A class measured the radius r, circumference C, and area A of various circular objects. The results are recorded in thistable. b. Does the equation A=1/2*r* C describe the relationships in the table? Explain your reasoning.YesNor (cm) C (cm) A (cm)42550

Deterministic.

The relationship between the variables is deterministic. A deterministic relationship refers to a relationship in which the dependent variable does not depend on other elements (variables) other than the independent element classified in the relationship. The independent variable (element) in the relationship possesses an exact value. Hence deterministic relationship is also named as the exact relationship between variables.

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Part a

The domain is the set of x-values, which is [tex][1, \infty)[/tex].

Part b

The range is the set of y-values, which is [tex][-3, \infty)[/tex].

Part c

As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex].

Part d

The x-intercept is when y=0, which is [tex](2, 0)[/tex].

Part e

The absolute minimum is the lowest point, which has a y-coordinate of [tex]-3[/tex].

Part a

The domain is the set of x-values, which is .

Part b

The range is the set of y-values, which is .

Part c

As , .

Part d

The x-intercept is when y=0, which is .

Part e

The absolute minimum is the lowest point, which has a y-coordinate of

The number of students that enrolled = 3,500 students.

This is defined as the intake of individuals into an organism or students into an institution through adherence to specific orders given by the administrative department of the organisation.

The number of students that apply= 20,000 students

The percentage of students that are accepted= 70% of 20,000

That is, 70/100× 20,000

= 1400000/100

= 14,000 students.

The quantity of students that actually enroll = 25% of 14,000

That is, 25/100× 14000

= 350000/100

= 3,500 students.

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Based on the linear relationship between the ticket numbers and the total cost, the cost of one ticket can be found to be A. $10.50

First, find the rate of change in ticket pricing assuming the number of tickets is x and the total cost is y.

The rate of change is:

= Change in y / Change in x

= (67.50 - 46.50) / (5 - 3)

= $10.50

Then find the y-intercept:

y = Slope(x) + y-intercept

67.50 = 10.50(5) + y-intercept

y-intercept  = 67.50 - 52.50

y-intercept = 15

Linear equation is:

Total cost = Rate of change (Tickets) + y-intercept

A single ticket would cost $10.50 which is the rate of change.

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The required rate of change and slope of the given relationship is $10.50.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope for the linear function is given as,
m = (y₂ - y₁) /  (x₂ - x₁)

From the table substitute the value in the above equation,
m = [67.50-46.50]/[5-3]
m = 21 / 2
m = 10.50

Thus, the required rate of change and slope of the given relationship is $10.50.

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Answer:

(4,-5)

Step-by-step explanation:

A is 5 units above the x axis so a' will be 5 units below the x axis.

The equation of the Pythagorean Theorem  in the triangle  is 25^2 = 24^2 + 7^2

From the question, the side lengths of the triangle are given as

25, 24 and 7

The Pythagorean Theorem states that:

Hypotenuse^2 = Sum of the squares of the other sides

Where

The other sides are the smaller sides

This in other words mean that:

Other sides = 24 and 7

Hypotenuse = 25

Substitute the known values in the above equation

25^2 = 24^2 + 7^2

Hence, the Pythagorean Theorem equation is 25^2 = 24^2 + 7^2

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Answer:

Surface area= 6(5·5)+6(3·3)-2(3·3)

Step-by-step explanation:

first figure out the surface area of both cubes

for the larger cube- 5 multiplied by 5 for the area of one side then multiplied by 6 for all faces

for the smaller cube- 3 multiplied by 3 for the area of one side then multiplied by 6 for all the faces.

the cubes are touching on one face, this is the whole area of one side of the 3 by 3 cube, meaning two of these faces must be subtracted to find the surface area of the whole shape

hope that helps

Hello!

First, let's write the coordinates of each vertex of this parallelogram:

• A (-4, 2)

• B (2, 2)

• C (5, -2)

• D (-1, -2)

As line AB is parallel to the x-axis, we can find its measurement without formulas. We just need to count the number of squares from one point to the other.

So,

We will follow the same reasoning to calculate CD (because it's also parallel to the x-axis).

Now we have to use the formula of the distance between two points to calculate the sides BC and DA. The formula is:

As we know the formula, let's replace it with the coordinates:

We can solve it using the same formula as I used to solve BC, but now I'll show you how to solve it using Pythagoras Theorem (I think it will be easier). Look:

Solving by Pythagoras, we'll obtain:

Remembering: the perimeter is the sum of all the sides of a figure. So, we will have:

We will have the following:

Now, we corroborate with one of the expression, in our case we will analyze y = x^2:

So, the expression taht represents the value given is:

We will determine the area of the green section as follows:

Here alpha is the angle [In radians] and r is the radius-

*First: We determine the angle:

Now, we transform it to radians:

*Second: We replace on the equation:

So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]

Answer:

A ≈ 43.4 cm²

Step-by-step explanation:

the area (A) of the green sector is calculated as

A = area of circle × fraction of circle

  given d = 12 then r = 12 ÷ 2 = 6 cm

the central angle of the green sector = 180° - 42° = 138°

then

A = πr² × [tex]\frac{138}{360}[/tex] ( simplify fraction by dividing numerator/denominator by 6 )

   = π × 6² × [tex]\frac{23}{60}[/tex]

   = 36π × [tex]\frac{23}{60}[/tex]

   = [tex]\frac{36\\pi (23) }{60}[/tex]

   ≈ 43.4 cm² ( to the nearest tenth )

The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.

There are two hypotheses. The first one is called the null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test.

The hypothesis which substitutes the null hypothesis is an alternate hypothesis.

We know that the Null hypothesis is the one that researchers try to disprove.

The null hypothesis must be rejected if we choose the 99.7 percent of  confidence level.

The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.

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Answer:

  y = -3x +6

Step-by-step explanation:

You want to solve the equation 6x +2y = 12 for y.

We can isolate the y-term by subtracting 6x from both sides.

  6x -6x +2y = -6x +12

  2y = -6x +12 . . . . . . . . . . simplify

Then we can get y by itself by dividing both sides by 2:

  2y/2 = -6x/2 +12/2

  y = -3x +6 . . . . . . . . . . . simplify

The expression for y is  y = -3x +6.

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The missing value is 1/3 from the table that represents Judy's rate which is the correct answer that would be an option (C).

In mathematics, relations are used to describe the link between the components of two sets. They aid in mapping items from one set (known as the domain) to elements from another set (known as the range), resulting in ordered pairs of the form (input, output).

We have been given the rates of time taken by Judy and Sal to complete a puzzle.

Sal's rate is r, as we can see from the table. Judy is said to take 3 hours to solve a puzzle by herself. It barely takes them two hours to work with Sal.

Because Judy completes the task in three hours, the portion of the puzzle finished in one hour is 1/3.

Therefore, the missing value is 1/3 from the table that represents Judy's rate

Hence, the correct answer would be an option (C).

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Step 1

Write the equation of a line in slope point form

Where;

Step 2

Find the equation to represent the cost of the topsoil.

The equation that represents the cost of the topsoil is

y=30x

Step 3

Find how the cost of the topsoil compares to the cost of the mulch.

The coordinates of G is (d+c, b)

This is because the opposite sides of any parallelogram are equal in length, and so the length of side HG is equal to the length of side EF.

a) The length of side HG is equal to the horizontal distance (x2 - x1): xG - 0

The length of side EF is equal to the horizontal distance (x2 - x1): d - (-c) = d +c

Thus:

xG - 0 = d + c

xG = d + c

Therefore the x-coordinate of G is d + c

b) To find the y-coordinate of G, we also apply the idea that sides GF and HE are equal.

The length of side GF is equal to the vertical distance (y2 - y1): yG - 0

The length of side HE is equal to the vertical distance (y2 - y1): b - 0

Thus:

yG - 0 = b -0

yG = b

Therefore the y-coordinate of G is b

Finally, the coordinates of G is (xG, yG) = (d+c, b)

The equation for constant proportionality is y ∝ m .

1760 is a constant of proportionality.

The ratio of two proportional values at a constant value is the proportionality constant. When either the ratio or the product of two variables results in a constant, the connection between the two is proportional. The ratio between the two stated quantities affects the proportionality constant's value.

The formula y = 1760m describes the relationship between a distance in yards (y) and a similar value in miles (m).

As a result, the graph of the aforementioned equation will be a straight line with a constant slope of 1760 that passes through the origin (0, 0).

As a result, a measurement in yards and a measurement in miles have the same proportionality relationship.

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The amount of coffee she bought is 5.16 pounds.

She received a $70 gift card for a coffee store.

She used it in buying some coffee that cost $8.36 per pound after buying a coffee she had $26.85 left.

