John and Maria solved the same equation using two different methods.

Compare and contrast John and Maria’s methods. Explain how they arrived at the same solution.

Answer:

[tex]x = \frac{-6y+7}{5}[/tex]

Step-by-step explanation:

[tex]6y + 5x = 7[/tex]

Isolate x ;

[tex]5x = 7-6y\\\\5x =-6y+7[/tex]

Divide both sides of the equation by 5

[tex]\frac{5x}{5} = \frac{-6y+7}{5} \\\\x = \frac{-6y +7}{5}[/tex]

Answer:

6 gallons per minute

Step-by-step explanation:

35÷7=6

Hey there! I'm happy to help!

There were 5 tests needed to make an average of 77. These numbers have to add up to 385 (77×5) because that is what you divide by 5 to find the average which is 77.

Now, we want to find an average of 80 with 6 numbers. We multiply 80 and 6, showing us that the sum of these 6 numbers must be 480. Since 5 of these numbers are the same as with the 77 average, we know that one test score (the one Brady needs to get) is added to 385 to give us 480.

480-385=95

Therefore, Brady needs to earn a 95% on the last test to receive a B in the class.

Answer:

74 fishes

Step-by-step explanation:

Total number of people = 1672

Let us represent:

Number of people over the age of 50 = a

Number of people below the age of 50 = b

People over the age of 50 she gave = 16 fish

People below 50 she gave = 96 fish. Only 3/4 of the over 50s collected their salmon

= 3/4a collected fish = 0.75a

If a should collect = 96 fishes

0.75a =

Cross Multiply

=0.75a × 96 fishes/ a

= 72 fishes

Therefore, 3/4 of the over 50s collected 72 fishes.

1/8 of the under 50s collected their fish.

= 1/8b collected fish = 0.125b

If b people should collect = 16 fishes

0.125b people =

Cross Multiply

0.125b × 16 fishes/b

= 2 fishes.

Therefore, the total number of fishes shared

= 72 fishes + 2 fishes

= 74 fishes

Answer:

Option 1: [tex]-2x+3[/tex]

Step-by-step explanation:

[tex]-\frac{1}{5}\left(5x+20\right)-\frac{1}{4}\left(4x-28\right)[/tex]

Expand:

[tex]-\frac{5x+20}{5}-\frac{4x-28}{4}[/tex]

[tex]-\left(x+4\right)-\left(x-7\right)[/tex]

Remove brackets:

[tex]-x-4-x+7[/tex]

Group similar terms together:

[tex]-x-x-4+7[/tex]

[tex]-2x+3[/tex]

Complete question is;

Vincent goes to the gym for 30 minutes every day. He starts a new exercise routine on a Monday and uses a function to model the amount of calories he has used, f(d), as a function of the number of days, d, he has exercised with the new routine.

Which statement represents a correct interpretation of f(d) ?

A. f(5) = 150 means Vincent has exercised for a total of 150 minutes after the fifth day of exercising with his

new routine

B. f(10) = 3500 means Vincent will use 3,500 calories on day 10 of exercising with his new routine.

C. f(15) = 5250 means after 15 days of exercising with his new routine, Vincent has used 5,250 calories.

D. f(30) = 10500 means the number of calories Vincent has used times 30 is equal to 10,500

Answer:

Option A: f(5) = 150 means Vincent has exercised for a total of 150 minutes after the fifth day of exercising with his

new routine .

Step-by-step explanation:

We are told that f(d), is a function of the number of days, d, he has exercised with the new routine.

We are also told that he goes to the gym for 30 minutes daily.

Thus;

For option A, f(5) means that he went to the gym for 5 days. At 30 minutes per day means he exercised for a total of: 30 × 5 = 150 minutes. So option A is correct

For option B, f(10) means that he went to the gym for 10 days. At 30 minutes per day means he exercised for a total of: 30 × 10 = 300 minutes. Thus, option B is wrong

For option C, f(15) means that he went to the gym for 15 days. At 30 minutes per day means he exercised for a total of: 30 × 15 = 450 minutes. Thus, option C is wrong.

For option D, f(30) means that he went to the gym for 30 days. At 30 minutes per day means he exercised for a total of: 30 × 30 = 900 minutes. Thus, option D is wrong.

