1. Fill in the blanks to complete the description of the track. (2 points)
The track has ____ sides of the square and the distance around ____ complete circle(s).















2. The length of one side of the square is the square root of its area. Use the table to find the approximate length of one side of the square. Explain how you used the table to find this information. (2 points)















3. Use your answers above to find the total length of the part of the track that is made up of sides of the square. (2 points)















4. The circumference of (distance around) a circle is π times the diameter, or C = πd. A side of the square is the diameter of each half circle.
In your answer to question 1, you gave the number of complete circles included in the track. Use this answer and C = πd to find the approximate length of the circular part of the track to the nearest tenth of a foot. Use 3.14 for π and show your work. (2 points)















5. Find the approximate length of the track, including the straight and circular sections. (2 points)

Answer:

The area of the circle would be 530.93 sq ft.

Step-by-step explanation:

The formula is A = π r². We know that the radius or r is 13, meaning that the new equation is A = π 13². 13 to the second power is 169 meaning that the formula would now be A = π(169). 169 times π is 590.93 getting you your answer. I hope this helped! :)

Answer:

1.121

Step-by-step explanation:

We can align them:

0.001

1 .010

0.1 10

Then we can add each horizontal line.

We get, 1.121

Answer:

I think the equation is this

a_n = -n^2/2 + 13n/2 - 5

If this helps the 5th term is 15

Hope this helps :)

Answer:

no they don't intersect

Step-by-step explanation:

line 1:

m=11-3/7-3=8/4=2

y-3=2(x-3)

y-3=2x-6

y=2x-3

line 2:

m=24-8/13-5=16/8=2

y-8=2(x-5)

y-8=2x-10

y=2x-2

no they don't intersect cause they are parallel and parallel lines don't cross

The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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Answer:5

Step-by-step explanation:

Answer:

4/5x + 8/5 = g(x)

Step-by-step explanation:

−4x−6=−5y+2

Solve for y

Subtract 2 from each side

−4x−6-2=−5y+2-2

-4x -8 = -5y

Divide each side by -5

-4x/-5 -8/-5 = -5y/-5

4/5x + 8/5 = y

Replace y with g(x)

4/5x + 8/5 = g(x)

The quadrilateral with the given vertices is a Rhombus , the correct option is (C) .

In the question ,

it is given that ,

the vertices of the quadrilateral are (0,2), (6,0), (0,-2), (-6,0)

let us rename , the coordinates as A(0,2) , B(6,0) , C(0,-2) , D(-6,0) .

the distance between two points (x₁,y₁) and (x₂,y₂) can be calculated using the formula

d = √(x₂ - x₁)² + (y₂ - y₁)²

distance between A(0,2) and B(6,0) is

AB = √(6 - 0)² + (0 - 2)²

AB = √(6² + (-2)²)

AB = √(36+4)

AB = √40

distance between B(6,0) and C(0,-2) is

BC = √(0 - 6)² + (-2 - 0)²

BC = √((-6)² + (-2)²)

BC = √(36+4)

BC = √40

distance between C(0,-2) and D(-6,0) is

CD = √(-6 - 0)² + (0 - 2)²

CD = √((-6)² + (-2)²)

CD = √(36+4)

CD = √40

distance between D(-6,0) and A(0,2) is

DA = √(0 -(-6))² + (2 - 0)²

DA = √(6² + 2²)

DA = √(36+4)

DA = √40

we see that the length of all the sides  is √40 ,

all the sides are same in Square and Rhombus ,

But from the graph below, we see that the quadrilateral formed is in the shape of the Rhombus .

Therefore , The quadrilateral with the given vertices is a Rhombus .

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Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

We need to find out how many combinations of pants, shirts, and shoes the software engineer can wear without repeating any combination.

1. Pants: The software engineer has 3 pairs of pants to choose from.
2. Shirts: They have 4 shirts to choose from.
3. Shoes: They have 3 pairs of shoes to choose from.

To find the total number of combinations, simply multiply the number of choices for each item together:

Combinations = (Number of pants) x (Number of shirts) x (Number of shoes)

Combinations = 3 (pants) x 4 (shirts) x 3 (shoes)

Combinations = 36

So, the software engineer can go 36 days without wearing the same combination of three items.

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Answer:

364

Step-by-step explanation:

Answer:

\(P = 4\sqrt{13}\)

Step-by-step explanation:

Given

\(W = (7, 2)\)

\(X = (5, -1)\)

\(Y = (3, 2)\)

\(Z =(5, 5)\)

Required

The perimeter

To do this, we first calculate the side lengths using distance formula

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2\)

So, we have:

\(WX = \sqrt{(5- 7)^2 + (-1 - 2)^2\)

\(WX = \sqrt{13}\)

\(XY = \sqrt{(3-5)^2 + (2--1)^2}\)

\(XY = \sqrt{13}\)

\(YZ = \sqrt{(5-3)^2 + (5-2)^2}\)

\(YZ = \sqrt{13}\)

\(ZW = \sqrt{(7 - 5)^2 + (2 - 5)^2}\)

\(ZW = \sqrt{13}\)

The perimeter is:

\(P = WX + XY + YZ + ZW\)

\(P = \sqrt{13}+\sqrt{13}+\sqrt{13}+\sqrt{13}\)

\(P = 4\sqrt{13}\)

Answer:

C on edge 2021

Step-by-step explanation:

I took the cumulative exam

Answer:

543

Step-by-step explanation:

4(138)-9

552-9

543

Answer:

543

Step-by-step explanation:

based on PEMDAS

paranthesis first 60+78= 138

then you would multiply 4x138=552

then you would 552-9= 543

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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Answer:

20.8 ft²

Step-by-step explanation:

area = (ab sin C)/2

area = (6 ft × 8 ft × sin 60°)/2

area = 20.8 ft²

Answer:

B

Step-by-step explanation:

On edge 2020

The graph of absolute value function f(x) and g(x) are:

On a coordinate plane, y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).

The correct answer is an option (B)

"A function of the form f(t) = |t| ."

"It is a set of points on the coordinate plane that follows given function."

For given question,

We have been given an absolute value function f(x) = |x|

and absolute value function g(x) = |-4(x - 7)|

The graph of f(x) = |x| is like a 'V', with its vertex at (0, 0).

Y = f (x) opens up and goes through (-4, 4), has a vertex at (0, 0), and goes through (4, 4)

Consider absolute value function, h(x) = |x - 7|

A function h(x) is the function f(x) is translated horizontally 7 units right.

The graph of h(x) = |x - 7| is like a 'V', with its vertex at (7, 0).

Now consider absolute value function g(x) = |-4(x - 7)|

A function g(x) is the function h(x) is compressed inside by factor 4.

So, the graph of y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4).

Therefore, the graph of absolute value function f(x) and g(x) are:

On a coordinate plane, y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).

The correct answer is an option (B)

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The value of the given integral is \((-1/18)ln|x| - (1/36)ln|6x^2-1|\)+ C, where C is the constant of integration.

To evaluate the integral, we can use integration by substitution. Let u = x² - x, then \(\frac{du}{dx}\) = 2x - 1 and dx = \(\frac{du}{(2x-1)}\). Substituting this in the integral, we get:

We can further simplify this by breaking the integral into partial fractions:

\(\frac{u}{(18x(2x-1))}\) = A/x + B/(2x-1)

u = A(2x-1) + Bx

Equating coefficients, we get A = -1/18 and B = 1/18. Substituting these values, we get:

∫ \(\frac{(x^2 - x)}{(36x^3 - 6x)}\) dx = (-1/18)∫ \(\frac{dx}{x}\) + (1/18)∫ dx/(2x-1)

= \((-1/18)ln|x|\) - (1/36)ln|2x-1| + C

Since the natural logarithm function is only defined for positive values, we need to use absolute values in the final answer to account for negative values of x. Therefore, the answer is  

\((-1/18)ln|x| - (1/36)ln|6x^2-1|\) + C.

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Angela's and Carlton's boards could be rectangles.

Given that:

Four students designed game boards for a class project.

The dimensions of their boards are provided.

Angela's board has a length of 20 cm, a width of 21 cm, and a diagonal of 29 cm.

Bradley's board has a length of 9 in., a width of 9 in., and a diagonal of 9 in.

Carlton's board has a length of 25 cm, a width of 30 cm, and a diagonal of 35 cm.

Della's board has a length of 10 in., a width of 12 in., and a diagonal of 15 in.

To determine whose board could be a rectangle,

We need to check if the Pythagorean theorem is satisfied for each board. The Pythagorean theorem states that for a right triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (length and width).
If this is true for a board, then it is a rectangle.

Angela's board:

diagonal² = length² + width²

29² = 20² + 21²

841 = 400 + 441

This is true, so Angela's board could be a rectangle.

Bradley's board:

diagonal² = length² + width²

9² = 9² + 9²

81 = 81 + 81

This is not true, so Bradley's board is not a rectangle.

Carlton's board:

diagonal² = length² + width²

35² = 25² + 30²

1225 = 625 + 900

This is true, so Carlton's board could be a rectangle.

Della's board:

diagonal² = length² + width²  

15²  = 10²  + 12²  

225 = 100 + 144

This is not true, so Della's board is not a rectangle.

Therefore, Angela's and Carlton's boards could be rectangles.

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The ice cream truck driver sold approximately 77 gallons of ice cream. The ice cream truck driver has a daily route with 94 gallons of ice cream, and they sold 82% of Ice cream. We calculate no. of gallons of ice cream sold.

To find the number of gallons of ice cream sold, we can follow these steps:

Calculate the amount of ice cream sold: Multiply the total amount of ice cream (94 gallons) by the percentage sold (82%). 94 gallons * 0.82 = 77.08 gallons.

Round the result: Since we are dealing with gallons, round the answer to the nearest whole number. In this case, the nearest whole number is 77.

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\(\\ \rm\rightarrowtail Area=Length\times Width\)

\(\\ \rm\rightarrowtail x(x-3)=378\)

\(\\ \rm\rightarrowtail x^2-3x=378\)

\(\\ \rm\rightarrowtail x^2-3x-378=0\)

\(\\ \rm\rightarrowtail x^2-21x+18x-378=0\)

\(\\ \rm\rightarrowtail (x+18)(x-21)=0\)

\(\\ \rm\rightarrowtail x=-18,21\)

Take it positive

Let the length be x

Let the width be x-3

Now,

\( \red \dashrightarrow \mathcal{Area = Length×Breadth}\)

\( \red \dashrightarrow \sf \: 378 = x \times (x - 3)\)

\( \red \dashrightarrow \sf \: 378 = {x}^{2} - 3x\)

\( \red \dashrightarrow \sf \: 378 - {x}^{2} + 3x = 0\)

\( \red \dashrightarrow \sf \: - 378 + {x}^{2} - 3x = 0\)

\( \red \dashrightarrow \sf \: {x}^{2} - 3x - 378= 0\)

\( \red \dashrightarrow \sf \: {x}^{2} + 18x - 21x - 378= 0\)

\( \red \dashrightarrow \sf \: x \times (x + 18) - 21(x + 18)= 0\)

\( \red \dashrightarrow \sf \: (x + 18) (x - 21)= 0\)

\( \red \dashrightarrow \sf \: x + 18= 0 \\ \red \dashrightarrow \sf \: x - 21= 0\)

\( \red \dashrightarrow \sf \: x = - 18 \\ \red \dashrightarrow \sf \: x = 21\)

\( \colorbox{lightyellow}{length = x = 21}\)

\( \colorbox{lightyellow}{breadth= x - 3= 21 - 3 = 18}\)

Answer:

\(\frac{3x^2}{y}\)

Answer:

42cm

Step-by-step explanation:

It's a rectangle so sides are 6, 6, 15, 15. Σs = 42.

Answer:

x = 8 base angle = 81 degrees

Step-by-step explanation:

Answer:

x = 8

base angle = 81 deg

Step-by-step explanation:

we observe that because the given triangle is a isosceles triangle, the base angles must be the same.

Hence the missing base angle must also be (10x+1)°

recall that all internal angles of an triangle must add up to 180 deg,

hence

180° = sum of all internal angles

180° = 18° + (10x+1)° + (10x+1)°

180° = 18° + 2(10x+1)°    (subtracting 18 from both sides)

180 - 18 = 2(10x+1)

162 = 2(10x+1)   dividing both sides by 2)

162 / 2 = 10x + 1

81 = 10x + 1    (subtracting 1 from both sides)

81 - 1 = 10x

10x = 80   (divide both sides by 10)

x = 80/10

x = 8   (answer)

substituting x = 8 into the expression for the base angle

base angle = (10x+1)

= 10(8) + 1

= 10 + 1

= 81

Amy play 11 games of Balloon bouncer. If Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.

An algebraic equation is a formula that expresses the equivalence of two expressions by applying the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and root extraction to a collection of variables. An algebraic equation, sometimes known as a polynomial equation, in mathematics is a formula of the form P=0, where P is a polynomial with coefficients in some field, typically the field of the rational numbers. A mathematical statement with variables, constants, coefficients, and algebraic operations is known as an algebraic expression. A good example of an algebraic expression is 5x2+6xyc. Algebraic expressions do not use equal signs, in contrast to algebraic equations.

Given

Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.

Algebraic Equation:

2 + 3g = 35

3g = 35 - 2

3g = 33

g = 11

Amy play 11 games of Balloon bouncer.

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The area of the drawing as required to be determined in the task content is; 71.25 m².

It follows from the task content that the area of the drawing is to be determined according to the given parameters.

Since the actual rectangular shape has dimensions 95m by 75m. Upon drawing using a scale of 1m to 10m.

It follows that the dimensions of the drawing becomes; 95/10 by 75/10.

Hence, since the dimension of the drawing by evaluation is; 9.5 by 7.5;

The area of the rectangle (A = l × b) is; 9.5 × 7.5 = 71.25 m².

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Answer:

Explanation:

So the equation it's asking you to do is like y=kx ,

so your k is 2/3.

y=2/3x

Then for x it's 3 1/2.

y= 2/3(3 1/2)

now your "y" is any variable to hold the other too.

Hope this helped!

y= 2/3( \(3\frac{1}{2}\)) is the  equation that relates the amounts of pretzels and peanuts in the snack mix.

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

Given that Emma is making a snack mix of pretzels and peanuts

For every batch, she uses 2/3 cup of peanuts and \(3\frac{1}{2}\) cups of pretzels

We need to find an equation that relates the amounts of pretzels and peanuts in the snack mix.

The equation will be in the form of y=kx

From the given information the value of k is 2/3

y=2/3x

y= 2/3( \(3\frac{1}{2}\))

Hence, y= 2/3( \(3\frac{1}{2}\)) is the  equation that relates the amounts of pretzels and peanuts in the snack mix.

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Answer:

I think it is 6x+3=y (y=6x+3)

Based on the alternate exterior angles theorem, the equation is: 15x - 3 = 14x + 2

The value of x = 5.

The angles, (15x - 3) and (14x + 2) are alternate exterior angles. Based on the alternate exterior angles theorem/postulate, they are congruent to each other.

Thus, the equation to create in solving for the value of x would be:

15x - 3 = 14x + 2

Subtract 14x from both sides of the equation

15x - 3 - 14x = 14x + 2 - 14x [subtraction property of equality]

x - 3 = 2

Add 3 to both sides

x - 3 + 3 = 2 + 3 [addition property of equality]

x = 5

In summary, based on the alternate exterior angles theorem, the equation is: 15x - 3 = 14x + 2

The value of x = 5.

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