4) Edgar builds a sand castle with a rectangular base. The side lengths of the base are 25 in, and 16 in. He wants
to surround the castle's base with a moat that is w inches wide. Write a quadratic function, A, in standard form to
represent the combined area taken up by the castle and the moat.
16in.
25 in.

The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.

The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.

In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.

For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).

A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.

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Answer:

D. trapezoid

Step-by-step explanation:

---------------

Answer:

4 is next in NUMBER OF DAYS

9 is the first in NUMBER OF TADPOLES

41 is the 2nd answer ON NUMBER OF TADPOLES

Step-by-step explanation:

hope this helps a lot!!

Answer:

[tex]c = 3 \tan(60 \degree) \\ c = 5.2 \\ hypotenuse \: of \: first \: triangle : \\ = \frac{ 5.2 }{ \sin(60 \degree) } \\ = 6 \\ \\ \frac{6}{4} = \frac{c}{b} \\ \frac{6}{4} = \frac{5.2}{b} \\ b = \frac{5.2 \times 4}{6} \\ b = 3.5[/tex]

Answer:

[tex](a)\ C(x) = 6312.50 + 8.75x[/tex]

[tex](b)\ R(x) = 34x[/tex]

[tex](c)\ P(x) = 6312.50 -25.25x[/tex]

[tex](d)\ Break\ Even = 250\ hours[/tex]

Step-by-step explanation:

Solving (a): The cost function.

Given

[tex]Cost = \$6312.50[/tex] --- cost of saxophone

[tex]Additional = \$8.75[/tex] per hour

The cost function is: sum of the cost of the saxophone and the extra cost per hour.

If an hour costs 8.75, then x hours will cost 8.75x

So, the cost function is:

[tex]C(x) = Cost + Additional[/tex]

[tex]C(x) = 6312.50 + 8.75x[/tex]

Solving (b): The revenue function

Given

[tex]Charges = \$34.00[/tex] per hour

The revenue function is the product of the unit charge by the number of hours.

If in an hour, she charges $34.00, then in x hours, she will cost 34x

So, the revenue function is:

[tex]R(x) = Charges * Hours[/tex]

[tex]R(x) = 34.00 * x[/tex]

[tex]R(x) = 34x[/tex]

Solving (c): The profit function

This is the difference between the cost function and the revenue function

i.e.

[tex]P(x) = C(x) - R(x)[/tex]

So, we have:

[tex]P(x) = 6312.50 + 8.75x - 34x[/tex]

[tex]P(x) = 6312.50 -25.25x[/tex]

Solving (d): The break even hours.

To do this, we simply equate the cost function and the revenue function, then solve for x

i.e.

[tex]C(x) =R(x)[/tex]

[tex]6312.50 + 8.75x = 34x[/tex]

Collect like terms

[tex]6312.50 =- 8.75x + 34x[/tex]

[tex]6312.50 = 25.25x[/tex]

Solve for x

[tex]x = \frac{6312.50}{25.25}[/tex]

[tex]x = 250[/tex]

Summary of slope of parallel lines:

Parallel lines have equal slopes. The parallel lines are equally inclined with regard to the positive x-axis, and this is taken into account when calculating a line's slope.

If one line has a slope of m1, another line has a slope of m2, and both lines are parallel, then we get m1 = m2.

The coefficients for "x" and "y" in the equations that depict parallel lines are identical.

Ax + by + c2 = 0 is the line that is parallel to ax + by + c1 = 0. Observation reveals that the x and y coefficients in both equations are equivalent.

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Answer:

5 + 3/4

Step-by-step explanation:

Answer:

23/4

Decimal Form:

5.75

Mixed Number Form:

5 3/4

Step-by-step explanation:

there ya goo

Sorry I over complicated the answer that i wrote, I think the answer is 18

All of the equations that are true include the following:

B. 56 + 70 = 14(4 + 5).

C. 28 + 49 = 7(4 + 7).

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

In order to determine the true equation, we would apply the distributive property of multiplication and then check whether or not the right-hand side is equal to the left-hand side.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

32 + 96 = 8(4 + 14)

32 + 96 = 32 + 112 (False).

56 + 70 = 14(4 + 5).

56 + 70 = 56 + 70 (True).

28 + 49 = 7(4 + 7).

28 + 49 = 28 + 49 (True).

27 + 36 = 3(9 + 13)

27 + 36 = 27 + 39 (False).

25 + 35 = 5(5 + 6)

25 + 35 = 25 + 30 (False).

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The total number of students in the student body is 110.

Percentage is the ratio of an amount expressed as a number out of 100. The sign that is used to represent percentage is %.

In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.

In order to determine the total number of students in the student body, divide the number of students that watch TV everyday by the given percentage.

Number of students in the student body = number of students that watch TV everyday / percentage

88 / 80%

= 88 / 0.8 = 110

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Answer: y = −0.7, -5

Step-by-step explanation:

Hi there!

[tex]\large\boxed{\text{ UVY} = 65^o, \text{ VYZ }= 65^o}[/tex]

We can begin by finding ∠VUY so we can solve for ∠UVY.

∠VUY is supplementary to ∠TUY, so:

180 = 144 + ∠VUY

∠VUY = 36°

In a triangle, angles sum up to 180°, so:

180 = 36° + 79° + m∠UVY

m∠UVY = 65°

Solve for m∠VYZ by comparing the angle to m∠UVY because the angles are alternating interior angles. Thus:

m∠UVY = m∠VYZ = 65°.

Answer:

6a. 0.02623

b. 0.5692

Thank you :)

Answer:

A.

Step-by-step explanation:

x=14

Step-by-step explanation:

the answer is 14

I just added 8 with 6

:)

On solving the provided question we can say that - the coordinates from the graphs will be P' = (0.0); Q' = (1,0); R' = (1,1); S' = (0,1)

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is r

A fixed point serves as the dilation's center.

Dk is used to represent dilation, where k is the scale factor.

Dk (x, y) = for a dilation centered on the origin (kx, ky)

Let's assume that you have a PQRS rectangle where

P = (0,0)

Q = (4,0)

R = (4,4)

S = (0,4)

You must multiply each coordinate by 1/4 to achieve the dilation of this PQRS to P'Q'R'S' with a scale factor of 1.

P' = (0.0)

Q' = (1,0)

R' = (1,1)

S' = (0,1)

You may plot both of these rectangles to see that they are the same size and are centered on the origin, but they have different shapes.

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The transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

An isometric transformation is one that keeps the angles and distances between the original and changed shapes the same. There are numerous techniques that can be used to alter any image in a plane.

The two figures are isometric only if they are congruent. In the given figure the angles remain the same however the lengths of the side are transformed as the figure is dilated.

Hence, the transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

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Given:

The given digits are 1,2,3,4,5, and 6.

To find:

The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).

Solution:

To form an even number, we need multiples of 2 at ones place.

In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.

We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.

Total number of ways to form a 5 digit even number is:

[tex]Total=6\times 6\times 6\times 6\times 3[/tex]

[tex]Total=3888[/tex]

Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.

The minimum number of pieces dan requires to achieve his objective of constructing a bigger square is; 4 pieces

We are told that dan is trying to construct a bigger square with a smaller square. That all the smaller square-shaped pieces of paper have similar dimensions.

Length = 2x

Width = x

Length = 2x

Width = 2x

Thus, the minimum number of pieces dan will require to construct the bigger square is 4 squares.

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Area of both the triangles :

= ½ × base × prepenicular

= ½ × 3 × 4

= 3 × 2

= 6 × 2 = 12 ( We have two triangles)

Area of semicircle :

= πr²/2

= 3.14 × 3 × 3 /2

= 28.26/2

= 14.13

Total area = 12 + 14.13 = 26.13 = 26.130

Answer:

The question doesn't make since so random guess

If you multiply $0.50 by 750 you get 375

If you multiply $0.25 by 750 you get 187.5

divide that by 85 and you get 2.2.

Step-by-step explanation:

Answer:

The answer is -4a + 22b

Step-by-step explanation:

12a + 26b -4b -16a

12a - 16a + 26b - 4b

-4a + 22b

Thus, The answer is -4a + 22b

-TheUnknownScientist

Step-by-step explanation:

[tex] \mathfrak{SOLUTION} _{(By\:Mister360)} \begin{cases} \\ \rm \mapsto \: 12a + 26b - 4b - 16a \\ \\ \rm \mapsto \: 12a - 16a + 26b - 4b \\ \\ \rm \mapsto \: (12 - 16)a + (26 - 4)b \\ \\ \rm \mapsto \: - 4a + 22b \\ \\ \rm \mapsto \: - (4a - 22b) \end{cases}[/tex]

On solving the inequality we know, Barrett should work 25 hours tutoring and 10 hours cutting grass to make $400.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.

Solution:-

given,

z=hours of cutting grass

y=hours of tutoring

Two equation can be made using given condition

15z+10y=400

and

z+y=35

Solving both equation simultaneously,

we get

y=25

z=10

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The candy bar will each person get will be 4 / 15.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally.

The amount of candy shared by each person will be,

Amount = ( 4 / 5 ) ÷ 3

Amount = 4 / 15

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Answer:

The coordinates of point R are (7,6), second option

Step-by-step explanation:

Coordinates of point R:

The coordinates of point R are , so (6,-7).

90° counterclockwise rule:

The rule for a rotation of 90º counterclockwise is given by:

(x,y) -> (-y,x)

What are the coordinates of point R?

(6,-7) -> (-(-7),6) = (7,6).

The coordinates of point R are (7,6), second option

Answer:

11.5

Step-by-step explanation:

[tex]14^{2} - 8^{2} = 132\\\sqrt{132}= 2\sqrt{33} = 11.48912529\\answer-is -11.5[/tex]

Answer:

11.48

Step-by-step explanation:

Pythagoras Therum

8^2 + x^2 = 14^2

64 +×^2 = 196

x^2 = 132

sqrt both sides

11.48

The expected values for each experiment are:

A) 3.4

B) 3.36

C) 3.33

If we have an experiment with the outcomes:

{x₁, x₂, ..., xₙ}

Each one with the correspondent probability:

{p₁, p₂, ..., pₙ}

Then the expected value of that experiment will be:

EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ

A) in this case we have 10 slips of paper, 8 of them with the number 3, and 2 of them with the number 5.

So the outcomes are:

{3, 5}

The probabilities are:

{8/10, 2/10}

Then the expected value is:

EV = 3*(8/10) + 5*(2/10) = 3.4

B) If we add another slip of paper with a number 3 on it, the new probabilities are:

{9/11, 2/11}

Then the new expected value is:

EV = 3*(9/11) + 5*(2/11) = 3.36

C) Finally, if we add 2 slips of paper with the number 3, now we will have a total of 12 slips of paper, then the new probabilities are:

{10/12, 2/12}

So the new expected value is:

EV = 3*(10/12) + 5*(2/12) = 3.33

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