Answer:

10

Step-by-step explanation:

2 1/2 ÷ 1/4 reduce

5/2 × 4/1 = 20/2

20 ÷ 2 = 10 pounds of flour per sugar

(I'm not very good at math so this might be wrong)

Answer:

it is a rational number

Answer:

1/12 or 0.083

Step-by-step explanation:

Answer:

[tex]y = \frac{2}{3} x + 5 \frac{2}{3} [/tex]

Step-by-step explanation:

Please see the attached pictures for the full solution.

Answer:

mean = 95, standard deviation of sampling distribution = 0.5

Step-by-step explanation:

sample space n = 25 snacks

mean = bar x = 95 calories

population standard deviation = 2.5 calories

the mean is already given as 95 calories

standard deviation of the sampling distribution = s.d/√n

= 2.5/√25

= 2.5/5

= 0.5

Therefore we have the mean = 95, and standard deviation of sampling distribution = 0.5

Answer:

The seats in the lower section are x= 1720 , in the upper section are 3x= 5160 and y=24,200 - 4x= 24,200 - 6880= 17320 tickets in the field.

Step-by-step explanation:

Let x represent the number of seats in the lower section then the number of seats in the upper section is 3x and y the number of seats in the field.

The equation can be written as

80x + 60 (3x) + 40 y= $1,140,000-----1

And x+ 3x+ y= 24,200------2

4x+ y= 24,200

or y= 24,200-4x----3

Solving Eq 1

80x + 180x + 40 y= $1,140,000

260x+ 40 y=$1,140,000-----4

Putting Eq 3 in Eq 4

260x+ 40 y=$1,140,000

260x+ 40(24,200-4x-)=$1,140,000

260x + 968,000- 160x= $1,140,000

100x= $1,140,000-968,000

100x= 172,000

x= 1720

The seats in the lower section are x= 1720 , in the upper section are 3x= 5160 and y=24,200 - 4x= 24,200 - 6880= 17320 tickets in the field.

Putting the values of x and y in Eq 1 we get the same revenue.

80x + 60 (3x) + 40 y= $1,140,000

80(1720) + 60 (5160) + 40( 17320)= $1,140,000

137600 + 309600 + 692800= $1,140,000

137600 + 1002400= $1,140,000

The total number of seats in the upper section is 5160, in the lower section is 1720 and the total number of seats in the field is 17320.

Given :

The following steps can be used in order to determine the total number of seats in each section:

Step 1 - In the lower section let the total number of seats be 'x'. So according to the given data, in the upper field, the total number of seats is '3x'. Now, let the total number of seats in the field be 'y'.

Step 2 - The linear equation that represents total revenue from the tickets.

[tex]\rm 80x + 60(3x)+40y = 1140000[/tex]

260x + 40y = 1140000    --- (1)

Step 3 - The linear equation that represents the total number of tickets is:

x + 3x + y = 24200

y = 24200 - 4x     --- (2)

Step 4 - Substitute the value of y in equation (1).

260x + 40(24200 - 4x) = 1140000

x = 1720 tickets

Step 5 - Substitute the value of 'x' in equation (2).

y = 24200 - 4(1720)

y = 17320 tickets

For more information, refer to the link given below:

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Answer:

Step-by-step explanation:

the answer i got was -57

Functions can be rewritten is several forms.

The new form of the function is: [tex]\mathbf{f(x) = \frac{x^2}{x - 1} + \frac{2}{x-1}}[/tex]

The function is given as:

[tex]\mathbf{f(x) = \dfrac{x^2+2}{x-1}}[/tex]

Split

[tex]\mathbf{f(x) = \frac{x^2}{x - 1} + \frac{2}{x-1}}[/tex]

The form is given as:

[tex]\mathbf{f(x) = p(x) + \frac{k}{x - 1}}[/tex]

So, by comparison

[tex]\mathbf{p(x) = \frac{x^2}{x - 1}}[/tex]

[tex]\mathbf{k =2}[/tex]

Read more about functions at:

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Answer:The simplified value: 4.8 divided by 3 or the answer you’ll get from that is 1.6

Step-by-step explanation:

4.2+0.6=4.8 0.9-0.5=0.4 5*0.4=2 3-2=1 4.8 divided by 3

Answer:

The answer is 2.4

Step-by-step explanation:

4.2 + 0.6 divided by 3 minus 5(0.9 minus 0.5) = 2.4

I got it right and used a calculater.

