solving joint variation​

The  value of the inequality is 1

In equality is a mathematical statement showing that two or more variables or quantities are not equal.

The given inequality is  6<2y+4

Making y the subject of the relation

6-4<2y

⇒2=2y

Making y the subject of the relation by dividing both sides by 2

therefore, y<1

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Answer:B. 1.50(5) + 2.00m ≤ 19.00

Step-by-step explanation:This inequality can be used to determine the maximum number of milkshakes that Donna can buy with her $19.00. The expression on the left side of the inequality represents the total cost of her purchase and the expression on the right side of the inequality represents the amount of money she has to spend. Since she must buy 5 ice cream cones, that is represented by the 1.50(5) term. The 2.00m term represents the cost of the milkshakes she can buy, with m representing the number of milkshakes. The inequality states that the total cost of her purchase must be less than or equal to the amount of money she has to spend, so the maximum number of milkshakes she can buy can be determined by rearranging the expression.

If Donna buys 5 ice cream cones, that adds up to, £10.00.

She is then left with £9.00.

9 divided by 1.50 = 6.

She is able to buy 6 milkshakes with the money she has left. However, she is now left with no money.

The answer would be B.1.50(5) +2.00m≤19.00

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The  inequalities represent the possible lengths for the third side, x is 4 < x < 14, the correct option is D.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. The set of values of the variable involved in the inequality for which the considered inequality holds true is called the solution set for that inequality.

Given;

One side of triangle =5

The other side of triangle=9

Now, the third side is between the difference and the sum of the other two sides;

9-5 < x < 9+5

4 < x < 14

Therefore, the inequality will be 4 < x < 14.

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Answer:

5

Step-by-step explanation:

The value of the function f(g(4)) is C) 4.

The diagram shows that f(1) = 0, f(2) = 1, f(3) = 4, and f(4) = 9. Therefore, the value of f(g(4)) is equal to f(9) = 4.

The other options are incorrect. Option A is incorrect because f(0) is not defined. Option B is incorrect because f(4) is not equal to 0. Option D is incorrect because f(1) is not equal to 9.

Here is the solution in steps:

The diagram shows that f(1) = 0, f(2) = 1, f(3) = 4, and f(4) = 9.

Therefore, the value of f(g(4)) is equal to f(9) = 4.

The other options are incorrect. Option A is incorrect because f(0) is not defined. Option B is incorrect because f(4) is not equal to 0. Option D is incorrect because f(1) is not equal to 9.

Therefore, the answer is C. 4.

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The value of n(B) in the set is 23

From the question, we have the following parameters that can be used in our computation:

n(A) = 108, n(A ∪ B) = 160, and n(A ∩ B) = 43,

The value of n(B) is calculated as

n(A u B) = n(A) + n(B) - n(A n B)

Substitute the known values in the above equation, so, we have the following representation

160 = 108 + n(B) - 43

This gives

n(B) = 160 + 43 - 180

Evaluate

n(B) = 23

Hence, the solution is 23

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The end behavior of the polynomial is:

x → ∞, F(X) → ∞

x → -∞, F(X) →-∞

Then the correct option is C.

Here we have the polynomial:

F(x) = x³ + 2x² - 1

And we want to see which ones of the given statements are true. At the end of the answer you can see the graph of the function so you can know how it behaves.

There we can see that there is one relative maximum and one relative minimum, and that the end behavior is:

x → ∞, F(X) → ∞

x → -∞, F(X) →-∞

Then the only correct option is C.

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The answer is 9:2 or 2:9. It depends if there is 9 women and 2 men or 2 women and 9 men.

Mark me branliest. :D

The given expression is a logarithm expression. The value of the log expression is -112.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is log (³√c⁵)/(a⁷b⁸).

The value of log a = 7, log b = 11, log c = 15

Applying the quotient formula log(a/b) = log a - log b in the given expression:

= log (³√c⁵) - log (a⁷b⁸)

Again applying the product formula log (ab) = log a + log b:

= log (³√c⁵) - log (a⁷) - log b⁸

Apply the power rule log (a^b) = b log a:

= (5/3) log c - 7log a - 8log b

Now putting the value of log a = 7, log b = 11, log c = 15:

= (5/3) × 15 - 7 × 7 - 8 × 11

= 5×5 - 49 - 88

= -112

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Solution set for y < 3/2 x – 4 is represented by Graph D.

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal.

Given inequality,

y < 3/2x - 4

Since there is less than sign, the region should be shaded below dotted line.

Equation for the dotted line

y = 3/2x - 4

comparing it with Slope intercept equation,

y = mx + c

slope m = 3/2

y - intercept = - 4 unit.

Only graph D has the shaded part below dotted line.

Hence, Graph D represents  y < 3/2 x – 4.

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A straight line can be drawn through all the points, and the line passes through the origin. Option C

We know that a relationship is proportional when we can be able to find an association between the variables. It is either the variables are increasing or that the variables are decreasing.

here, we have,

Thus, we would notice that if there is an association between the variables then the graph would be a straight line graph and the graph would have to pass through the origin.

