What is the angle of rotation from figure A to figure A’? Assume that the center of rotation is the origin. A. 180° clockwise B. 90° counterclockwise C. 180° counterclockwise D. 270° counterclockwise

Answer:

1st 2nd 4th 5th

Answer:

1. Use a straightedge

2. Draw dots on the line to mark the starting point  

3. Place the point of the compass on the point you made or was given

4. Extend the compass so that the pencil is on the 2nd point & make a an arc thru point B

5. Place the compass point on the starting point dot on the line and draw w/ the pencil to create an arc crossing the line.

Answer:

Step 1: Mark the point that will be the vertex of the new angle, and label it P.

Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.

Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.

Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.

Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.

Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.

Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.

Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.

Step-by-step explanation:

edmentum

Answer:

x = 6

Step-by-step explanation:

2x + 3(3x - 5) = 51

Expand the brackets.

2x + 9x - 15 = 51

Add like terms.

11x - 15 = 51

Add 15 on both sides.

11x = 51 + 15

11x = 66

Divide both sides by 11.

x = 66/11

x = 6

The solution to the equation 2x+3(3x-5)=51 is x = 6

The equation is given as:

2x+3(3x-5)=51

Expand

2x + 9x - 15 = 51

Evaluate the like terms

11x = 66

Divide both sides by 11

x = 6

Hence, the solution to the equation 2x+3(3x-5)=51 is x = 6

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Answer:

100 times

Step-by-step explanation: vibration per second: 50 times

                               vibration for 2 seconds; 50*2=100 times

Answer:

100 times

Step-by-step explanation:

2 seconds=100 times

100÷50=2

So now you can do

Answer:

arccos (0.5) is [tex]\frac{\pi}{3}[/tex]

Step-by-step explanation:

With the arccos(0.5)  in this problem, you are asked which angle renders its cosine equal to 0.5 (or 1/2).

Recall that there are special angles in the unitary circle that render well know values like 1/2. There are two angle values between 0 and the full circle ([tex]2\pi[/tex] radians), that render cosine function equal 1/2, and they are: [tex]\frac{\pi}{3}[/tex], and [tex]-\frac{\pi}{3}[/tex].

The arccos uses just the first one as answer over the restricted domain between 0 and [tex]\pi[/tex], since otherwise it will not be considered a function.

So the answer is that the arccos (0.5) is [tex]\frac{\pi}{3}[/tex]

Answer:

The 25,000 registered voters

Step-by-step explanation:

Population includes the entirety of the set of data, it consists of all the elements of a data set. For example all the students in a school, all the citizens of a country etc.

While the sample is the elements of the population from which observations are drawn from.

Therefore, for the case above, the population is the entirety of the registered voters in the city, that is all the 25,000 registered voters.

Answer:

182.8125

Step-by-step explanation:

Given:

y = x^3

from [2,5] using 6 subdivisions

deltax = (5 - 2)/6 = 3/6 = 0.5

hence the subdivisions are:

[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]

hence the right endpoints are:

x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5

now the area is given by:

A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]

A = 0.5*365.625

A = 182.8125

Area using Right Endpoint approximation is 182.8125

The area of the region is an illustration of definite integrals.

The approximation of the area of the region R is 182.8125

The given parameters are:

[tex]\mathbf{f(x) = x^3}[/tex]

[tex]\mathbf{Interval = [2,5]}[/tex]

[tex]\mathbf{n = 6}[/tex] ------ sub intervals

Using 6 sub intervals, we have the partitions to be:

[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]

List out the right endpoints

[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]

Calculate f(x) at these partitions

[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]

[tex]\mathbf{f(3) = 3^3 = 27}[/tex]

[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]

[tex]\mathbf{f(4) = 4^3 = 64}[/tex]

[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]

[tex]\mathbf{f(5) = 5^3 = 125}[/tex]

So, the approximated value of the definite integral is:

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]

This becomes

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]

Hence, the approximation of the area of the region R is 182.8125

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Answer:

x = 85 deg

Step-by-step explanation:

We can see that there are two straight lines that intersect and that the two angles given are opposite angles.

Because they are opposite angles, the two angles have the same value, i.e

(x + 5) = 90     (subtract 5 from each side)

x = 90 - 5

x = 85 deg

Answer:

t = 5,-1,3

Step-by-step explanation:

r=0.01t^3-0.07t^2+0.07t+0.15

For simplification let's multiply the equation by 100

100r = t³ - 7t² + 7t + 15

When r= 0

t³ - 7t² + 7t + 15= 0

Let's look for the value of t.

Let's try a possible division

(t³ - 7t² + 7t + 15)/(t-5) = t² -2t -3

So we've gotten one as t-5

Let's factorize t² -2t -3

= t² +t -3t -3

= t(t+1) -3(t+1)

= (t+1)(t-3)

So we have

(t-5)(t+1)(t-3)

What it means is that the possible values are when

t = 5,-1,3

These are also called the roots of the equation

Answer:I don’t know

Step-by-step explanation: fruit flys are weird

Answer:

Piecewise function;

y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Step-by-step explanation:

Function graphed represents the piecewise function.

1). Equation of the line with y-intercept (-2) and slope 'm'.

 Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

                                        = [tex]\frac{2}{1}[/tex]

                                        = 2

 Therefore, equation of this segment will be in the form of y = mx + b,

 ⇒ y = 2x - 2 where x < 2

2). Equation of a horizontal line,

 y = 4  where 2 ≤ x ≤ 5

3). Equation of the third line in the interval x > 5

 Let the equation of the line is,

 y = mx + b

 Where m = slope of the line

 b = y-intercept

 Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

                           = [tex]\frac{2}{2}[/tex]

                           = 1

 Equation of this line will be,

 y = 1(x) + b

 y = x + b

 Since, this line passes through (5, 6),

 6 = 5 + b

 b = 6 - 5 = 1

 Therefore, equation of this line will be,

 y = x + 1 where x > 5

 Graphed piecewise function is,

 y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Answer:

D. 0.002

Step-by-step explanation:

Given;

total number of sample, N = 500 elements

50 elements are to be drawn from this sample.

The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample

The probability of the first selection = 1 / 500

The probability of the first selection = 0.002

Therefore, on the first selection, the probability of an element being selected is 0.002

The correct option is "D. 0.002"

On the first selection, the probability of an element being selected is 0.002. Option D is correct.

Given information:

A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .

We want to draw a simple random sample of 50 elements.

The probability is defined as the preferred outcomes divided by the total number of samples.

So, the probability of first selection will be calculated as,

[tex]P=\dfrac{1}{500}\\P=0.002[/tex]

Therefore, on the first selection, the probability of an element being selected is 0.002.

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Answer:

Step-by-step explanation:

The perimeter of the triangle △SMP is the sum of al the sides of the triangle.

Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.

Given LM=9, NR=16 and SR=8

NR = NP+PR

Since NP = PR

NR = NP+NP

NR =2NP

NP = NR/2 = 16/2

NP = 8

From △LSM,  NP = PR = MS = 8

Also since LM = MN, MN = 9

From △SRP, SR = RP = PS =  9

Also SR = MP = 8

From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

perimeter of △SMP = 8+8+9

perimeter of △SMP = 25

Answer:

120 inches cubed

Step-by-step explanation:

The formula for finding the volume of a rectangular prism is length * width * height.

In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.

So multiplying all of those together gets you 120 inches cubed.

Answer:

w = 15

Step-by-step explanation:

-9(w + 585) = -360w

-9w -5265 = -360w

351w = 5265

w=15

Answer:

1/64

Step-by-step explanation:

1/4 × 1/4 × 1/4

Multiply the fractions.

1/4³

= 1/64

Answer:

The answer is 1/64.

Step-by-step explanation:

1/4 x 1/4 x 1/4 = 1/64

In other ways, you can write this as: 1/4³

Hope this helped!

Answer:

Step-by-step explanation:

y = -3x - 2

5x + 2y = 15

5x + 2(-3x -2) = 15

5x -6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

y = -3(-19) - 2

y = 57 - 2

y = 55

(-19, 55)

solution is b

Answer:

A

90 degrees

anticlockwise.

Step-by-step explanation:

It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.

1 A

The center of rotation is where the 90 degree angle has its vertex. So that would be A.

1 B

Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.

1 C

The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.

Answer: n = -2

Step-by-step explanation:

answer:

-2                                                    

step by step explanation:

Answer:

30, 150, 120, and 60 degrees

Step-by-step explanation:

Since the sum of the interior angles in a quadrilateral is 360 degrees:

y+5y+4y+2y=360

12y=360

y=30

2y=60, 4y=120, 5y=150

Hope this helps!

Step-by-step explanation:

y+5y+ 4y + 2y=360°(sum of a Quadrilateral)

12y=360°

divide both sides by 12

y=30°

5y=(5×30)=150°

4y=(4×30)=120°

2y=(2×30)=60°

Answer:

57,838.4 - 57,491.9 = 346.5 miles

346.5/17.5 = 19.8 miles per gallon.

Hope this helps :-)

Step-by-step explanation:

Answer:

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, we failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.

Step-by-step explanation:

Refer to the attached data.

The Null and Alternate hypothesis is given by

Null hypotheses = H₀: μ₁ = μ₂

Alternate hypotheses = H₁: μ₁ ≠ μ₂

The test statistic is given by

[tex]$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } } $[/tex]

Where [tex]\bar{x}_1[/tex] is the sample mean of people who do not exercise regularly.

Where [tex]\bar{x}_2[/tex] is the sample mean of people who do exercise regularly.

Where [tex]s_1[/tex] is the sample standard deviation of people who do not exercise regularly.

Where [tex]s_2[/tex] is the sample standard deviation of people who do exercise regularly.

Where [tex]n_1[/tex] is the sample size of people who do not exercise regularly.

Where [tex]n_2[/tex] is the sample size of people who do exercise regularly.

[tex]$ t = \frac{72.7 - 69.7}{\sqrt{\frac{10.9^2}{16} + \frac{8.2^2}{12} } } $[/tex]

[tex]t = 0.83[/tex]

The given level of significance is

1 - 0.95 = 0.05

The degree of freedom is

df = 16 + 12 - 2 = 26

From the t-table, df = 26 and significance level 0.05,

t = 2.056 (two-tailed)

Conclusion:

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, We failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.

Answer: -32

Step-by-step explanation:

I'm just going to plug in and break down the equation to make it more understandable and easier to comprehend

-(3^2) - (4*3) -11

-(9)- (12) -11

-9 - 12 - 11

-21 -11

-32

Answer:

Step-by-step explanation:

Hello,

Factor x^2 + 64.

[tex]\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}[/tex]

Factor 16x^2 + 49.

[tex]\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}[/tex]

Find the product of (x + 9i)^2.

[tex]\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}[/tex]

Find the product of (x − 2i)^2.

[tex]\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}[/tex]

Find the product of (x + (3+5i))^2.

[tex]\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

x = 1, x = .333

Step-by-step explanation:

Answer:

x = 1 and x = 1/3

Step-by-step explanation:

Here the coefficients of this quadratic are a = 3, b = -4 and c = 1.

The discriminant is b^2 - 4ac, or (-4)^2 - 4(3)(1) = 16 - 12 = 4.

Thus, the roots are:

      -(-4) ± √4        4 ± 2

x = ---------------- = -------------   =>  x = 1 and x = 1/3

          2(3)                  6

Answer:  The ramp must be 32 feet long.  In inches, 384.

Step-by-step explanation:

For each 16 inches of run, there is one inch of rise. To get 24 inches of rise, multiply 16 by 24 to get 384 inches. To convert to a more useful measurement, convert to feet.  12 inches per foot.  384/12 = 32

Measurement is the process of assigning numbers to physical quantities and phenomena.

If a 1-inch rise for a 16-inch run makes it easier for the wheelchair rider, this can be expressed as:

1inch rise = 16-inch run

In order to determine how long must a ramp be to easily accommodate a 24-inch rise to the door, we can write:

24in rise = x

Divide both expressions:

[tex]\dfrac{1}{24}=\dfrac{16}{x}\\[/tex]

Cross multiply:

[tex]x=16 \times 24\\x=384inches[/tex]

Hence the ramp must be 384inches long in order to easily accommodate a 24-inch rise to the door.

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Answer:

The roots are where the graph intercepts the x-axis

Step-by-step explanation:

Alternatively, you could factor and then solve algebraically.

Answer:

(- 5, - 7 )

Step-by-step explanation:

Equate f(x) and g(x), that is

2x + 3 = - 4x - 27 ( add 4x to both sides )

6x + 3 = - 27 ( subtract 3 from both sides )

6x = - 30 ( divide both sides by 6 )

x = - 5

Substitute x = - 5 into either of the 2 functions for y- coordinate

Substituting into f(x)

f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7

Thus point of intersection = (- 5, - 7 )

Answer:

the correct answer is a reflection over the y axis

Step-by-step explanation:

The best description of the transformation shown will be;

''Reflection over the y - axis.''

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The transformation is shown in figure.

Now,

Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.

So, The best description of the transformation shown will be;

''Reflection over the y - axis.''

Thus, The best description of the transformation shown will be;

''Reflection over the y - axis.''

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Answer:

Right-angle triangle

Step-by-step explanation:

Answer:

x=35

Step-by-step explanation: