanda was when they married, we first need to establish the current ages of Xavier and Yolanda based on the information given.

Let's denote Xavier's current age as x years. Consequently, Yolanda's current age will be x + 4 years (since she is 4 years older than Xavier). According to the problem, the sum of their ages now is 126 years. We can set up the following equation based on this information:

x + (x + 4) = 126

By solving the equation:

Combine like terms: 2x + 4 = 126

Subtract 4 from both sides: 2x = 122

Divide both sides by 2: x = 61

This means that Xavier is now 61 years old, and Yolanda is x + 4, which is 65 years old. Since they have been married for 40 years, we subtract 40 from their current ages to get their ages at the time they got married. So, Yolanda was 25 years old when she got married.

Answer: Yes.

Step-by-step explanation: if y=12, then 24-12=24 aka 24-y=12

The solutions are - 0.8 and 1

Step-by-step explanation:

In the quadratic equation ax² + bx + c = 0

Assume that the solutions of the equations are m and n

∵ 5x² - x - k = 0

- By comparing it by the form above

∴ a = 5, b = -1 , c = -k

- Use the rule of the sum of the two solutions above

∵ The sum of the two solutions = [tex]\frac{-b}{a}[/tex]

∴ The sum of the two solutions = [tex]\frac{-(-1)}{5}=0.2[/tex]

∵ The two solutions are m and n

∴ m + n = 0.2 ⇒ (1)

∵ The difference of the two solutions is 1.8

∴ m - n = 1.8 ⇒ (2)

Now we have a system of equations to solve

Add Equations (1) and (2) to eliminate n

∴ 2m = 2

- Divide both sides by 2

∴ m = 1

- Substitute the value of m in equation (1) to find n

∴ 1 + n = 0.2

- Subtract 1 from both sides

∴ n = -0.8

The solutions are - 0.8 and 1

If you want to find the value of k

∵ The product of the solutions is [tex]\frac{c}{a}[/tex]

∴ The product of the solutions = [tex]\frac{-k}{5}[/tex]

∵ m × n = 1 × (-0.8) = - 0.8

- Equate  [tex]\frac{-k}{5}[/tex]  by - 0.8

∴ [tex]\frac{-k}{5}=-0.8[/tex]

- Multiply both sides by -5

∴ k = 4

∴ The equation is 5x² - x - 4 = 0

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Answer:

x = 1; x = -0.8

Step-by-step explanation:

Here is a simpler approach if needed for future students:

5x^2-x-k = 0,

System of Equations: x1 - x2 = 1.8 & x1 + x2 = 1/5 = 0.2 (if x1 and x2 are roots)

Now let's add the two:

x1 - x2 = 1.8

+ x1 + x2 = 0.2

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

2x1 = 2,

x1 = 2/2 = 1

- x2 = 1.8 - 1 = 0.8 => x2 = -0.8

Answer:

Therefore the Speed of a wave is 340 m/s.

Step-by-step explanation:

Given:

Wave Length = 5 m

Frequency = 68 hertz

To Find:

Speed = ?

Solution:

Wave Speed:

Wave speed is the distance a wave travels in a given amount of time, such as the number of meters it travels per second.

Wave speed is related to wavelength and wave frequency.

The Formula is given by

[tex]Speed = Wavelength\times Frequency[/tex]

Substituting the values we get

[tex]Speed = 5\times 68=340\ m/s[/tex]

Therefore the Speed of a wave is 340 m/s.

Answer:

just use mathpapa it's a game changer itll change your life

Answer:

see the explanation

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x ----> the time in seconds

y ---> the distance in meters

In this problem we have a proportional relationship between the variables x and y

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

For x=2, y=25 ---> [tex]k=\frac{25}{2}=12.5[/tex]

For x=4, y=50 ---> [tex]k=\frac{50}{4}=12.5[/tex]

For x=6, y=75 ---> [tex]k=\frac{75}{6}=12.5[/tex]

For x=8, y=100 ---> [tex]k=\frac{100}{8}=12.5[/tex]

so

The value of k is [tex]12.5\ \frac{m}{sec}[/tex]

In this problem the value of k or slope represent the speed of the train

The linear equation is equal to

[tex]y=12.5x[/tex]

or

[tex]Distance=12.5Time[/tex]

Answer:

24 degrees

Step-by-step explanation:

The distance from 15 degrees to 0 degrees is 15, and the distance from 0 degrees to -9 degrees is 9, so then the total distance from 15 degrees to -9 degrees is (15+9 degrees) which adds up to be 24 degrees

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\x-\text{number of wrapping paper of Mr. Smith's class}\\y-\text{number of magazines of Mr. Davis' class}\\\$3.50x-\text{the amount obtained from the sale of wrapping paper}\\\$2.75y-\text{the amount obtained from the sale of magazines}[/tex]

[tex]\bold{SYSTEM\ of\ EQUATIONS:}\\\\\left\{\begin{array}{ccc}x+y=72&\text{subtract}\ y\ \text{from both sides}\\3.5x+2.75y=222\end{array}\right\\\\\left\{\begin{array}{ccc}x=72-y&(1)\\3.5x+2.75y=222&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3.5(72-y)+2.75y=222\qquad\text{use the distributive property}\\\\(3.5)(72)+(3.5)(-y)+2.75y=222\\\\252-3.5y+2.75y=222\qquad\text{substract 252 from both sides}\\\\-3.5y+2.75y=222-252\qquad\text{combine like terms}[/tex]

[tex]-0.75y=-30\qquad\text{divide both sides by (-0.75)}\\\\\boxed{y=40}\\\\\text{Put it to (1):}\\\\x=72-40\\\\\boxed{x=32}\\\\\$3.5x=\$3.5\cdot32=\$112\\\\\$2.75\cdot40=\$110\\\\\$112-\$110=\$2[/tex]

Answer:

If you want the mixed number,it is 7 1/9

Step-by-step explanation:

Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

y < –12

Solution:

Step 1: Given inequality is y + 15 < 3.

To find the solution to the inequality.

Step 2: Subtract –15 on both sides to equal the expression.

⇒ y + 15 –15 < 3 –15

Step 2: Using addition identity property, any number adding with zero gives the number itself.

⇒ y + 0 < –12

⇒ y < –12

Hence the solution to the inequality is y < –12.

Answer:

Step-by-step explanation:

It’s b

Answer:

It is important to use mixed numbers in real life, because it can help you find the measurements for when you are buying ingredients or baking something.

Hope this helps ;)

Step-by-step explanation:

Answer:

The total weight of the water in a full tank, to the nearest pound is 3527 pounds per cubic foot

Step-by-step explanation:

Given:

Diameter  of the hemispherical tank = 6 feet

Weight of water per cubic foot =  62. 4 pounds

To Find:

The total weight of the water in a full tank, to the nearest pound?

Solution:

We know that the volume of a sphere is:

[tex]V =\frac{4}{3}\pi r^3[/tex]

where  

r = is the radius

In the question we are given with diameter,

So

[tex]radius = \frac{diameter}{2}[/tex]

radius = [tex]\frac{6}{2}[/tex]

Radius = 3

We need the volume of the hemisphere

So the volume of the hemisphere will be half of the volume of teh sphere

[tex]\frac{V}{2} = \frac{2}{3}\pi r^3[/tex]

Thus the volume of the hemisphere is

[tex]V =\frac{2}{3} \pi r^3[/tex]

Now substituting the values

[tex]V = \frac{2}{3} \pi(3)^3[/tex]

[tex]V = \frac{2}{3}\pi(27)[/tex]

[tex]V = \frac{54 \pi}{3}[/tex]

[tex]V = \frac{169.56}{2}[/tex]

V=  56.52 cubic foot

Now, the total weight of water of:

W =  56.52 x 62.4

W= 3526.848 pounds per cubic foot

To the nearest pounds

W= 3527 pounds per cubic foot

Answer:

3529

Step-by-step explanation:

If you are here from delta math this is the Answer