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You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.

Businesses, a noun in plural. a group of people who are connected or who have joined together. a guest or guests: We're having people over for dinner. a collection of individuals together for social purposes. association, camaraderie, and fellowship She is a lot of joy to be around.

The Old French word "compagnie," which was first used in the Salic code and meaning "one who eats bread with you," is where the English word "company" originates. To describe a "society, friendship, closeness, or body of troops," it was first used in 1150.

You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.

Total Amount to be when start the company is $12000 + $12000

= $24000

Out of which company owns land and a building worth $8,878 and equipment worth $4,230 and have retained $1,291 in earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term investment.

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The set of pairs for which x and y vary inversely is given as follows:

{(-1, -2/7), (4, 1/14), (6, 1/21)}

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse relation, the relation is modeled as follows:

y = k/x.

Meaning that when x increases, y decreases at a constant rate.

The constant is then given as follows:

k = yx.

Hence the third relation is then the relation for which x and y vary inversely, as:

k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.

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If George painted 1/5 of the room and Adam painted 0.35 of the room then the total percentage of the room painted by Adam and George collectively is 55%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The amount of room painted by George is = 1/5

The amount of room painted by George is = 0.35

Convert the fraction into percentage -

Percentage = 1/5 × 100

Percentage = 20%

Convert the decimal into percentage -

Percentage = 0.35 × 100

Percentage = 35%

The total percentage of room painted by George and Adam is -

Total % of room painted = % of room painted by George + % of room painted by Adam

Substitute the values into the equation -

Total % of room painted = 20 + 35

Total % of room painted = 55

Therefore, 55% of the room was painted.

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George and Adam painted the game room together. George painted 1/5 of the room, and Adam painted 0.35 of the room.

What is the total percentage of the room painted by Adam and George?

The proportional relationship modeling the number of eggs needed to make x pies is given as follows:

y = 3x.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

3 large eggs, hence the constant of the proportional relationship is given as follows:

k = 3.

Then the equation of the proportional relationship is given as follows:

y = 3x.

Which is a linear function with a slope of 3 and an intercept of zero.

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Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]\angle B=180^{\circ}-115.5^{\circ}-27.2^{\circ} \longrightarrow \boxed{\angle B=37.3^{\circ}}[/tex]

Using the Law of Sines:

[tex]\frac{AC}{\sin 37.3^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{AC=\frac{76\sin 37.3^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]

[tex]\frac{BC}{\sin 27.2^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{BC=\frac{76\sin 27.2^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]

sin(A) / a = sin(B) / b = sin(C) / c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

Answer:  C. 120!

Step-by-step explanation:

Okay so, first we need to find out our percentages of course.
I learned this trick that can help us with this question easily!

14% of 500 - 70 - Drama
14 * 5 = 70.

22% of 500 - 110 - Sports
22 * 5 = 110

20% of 500 - 100 - Reality
20 * 5 = 100

20% of 500 - 100 - Sci-fi
20 * 5 = 100

70 + 110 + 100 + 100 = 380

500 - 380 = 120

Therefore, documentaries is labeled as 24% of 500 or 120 out of 500.

Your welcome! ^^

Therefore , the solution of the given problem of percentage comes out to be $387.704 is the weekly unemployment amount.

In mathematics, a percentage is any amount that can be stated as a proportion of 100. Also occasionally used are the abbreviations "pct.," "pct," or "pc." But the "%" mark is usually used to indicate it. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. A number should be preceded by the percent sign (%) to denote it is a percent.

Here,

Given :

A weekly unemployment amount is calculated using the following three components:

1. Determine the quarterly wage total (consecutive)

2. Multiply the sum by 26.

3.Multiplying by the rate of unemployment

Calculate the total of a quarterly salaries first:

=> (12950.80 + 12250.10) / 26

=>  25,200.9/26

=> 969.26 * 40 %

=> 387.704

Therefore , the solution of the given problem of percentage comes out to be $387.704 is the weekly unemployment amount.

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Answer:

b, education

Sana makatulong

Answer:

40

Step-by-step explanation:

Assign the variable x to Devaughn's age. If Devaughn is 7 years older than Sydney, then Sydney must be 7 years younger than him, so the expression x - 7 can represent Sydney's age.

The sum of their ages would be x + x - 7 or 2x - 7 which is also said to equal  87. Therefore, this can be written as an equation and be solved accordingly:

2x - 7 = 87

2x = 94

x = 47

Therefore, Devaughn is 47 and Sydney, who is 7 years younger, is 40.

Sydney's age is determined by setting up and solving a simple algebraic equation based on the information provided. The equation that represents this situation is S + (S + 7) = 87, which leads to the conclusion that Sydney is 40 years old.

Devaughn is 7 years older than Sydney. Given that the sum of their ages is 87, we can represent this situation with algebra. Let's denote Sydney's age as S.

Considering Devaughn is 7 years older, we can represent his age as S + 7. Given that the sum of their ages is 87, we can write down this equation: S + (S + 7) = 87.

Solving this equation will help us find Sydney's age. First, simplify the left side: 2S + 7 = 87. Then, subtract 7 from both sides: 2S = 80. Finally, divide both sides by 2 to solve for S, yielding Sydney's age: S = 40.

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The given equation would be, 5(6b-3) - 3b = 0 and b can take infinite number of values to make the equation true.

What equation system has an infinite number of solutions ?

The prerequisite for a situation in which an equation has an endless number of solutions is that the right and left sides of the equation are equal.

The equation is already complete and has infinitely many solutions.

The unknown variable is b, and there are an infinite number of values that b can take to make the equation true.

5(6b-3) - 3b = 0

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The inequality and graph of the solutions will be x + 0.80y ≤ 20 and any value on the line or below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Dion is buying a balloon bouquet. His favorite colors are silver and purple. Silver balloons cost $1.00 and purple balloons cost $0.80.

Let 'x' be the number of silver balloons and 'y' be the number of purple balloons. And if he doesn't spend more than $20. Then the inequality is given as,

$1 x + $0.80 y ≤ $20

x + 0.80y ≤ 20

Take any value on the line or below.

The inequality and graph of the solutions will be x + 0.80y ≤ 20 and any value on the line or below.

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Answer:

But the 2lbs.

Step-by-step explanation:

Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.

You're welcome.

It will take 5 minutes to paint this cone

Since the area of the base of the cone is doubled, the new base area becomes 2 * 49π in² = 98π in².

The radius of the original cone can be found by using the formula for the area of a circle:

49π = πr^2

r = 7 in

The height of the new cone can be calculated using the same lateral height as the original cone:

h = 8 in

Using the formula for the volume of a cone, we can calculate the volume of the new cone:

V = (1/3)πr^2h = (1/3)π(7^2)(8) = (1/3)π(392)

The surface area of the original cone can be found using the formula for the surface area of a cone:

A = πr^2 + πrs

where s is the slant height of the cone.

s = √(r^2 + h^2) = √(7^2 + 8^2) = √(49 + 64) = √(113)

So, we have

A = πr^2 + πrs = π(7^2) + π(7)(√(113)) = 49π + 7π(√(113))

The surface area of the new cone can be found using the same formula:

A = πr^2 + πrs = π(7^2 * 2^2) + π(7 * 2)(√(113)) = 98π + 14π(√(113))

When the equations are compared, we have

2 * 49π + 7π(√(113)) = 98π + 14π(√(113))

Since the new cone has twice the surface area of the original cone and can be painted at the same rate,

It will take 2.5 * 2 = 5 minutes to paint this cone.

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Answer:

Step-by-step explanation:

I took the test the answer is 4.2

1600 units were produced , If you spend $3000 on production cost.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The cost of producing X units of a product is 1.25. Per unit plus $1000 in flat production cost.

If you spend $3000 on production cost.

let, x units were produced.

so, we get,

1.25x+1000 = 3000

1.25x= 2000

x= 1600

Hence, 1600 units were produced , If you spend $3000 on production cost.

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Answer:

D: ( - ∞, 5)

R: [- 3, ∞)

Step-by-step explanation:

The domain is the set of possible x values. The function has values from below five while not including 5(as shown by the open circle). Therefore the domain would be ( - ∞, 5). (Open brackets are non-inclusive while closed brackets are inclusive).

The range is the set of possible y values. The minimum of this graph seems to be at y = -3, and there is not a maximum as while the x values decrease, the y-values infinitely increase. Therefore, the range is [- 3, ∞)

Answer:

5.2

Step-by-step explanation:

8.6 Pounds + P = 14.2 Pounds

-8.6 Pounds -8.6 Pounds

P = 5.2

Rufus gained 5.6 pounds between his first and second visits to the veterinarian.

We have,

To find the number of pounds Rufus gained between visits, we need to subtract his initial weight from his weight at the second visit.

Therefore, we have:

pounds gained = weight at second visit - weight at the first visit

p = 14.2 - 8.6

p = 5.6

Therefore,

Rufus gained 5.6 pounds between his first and second visits to the veterinarian.

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The step-by-step process of making simplified algebraic expressions are shown below

Below are six simplified algebraic expressions with step by step solutions:

1. Simplify: 2x + 3x

Step 1: Combine like terms: 2x + 3x = 5x

Step 2: Simplified expression: 5x

2. Simplify: 7x - 4x

Step 1: Combine like terms: 7x - 4x = 3x

Step 2: Simplified expression: 3x

3. Simplify: 5y + 2y + 3y

Step 1: Combine like terms: 5y + 2y + 3y = 10y

Step 2: Simplified expression: 10y

4. Simplify: 8z - 6z

Step 1: Combine like terms: 8z - 6z = 2z

Step 2: Simplified expression: 2z

5. Simplify: 4a + 6a - 3a

Step 1: Combine like terms: 4a + 6a - 3a = 7a

Step 2: Simplified expression: 7a

6. Simplify: 9b - 7b + 5b

Step 1: Combine like terms: 9b - 7b + 5b = 7b

Step 2: Simplified expression: 7b

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