Jacqueline is buying grapes and apples from the Walmart produce section. Grapes are $3
per pound and apples are $4 per pound. Jacqueline’s mother gave her $20 to spend. To
determine the combinations of grapes and apples that she can afford to purchase,
Jacqueline wrote the inequality 3 + 4 ≤ 20.

1. Define the variables Jacqueline used based on the context.
Let represent _______________________________________________.
Let represent _______________________________________________.
2. Explain why the inequality sign ≤ makes sense in this context.
3. Graph the inequality 3 + 4 ≤20.

4.The ordered pair (3, −4) is a solution to the inequality 3 + 4 ≤ 20.

Explain why
this is not a viable solution in the context of buying grapes and apples.

5. The ordered pair (4, 2) is a point on the boundary line. Explain what the ordered
pair represents in the situation.

On solving the provided inequality equation we cans ay that therefore, 60x + 45 <250 is the necessary inequality for the given situation.

An inequality in mathematics shows how two values are related in an imbalanced algebraic expression. According to inequality signals, one of the two variables on either side of the inequality may be larger than, greater than or equal to, less than, or less than or equal to another value.

If the daily cost for each crew member is $60, the daily wage for crew members is $60, and the daily cost of operations is $45; the amount paid equals the total of the wages for each crew member plus the cost of operations. In this case, let x indicate the size of the crew.

= 60x + 45

Since the maximum daily payment is $250,

In other words, the total payment cannot be more than $250.

60x + 45 ≤ 250

Therefore , the required inequality for given problem is 60x + 45 ≤ 250.

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Answer:

47.07, 47.16, 47.3, 47.4, 48.1

Step-by-step explanation:

lol

Answer: The formula for the surface area of a cone is S = π * r * s + π * r², where r is the radius of the base and s is the slant height of the cone.

To find the surface area of a cone, you first need to find the radius of the base. Since the base diameter is given as 7cm, you can divide this by 2 to find the radius of the base:

r = 7cm / 2 = 3.5cm

Next, you need to find the slant height of the cone. You can use the Pythagorean theorem to do this.

slant height = sqrt(r^2 + h^2) = sqrt(3.5² + 8²) = sqrt(12.25 + 64) = sqrt(76.25) = 8.766cm

Now you can substitute these values into the formula for the surface area of a cone and find the surface area of the cone.

S = π * r * s + π * r² = π * 3.5cm * 8.766cm + π * 3.5² cm² = 12.571 cm² + 38.485 cm² = 51.056 cm²

So the surface area of a cone with a base diameter of 7cm and height of 8cm is 51.056 cm²

Step-by-step explanation:

The total quantity of water that the container would have to hold is given as 8.

We know that the container holds 1 gallon of water, and that each bottle holds 1/8 of a gallon. To find out how many bottles the container can hold we need to divide the container size by the size of each bottle.

We can use the following formula to find the number of bottles:

Number of bottles = Container size / Size of each bottle

We can substitute the values into the formula:

Number of bottles = 1 / (1/8) = 8

So the container can hold 8 bottles of water.

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Using the provided values and information, The answer is each person would receive 1/5 of the original bread loaf.

A proportion is a mathematical statement that compares two ratios. It is an equation that states that two ratios are equal, such as "a/b = c/d." Proportions are often used to solve problems involving fractions, decimals, and percentages. For example, if you know that a particular recipe calls for two cups of flour for every one cup of sugar, you can use this proportion (2/1 = x/3) to figure out how much sugar you need if you want to triple the recipe. The proportion can also be written as 2:1 = x:3.

A ratio is a mathematical comparison of two or more quantities, typically represented as a fraction. It is a way to compare the size of two or more things. For example, if a recipe calls for 2 cups of flour to 1 cup of sugar, the ratio of flour to sugar is 2:1. This means that for every 2 units of flour, there is 1 unit of sugar. Ratios can also be written using the colon symbol (:) or the word "to". For example, the ratio 2:1 can also be written as 2/1 or 2 to 1. Ratios can be simplified by dividing both the numerator and denominator by a common factor and can be used to compare quantities in different units.

Each person would get 1/5 of the original bread loaf. If the bread is divided equally among four people, then each person would receive 1/4 of the total amount. Since 1/5 is the same as 4/20, and 4 people are receiving the bread, then each person would receive 1/5 of the original bread loaf.

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Answer:

For this example they are all the same thing.  

530:1 or 530 mph

Step-by-step explanation:

A unit rate is when the denominator is 1.  In this case, the denominator is already 1 hour.

3.) x = 15.25 or 15 1/4 ( not sure if you'll need to round your answer )

4.) x =6

5.) x = 10

6.) x = 9

Explanation:

1.) write your equation down 8x + 9 = 131

2.) Subtract +9 from 131. you'll get 122

3.) divide 8x and 122.

4.) Then there's your answer 15.25

you'll do the same thing throughout each equation. write down your equation but with the 22x and 23x you're going to subtract 22x from 23x. and you'll get 1x then continue on the same way as with the last equation.

Answer:

Step-by-step explanation:

(9x-12)-(5x-7)=9x-12-5x+7=9x-5x-12+7=4x-5

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The coordinates of B are (6,0).

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is given by the coordinates:

In this problem, we're given that the midpoint is (2, 4) and we need to find the coordinates of point B. Since we know the coordinates of the midpoint, we can set up the equation:

We know that point A = (-2,9) is one endpoint, so we can substitute it into the equation

Solving for x2 and y2, we get x2 = 6 and y2 = 0 which is the coordinates of point B.

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Answer:

x ≈ 10.6

Step-by-step explanation:

using the cosine ratio in the right triangle

cos35°= [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{13}[/tex] ( multiply both sides by 13 )

13 × cos35° = x , then

x ≈ 10.6 ( to the nearest tenth )

The solution is Option C and Option D.

The exponential function is given by f ( x ) = 2 ( 3 )ˣ

The exponential function is given by f ( x ) = 800 / 4ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 7 , 19 , 31 , 43 }

The equation of line is y = 12x + 7

This is a linear equation

b)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 5 , 10 , 15 , 30 }

The equation is a quadratic equation

c)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 2 , 6 , 18 , 54 }

The equation is y = 2 ( 3 )ˣ

This is an exponential function

d)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 800 , 200 , 50 , 12.5 }

The equation is f ( x ) = ( 800 / 4ˣ )

This is an exponential function

Hence , the exponential equations are solved

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Answer:

215/100

Step-by-step explanation:

it is asking for improper fraction

improper fractions are just the bottom number multiplied by the number outside of the fraction so in this case it is

2*100 which is 200 then add that to the top number

which leaves you with 215/100

The solutions for all the equations would be

1. p = 30

2. h = 99

3. t = 31.4

4. r = 57

5. t = 5

6. w = 8

7. y = 9

8. p = 7

9. a = 13

10. w = 12

11. h = 24

12. g = 128

13. a = 21

14. y = 39

15. d = 16

16. w = 25

What is an equation?

An equation is a statement that asserts the equality of two expressions. The expressions on either side of the equation are separated by an equals sign (=), and they must have the same value for the equation to be true.

1) 30p = 900

  p = 900/30

  p = 30

2) h/9 = 11

   h = 9 * 11

   h = 99

3) t + 32.4 = 62

   t = 62 - 32.4

   t = 31.4

4) r - 17 = 40

   r = 40 + 17

  r = 57

5)  5t = 25

      t = 25/5

      t = 5

6) 8w = 64

    w = 64/8

   w = 8

7)  9y = 81

     y = 81/9

     y = 9  

8) p + 5 = 12

   p = 12 - 5

   p = 7

9)  a + 2 = 15

    a = 15 - 2

    a = 13

10)  w + 8 = 20

      w = 20 -8

      w = 12

11)  h/6 = 4

    h = 6 * 4

    h = 24

12) g/8 = 16

    g = 16 * 8

    g = 128

13) a/7 = 3

    a = 3 * 7

    a = 21

14) y - 11 = 28

    y = 28 + 11

    y = 39

15) d - 4 = 12

    d = 12 + 4

    d = 16

16) w - 10 = 15

    w = 15 + 10

    w = 25

Hence, solutions for all the equations would be

1. p = 30

2. h = 99

3. t = 31.4

4. r = 57

5. t = 5

6. w = 8

7. y = 9

8. p = 7

9. a = 13

10. w = 12

11. h = 24

12. g = 128

13. a = 21

14. y = 39

15. d = 16

16. w = 25

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The answer as an exact decimal = -0.84 and simplified fraction = −21/25.

Simplifying a fraction is the process of reducing a fraction to its most basic form. If the numerator and denominator of a fraction have no common factors other than one, the fraction is in its simplest form.

When solving fraction problems, we must first simplify them. Even if we simplify them, the fraction's value will remain unchanged. This means that the simplified and actual fractions are equivalent fractions.

Given that

-67/50 + 1.5 − 100% = ?

Lets solve

= -67/50 + 1.5 − 100%

= -67/50 + 1.5 − (100 × 0.01)

= -67/50 + 3/2 - 1

= -67/50 + 75/50 - 50/50

= (-67 + 75- 50)/50

= −42/50

= −21/25

= -0.84

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The value of x is 20

Now, According to the question:

The given equation is:

3x + 32 = 5x - 8

To solve the equation for finding the value of x .

32 + 3x = -8 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.

32 + 3x  -5x = -8 + 5x  -5x

Combine like terms:

3x  -5x = -2x

32  -2x = -8 + 5x  -5x

Combine like terms: 5x  -5x = 0

32  -2x = -8 + 0

32  -2x = -8

Add '-32' to each side of the equation.

32  -32 -2x = -8  -32

Combine like terms: 32  -32 = 0

0 -2x = -8  -32

-2x = -8  -32

Combine like terms: -8  -32 = -40

-2x = -40

Divide each side by '-2'.

x = 20

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Answer: first u have to find the perimiter for each side

Step-by-step explanation:

the answer is 100 d z

Answer:

2 ≥ p

Step-by-step explanation:

-14 ≤ -7p

Divided both sides by -7. Because divided by a negative number, the < will turn to >

So, the equation is

2 ≥ p

Because there is an equal, the circle will be close and to the left of 2.

Answer:

2 ≥ p

Step-by-step explanation:

Have a great day :) <3

There are four fundamental types of inequality: less than ( < ), larger than( > ), less than or equal to ( ≤ ), and more than or equal to( ≥ ).

The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.

The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.

Steps to solve the inequality:

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Each state is given a specific amount of "votes" under the "Electoral College" system. The amount of "votes" each state receives is proportionate to its size.

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Answer:

25

Step-by-step explanation:

so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.

Answer:

51.50004959055205

Step-by-step explanation:

[tex]sin (x) = \frac{18}{23}[/tex]

Answer:

you can eliminate the x terms in this system by multiplying each side by 3.

Step-by-step explanation:

in order to eliminate a variable from a system of equations, you must multiply whatever variable you want to eliminate (in this case, x) by a number that will make the variable you want to eliminate in the first (4y+3x=-6) and second (which is y-x= -5) equations cancel out when adding them together

a written example for further clarification:

step 1:

4y + 3x = -6

3*(y - x = -5)

up here, you can see i'm multiplying the bottom equation by 3 in order to change the value of x from x to -3x, so that when you add the top and the bottom equations together, x is nowhere to be found in the resulting equation (this is what you want)

step 2:

distribute the 3 to all terms in the second equation. this gives you:

(3y-3x = -15).

step 3:

now add this new equation to the first equation (4y+3x=-6).

This gives you:

4y+3x=-6

+

3y-3x=-15

then just add the like terms (4y and 3y, 3x and -3x, -6 and -15).

which gives you (7y=-21)

see how x is not in the resulting equation? you have now successfully eliminated it :] hope this helped!

The equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that a line has a slope of 1/5 and passes through the point (3, 10)

We can write the slope of the line as -

m = 1/5

For the point (3, 10), we can write -

y = (1/5)x + c

10 = (1/5) x 3 + c

c = 10 - 3/5

c =  47/5

Therefore, the equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).

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the length of side x = 12.5.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, we have,

From the given figure, we get.

These two figures are similar.

so, we have,

8/x=y/5 ............(1)

10/15=4/z ......(2)

8/15=y/z .....(3)

Solving we get,

x=12.5

Hence,  the length of side x = 12.5.

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Answer:

A

Step-by-step explanation:

each text message is .17 text messages are x the total bill is 28.45. the service charges are 24.20.

.17x + 24.50 = 28.45

Answer:

They are parallel line.

Jake and Hakeem's rocket's flight is approximately modeled by the equation h(t) = - 12t ^ 2 + 36t + 3. The rocket's highest point is 30m

Generally, Since we are not instructed on what to look for, we are able to determine the highest point that the rocket ever achieved.

Given that the rocket's flight can be approximated approximatively using the equation,

h(t) = - 12t ^ 2 + 36t + 3

At maximum height dh/dt = 0

dh/dt = --24t + 36

0 = -24t + 36

24t = 36

t= 36/24

t = 1.5s

Find out the maximum height.

h(1.5) = - 12 (1.5)^ 2 + 36(1.5) + 3

h(1.5) = - 12(2.25) + 54 + 3

h(1.5) = -27 + 57

h(1.5) = 30m

As a result, the rocket is only capable of reaching a height of 30 meters at its highest point.

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The term 5 in 5x is known as the coefficient of the expression.

A coefficient is defined as a term or a number which is multiplied by a variable. This constant terms generally precedes the variable term.

A coefficient is a generally a multiplicative factor in a polynomial series, or in an  equation.

Expressions are mathematical statements which are composed of two terms in which at least one contain variables, numbers, or both. These terms are either numbers or variables or numbers and variables multiplying each other. These expressions are a combination of numbers with mathematical ,operators are used to separate them.

Eg, 2x - 90 =45

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