Therefore, base on the card, the number of pounds of coffee she bought can be calculated as follows;

Hence,

let

the amount of coffee she bought in pounds = x

Hence,

70 = 8.36x + 26.85

70  - 26.85 = 8.36x

43.15 = 8.36x

divide both sides by 8.36

43.15 / 8.36 = x

x = 5.16148325359

Therefore, the amount in pounds is 5.16 pounds.

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800 miles is going to be the distance that separates the two aircraft. The distance between the two airplanes will be 1,300 kilometers at the very least.

It is important to keep in mind that the two aircraft's combined speed will be equal to the sum of their separate speeds when calculating their overall speed. In addition, the pilots of the two aircraft have one hour to find each other.

According to the information that was provided, the distance that separates the aircraft after they have flown for forty-five minutes is two hundred miles. As a result, the following will constitute the remaining distance:

= 1 hour - 45 minutes = 15 minutes.

When this occurs, the distance between the planes will be as follows:

= 200/15 × 60

= 200 × 4

= 800 miles

As a result, there will be a gap of 1300 kilometers between the two aircraft.

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Given

x - y + (- z) where x and z are positive real numbers and y is a negative real number.

Find

i) What are the directions of motion for this calculation ?

ii) Is the final answer positive , negative , or undetermined ?

Explanation

i) as we have given

x - y + (- z)

x - y - z

(x - y) - z

right -left - left

ii) for this we take examples

let x = 2 , y = -1 and z = 2

2- (- 1) + (- 2) = 1 , positive

now

let x = 2 , y = -1 and z = 5

2 - (- 1) + (- 5) = 3 - 5 = -2 , negative

so , it is both negative or positive

hence it is undetermined

Final Answer

Hence , the correct option is

i) Right, left , left

ii) Undetermined

By the concept of measurement of length we get the remaining length of the pipe 65 cm.

The total length of pipe before it was used by the plumber was 2.5 metre = (2.5 x 100)cm = 250cm.

Since,the plumber needs to cut lengths of 60cm, 35cm and 90cm

Thus,total Length of the pipe cut  by the plumber = 60cm + 35cm + 90cm = 185cm

After subtracting the length of pipe used by the plumber from the original length of the pipe, we get,

The remaining length of the pipe = 250 - 185 = 65cm

Hence, the remaining length of the pipe is 65 cm.

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Answer:

S': (2, 1)

T': (5, 3)

U': (1, -4)

S'': (1, 3)

T'': (4, 5)

U'': (0, -2)

Step-by-step explanation:

Hi!

For Reflection Across the X-Axis use this :

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

So :

S': (2, 1)

T': (5, 3)

U': (1, -4)

and then the question also asks for a translation so we follow what it gave us:

S'': (1, 3)

T'': (4, 5)

U'': (0, -2)

Please ask me any questions that you still may have!

and Have a great day! :)

Answer:

S' (2, 1)         S'' (1, 3)

T' (5, 3)        T'' (4, 5)

U' (1, -4)       U'' (0, -2)

Step-by-step explanation:

The preimage is S (2,-1), T (5, -3) U(1,4).

Preimage: the original figure prior to a transformation.

The directions say to reflect the preimage over the x-axis.

To do this, follow this transformation rule: (x, y) → (x, -y)

This means keep the x-coordinate as it is, but then change the sign of the y-coordinate.

S (2, -1) → S' (2, 1)

T (5, -3) → T' (5, 3)

U (1, 4) → U' (1, -4)

Next, take the coordinates from the last transformation then translate it using the rule: (x, y) → (x-1, y+2)

This means subtract 1 from the x-coordinate, then add 2 to the y-coordinate.

S' (2, 1) → S'' (1, 3)

T' (5, 3) → T'' (4, 5)

U' (1, -4) → U'' (0, -2)

Notice that each time you do a transformation, you add an apostrophe next to the letter. In math, this symbol is called a 'prime symbol.'

I hope this helped! Let me know if you have any questions.

Using equations we now know that the distance of the first part of the Yuna's swim is 0.7 miles.

So, let 'x' be the distance of the 1st part and 'y' be the time in hours of the 1st part.

Plot the equations on the graph as follows:

(Refer to the graph attached below)

Be obtain:

Therefore, using equations we now know that the distance of the first part of the Yuna's swim is 0.7 miles.

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The complete question is given below:
In training for a triathlon, Yuna swam 1.9 miles in the open ocean, which took her 2 hours. For the first part of her swim, she averaged 1.4 miles per hour. For the second part of her swim, she swam against the current and started to tire, so her average speed decreased to 0.8 mph. What was the distance of the first part of Yuna's swim? Round to the nearest tenth as needed. The distance in the first part of her swim was miles.

Answer:

.7

Step-by-step explanation:

The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer ; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

Let's assume that first, even integer is x

Then the second and third will be x + 2,x + 4 respectively.

As per the given,

1 less than 4 times the third → 4(x+4) - 1

It is equal to the 5 more than the sum of x and x + 2

So, x + x + 2 + 5

Therefore,  4(x+4) - 1 = x + x + 2 + 5

4x + 16 - 1 = 2x + 7

4x + 15 = 2x + 7

2x = 7 - 15

x = -4

So integers are -4,-2,0

Hence "The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0".

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The figure above is a rectangle

The classifications of a rectangle are:

1. A rectangle has 4 sides and angles, therefore, it is a quadrilateral.

2. Each interior angle is a right-angle, that is 90⁰

3. The sum of the interior angles equals 360

4. The opposite sides are parallel

5. The opposite sides are equal

6. The diagonals bisect each other

7. The diagonals have the same length

The rational numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49

A rational number can simply be described as a number that is expressed as the ratio of two even or odd integers.

The denominator of the fraction or ratio must be greater than zero.

Rational numbers are represented mathematically as a quotient, say x/y of two integers such that y ≠ 0, that is, the denominator is not equal r equivalent to zero.

It is formed from dividing on integer(whether odd or even) by another integer.

The numbers; √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49 are all rational numbers

Hence, the numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49

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Answer:  The slope is [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

[tex]Slope = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-1-2}{1-7} =\frac{-3}{-6} =\frac{3}{6}=\frac{1}{2}[/tex]

A place where two or more curves, lines, or edges converge is known as a vertex in geometry (plural: vertices or vertexes), and it is frequently identified by letters like,,,. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The solutions are:

P' = (-4,-7)

Q ' = (-8,-7) (-8,-7)

R ' = (-3,3) (-3,3)

All you have to do is flip the provided points P, Q, and R's x and y coordinates.

The common principle is (x,y) —-> (y,x)

Thus, when we reflect across the line y = x, something like P = (-7,-4) becomes P'= (-4,-7). The similar approach is taken with the other points.

How do you locate a triangle's vertices?

Finding the triangle's vertices on the line y = x as an image

The steps below are used to locate a triangle's vertices using its midpoints:

Identify the midpoints' x and y values;

Calculate the midpoint using the following equations: A = (x 1+ x 3 - x 2, y 1 + y 3-y 2); B = (x 1+x 2-x 3, y 1+y 2-y3); C = (x 2+x 3-x 1, y 2 + y 3 -y 1);.

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The measure of ∠E will be equal to 38°.

Given,

m∠BFE = 118° and m∠C = 86°

And BF bisects ∠ABD

From the Property of Linear Pair,

∠AFB + ∠BFE = 180°

=> ∠AFB + 118° = 180°

=> ∠AFB = 62°

Now, we can see that ∠AFB and ∠FBD are equal because they are alternate angles.

And ∠FBD and ∠ABF are equal because BF bisects ∠ABD.

So, In ∆ABF,

∠AFB + ∠ABF + ∠BAF = 180° (because of the angle sum property of a triangle)

=>62° + 62° + ∠BAF = 180°

=>∠BAF = 180° - 124°

=> ∠BAF = 56°

Similarly, in ∆ABE,

∠A +∠C  +∠E = 180°

=> 56° + 86° + ∠E = 180°

=> ∠E = 38°

Therefore, m∠E = 38°.

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Answer:

Question 4

Answer: Alternative C - 0

Step-by-step explanation:

Since x→∞, we can substitute the values of x for values as 10, 100, 1000 and see the tendency of the function when the values are getting higher (closer to ∞):

For x = 10

f(10) = 0.5*10^(-3/4)

f(10) = 0.089

For x = 100

f(10) = 0.5*100^(-3/4)

f(10) = 0.016

For x = 1000

f(10) = 0.5*1000^(-3/4)

f(10) = 0.003

As we can see, when the x-values are getting closer to infinite, the y-values tends to zero. Thus, alternative C is correct.