MATHEMATICS HIGH SCHOOL

Which of the following represents a polygon that is two times the size of the original polygon?A: (x' , y') = (0.2x,0.2y)
B: (x' , y') = (1/2x, 1/2y) <-- Fractions
C: (x' , y') = (4x,4y)
D: (x' , y') = (2x,2y)

Answers

Answer 1
Answer:

The expression representing two times the size of the original polygon is (x' , y') = (2x,2y), hence, option (D) is the correct answer.

What is dilation?

A dilation is a transformation that yields a picture that differs in size while maintaining the original image's shape.

The size of the polygon will be doubled if its coordinates are multiplied by 2.

The expression representing the two times the size of the original polygon is (x' , y') = (2x,2y)

Hence, option (D) is the correct answer.

Learn more about the dilation:

brainly.com/question/13176891

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Answer 2
Answer: The answer is D. (2x,2y) because when you two times an ordered pair you multiply it by two.

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Create an equation. Use the graph below to create the equation of the rainbow parabola.Graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0.
Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function. Remember to include the two points of intersection in your table.

Answers

Remember that a quadratic with two real zeroes can be written as a(x - r_1)(x - r_2), where a is a constant and r_1 and r_2 are the zeroes (or roots) of the function. Since the graph shows that the two zeroes are at -6 and 6, the equation has to be of the form

y = a(x - ({-6}))(x - 6), or
y = a(x + 6)(x - 6)

To solve for a, let's use the point at the vertex (0, 36) and plug that in:

36 = a(0 + 6)(0 - 6)
36 = {-36}a
a = {-1}
(It makes sense that a is negative since the parabola opens down.)

So, the equation of the parabola is

y = -(x + 6)(x - 6), or
\bf y = -x^2 + 36

Now for the second part, just pick any two points with which we can draw a line with a positive slope. I'll use x = -2 and 1:

y = -({-2})^2 + 36 = {-4} + 36 = 32
y = -(1)^2 + 36 = {-1} + 36 = 35

So, our two points are (-2, 32) and (1, 35). To find the equation of the linear function that goes through these two points, let's use slope-intercept form, which is f(x) = mx + b. The slope m is given by (y_2 - y_1)/(x_2 - x_1), so

m = (y_2 - y_1)/(x_2 - x_1) = \frac{35 - 32}{1 - ({-2})} = 1
So, the equation of the linear function so far is just f(x) = x + b, and we can find b by plugging in one of the points on the line:

35 = 1 + b
b = 34

Thus, the equation of the linear function is

\bf f(x) = x + 34

And you can find more points on the line simply by plugging other values of x, such as (0, 34) and (5, 39).

If two lines are parallel, which statement must be true?A. Their slopes are reciprocals.
B. Their slopes are opposites.
C. Their slopes are equal.
D. Their slopes are negative reciprocals.

Answers

I believe the correct answer from the choices listed above is option C. If two lines are parallel, their slopes are equal. Having equal slopes mean that the rise and run of the points of the lines are the same. Parallel lines do not intersect even when extended infinitely.

Answer:

C. Their slopes are equal.

Step-by-step explanation:

Given : If two lines are parallel.

To find  : which statement must be true.

Solution : We have given that If two lines are parallel.

We know that two parallel line have same slope

By rise over run :

Therefore, C. Their slopes are equal.

Refer to the figure and find the volume V generated by rotating the given region about the specified line.R3 about AB

Answers

Answer:

Hence, volume is: (34\pi)/(45) cubic units.

Step-by-step explanation:

We will first express our our equation of the curve and the line bounded by the region in terms of the variable y.

i.e. the curve is rex=(1)/(16)y^4

and the line is given as:  x=(1)/(2)y

Since after rotating the given region R_(3) about the line AB.

we see that for the following graph

the axis is located at x=1.

and the outer radius(R) is: (1)/(16)y^4

and the inner radius(r) is:  (1)/(2)y

Now, the area of the graph= area of the disc.

Area of graph=\pi(R^2-r^2)

Now the volume is given as:

Volume=\int\limits^2_0 {Area} \, dy

On calculating we get:

Volume=(34\pi)/(45) cubic units.

The volume V generated by rotating the given region about the specified line R3 about AB is \boxed{\frac{{34\pi }}{{45}}{\text{ uni}}{{\text{t}}^3}}.

Further explanation:

Given:

The coordinates of point A is \left( {1,0} \right).

The coordinates of point B is \left( {1,2} \right).

The coordinate of point C is \left( {0,2} \right).

The value of y is y = 2\sqrt[4]{x}.

Explanation:

The equation of the curve is y = 2\sqrt[4]{x}.

Solve the above equation to obtain the value of x in terms of y.

\begin{aligned}{\left( y \right)^4}&={\left( {2\sqrt[4]{x}} \right)^4} \n{y^4}&=16x\n\frac{1}{{16}}{y^4}&= x\n\end{aligned}

The equation of the line is x = (1)/(2)y.

After rotating the region {R_3} is about the line AB.

From the graph the inner radius is {{r_2} = (1)/(2)y and the outer radius is {{r_1}=\frac{1}{{16}}{y^4}.

{\text{Area of graph}}=\pi\left( {{r_1}^2 - {r_2}^2} \right)

Area = \pi\left( {{{\left({\frac{1}{{16}}{y^4}} \right)}^2} - {{\left({(1)/(2)y} \right)}^2}}\right)

The volume can be obtained as follows,

\begin{aligned}{\text{Volume}}&=\int\limits_0^2 {Area{\text{ }}dy}\n&=\int\limits_0^2{\pi \left( {{{\left({\frac{1}{{16}}{y^4}} \right)}^2} - {{\left( {(1)/(2)y} \right)}^2}} \right){\text{ }}dy}\n&= \pi \int\limits_0^2 {\left( {\frac{1}{{256}}{y^8} - (1)/(4){y^2}} \right){\text{ }}dy}\n\end{aligned}

Further solve the above equation.

\begin{aligned}{\text{Volume}}&=\pi \left[ {\int\limits_0^2 {\frac{1}{{256}}{y^8}dy - } \int\limits_0^2{(1)/(4){y^2}{\text{ }}dy} } \right]\n&= \frac{{34\pi }}{{45}}\n\end{aligned}

The volume V generated by rotating the given region about the specified line R3 about AB is \boxed{\frac{{34\pi }}{{45}}{\text{ uni}}{{\text{t}}^3}}.

Learn more:

1. Learn more about inverse of the functionbrainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Volume of the curves

Keywords: area, volume of the region, rotating, generated, specified line, R3, AB, rotating region.

Find the domain of the parent function below.y=x^2
A.
all real numbers
B.
all positive numbers
C.
all negative numbers
D.
all real numbers except 0

Answers

Hello,

Answer A
There are no value to exclude with a square.

IF the navy pier ferris wheel in chicago has a circumference that is 56% of the circunference of the first ferris wheel built in 1893. a. What is the radius of the navy pier wheel?
b. what was the radius of the first ferris wheel?
c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?

Answers

Answer:

a. The radius of the navy pier wheel is 56% of the radius of the first ferris wheel

b. The radius of the first ferris wheel was 179% of the radius of the navy pier ferris wheel

c. The wheel was moving at 0.70 (rad)/(min)

Step-by-step explanation:

Navy pier wheel circumference = Cn

First ferris wheel circumference = Cf

Cn = 0.56*Cf

a.

Circumference Perimeter = 2*π*Radius

Navy pier wheel radius = Rn

First ferris wheel radius = Rf

Cn = 0.56*Cf

2*π*Rn = 0,56*2*π*Rf        (equation 1)

dividing both sides by 2π

Rn = 0,56*Rf

b.

From equation 1

2*π*Rn = 0,56*2*π*Rf

dividing both sides by 2π

Rn = 0.56*Rf

dividing both sides by 0.56

Rf = (1)/(0.56)*Rn

Rf = 1.79*Rn

c.

9 minutes / revolution

1 revolution = 2π radians

The wheel makes 2π radians in 9 minutes

Wheel velocity = (2\pi )/(9)  (rad)/(min)

Wheel velocity = 0.70 (rad)/(min)
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