Find three consecutive numbers whose sum is 84

The gallons of milk per day is an illustration of unit rates.

Ken needs to buy 2 gallons to last them for 3 days.

Given that:

\(Rates= \frac 23\) gallons per day

\(Days = 3\)

The number of gallons that will last 3 days is:

\(Gallons = Rate\times Days\)

So, we have:

\(Gallons = \frac 23 \times 3\)

Multiply 2 and 3

\(Gallons = \frac 63\)

Divide 6 by 3

\(Gallons = 2\)

Hence, 2 gallons will last Ken's family for 3 days.

Read more about unit rates at:

https://brainly.com/question/18065083

The equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4 will be y=2x-11.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

It is given that,  

y=2x-4

We have to write an equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4.

The slope of the given equation,

y=2x-4

m=2

The slope of the parallel lines is equal,

m=2

The equation of a line that passes through the point (5,-1) with slope 2 is,

y-y₁=m(x-x₁)

y-(-1)=2(x-5)

y+1=2(x-5)

y+1=2x-10

y=2x-11

Thus, the equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4 will be y=2x-11.

Learn more about the straight line here:

brainly.com/question/3493733

#SPJ1

The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error, Chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards,

Given that the directions on a sewing pattern say to cut an extra 15% of fabric to account for an error, and Chloe needs a 0.75 yard of fabric to make a skirt, so she cuts 0.1125 yard, to determine if Chloe cut the correct amount of fabric the following calculation must be made:

0.75 x 1.15 = X

0.8625 = X

0.8625 - 0.1125 = 0.75

Therefore, the amount of fabric that Chloe cut is correct.

To learn more about proportions, click here https://brainly.com/question/870035

#SPJ4

Answer:

Let c = number of children

a = number of adults

$15.50c + $20a = $3,782

c + a = 217

$15.50c + $20(217 - c) = $3,782

$15.50c + $4,340 - $20c = $3,782

$4,340 - $4.50c = $3,782

$4.50c = $558

c = 124, a = 93

{(c, a)} = {(124, 93)}

Answer:

yes

Step-by-step explanation:

because although some of the other are missing to be a function, it has to have an element of x and of y, it does not matter that some do not have it with one of y and one of x is enough

And if you are talking about relation it is also because they comply with the rules

Answer:

the answer is 86!

hope this helped

Answer:

the answer to your question is 86

(x+3) x (x+2)

Step-by-step explanation:

it should be *(x+3) x (x+2)* because area of rectangle = length x breadth

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

The particular solution that satisfies the differential equation and the initial condition f(0) = a is: f(x) = -sin(x) + C1x + a.

To find the particular solution that satisfies the differential equation f''(x) = sin(x) and an initial condition, we need to integrate the equation twice and apply the initial condition.

1. First Integration:

Integrating the differential equation f''(x) = sin(x) with respect to x once gives us:

f'(x) = -cos(x) + C1

where C1 is the constant of integration.

2. Second Integration:

Integrating f'(x) = -cos(x) + C1 with respect to x again gives us:

f(x) = -sin(x) + C1x + C2

where C2 is another constant of integration.

3. Applying the Initial Condition:

To apply the initial condition, we need to use the given information about the problem. Let's say the initial condition is given as f(0) = a, where 'a' is a specific value.

Substituting x = 0 and f(x) = a into the equation, we get:

a = -sin(0) + C1(0) + C2

a = 0 + 0 + C2

C2 = a

Therefore, the particular solution that satisfies the differential equation and the initial condition f(0) = a is:

f(x) = -sin(x) + C1x + a

In this particular case, the initial condition f(0) = a determines the value of the constant C2, which becomes C2 = a. The resulting particular solution incorporates the constant C1 from the first integration and the constant a from the initial condition.

Note that without a specific initial condition or boundary condition, the constants C1 and C2 remain arbitrary and can be adjusted to fit different situations or additional information if provided.

for more such question on equation visit

https://brainly.com/question/17145398

#SPJ8

Answer:

294 calories per 6 servings

You just divide to fine the unit rate

You want to find how many calories is 1 serving

294/6 is 49

So its 49 calories PER serving

Answer:

110

Step-by-step explanation:

Answer:

i would think about 20 miles away

Step-by-step explanation:

The another equivalent expression of total liquid is (x+2)/4.

Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.

x quarts liquid in the container 3/4 part of liquid is removed

Then remaining liquid in container = X - \(\frac{3}{4}X\)

Then remaining liquid in container = x/4quarts

Another 1/2 quart is poured into container

Then total liquid = \(X-\frac{3}{4}X+\frac{1}{2}\) quarts

total liquid = \(\frac{X+2}{4}\) quarts

So, then the another equivalent expression of total liquid is (x+2)/4.

To learn more about simplification of expression link is here

brainly.com/question/14526172

#SPJ4

The equation used to determine the value of the car ,v, after 5 years is V= 12500*4.5*5/100-D.

An equation represents equality of two or more mathematical expression.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

Given;

A car depreciates ( loses value ) at a rate of 4.5% annually

Greg purchased a car for 12,500

Time= 5years

Here, the depreciation is equal to the simple interest but in depreciation

So, Let the depreciation be D

D=P*R*T/100

D=12500*4.5*5/100

=2812.5

Now, value of car v;

V= 12500*4.5*5/100-D

Therefore, the equation will be V= 12500*4.5*5/100-D

Learn more about solving equations here;

https://brainly.com/question/18015090

#SPJ1

The thief stole 22 oranges using algebraic equations.

To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.

According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.

We also know that the thief was left with only 9 oranges. So we can set up the equation:

x - [(1/2)x + 2] = 9

Simplifying this equation:

(1/2)x - 2 = 9
(1/2)x = 11
x = 22

Therefore, the thief stole 22 oranges.

The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.

To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.

In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.

To learn more about algebraic equations, refer here:

https://brainly.com/question/953809#

#SPJ11

THE QUESTION CAN BE WRITTEN AS THIS;

It is given that ∠ABC and ∠CBD are a____________ So, m∠ABC+m∠CBD=90° using the b____________. It is also given that ​m∠ABC=35°​. Using the substitution property of equality, you have c________+ ​m∠CBD=90°​. Therefore, using the subtraction property of equality, ​m∠CBD=55°

Answer:

a)COMPLIMENTARY ANGLE

b)DEFINITION OF COMPLEMENTARY ANGLES

c)35°+ m<CBD = 90 degrees.

Step by step Explanation:

a)It's given that <ABC and <CBD are (COMPLIMENTARY ANGLE)

We know that the Sum of Complementary angles equal to 90 degrees.Those angles don't have to be next to each other, just so long as the total is 90 degrees. That's why the Sum of m<ABC and m<CBD equals 90 degrees that is m<ABC + m<CBD = 90 degrees

b)using the (DEFINITION OF COMPLEMENTARY ANGLES) It is also given that m<ABC = 35 degrees.

c)Using substitution property of equality, you have (35°+ m<CBD = 90 degrees.)

If we subtract 35 from both sides, we get 35-35+ m<CBD = 90-35.

Therefore, m<CBD = 55 degrees.

PLEASE CHECK THE ATTACHED FIGURE TO SEE HOW THE QUESTION LOOKS LIKE

Answer:

Step-by-step explanation:

The correct response since I just took this test is:

It is given that ∠ABC and ∠CBD are complementary angles. So, m∠ABC+m∠CBD=90° using the definition of complementary angles. It is also given that ​m∠ABC=35°​. Using the substitution property, you have 35° + ​m∠CBD=90°​. Therefore, using the subtraction property of equality, ​m∠CBD=55°

After answering the presented question, we may conclude that  expressions As a result, Ms. Jimenez contributes roughly $41.54 to her retirement fund each week.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

We need to do the following to figure out how much money Ms. Jimenez puts into her retirement fund each week:

Ms. Jimenez's yearly retirement fund contribution is calculated as follows:

8% of $27,000 = annual retirement fund contribution

= 0.08 x $27,000

= $2,160

To calculate the weekly retirement fund contribution, divide the yearly payment by the number of weeks in the year:

Contribution to a retirement fund on a weekly basis = Annual contribution to a retirement fund divided by the number of weeks in a year

= $2,160 / 52

≈ $41.54

As a result, Ms. Jimenez contributes roughly $41.54 to her retirement fund each week.

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

The derivative of the given function is 80e^-t. By evaluating this expression at t=4, we get 80e^-4. When t = 4 the marginal cost is approximately $14.874 million.

C(t) = 120 − 80e^-t

dC/dt = 0 - (-80)(-e^-t)

= 80e^-t

80e^-4 ≈ 80(0.01832) [using e^-4 ≈ 0.01832]

≈ 1.4656

However, the question asks for the answer in millions of dollars

1.4656 / 1 million ≈ 0.014874

Rounding this to three decimal places, we get the answer as approximately $0.015 million or $15,000.

Therefore, the marginal cost when t = 4 is:

dC/dt | t=4 = 80e^-4

dC/dt | t=4 ≈ 14.874

To learn more about cost follow the link: brainly.com/question/30045916

#SPJ4

The complete question is:

A company's total cost, in millions of dollars, is given by C(t) = 120 − 80e^-t where t = time in years. Find the marginal cost when t = 4.

Answer:

aₙ = 30 - 5n

Step-by-step explanation:

25,20,15,10, ...

We see from the given series that it is AP with:

Then formula is:

Answer:

never true................

The total cost to lay the garden path is $1952.64. To find the total cost to lay a rectangular garden path, we first need to find the area of the path.

The area of a rectangle is found by multiplying its length and width.

In this case, the length of the path is 18 feet and the width of the path is 9 2/5 feet. To multiply these two measurements, we first need to convert the mixed number 9 2/5 into a fraction: 9 2/5 = 9 + 2/5 = 9.4

So the area of the path is:

18 feet * 9.4 feet = 162.72 square feet

Next, we multiply the area of the path by the cost per square foot, which is $12:

162.72 square feet * $12/square foot = $1952.64

So the total cost to lay the garden path is $1952.64.

To learn more about rectangular garden path please click on below link.

https://brainly.com/question/17493797

#SPJ4

A landscaper charges 12 dollars per square foot how much does he charge to lay a rectangular garden path that is 18 feet long by 9 2/5 feet wide?

The inverse transformation T⁻¹ takes the point (x, y, z) to (2z - x, y - z, x - y).

The inverse transformation T⁻¹ of a linear transformation T is defined as the transformation that undoes the action of T. That is, if T takes a point (u, v, w) to (u + v + w, u + v, u), then T⁻¹ will take the point (u + v + w, u + v, u) back to (u, v, w).

To find what T⁻¹ does to the point (x, y, z), we need to solve the system of equations:

u + v + w = xu + v = yu = z

Substituting the third equation into the first two equations gives us:

v + w = x - zv = y - z

Subtracting the second equation from the first equation gives us:

w = x - y

Substituting the equations for v and w back into the first equation gives us:

u + (y - z) + (x - y) = xu = 2z - x

So, the inverse transformation T⁻¹ takes the point (x, y, z) to (2z - x, y - z, x - y).

Therefore, T⁻¹(x, y, z) = (2z - x, y - z, x - y).

Learn more about Transformation:

https://brainly.com/question/27224272

#SPJ11

Answer:

1

Step-by-step explanation:

3 divided by 1/3 is 9, and 9-9=0

0+1=1

1

Step-by-step explanation:

The solutions to the quadratic equation x² = -7x - 8 are x equals  \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Given the quadratic equation in the question:

x² = -7x - 8

To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.

x² = -7x - 8

x² + 7x + 8 = 0

a = 1, b = 7 and c = 8

Plug these into the quadratic formula: ±

\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)

Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Learn more about quadratic equations here: brainly.com/question/1863222

#SPJ1

Answer:

1/2

Step-by-step explanation:

We know that each team has the following:

36Players + 3Coaches + ?Assistants = Sports League

We know that the ratio of assistants to players is 1/6, rewrite the equation accordingly:

36Players + 3Coaches + 6Assitants = Sports League

Now find the ratio of coaches to assistants:

3Coaches / 6Assistants = 1/2

Answer: It will take 2.5 hours for her to walk 7.2 miles

Step-by-step explanation:

Divide the total mile by the number of miles per hour

7.2/2.88=2.5

since it takes an hour walk of 2.88 miles per hour, multiply 2.5 by 1

2.5*1=2.5

It will take 2.5 hours for her to walk 7.2 miles

The probability that a randomly purchased item from the manufacturer will last longer than 10 years is approximately 0.205 (rounded to three decimal places).

To find the probability that an item will last longer than 10 years, we can use the properties of the normal distribution. First, we need to standardize the value of 10 years using the formula: z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

Using the given values, we can calculate z as: z = (10 - 13.8) / 4.6 = -0.826.

Next, we need to find the cumulative probability to the right of this z-score. We can consult the standard normal distribution table or use a calculator to find this value. From the table or calculator, we find that the cumulative probability for a z-score of -0.826 is approximately 0.205.

Therefore, the probability that the item will last longer than 10 years is 0.205 (rounded to three decimal places).

To learn more about probability click here

brainly.com/question/32117953

#SPJ11