Answer:$15.18

Step-by-step explanation:

Answer:

$0.39

Step-by-step explanation:

39¢

5.99 ÷ 15 = 0.39

Answer:

The fourth graph in the second image.

Step-by-step explanation:

After plotting all the points in a calculator, the fourth graph matches the calculator.

APEX

5th graph with the large spike on the second to last bar

Answer:

The number of cars that brings the same profit is 9 and 0

Step-by-step explanation:

Given

[tex]x^2 - 4x = 5x[/tex]

Required

Determine the possible values of x

[tex]x^2 - 4x = 5x[/tex]

Subtract 5x from both sides

[tex]x^2 - 4x - 5x = 5x - 5x[/tex]

[tex]x^2 - 9x = 0[/tex]

Factorize

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

Split the equation

[tex]x = 0[/tex]         or        [tex]x - 9 = 0[/tex]

[tex]x = 0[/tex]         or        [tex]x = 9[/tex]

Hence, the number of cars that brings the same profit is 9 and 0

Answer:

I will tell you in the explanation...

Step-by-step explanation: God created us and god knows the answer. :)

Answer: 54 teaspoons of oregano

Step-by-step explanation: 1 can is 6 teaspoons so 9 cans would be 54 teaspoons because 9 x 6 = 54.

Hope this helps!

Answer:

a = -10

Step-by-step explanation:

Simplifying

7 + 4(2a + 15) = -13

Reorder the terms:

7 + 4(15 + 2a) = -13

7 + (15 * 4 + 2a * 4) = -13

7 + (60 + 8a) = -13

Combine like terms: 7 + 60 = 67

67 + 8a = -13

Solving

67 + 8a = -13

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-67' to each side of the equation.

67 + -67 + 8a = -13 + -67

Combine like terms: 67 + -67 = 0

0 + 8a = -13 + -67

8a = -13 + -67

Combine like terms: -13 + -67 = -80

8a = -80

Divide each side by '8'.

a = -10

Simplifying

a = -10

Answer:

8

Step-by-step explanation:

There are no values for which the equation has only one solution for no solution the missing value can be anything except 16.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The equation shown has a missing value.

-2(2x - ?) + 1 = 17 - 4x

Applying the distributive property:

-4x + ? + 1 = 17 - 4x

? + 1 = 17

There are no values for which the equation has only one solution or unique solutions.

For no solution the missing value can be anything except 16

? + 1 = 17

? = 17 - 1

? = 16

Thus, there are no values for which the equation has only one solution for no solution the missing value can be anything except 16.

Learn more about the linear equation here:

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Answer: Group 12

Step-by-step explanation: The element is Mercury.

Answer:

The t-distribution is a kind of probability distribution that is bell-shaped (like the normal distribution) but has a good number of values at the tails, making the tails fatter and the curve flatter.

Step-by-step explanation:

The t-distribution is a kind of probability distribution that is bell-shaped (like the normal distribution) but has a good number of values at the tails, making the tails fatter and the curve flatter.

The smaller the sample size n, the flatter the t-distribution curve but the larger the sample size n, the closer in identity to the normal distribution, the t-distribution will be.

Answer:

∫ₑ°° 1 / (x (ln x)¹⁰) dx

∫₁°° x⁻³ dx

Step-by-step explanation:

A p-series 1 / xᵖ converges if p > 1.

∫ₑ°° 1 / (x (ln x)¹⁰) dx

If u = ln x, then du = 1/x dx.

When x = e, u = 1.  When x = ∞, u = ∞.

= ∫₁°° 1 / (u¹⁰) du

p = 10, converges

∫₁₀°° x^(-⅔) dx

= ∫₁₀°° 1 / (x^⅔) dx

p = ⅔, diverges

∫₁°° 2 / x^0.5 dx

= 2 ∫₁°° 1 / x^0.5 dx

p = 0.5, diverges

∫₁°° x⁻³ dx

= ∫₁°° 1 / x³ dx

p = 3, converges

∫₂°° 1/(3x) dx

= ⅓ ∫₂°° 1/x dx

p = 1, diverges

Answer:

least to greatest: -16/32, -8/20, 3/5

Step-by-step explanation: