Fay has a lemonade stand.
She spends £42 on ingredients.
She sells each glass of lemonade for £1.20.
If she sells 50 glasses of lemonade, what is her total profit?

The system of equations that represents this situation is D + Q  =24 and 10D + 25Q = 465 with 15 and 9 quarters and dimes respectively.

Given that

let the quarter be represented by Q and dimes with D

D + Q  =24 (multiply this by 10)

10D  + 10Q = 240

10D + 25Q = 465

Subtracting both the equations:

15Q  =225

Q = 225/15 = 15 quarters

Now putting this value in equation 1st we get

D = 24-15 = 9 dimes

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Answer:

4 or t = -8

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are solving for the variable, t. Note the equal sign, what you do to one side, you do to the other.

To isolate t, add 7 to both sides of the equation:

21 = t - 7

21 (+7) = t - 7 (+7)

21 + 7 = t

t = 28

t = 28 is your answer.

Check: Plug in 28 for t in the given equation:

21 = t - 7

21 = (28) - 7

21 = 21 (True).

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Due to the corresponding angle property, which requires that the sum of neighboring opposite angles be 180, the angles are 90 and 79.8.

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are positioned. When two planes collide, an angle is also created. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, also known as the sides of the angle, converge.

given

Due to the property of matching angles,

the angles are 90 and 21x + 8

90 + 21x + 18 = 180

= 108 + 21x = 180

= 21x = 72

x = 3.42

Due to the corresponding angle property, which requires that the sum of neighboring opposite angles be 180, the angles are 90 and 79.8.

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To display the relationship between data objects, tables of values are utilized. In scientific class, you might employ a table of values.

A group of numbers, often known as "terms," such as 2, 5, or 8, make up a sequence. Some sequences can be made infinitely long by utilizing a specific pattern that they follow. Add 3 and use the example of 2,5,8 to continue the series. There, you can find formulas that outline where to hunt for terms in a series. A collection of elements in some order is what is referred to as a sequence informally in mathematics (or events). Like a set, it is made up of parts (also called elements or terms). The entire, perhaps indefinite number of arranged objects is referred to as the length of the sequence. the process of logically ordering two or more objects. Chronological.

given

To display the relationship between data objects, tables of values are utilized. In scientific class, you might employ a table of values. Researchers and scientists record their data using tables of numbers, then examine the data to look for patterns.

This pattern can then be applied to generate forecasts.

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Answer:

56.8x+39.2 Welcome :D

Step-by-step explanation:

Answer:

[tex]56.8x+39.2[/tex]

Step-by-step explanation:

First, you must distribute the 2's to the expressions:

2(4.4x+7.6) = 2(4.4x) + 2(7.6) which is equal to 8.8x + 15.2 and;

2(24x+12) = 2(24x) + 2(12) = 48x + 24

Now add both: 8.8x + 48x + 24 + 15.2 ; combine like terms.

56.8x + 39.2 is what you get from doing that.

This cannot be simplified any further, and therefore is your answer:

56.8x + 39.2

Answer: To find the capacity of the tin can, we can use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length is 5 cm, the width is 4 cm, and the height is 15 cm. So the volume of the tin can is 5 x 4 x 15 = 300 cubic cm.

To find the capacity of the plastic cylinder, we can use the formula for the volume of a cylinder, which is pi x radius squared x height. The diameter of the circular base is 7 cm, so the radius is half of that, or 3.5 cm. So the volume of the plastic cylinder is pi x (3.5 cm)^2 x 10 cm = 385.4 cubic cm.

So the plastic cylinder has a greater capacity by 385.4 - 300 = 85.4 cubic cm.

Step-by-step explanation:

There are number of factors of 36 are 9 and number of array Courtney can make with the photo is 9.

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

In math, an array refers to a set of numbers or objects that will follow a specific pattern.

the arrays can Courtney make with the 36 photos are,

1 by 36,

36 by 1,

2 by 18,

18by 2,

3 by 12,

12 by 3,

4 by 9,

9 by 4,

6 by 6.

the factors of 36 are,

1, 2, 3, 4, 6, 9, 12, 18, 36

∴ 9 ( factors ) = 9 ( arrays )

Therefore, there are number of factors of 36 are 9 and number of array Courtney can make with the photo is 9.

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Answer: The perimeter of a rectangle is the sum of the lengths of its four sides which is given by the expression: P = 2l + 2w (where l is the length and w is the width)

The expression that does not show this relationship is P = l + w

It doesn't show the relationship because it doesn't take into account the two sides that are equal to the width and the two sides that are equal to the length.

P = 2l + 2w shows the relationship as it considers both length and width of the rectangle twice, once for each pair of sides.

Step-by-step explanation:

The procedure of solving linear equations in two variables by substitution includes selecting one eqn and solving it for one variable, substituting the result in another equation, solving the new eqn, and finally substituting the value into any of the eqns and solving for another variable.

An equation is a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b (≠ 0).

To solve systems using substitution, follow these steps:

Step 1. Select one equation and solve it for one of its variables.

Step 2. In the other equation, substitute the value get from step 1.

Step 3. Solve the new equation.

Step 4. Substitute the value found into any equation involving both variables and solve for the other variable.

Step 5. Check the solution in both original equations.

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The correct answer is -60

When you look at -70 it looks like it would be higher then -60 but -60 is actually higher then -70 because it has a negative line.

Therefore, the correct answer is -60

The expression " [tex]\frac{2}{3}[/tex] to the exponent of 3" is represented as , [tex](\frac{2}{3} )^{3}[/tex] , and the value of  [tex]\frac{2}{3}[/tex] to the exponent of 3 is [tex]\frac{8}{27}[/tex] .

What are Exponents ?

The Exponents are defined as the representation of a number that is multiplied by several to itself .

For Example : 8 multiplied by two times to itself , can be represented in exponential form as  8² .

We have to find the value of  " [tex]\frac{2}{3}[/tex] to the exponent of 3" ;

the given exponential expression can be solved further as :

⇒ [tex](\frac{2}{3} )^{3} = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3}[/tex]

On simplifying ,

we get ;

⇒ [tex]\frac{2\times 2 \times 2}{3 \times 3\times 3}[/tex]

⇒ [tex]\frac{8}{27}[/tex] .

Therefore , the value of  " [tex]\frac{2}{3}[/tex] to the exponent of 3" is [tex]\frac{8}{27}[/tex] .

The given question is incomplete , the complete question is

What is [tex]\frac{2}{3}[/tex] to the exponent of 3 ?

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The inequality can be written as g * 37.5 >= 120.

What is linear inequality?

A linear inequality is a mathematical statement that describes a relationship between two or more variables that form a half-plane when graphed. The equation of a linear inequality is in the form of "ax + by < c" or "ax + by > c" or "ax + by <= c" or "ax + by >= c", where x and y are variables, and a, b and c are constants.

An inequality that could be used to determine the minimum number of gallons, g, of gasoline Darla would need to drive 120 miles to her brother's house is:

g >= 120/37.5

This inequality states that the number of gallons, g, must be greater than or equal to the number of miles Darla needs to drive, 120, divided by the number of miles per gallon her car gets, 37.5. This is because Darla wants to ensure that she has enough gasoline to make the trip, and she may not want to risk running out of gas on the way.

Another way to write this inequality is

g * 37.5 >= 120

This inequality represents the same meaning as before, we multiply g by the number of miles per gallon the car gets, 37.5 and it should be greater than or equal to the distance she needs to travel which is 120 miles.

Hence, the inequality can be written as g * 37.5 >= 120.

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To determine if the set of ordered pairs satisfies an exponential function, x -coordinates must have a constant increment.

We know that generally exponential function is written in the form function can be written in the form y = ab^x ,

where a and b are real numbers such that, a ≠ 0 , b > 0 , and b ≠ 1

a is called the initial value of function

and b is the constant ratio

We know that as x increases by a constant value, the value of y increases by a common ratio. This is characteristic of all exponential functions.

To determine whether the set of ordered pairs satisfies an exponential function, the condition that 'The x -coordinates must have a constant increment' must be satisfied.

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340 feet deep was well dug relative to ground level

Two or more expressions with an Equal sign is called as Equation.

Given that Mr. Jakarta is having a well built in his backyard.

On Monday 175 feet of the well was drug

Another 165 feet was dug tuesday.

We need to find the how many feet deep was well dug relative to ground level

To find the number of feet, we simply make an addition of the number of feet dug on both days

The total will be 175 feet + 165 feet = 340 feet

Hence, 340 feet deep was well dug relative to ground level

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The polynomial h(x)=x^4+2x^3-13x^2-14x+24 in the factored form is (x−1)(x+2)(x−3)(x+4). The real roots of the polynomial is x= 1, x = 3, x = -2, x  = -4.

What is a polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

The polynomial function is -

h(x)=x^4+2x^3-13x^2-14x+24

Divide the polynomial h(x) by (x-1) -

(x^4+2x^3−13x^2−14^x+24)=(x−1)(x3+3x2−10x−24)

Divide (x^3+3x^2−10x−24) by (x+2) -

(x−1)(x^3+3x^2−10x−24)=(x−1)(x+2)(x^2+x−12)

Solve the quadratic equation x^2+x−12=0.

x^2+x−12=0

x^2+4x-3x-12=0

x(x+4)-3(x+4)=0

(x+4)(x-3)=0

So, (x−1)(x+2)(x^2+x−12)=(x−1)(x+2)(x−3)(x+4)

Therefore, x^4+2x^3−13x^2−14x+24=(x−3)(x−1)(x+2)(x+4) .

The Rational Root Theorem tells us that if the polynomial has a rational zero then it must be a fraction q/p, where p is a factor of the constant term and q is a factor of the leading coefficient.

We can see that p(1)=0 so x=1 is a root of a polynomial h(x).

Divide the polynomial by (x-1) -

(x^4+2x^3−13x^2−14x+24)/(x-1)=(x^3+3x^2−10x−24)

Divide (x^3+3x^2−10x−24) by (x-3) -

(x^3+3x^2−10x−24)/(x-3) = (x^2+6x+8)

To find the last zero, solve equation x+4=0

x=-4

Therefore, the real roots are - x = 1, 3, -2, -4.

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No, the set of 2nd coordinates is not a set. It is a pair of numbers that identifies a particular point on a coordinate plane.

1. It is not a collection of items.

2. It is not an ordered list.

3. It is not a group of elements.

4. It is not a set of elements.

5. It is not a collection of points.

6. It is not a grouping of numbers.

7. It is not a sequence of numbers.

8. It is not a selection of numbers.

9. It is not a combination of numbers.

10. It is not a union of numbers.

11. It is not a cluster of numbers.

12. It is not a set of components.

13. It is not a combination of values.

14. It is not a sequence of values.

15. It is not a selection of values.

16. It is not a union of values.

17. It is not a set of points.

18. It is not a set of data points.

19. It is not a selection of coordinates.

20. It is not a set of ordered pairs.

21. It is not a set of numbers.

22. It is not a set of measurements.

23. It is not a set of data.

24. It is not a set of variables.

25. It is not a set of parameters.

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Answer:

It seems that your question is missing something, it looks like a question to a previous question. Please add all info when making a question. Also you can comment underneath my reply with that additional info.

Answer:

yes

Step-by-step explanation:

a^2 + b^2 = c^2

so

32^2 + 60^2 = 68^2

1024 + 3600 = 4624

On solving the question, unit rate by using the given graph could be 2.4 potatoes/pound

Graph can be defined as the visual representation which is used to represent the data.

The unit rate is the slope of the line.

The slope of the line =  (change in y-value)/(change in x-value)

= (36 potatoes - 12 potatoes)/(15 pounds - 5 pounds)

= (24potatoes)/(10 pounds)

= 2.4 potatoes/pound

The relationship here is proportional, so the line goes through the point (0, 0) and the unit rate can be figured from any point:

(12 potates)/(5 pounds)

= (24 potatoes)/(10 pounds)

= (36 potatoes)/(15 pounds) = 2.4 potatoes/pound

Hence, The unit rate by using the given graph could be 2.4 potatoes/pound .

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The correct question is -

Identify the unit rate in the graph.

A. 40mph

B. 75mph

C. 50mph

D. 25mph

An equation that has one solution for y for each value of x is referred to be a function. A function pairs each input of a particular type with exactly one output.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function.  Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

An equation that has one solution for y for each value of x is referred to be a function.

A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.

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Answer:

Function A

Step-by-step explanation:

doesn't have vertical points

The sum of: (-14.2b - 97.35) + (6.76d - 118.7 - 3.4d ) is -14.2b + 3.36d -216.05

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

(-14.2b - 97.35) + (6.76d - 118.7 - 3.4d )

Remove the brackets

So, we have

-14.2b - 97.35 + 6.76d - 118.7 - 3.4d

Evaluate the like terms

-14.2b + 3.36d -216.05

Hence, the sum is -14.2b + 3.36d -216.05

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The length 4.5 cm 3.5 cm 6.4 cm can be the dimensions of a triangle according to rule.

Considering the dimensions of triangle, the one side of the triangle should be less than the sum of other two sides. Based on the rule, let us say that 4.5, 3.5 and 6.4 cm is side a, b and c.

Keep the values to compare the sides

Side a + side b > side c

4.3 + 3.5 > 6.4

Add the digits

7.8 > 6.4

Side b + side c > side a

3.5 + 6.4 > 4.5

Add the digits

9.9 > 4.5

side c + side a > side b

6.4 + 4.5 > 3.5

Add the digits

10.9 > 3.5

All the sides follow the rule. Therefore, the mentioned lengths are possible for a triangle.

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The rider has 141 laps left to finish the race.

If a rider has already cycled 4.75 km, and each lap measures 0.25 km, we can determine how many laps the rider has completed by dividing the distance already cycled by the distance per lap.

To find out how many laps the rider has left to finish the race, we will use the information on the total number of laps to complete the race: 160 laps.

The rider has completed:

4.75 km / 0.25 km = 19 laps

The rider has yet to finish:

160 laps - 19 laps = 141 laps

So the rider has 141 laps left to finish the race.

Therefore, the rider has 141 laps left to finish the race.

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If rectangle is similarity to rectangle, to find the value of x we use proportion (c) 5/12 = 2/x.

When applying a scale factor, similar shapes are enlarged versions of one another.

All of the matching angles and lengths in related shapes are equal and in the same ratio.

If two figures share the same shape, congruent corresponding angles (which means the angles in the same places of each shape are the same), and identical scale factors, they are said to be "similar figures."

Given that rectangle EFGH is similar to rectangle JKLM, it means the corresponding sides of both rectangles are similar, and as such the ratios if the corresponding sides of rectangle EFGH and rectangle JKLM would be equal.

Thus, EF/JK = FG/KL

Since, EF = 5; JK = 12; FG = 2; and KL= x, therefore, the proportion to use in finding x would be:

5/12= 2/x

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The equation for the nth term of this sequence is  [tex]a_{n}[/tex] = 8n - 14. The solution has been obtained by using the concept of arithmetic progression.  

What is arithmetic progression?

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

We are given that the third term is 10.

This means that [tex]a_{3} =10[/tex]

So, n=3

Substituting this value in the given equations, we get

1)  [tex]a_{n}[/tex] = 8*3+10 = 34

2)  [tex]a_{n}[/tex] = 8*3 - 14 = 10  

3)  [tex]a_{n}[/tex] = 16*3+10 = 58

4)  [tex]a_{n}[/tex] = 16*3 - 38 = 10

So, the second and the fourth equation satisfy the condition.

We are also given that the fifth term is 26.

This means that [tex]a_{5} =26[/tex]

So, n=5

Substituting this value in the given equations, we get

2)  [tex]a_{n}[/tex] = 8*5-14 = 26  

4)  [tex]a_{n}[/tex] = 16*5 - 38 = 42

So, the second equation satisfies the condition.

Hence,the equation for the nth term of this sequence is  [tex]a_{n}[/tex] = 8n - 14.

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The amount invested in each mutual fund is $400 and $1200 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 10 and 8x − 4y = 2

Let represent the amount the first fund get by x and the amount the second fund get by y.

Therefore x+y = 1600 equation 1

and 9/100 × x + 4/100 × y = 84

9x/100 + 4x/100 = 84

multiply through by 100

9x + 4x = 8400 equation 2

using elimination method

9x+ 9y = 14400 equation 3

9x + 4y = 8400 equation 4

subtract equation 4 from 3

5y = 6000

divide both sides by 5

y = 6000/5

y = $1200

substitute 1200 for y in equation 1

1200+x = 1600

x = 1600-1200

x = 400

Therefore the first fund will get $400 and the second fund will get $1200

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Therefore , the solution of the given problem of triangle comes out to be the planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.

Since a triangle has three sides or three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to one of a triangle that has endpoints A, B, and C. When the points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where its three sides meet are known as the triangle's corners. The product of three triangle angles is 180 degrees.

Here,

Using the ABC/XYZ technique, planned units (characteristic product combinations, SKUs) are grouped according to their value (income or product sales) and consumption or sales dynamics.

The planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.

Therefore , the solution of the given problem of triangle comes out to be the planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.

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Answer:

:Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded

Step-by-step explanation:

Answer:  Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.

Step-by-step explanation: