Triangle D has been dilated to create triangle D′. Use the image to answer the question.

image of a triangle labeled D with side lengths of 12, 16, and 20 and a second triangle labeled D prime with side lengths of 6, 8, and 10

Determine the scale factor used.

Scale factor of one third
Scale factor of 3
Scale factor of one half
Scale factor of 2

The following are the values for the angles and side of the right triangle using the trigonometric ratio: P = 28.6137, Q = 61.3863, and r = 14.0112

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tan P= 6.71/12.3 {opposite/adjacent}

P = tan⁻¹(6.71/12.3)

P = 28.6137

Q = 180 - (90 + 28.6137) {sum of interior angles of a triangle}

Q = 61.3863

sin P = 6.71/r {opposite/hypotenuse}

sin 28.6137 = 6.71/r

r = 6.71/sin 28.6137 {cross multiplication}

r = 14.0112

Therefore, the values for the angles and side of the right triangle using the trigonometric ratio are: P = 28.6137, Q = 61.3863, and r = 14.0112

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A saleswoman earns 3% commission on all the merchandise that she sells. Last month she sold 8000 worth of merchandise. the commission earned last month is  $240

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

3%

= 3 percent

= 3 / 100

= 0.03

The factor 0.71 is added to 1 and multiplied by revenue generated from sales to get the amount earned last month

the addition

= 1 + 0.03.

= 1.03

the multiplication

= 1.03 * 8000

= 8240

The commission earned last month is

= 8240 - 8000

= 240

The commission earned last month = $240

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Answer:

(-6)(+5-5) is the answer

The fraction represented by point A, it is crucial to have information about the scale, intervals, and the relative position of point A on the number line.

With these details, you can calculate the fraction accurately.

Point A on the number line represents a fraction that requires additional information to determine its precise value.

I can provide you with a general approach to finding the fraction corresponding to a given point on the number line.

A number line represents a range of values, typically with a specific scale or interval.

The scale can be divided into equal parts, such as units or fractions.

To determine the fraction represented by point A, we need to know the scale and the position of point A relative to that scale.

Let's consider a number line that ranges from 0 to 1, with evenly spaced tick marks representing tenths.

If point A is located halfway between the tick marks representing 0.4 and 0.5, then it represents the fraction 0.45 (or 9/20 in simplified form).

If the number line has a different scale or is divided into different intervals, the fraction represented by point A will be different.

Without specific details about the number line and the position of point A, it is impossible to determine the fraction precisely.

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Step-by-step explanation:

Hello please could u re take the picture again

Answer:

b=10cm²

Step-by-step explanation:

4inx5in=20

20/2=10cm²

Let me know if this helps

Answer: yum!!!

Step-by-step explanation:

Answer: 575

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(14^2 = b^2+6^2\\b^2 = 14^2-6^2\\b = \sqrt{14^2-6^2} \\ = \sqrt{160}\\ = 12.6491106407\)

Rounding off to nearest tenth:

b ≈ 12.6

tanθ = 6/12.6

\(tan^{-1} (6/12.6)\\ = 25.46334506\\\)

Hence angle A ≈ 25.5

Angle B = 180-25.5-90

Angle B = 64.53665494

Hence, Angle B ≈ 64.5

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Answer:

50.24

Step-by-step explanation:

→To find a circle's (compass) area, you must use the following formula:

A = π\(r^2\)

→All you need to do is plug in 4 for the "r," (radius), and solve:

A = π\(4^2\)

A = π\((16)\)

→When you multiply 16 by pi, we're going to use 3.14:

A = 3.14(16)

A = 50.24

The measurement of angle x in the given figure is 11°

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.

Given is a figure, we need to find the measure of angle x,

The labeled figure is attached,

We have,

∠ 1 = 85° [vertically opposite angles]

∠ 3 = 96° [corresponding angles between parallel lines]

∠ 2 + ∠ 3 = 180° [linear pair angles]

∠ 2 = 180°-96°

∠ 2 = 84°

Now,

∠ 1 + ∠ 2 + x = 180° [angles sum property of a triangle]

85° + 84° + x = 180°

x = 180°-169°

x = 11°

Hence, the measurement of angle x in the given figure is 11°

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Answer:

1/9

Step-by-step explanation:

probability equals number of desired outcomes over total possible outcomes

Total possible outcomes = 36

possible sums of 5:

2,3   1,4  3,2.  4,1

4/36= 1/9

Answer:

82.63 miles/min

Step-by-step explanation:

Unit rate in minutes per mile = 2727/ 33

Unit rate in minutes per mile = 82.63 min

=》 Peter runs 1 mile in about 82.63 minutes (approx - 83 minutes).

Hope it helps ⚜

Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

Answer:

line one should have a y-intercept at (0,2).

Step-by-step explanation:

Answer: A

Step-by-step explanation: line one should have a y-intercept at (0,2).

The equations are 4x - y - 2 = 0 and x + 3y + 6 = 0. The solution has been obtained using two-point form.

What is two-point form?

One of the crucial forms for algebraically representing a straight line is the two-point form. Each and every point on a line fulfils the equation for that line, making it the representation of the entire line.

We are given two lines on the graph

Both the lines meet on the y-axis at (0,-2)

This means (0,-2) is the common solution.

Another point of the steeper line is (1,2)

Another point of the flatter line is (3,-3)

Now, as we know the two points of the line, using the two-point form, we get

\(\frac{y - y_{1}}{x-x_{1} } = \frac{y_{2} - y_{1}}{x_{2} -x_{1} }\)

⇒ (y+2)/(x-0) = (2+2)/(1-0)

⇒ y+2 = 4x

⇒ y = 4x-2

⇒ 4x - y - 2 = 0

Similarly,

⇒ (y+3)/(x-3) = (-2+3)/(0-3)

⇒ (y+3)/(x-3) = -1/3

⇒ (y+3) = -(x-3)/3

⇒ y+3 = -x/3 + 1

⇒ y = -x/3 - 2

⇒x + 3y + 6 = 0

Hence, the equations are 4x - y - 2 = 0 and x + 3y + 6 = 0.

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Since there are multiple questions so, the question answered above is attached below

Answer:

a) The angular velocity is 0.4π radians/second ⇒1.25664 radians/second

b) The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters

Step-by-step explanation:

The angular velocity ω = 2 π n ÷ t, where

The distance that moving by the angular velocity is d =  ω r t, where

a)

∵ A wheel completes 12 revolutions in 1 minute

∴ n = 12

∴ t = 1 minute

→ Change the minute to seconds

∵ 1 minute = 60 seconds

∴ t = 60 seconds

→ Substitute n and t in the rule above

∵ ω = 2 (π) (12) ÷ 60

∴ ω = 24π ÷ 60

∴ ω = 0.4π radians/second

∴ The angular velocity is 0.4π radians/second ⇒1.25664 radians/second

b)

→ To find the distance in 5 minutes multiply ω by the radius by the time

∵ The wheel has a radius of 33 cm

∴ r = 33 cm

→ Change it to meter

∵ 1 m = 100 cm

∴ r = 33 ÷ 100 = 0.33 m

∵ t = 5 minutes

→ Change it to seconds

∴ t = 5 × 60 = 300 seconds

→ Substitute them in the rule of the distance above

∵ d = 0.4π (0.33) (300)

∴ d = 39.6π meters ⇒ 124.407 meters

∴ The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters

1.) Probability of getting 1: 0.12 or 12%.

2.) Probability of getting 2: 0.16 or 16%.

3.) Probability of getting 3: 0.25 or 25%.

4.) Probability of getting 4: 0.18 or 18%.

5.) Probability of getting 5: 0.15 or 15%.

6.) Probability of getting 6: 0.14 or 14%.

To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:

Number: 1 2 3 4 5 6

Times: 12 16 25 18 15 14

To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):

Probability of getting 1 = 12 / 100 = 0.12.

Probability of getting 2 = 16 / 100 = 0.16.

Probability of getting 3 = 25 / 100 = 0.25.

Probability of getting 4 = 18 / 100 = 0.18.

Probability of getting 5 = 15 / 100 = 0.15.

Probability of getting 6 = 14 / 100 = 0.14.

Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:

1: 0.12 or 12%,

2: 0.16 or 16%,

3: 0.25 or 25%,

4: 0.18 or 18%,

5: 0.15 or 15%,

6: 0.14 or 14%.

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If we use more than 133 minutes then the 2nd plan will be preferable.

Given:

The first plan charges a rate of 26 cents per minute. The second plan charges charges a monthly fee of $19.95 plus 11 cents per minute.

26 cents = $0.26

Let m be the minutes

19.95 + .17m < .32m

Subtract .17m from both sides

19.95 < .32m - .17m

19.95 < .15m

Divide both sides by .15

19.95/.15 < m

133 < m

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Based on the dimensions of the wall and the triangular glass, the number of mirrors needed is 215 mirrors.

First find the area of the wall:

= 36 x 93

= 3,348 m²

The area of the triangle, assuming it is an equilateral triangle is:

= (√3/4) x 6²

= 15.59 m²

The number of mirrors needed is:

= 3,348 / 15.59

= 215 mirrors

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Answer:

11 hours

Step-by-step explanation:

Answer:

\((f + g)(4) = 191\)

Step-by-step explanation:

Given

\(f(x) = 5x^2 - 5x + 15\)

\(g(x) = 6x^2 + 7x - 8\)

Required

\((f + g)(4)\)

First, calculate \((f + g)(x)\)

This is calculated as:

\((f + g)(x) = f(x) + g(x)\)

So, we have:

\((f + g)(x) = 5x^2 - 5x + 15+6x^2 + 7x - 8\)

Collect like terms

\((f + g)(x) = 5x^2 +6x^2 - 5x+ 7x + 15 - 8\)

\((f + g)(x) = 11x^2 + 2x + 7\)

Substitute 4 for x

\((f + g)(4) = 11*4^2 + 2*4 + 7\)

\((f + g)(4) = 191\)

Answer:

Step-by-step explanation:

\(\sqrt{2} cos x-1=0\\cos x=\frac{1}{\sqrt{2} } =cos (\frac{\pi }{4} ),cos (2\pi -\frac{\pi }{4} )\\cos x=cos(2n\pi +\frac{\pi }{4} ),cos(2n\pi +\frac{7\pi }{4} )\\x=2n\pi +\frac{\pi }{4} ,2n\pi +\frac{7\pi }{4} \\n=0\\x=\frac{\pi }{4} ,\frac{7\pi }{4}\)

Answer:

6n-3

Step-by-step explanation:

You can see the sequence is ascending by 6 each time so the nth term is 6n.

The 'zero term' would be -3 so the equation would be 6n-3.

Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)