In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
A) 6 B) 7 C) 8 D) 9

Hey there!

Unless the smaller object was rotated 360° (in which case the rotation wouldn't have to be mentioned), you can see that all of the lines are still in the same place and that it wasn't rotated at all. This eliminated any answer option that mentions a rotation, which is A and C.

Also, if you count the units of one of the straight lines – for example, line AB and A'B' – you can see that the smaller object is four times smaller than the larger object. In the case of line AB and A'B', line AB is 8 units long and A'B' is 2 units long. This means that the scale factor is [tex]1[/tex].

Lastly, the smaller object was moved from its initial location, which would be in the center of the larger object if it wasn't moved after being scaled down.

The answer will be, "a dilation with a scale factor of [tex]1[/tex] and then a translation."

Hope this helped you out! :-)

Answer:

The number that belongs in the green box is equal to 909.

General Formulas and Concepts:
Algebra I

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 30

b = 3

c = x

Step 2: Find x

Let's solve for the general equation that allows us to find the hypotenuse:

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.

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Topic: Trigonometry

Answer:

6

Step-by-step explanation:

By the alternate exterior angles theorem,

120=15(x+2)

8=x+2

x=6

The ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

We have ABCD is a parallelogram.

BE is perpendicular to FC

FA is perpendicular to FC

As we know in the parallelogram ABCD:

AB ≅ DC

AD ≅ CB

As the DC is extended to F

So, AB ≅ FE

And BE is perpendicular to FC

       FA  is perpendicular to FC  (given)

∴ FA ≅ BE

∴ ABEF is a parallelogram.

Thus, the ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

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Cassie need to make the model is 2250 cm²

A square pyramid has a square base and four lateral faces in geometry. A pyramid is a polyhedron with a base and three or more triangular faces that meet above it .

The complete question is attached below:

We know,

A= a(a+ √(a²+4h²))

and, a =25cm, h=30 cm

So,

A= 25(25+ √(25²+4*30²))

=25(25+65)

= 2250 cm²

Hence, Cassie need to make the model is 2250 cm²

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Answer:

9%

Step-by-step explanation:

(final - initial )/ initial * 100

3.87 / 43 * 100

= 9%

Answer:

The definition for the given piecewise-defined function is:   [tex]\boxed{\displaystyle\sf\ Option\:D:\:\: f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}[/tex].

Step-by-step explanation:

A piecewise-defined function represents specific rules over different intervals of the domain.  

Open interval: This means that the endpoint is not included in the interval.

We can use the following symbols to indicate the exclusion of endpoints in the interval:

Closed interval: This implies the inclusion of endpoints in the interval.

We can use the following symbols to indicate the inclusion of endpoints in the interval:

The best way to determine which piecewise-defined function represents the graph is by observing the endpoints and orientation of both partial lines.

Based on our observations from the previous step, we can infer that x > -1 or x ≤ -1 apply to piecewise-defined functions A or D. However, only one of those two options represent the graph.

    [tex]\boxed{\displaystyle\sf Option\:A)\:\:\:f(x) = \begin{cases}\displaystyle\sf\ 2x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ x + 4 & \sf\:{if\:\:x > -1}\end{cases}}[/tex]

We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a closed dot.

Substitute x = -2 into f(x) = 2x + 2:  

⇒ The output value of f(-2) = -2 is not included in the graph of the partial line whose endpoint is at (-1, 1).

We must choose a domain value that falls within the interval of x > -1 whose output is included in the graph of the partial line with an open dot.

Substitute x = 0 into  f(x) = x + 4:

⇒ The output value of f(0) = 4 is included in the graph of the partial line whose endpoint is at (-1, 2).

Conclusion for Option A:

Option A is not the correct piecewise-defined function because one of the pieces, f(x) = 2x + 2, does not specify the interval (-∞, -1].

    [tex]\boxed{\displaystyle\sf Option\:D)\:\:\:f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}[/tex]

We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a closed dot.

Substitute x = -2 into f(x) = x + 2:

⇒ The output value of f(-2) = 0 is included the graph of the partial line whose endpoint is at (-1, 1).

We must choose a domain value that falls within the interval of x > -1 whose output is included is included in the graph of the partial line with an open dot.

Substitute x = 0 into f(x) = 2x + 4:

⇒ The output value of f(0) = 4 is included in the graph of the partial line whose endpoint is at (-1, 2).  

We can infer that the piecewise-defined function that represents the graph is:

[tex]\boxed{\displaystyle\sf\ Option\:D:\:\: f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}[/tex].

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Answer:

it's C just did the quiz and go it right

Volume is a three-dimensional scalar quantity. The volume of the rectangular prism is 200 in³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the rectangular prism of the length of 8 inches, the width of 2 inches, and the height of 12 1/2 inches can be written as,

The volume of the rectangular prism = 8in × 2in × 12.5in

                                                               = 200 in³

Hence, The volume of the rectangular prism is 200 in³.

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Answer:

y = -x - 1

Step-by-step explanation:

y = mx + b

slope (m): Since the line is going downhill, the slope will be negative

slope = rise / run

slope = 1 / 1

slope = 1

m = -1

y - intercept (b): this when x = 0, the line is crossing the vertical line (y-axis)

b = -1

so y = mx + b is

b = -1, m = -1

y = (-1)x + (-1)

Answer:

y = - x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1-0}{0-(-1)}[/tex] = [tex]\frac{-1}{0+1}[/tex] = [tex]\frac{-1}{1}[/tex] = - 1

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - x - 1 ← equation of blue line

The population mean (μ) is: 74

The standard deviation (σ) is: 30.6

There is an outlier, 15.

Population mean (μ) = sum of data points / number of data points

Standard deviation (σ) = √(sum of squares/number of data points) = √(SS/n)

Given the data, 15, 75, 88, 92, 100:

Population mean (μ) = (15 + 75 + 88 + 92 + 100)/5 = 74

Standard deviation (σ) = √(4678/5)

σ = √935.6

σ = 30.6

15 is more smaller compared to most of the data points in the data, so, it is an outlier.

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Answer:

The angle shows 90° so that means

90° - 42° = 48°

Therefore the angle of the depression is 48°

The angle of depression from C to point A 48°. The correct option is c. 48°

From the question, we are to determine the angle of depression from C to point A

The angle of depression is the angle formed between the horizontal line and the line of sight when an observer looks downwards at an object

Thus, in the given diagram

The angle of depression is 90° - 42°

Angle of depression = 48°

Hence, the angle of depression from C to point A 48°. The correct option is c. 48°

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Answer:

[tex]x = 2\\ \\x= -\dfrac 78[/tex]

Step-by-step explanation:

[tex]~~~~~~~8x^2 -9x -14=0\\\\\implies 8x^2+7x-16x-14=0\\\\\implies x(8x+7)-2(8x+7)=0\\\\\implies (x-2)(8x+7) = 0\\\\\implies x = 2,~ x= -\dfrac 78[/tex]

Answer:

1

Step-by-step explanation:

The points go rise:1 up:1 so the slope is 1.

Answer:

hey!! we can taIk here

Step-by-step explanation:

Using the tangent ratio, the height of the lighthouse from the top of the cliff ≈ 161.2 meters.

For solving a right triangle, the tangent ratio that can be applied is: tan ∅ = opposite length / adjacent length.

Find the height of the light house and the cliff using the tangent ratio:

tan 51.3 = height/980

Height of lighthouse + cliff = (tan 51.3)(980)

Find the height of the cliff only using the tangent ratio:

tan 47.3 = height/980

Height of cliff = (tan 47.3)(980)

Height of the lighthouse from the top of the cliff = (tan 51.3)(980) - (tan 47.3)(980)

Height of the lighthouse from the top of the cliff ≈ 161.2 meters.

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f(x) = | x + 61 | function is a translation of the parent absolute value function.Option B is correct.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

A single vertical parenthesis separating the equation on either side identifies an absolute value function. Option B is the only one with this indication.

B. f(x) = | x + 61 |

There are two ways to answer this equation;

1.f(x) = - (x + 61)

2.f(x) = x + 61

Hence,f(x) = | x + 61 | function is a translation of the parent absolute value function.

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Explanation:

We want the relative frequency of the purple candies.

There are 16 purple out of 18+20+10+16 = 64 total

Divide the values to get 16/64 = 0.25

Exactly 25% of the candies are purple. This converts to the fraction 1/4.

The correct answer is 25%

First calculate the the total number of frequency

18+20+10+16

= 64

The total number of frequency is 64

Hence the relative frequency of purple is 16/64

Therefore , relative frequency of purple is 1/4 = 0.25

Therefore 25% of purple candies are there

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Answer:

4

Step-by-step explanation:

35-10=25

25÷5.75= 4.3

Answer:

4 and 7/12

Step-by-step explanation:

This is addition with fractions.

We must convert to the same denominator.

1/3 and 1/4 becomes 4/12 and 3/12

This makes 7/12

1 add 3 add 7/12 is 4 and 7/12

Answer:

24

Step-by-step explanation:

Hello there!

To determine the amount (percentage) as from our question above, we have to divide the given percentage by 100% (original percentage) and then multiply by 120.

This is as shown below;

[tex] \frac{20\%}{100\%} \times 120 \\ \\ = 0.2 \times 12 \\ = 24[/tex]

. ° . = 24 <<<<<< Ans

I hope this helps.

Have a nice studies.

The scale factor have been categorized into Expansion and Contraction.

It is the measure by which two figures are same in appearance but different in size.

It can be positive or negative as the figure is getting bigger or smaller.

Different scale factors are given and it has been asked they describe which type of dilation.

1.  -2/3  This will contract the figure

2. 3.25 This shows expansion

3. 2/3 This will contract the figure

4. -3 This will expand but the image will be form on the other side of Center of Enlargement.

Therefore the scale factor have been categorized into Expansion and Contraction.

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Answer:

y= -2/3x - 4

Step-by-step explanation:

the 2/3 comes from going up 2 spaces and over left 3 spaces. the b is negative 4 because of where it falls. the line is negative because of the direction it is in.

The number of regular cones sold on Wednesday is 60, while the number of deluxe ones sold is 26.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of regular cones sold be x, and the number of Deluxe cones sold be y. Therefore, total number of cones sold can be written as,

x + y = 86

x = 86 - y

Now, the total money collected can be written as,

5x + 9y = 534

5(86 - y) + 9y = 534

430 - 5y + 9y = 534

4y = 104

y = 26

substitute the value of y in the first equation,

x = 86 - 26

x = 60

Hence, the number of regular cones sold on Wednesday is 60, while the number of deluxe ones sold is 26.

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The rule for the linear function that describes the length of the vine is L = 1.3 + 0.2d

The number of days it would take the vine to grow to be 10.3 inches long is 45 days

From the question, we are to determine a linear function that describes the situation

From the given information,

Then vine is 1.3 inches long now

and it grows 0.2 inches a day

∴ After the days, the vine will increase by 0.2d in length

Then,

If L represents the length of the vine, d represent the number of days

The length of the vine after d number of days will be

L = 1.3 + 0.2d

Hence, the rule for the linear function that describes the length of the vine is L = 1.3 + 0.2d

Now, we are to determining the number of days it will take the vine to grow to be 10.3 inches long

Using the above linear function

L = 1.3 + 0.2d

10.3 = 1.3 + 0.2d  

0.2d = 10.3 - 1.3

0.2d = 9

d = 9 / 0.2

d = 45

Hence, the number of days it would take the vine to grow to be 10.3 inches long is 45 days

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The probability of having a height that is between 158 cm and 163 cm is 0.69011 and the value of x is 169 centimeters

The given parameters are:

Calculate the z-scores at x = 158 and x = 163 using:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

So, we have:

[tex]z = \frac{158 - 161}{6} = -0.5[/tex]

[tex]z = \frac{163 - 161}{6} = 0.33[/tex]

The probability is then represented as:

P(158 ≤ x ≤ 161) = P(-0.5 ≤ z ≤ 0.33)

Using the z table, we have:

P(158 ≤ x ≤ 161) =  0.69011

Hence, the probability of having a height that is between 158 cm and 163 cm is 0.69011

The probability is represented as:

P(X ≥ x) = 1%

Express as decimal

P(X ≥ x) = 0.10

The z-score at p = 0.10 is:

z = 1.282

Substitute z = 1.282 in [tex]z = \frac{x - \mu}{\sigma}[/tex]

[tex]1.282 = \frac{x - \mu}{\sigma}[/tex]

Make x the subject

[tex]x = 1.282\sigma + \mu[/tex]

Substitute values for standard deviation and mean

x = 1.282 * 6 + 161

Evaluate

x = 168.692

Approximate

x = 169

Hence, the value of x is 169 centimeters

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Answer:

900π

Step-by-step explanation:

Hello!

The radius is represented by the function [tex]r(t) = 15\sqrt{t +2}[/tex].

The radius of the ripple can be found when [tex]t=2[/tex]

Solve:

The radius of the ripple is 30 inches

The area of a circle is calculated by the formula [tex]A = \pi r ^2[/tex]

Given the radius is 30, we can find the area of the circle.

Solve:

Step-by-step explanation:

both halves of a diagonal must be equal.

so,

8b - 30 = 6b + 6

2b = 36

b = 18

and

9a - 13 = 5a + 5

4a = 18

a = 18/4 = 4.5

Answer:

i can't send full page of it sorry

The equation y = 15000 - 950x best models the depreciation.

Option C is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The equation y = 15000 - 950x.

Here, y represents the value of the car after x years.

The initial value of the car is $15,000, which means the value of the car at x = 0 is $15,000.

The car depreciates by $950 each year, so after one year, the value of the car will be $15,000 - $950 = $14,050.

After two years, the value of the car will be $14,050 - $950 = $13,100, and so on.

This linear relationship between the value of the car and the number of years can be modeled by the equation y = 15000 - 950x,

where 15000 is the initial value and -950x represents the amount of depreciation each year.

Thus,

The equation y = 15000 - 950x best models the depreciation.

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