Dianne drew a triangle with coordinates (1,3), (3,2), and (4,2). She drew an image of thetriangle with coordinates (-1,3), (-3, 2), and (-4, 2). Which rule describes thetransformation she performed?(x,y) -> (x, y-2)(x,y) -> (x, -y)(x,y) -> (x, y-6)(x,y) -> (-x, y)

Answer:

1. 170.083 in³

2. 126π in³

3. 92.106 m³

4. 2412.74 in³

5. 612π m³ and 1922 m³

Step-by-step explanation:

1.

Cylinder:

\(V = \pi r^{2}h\)               *Plug in numbers*

\((3.14)(2.5)^{2}(7)\)         *Square 2.5*

\((3.14)(6.25)(7)\)        *Solve*

≈ \(137.375in^{3}\)

Sphere:

\(V = \frac{4}{3}\pi r^{3}\)              *Plug in numbers*

\(\frac{4}{3} (3.14)(2.5)^{3}\)         *Cube 2.5*

\(\frac{\frac{4}{3}(3.14)(15.625)}{2}\)         *Divide by 2 and Solve*

≈ \(32.7083 in^{3}\)

Add both volumes

\(137.375 + 32.7083\) ≈ \(170.083in^{3}\)

2.

Cylinder:

\(V = \pi r^{2}h\)         *Plug in numbers*

\(\pi (3)^{2}(10)\)            *Square 3*

\(\pi (9)(10)\)             *Multiply*

\(90\pi\)

Sphere:

\(V = \frac{4}{3}\) π \(r^{3}\)            *Plug in numbers*

\(\frac{4}{3}\pi (3)^{3}\)                   *Cube 3*

\(\frac{4}{3} \pi (27)\)                   *Multiply*

\(36\pi\)

Add both Volumes to get total

\(90\pi + 36\pi = 126in^{3}\)

3.

Sphere:

\(V = \frac{4}{3}\pi r^{3}\)              *Plug in numbers*

\(\frac{4}{3} (3.14)(3)^{3}\)            *Cube 3*

\(\frac{4}{3} (3.14)(27)\)            *Multiply*

\(113.04m^{3}\)

Cone:

\(V = \frac{\pi r^{2}h}{3}\)             *Plug in numbers*

\(\frac{(3.14)(2)^{2}(5)}{3}\)           *Square 2*

\(\frac{(3.14)(4)(5)}{3}\)             *Solve*

\(20.93m^{3}\)

Subtract the volumes to get the volume of the blue area

\(113.04 - 20.93 = 92.106m^{3}\)

4.

Sphere:

\(V = \frac{4}{3} \pi r^{3}\)            *Plug in numbers*

\(\frac{4}{3}\pi (8)^{3}\)                 *Cube 8*

\(\\\frac{4}{3}\pi (512)\)               *Multiply*

\(\\\\\pi (682.6)\)              *Solve*

\(2133.66in^{3}\)           *Divide by 2 since it's a hemisphere*

Cone:

\(V = \frac{\pi r^{2}h}{3}\)            *Plug in numbers*

\(\frac{\pi (8)^{2}(20)}{3}\)              *Square 8*

\(\frac{\pi (64)(20)}{3}\)              *Multiply and Divide*

\(1340.41 in^{3}\)

Add both volumes

\(1072.33 + 1340.41 = 2412.74in^{3}\)

5.

Cylinder:

\(V = \pi r^{2}h\)            *Plug in numbers*

\(\pi (6)^{2}(16)\)              *Square 6*

\(\pi (36)(16)\)             *Multiply*

\(576\pi\)

Cone:

\(V = \frac{\pi r^{2}h}{3}\)            *Plug in numbers*

\(\frac{\pi (6)^{2}3}{3}\)                  *Square 6*

\(36\pi\)

Add both volumes

\(576\pi + 36\pi = 612\pi m^{3}\)

Alternative: *Multiply π*

\(1922m^{3}\)

Answer:

1) 175 \(in^2\)

2) 1st option

3) 92 \(m^2\)

4) 2412 \(in^3\\\)

5) 2nd option

Step-by-step explanation:

\(1)\ A = D * Pi = 5 * 3.14 = 15.7\\\)

\(2)\ V_{1} = 15.7 * 7 = 109.9\)

\(3)\ V_{2} = 4Pi*\frac{R^3}{3} = 12.56*\frac{15.625}{3} = 65.41(6)\)

\(4)\ V_1 + V_2 = 65.4 + 109.9 = 175.3\) which is close to 175

\(1)\ A = Pi * R^2 = 3.14 * (\frac{6}{2})^2 = 3.14 * 3^2 = 28.26\\\)

\(2)\ V_1 = A * h = 28.26 * 10 = 282.6\)

\(3)\ V_2 = \frac{4}{3} * Pi * R^3 = \frac{4}{3} * 3.14 * (\frac{6}{2})^3 = 113.04\)

\(4)\ V_1 + V_2 = 282.6 + 113 = 395.6\) which is very close to 396

\(5)\ 396 = 126 * pi\)

\(1) V_1 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * 3.14 * 2^2 * 5 = 20.9(3)\) =

\(2)\ V_2 = \frac{4}{3} * Pi * R^3 = \frac{4}{3} * 3.14 * 3^3 = 113.04\\\)

\(3)\ V_2 - V_1 = 113.04 - 20.93 = 92.14\) which is very close to 92

\(1)\ V_1 = \frac{\frac{4}{3} * Pi * R^3}{2} = \frac{\frac{4}{3} * 3.14 * 512}{2} = 1,071.786\\\)

\(2)\ V_2 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * 3.14 * 64 * 20 = 1,339.733\)

\(3)\ V_1 + V_2 = 1072 + 1340 = 2,411 = 2412\)

\(1)\ A = Pi * R^2 = 36*Pi\\\)

\(2)\ V_1 = 36*Pi * 16 = 576 * Pi\\\)

\(3)\ V_2 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * Pi * 36 * 3 = 36 * Pi\)

\(4) V_1 + V_2 = 576Pi + 36Pi = 612Pi\)

Answer:

BAC and DAE are two acronyms for BAC and DAE, respectively. Since they are angles at a point, an arc measuring 204 degrees is 360 degrees. BAC is measured at 11 degrees. 5(11)° = 55° is the measure of DAE.

Step-by-step explanation:

\(3\leqslant |x+2|\leqslant 6\implies \begin{cases} 3\leqslant |x+2|\\\\ |x+2|\leqslant 6 \end{cases}\implies \begin{cases} 3 \leqslant \pm (x+2)\\\\ \pm(x+2)\leqslant 6 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(3\leqslant +(x+2)\implies \boxed{3\leqslant x+2}\implies 1\leqslant x \\\\[-0.35em] ~\dotfill\\\\ 3\leqslant -(x+2)\implies \boxed{-3\geqslant x+2}\implies -5\geqslant x \\\\[-0.35em] ~\dotfill\\\\ +(x+2)\leqslant 6\implies \boxed{x+2\leqslant 6}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ -(x+2)\leqslant 6\implies \boxed{x+2\geqslant -6}\implies x\geqslant -8\)

Create a frequency distribution with 10 intervals for 60 cases that range in score from 4 to 84, each interval will have an approximate width of 8 units.

To determine the width of each interval in a frequency distribution, we need to calculate the range of the data and divide it by the desired number of intervals.

Given that the scores range from 4 to 84, the range of the data is 84 - 4 = 80 units.

To distribute these 80 units into 10 intervals, we divide the range by the number of intervals:

Interval width = Range / Number of Intervals

Interval width = 80 / 10 = 8 units

Therefore, each interval in the frequency distribution will have an approximate width of 8 units.

In practice, it's important to note that the width of intervals can be adjusted slightly depending on the specific requirements or characteristics of the data. It's also worth considering whether the interval width provides an appropriate level of detail and captures the variation in the data effectively.

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Answer:

Both 6

Step-by-step explanation:

Considering the given scale, it is found that:

1. The distance between the two cities is of 325 km.

2. 43.3 cm should be used to represent the distance.

3. The scale of the map is of 1:9000000.

A scale is how much each unit in the drawing represents in actual distance.

For item 1, the scale of 1:5000000 means that each unit on the graph represents 5,000,000 units of actual distance.

The distance on the map is of 6.5 cm, hence the actual distance is of:

6.5 x 5000000 = 32,500,000 cm = 325 km.

For item 2, the scale is of 1:1500000, meaning that each cm of drawing is equivalent to 1,500,000 cm of real distance = 15 km.

Hence, the number of centimeters to represent a distance of 650 km is given by:

650/15 = 43.3 cm.

For item 3, we have that 7 cm represent 630 km = 63,000,000 cm, hence:

63,000,000/7 = 9000000.

Meaning that the scale is given by:

1:9000000.

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The cosine function with amplitude 2 and period 6π is given by:

y = 2cos(x/3).

The standard cosine function is given by:

y = Acos(Bx).

In which:

For a cosine function with amplitude 2 and period 6π, we have that A = 2 and B = 1/3, hence:

y = 2cos(x/3).

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Answer:

x = 7

Step-by-step explanation:

We can find our answer by getting x alone.

1/7 * x = 1

Multiply 1/7 to x.

x/7 = 1

Multiply 7 to both sides to isolate x.

x = 7

Answer:

$67.20

Step-by-step explanation:

84 x .05

4.2

84 x .25

21

84-21

63

63 + 4.2

67.20

The Density of object is 10,490 kg/m³

What is Density, Mass and Volume ?

Given,

Mass = 73,430 Kg

Volume = 7 m³

We know,

Density = Mass / volume

Now, plug in the values

Density = 73430/7

             = 10, 490 kg/m³

Hence, the Density of object is 10,490 kg/m³

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Answer:

\(\frac{1}{2^5}\)

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

2x - 6 = 2x + 6 ( add 6 to both sides )

2x = 2x + 12 ( subtract 2x from both sides )

0 = 12 ← false statement

this false statement indicates the equation has no solution

Answer:

Step-by-step explanation:

A cube has a surface area of 60 in2. Find the volume in in3.

60 : 6 = 10 in²

√10 = 3,162277660168379

3,162277660168379³ =

99,99999999999996

round

100in³

Answer:

Yes

Step-by-step explanation:

Answer:

Y/X = 2/3 x^2 + 16/3

Y= 2/3 x^3 + 16/3 x

Just replace y with y/X and X with x^2

You can use the definition of logarithms and some basic properties to find out the solution to the given equation.

The solution for Tenisha's system of equations is given approximately by  x = -4.805

When you raise a number with an exponent, there comes a result.

Lets say you get

\(a^b = c\)

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

\(b = log_a(c)\)

Some properties of logarithm are:

\(log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b) + log_b(c) = log_a(c)\)

The given equation is

\(log_3(5x) = log_5(2x + 8)\)

Simplifying and using above properties, we get:

\(log_3(5x) = log_5(2x + 8)\\\\log_3(5) + log_3(x) = log_5(2) + log_5(x+4)\\\\\text{Adding}\: \rm log_5(3) \text{ on both the sides}\\\\log_5(3) + log_3(x) + log_3(5) = log_5(2) + log_5(x+4) + log_5(3)\\\\log_5(x) + log_3(5) - log_5(2) - log_5(3) = log_5(x+4)\\\\\text{Using the values of constant logs from calculator}\\\\\log_5(x) - log_5(x+4) = 1.11\\\\log_5(\dfrac{x}{x+4}) = 1.11\\\\\dfrac{x}{x+4} = 5^{1.11}\\\\x = 5.968 \times (x+4)\\4.968x = -23.872\\\\x \approx -4.805\)

Thus,

The solution for Tenisha's system of equations is given approximately by  x = -4.805

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B) (1.0, 1.4)

I got it right on the quiz on Ed2020

Some other questions from the quiz and their answers (people will get different questions even on ed, but may have some in common if not all of them so im hoping this will help someone. )

Which system of equations could be graphed to solve the equation below? log Subscript 0.5 Baseline x = log Subscript 3 Baseline 2 + x

Answer: D

What is the approximate value of q in the equation below?

q+log26=2q+2

Answer: C (0.585)

Devonte used the change of base formula to approximate log Subscript 8 Baseline 25. Which expression did Devonte use?

Answer: D

Which system of equations could be graphed to solve the equation below? log (2 x + 1) = 3 x minus 2

Answer: B

Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a Not-equals 1 and b Not-equals 1?

log Subscript x Baseline x

Answer: Not B lol I got it wrong

Which is equivalent to log Subscript 2 Baseline n = 4?

Answer: D

Tenisha solved the equation below by graphing a system of equations.

log Subscript 3 Baseline 5 x = log Subscript 5 Baseline (2 x + 8)

Answer: B

Consider the equation below.

log Subscript 4 Baseline (x + 3) = log Subscript 2 Baseline (2 + x) Which system of equations can represent the equation?

Answer: A

Which expression results when the change of base formula is applied to log Subscript 4 Baseline (x + 2)?

Answer: A

What is the approximate value of x in the equation below?

log Subscript 5 Baseline 15 = x + 3

Answer: B

Using degree of freedom,

Two degrees of freedom would we report when we report the results of our study is (2,24).

Degree of freedom:

The statistical degrees of freedom (DF) indicate the number of independent values that can be changed in the analysis without violating the constraints.

degrees of freedom is the number of independent values that can be estimated in a statistical analysis. It can also be thought of as the number of values that are free to vary when estimating the parameters

DF = N – P

Where:

N = sample size

P = the number of relationships

We given that,

Number of groups , k = 3

Number of total participants, n = 27

Degrees of freedom for F-test is F(k-1,n-k)

= F(3-1 , 27-3)

= F(2,24)

Hence, (2,24,) are required two degrees of freedom.

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Therefore, the set of points that does not determine a spherical triangle is any set of three non-collinear points that do not lie on a great circle of the sphere.

Explanation: A spherical triangle is a triangle formed on the surface of a sphere by three great circle arcs intersecting pairwise to form three vertices. Any three points that do not lie on a great circle of the sphere will not determine a spherical triangle. Therefore, the set of points that does not determine a spherical triangle is any set of three non-collinear points that do not lie on a great circle of the sphere. Any set of three non-collinear points that do not lie on a great circle of the sphere does not determine a spherical triangle.

Therefore, the set of points that does not determine a spherical triangle is any set of three non-collinear points that do not lie on a great circle of the sphere.

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Answer: 3.9 ft

Step-by-step explanation:

From the question, the distance across the window which is 2.5 ft is the diameter. Therefore, radius will be:

= 2.5 / 2

= 1.25 ft

Then, we calculate the circumference of the circle which will be:

= 2πr

= 2 × 3.14 × 1.25

= 7.85 ft

Nite that it's a semi circle, therefore we divide the perimeter by 2. This will be:

= 7.85/2

= 3.9 feet

Answer:

b

Step-by-step explanation:

Therefore, the dimensions of triangle ABC and the angles opposite to these sides are:

a ≈ 6.85 units

b = 13 units

c ≈ 9.39 units

A ≈ 40 degrees

B = 97 degrees

C = 43 degrees

A triangle is a geometrical shape that has three sides and three angles. It is formed by connecting three non-collinear points in a plane with straight line segments. The three sides may have different lengths, and the three angles may have different measures. The sum of the angles in a triangle is always 180 degrees. Triangles are used in many fields of mathematics, as well as in science, engineering, and everyday life. They can be classified by their side lengths and angle measures, and there are various formulas and theorems that apply to triangles.

Here,

We can use the Law of Sines to find the missing measures of the triangle.

Recall that the Law of Sines states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides opposite to the angles A, B, and C, respectively.

Given that b=13 units, and angle B=97 degrees, we can set up the proportion:

13/sin(97) = c/sin(43)

Solving for c, we get:

c = (13*sin(43))/sin(97) ≈ 9.39

Now, to find the remaining angle and side, we can use the fact that the angles of a triangle sum up to 180 degrees. We know that angle C is 43 degrees, so we can find angle A as:

A = 180 - 97 - 43 = 40 degrees

And we can find side a using the Law of Sines:

a/sin(40) = 13/sin(97)

Solving for a, we get:

a = (13*sin(40))/sin(97) ≈ 6.85

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The image of point A(-6,-3) after being rotated 196° clockwise around point (-5,5) will be located in the fourth quadrant at approximately (-3.92,-7.49).

To determine the location of the image of point A(-6,-3) after being rotated 196° clockwise around point (-5,5), we need to follow these steps:

1. Draw the coordinate axes and plot point A(-6,-3).
2. Plot the center of rotation, point (-5,5).
3. Draw a line connecting point A to the center of rotation (-5,5).
4. Determine the distance between point A and the center of rotation (-5,5), which is 10 units (using the distance formula).
5. Rotate point A 196° clockwise around point (-5,5) by keeping the distance of 10 units and finding the new coordinates of the point.
6. The new coordinates of point A will be located in the fourth quadrant because the rotation is clockwise and the starting point A(-6,-3) is in the third quadrant.

Using trigonometry, we can determine the new coordinates of point A after rotation as follows:

- The angle of rotation is 196° clockwise, which is equivalent to 164° counterclockwise (360° - 196°).
- The distance between point A and the center of rotation (-5,5) is 10 units.
- The angle between the x-axis and the line connecting point A to the center of rotation is 116.57° (using inverse tangent function: tan⁻¹(3/6) = 26.57°, then 90° + 26.57° = 116.57°).
- The angle between the x-axis and the line connecting the new location of point A to the center of rotation is 280.57° (116.57° + 164°).
- The x-coordinate of the new location of point A can be found using the cosine function: cos(280.57°) = -3.92 (rounded to two decimal places).
- The y-coordinate of the new location of point A can be found using the sine function: sin(280.57°) = -7.49 (rounded to two decimal places).

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Answer:

it answer is 3 because it is trigonometry

Answer:b

Step-by-step explanation:

Answer:

17.5%

Step-by-step explanation:

We know that there are 35 out of 200 allergic to peanut

So we take

35 divided by 200, then times 100% = 17.5%

So, 17.5  of children are allergic to peanut

Question:

Solution:

If Jon ran around the track 24 times, then we have that Jon ran:

then the correct answer is

3 miles.

Answer:

he ran 3 miles

Step-by-step explanation: