Point A is the incenter of triangle DEF. Point A is the incenter of triangle D E F. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Y, and A Z. Which must be true? Select three options

The given equation is rearranged to obtain 9x - 1 - (41 - 5x) = 0. By simplifying and solving the equation, we get x = 3.

To solve this equation, we first simplify it by subtracting what is to the right of the equal sign from both sides of the equation. This gives us 9x - 1 - 41 + 5x = 0, which simplifies to 14x - 42 = 0. We then pull out the like factor of 14 to obtain 14(x - 3) = 0.

Next, we use the zero product property to find the values of x that make the equation true. We know that 14 can never equal 0, so we focus on the expression inside the parentheses. Setting x - 3 equal to 0, we get x = 3.

Therefore, the solution to the given equation is x = 3.

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Complete Question:

Simplify 9x-1=41-5x.

Answer:

Step-by-step explanation:

area of rectangle=120

find area of CPD

area=1/2  (area of the rectangle)

area =  1/2×120=60

The area of triangle CPD IS 30 square units.

If the area of the rectangle is 120, then the area of triangle CPD is 30.

The area of a rectangle is given by the formula:

Area = length × width

In this case, the length of the rectangle is 120/width.

The area of a triangle is given by the formula:

Area = (1/2) × base × height

The base of triangle CPD is the width of the rectangle, and the height of triangle CPD is half the length of the rectangle.

Therefore, the area of triangle CPD is:

(1/2) × width × (120/width) = 30

So the answer is 30.

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Answer: 23, 27,29

Those im absolutely positive about.

Im not sure abt the rest

Step-by-step explanation:

Answer:

\(\dfrac{2}{3}\)

Step-by-step explanation:

To find the scale factor of the dilation of a figure, simply divide the x-value (or y-value) of a vertex of the dilated image Q'R'S'T' by the x-value (or y-value) of the corresponding vertex of the pre-image QRST.

\(\implies \sf Scale\;factor=\dfrac{x_{Q'}}{x_{Q}}=\dfrac{-2}{-3}=\dfrac{2}{3}\)

\(\implies \sf Scale\;factor=\dfrac{y_{T'}}{y_{T}}=\dfrac{4}{6}=\dfrac{2}{3}\)

Therefore, the scale factor is 2/3.

To find the scale factor of the dilation of a figure, first find the lengths of corresponding sides using the distance formula.

\(\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}\)

From inspection of the given diagram:

\(\implies QR=\sqrt{(x_R-x_Q)^2+(y_R-y_Q)^2}\)

\(\implies QR=\sqrt{(3-(-3))^2+(6-9)^2}\)

\(\implies QR=\sqrt{(6)^2+(-3)^2}\)

\(\implies QR=\sqrt{36+9}\)

\(\implies QR=\sqrt{45}\)

\(\implies QR=3\sqrt{5}\)

From inspection of the given diagram:

\(\implies Q'R'=\sqrt{(x_{R'}-x_{Q'})^2+(y_{R'}-y_{Q'})^2}\)

\(\implies Q'R'=\sqrt{(2-(-2))^2+(4-6)^2}\)

\(\implies Q'R'=\sqrt{(4)^2+(-2)^2}\)

\(\implies Q'R'=\sqrt{16+4}\)

\(\implies Q'R'=\sqrt{20}\)

\(\implies Q'R'=2\sqrt{5}\)

To find the scale factor of dilation that maps QRST onto Q'R'S'T', divide the length of Q'R' by the length of QR:

\(\implies \dfrac{Q'R'}{QR}=\dfrac{2\sqrt{5}}{3\sqrt{5}}=\dfrac{2}{3}\)

Therefore, the scale factor is 2/3.

The probability that the sample mean will be less than 200 pounds is approximately 0.9015 or 90.15%.

Step-by-step explanation:

To solve this problem, we can use the central limit theorem, which states that the sampling distribution of the mean of a large sample (n >= 30) will be approximately normal, regardless of the distribution of the population.

We are given that the population mean is 196 pounds and the standard deviation is 22 pounds. The sample size is 50, which is large enough to apply the central limit theorem.

To find the probability that the mean of the sample will be less than 200 pounds, we need to standardize the sample mean using the formula:

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (200 - 196) / (22 / sqrt(50)) = 1.59

Now we need to find the probability that a standard normal variable is less than 1.59. We can use a standard normal table or calculator to find this probability, which is approximately 0.944.

Therefore, the probability that the mean of the sample will be less than 200 pounds is 0.944 or 94.4% (rounded to one decimal place).

So, we can say that there is a 94.4% chance that the mean weight of 50 randomly selected individuals will be less than 200 pounds.

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The number of ways to draw four marbles from the bag is 330.

The number of ways to draw four marbles if two must be red and two must be white from the bag is 150.

The number of ways to draw four marbles if all must be the same color from the bag is 20.

To find the number of ways the concept of combination is used. The formula for finding combination is as follows,
\(^nC_r=\frac{n!}{r!(n-r)!}\)

Where C is for combination, n is number of terms out of which r is selected terms, and ! is a sign of factorial.

Now, finding the number of ways to draw four marbles from the bag,

Total number of marbles = 5 + 6 = 11

Here, n = 11 and r = 4, so putting the values in the formula,

\(^{11}C_4=\frac{11!}{4!(11-4)!}\\\\=\frac{11\times10\times9\times8\times7!}{4\times3\times2\times1\times7!} \\\\=330\)

Similarly, now finding the number of ways to draw four marbles if two must be red and two must be white from the bag,

Here, n = 5 for red and r = 2 and n = 6 and r = 2, so putting the values in the formula,

\(^{5}C_2\times^{6}C_2=\frac{5!}{2!(5-2)!}\times\frac{6!}{2!(6-2)!}\\\\=\frac{5\times4\times3!}{2\times1\times3!}\times \frac{6\times5\times\times4!}{2\times1\times4!}\\\\=150\)

Similarly, now finding the number of ways to draw four marbles if all must be the same color from the bag,

Here, n = 5 for red and r = 2 and n = 6 and r = 2, so putting the values in the formula,

\(^{5}C_4+^{6}C_4=\frac{5!}{4!(5-4)!}+\frac{6!}{4!(6-4)!}\\\\=\frac{5\times4!}{4!\times1!}+\frac{6\times5\times\times4!}{4!\times2\times1}\\\\=5+15\\\\=20\)

Therefore, The number of ways to draw four marbles from the bag is 330 and the number of ways to draw four marbles if two must be red and two must be white from the bag is 150 and the number of ways to draw four marbles if all must be the same color from the bag is 20.

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Answer:

it that all the question

Step-by-step explanation:

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol \(^nC_{r}\).

There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.

So the 3 software engineers =3! ways, 2 nurses =2! ways,

doctor =1! way , 2 technicians =2! ways.

We must determine how many different configurations are possible so that no two pieces of software may coexist.

In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.

\(We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.\)

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Polar Coordinates

Given a point in coordinates (r, θ), the equivalent point in cartesian coordinates (x, y) can be found as:

x = r cos θ

y = r sin θ

We are given the point:

Converting to cartesian coordinates:

The cartesian coordinates are:

Answer:

Option D

Step-by-step explanation:

By applying Pythagoras theorem in triangle ABC,

(Hypotenuse)²= (Leg 1)² + (Leg 2)²

AC² = AB² + BC²

AC² = (40 - 15)² + (80 - 75)²

AC² = (25)² + 5²

AC² = 650

AC = √650

AC = 25.495 ft

Since, area of a rectangle = Length × Width

Therefore, area of the garden = 25.495 × 6

                                                  = 152.97

                                                  ≈ 153 ft²

Since, 150 is very close to 153, approximate area of the rectangular garden is 150 ft².

Option D is the answer.

The third-degree Maclaurin polynomial for f(x) = sin(x) is P3(x) = x - (x^3) / 6.

To find the nth Maclaurin polynomial for the function f(x) = sin(x) when n = 3, we need to compute the polynomial up to the third-degree term.

The Maclaurin polynomial for a function f(x) centered at x = 0 is given by the formula:

Pn(x) = f(0) + f'(0)x + (f''(0)x^2) / 2! + (f'''(0)x^3) / 3! + ...

Let's calculate the nth Maclaurin polynomial for f(x) = sin(x) when n = 3:

First, we find the values of the function and its derivatives at x = 0:

f(0) = sin(0) = 0

f'(x) = cos(x), so f'(0) = cos(0) = 1

f''(x) = -sin(x), so f''(0) = -sin(0) = 0

f'''(x) = -cos(x), so f'''(0) = -cos(0) = -1

Using these values, we can write the Maclaurin polynomial:

P3(x) = 0 + 1x + (0x^2) / 2! + (-1x^3) / 3!

Simplifying further, we have:

P3(x) = x - (x^3) / 6.

Therefore, the third-degree Maclaurin polynomial for f(x) = sin(x) is:

P3(x) = x - (x^3) / 6.

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After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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answer:

$4.24

explanation:

hope this helped <3

Given the equation 9sin θ - 1 = 0  we have no solution for t when θ=2π

To solve for t when θ=2π and 9sin θ - 1 = 0, we can use the following steps:

Step 1: Substitute the value of θ into the equation:
9sin(2π) - 1 = 0

Step 2: Simplify the equation by using the trigonometric identity sin(2π) = 0:
9(0) - 1 = 0
-1 = 0

Step 3: Since -1 ≠ 0, there are no solutions for t when θ=2π.

Therefore, the answer is that there are no solutions for t when θ=2π. This can be written as t = ∅, where ∅ represents the empty set. Note that the answer does not need to be rounded to two decimal places, as there are no solutions.

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Answer:

10 or 70

Step-by-step explanation:

10= 40-30=10

70=40+30=70

The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.

To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.

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Answer:

9.42

Step-by-step explanation:

Breaking the phrase down:

'Nine' would be the number 9 in the ones place.

'And' represents the decimal in a number. ('.')

'Forty-Two Hundredths" is 0.42.

So, "nine and forty-two hundredths" would be 9.42.

Hope this helps.

When a cylinder is sliced in such a way that the plane passes through the cylinder in a slanted direction without going through either base, the resulting cross section is an elliptical shape.

To visualize this, imagine a cylinder with circular bases. When a plane intersects the cylinder in a slanted direction, it cuts through the curved surface of the cylinder, creating an elliptical cross section.

The exact shape and size of the elliptical cross section will depend on the angle at which the plane intersects the cylinder and the specific orientation of the cylinder. The major axis of the resulting ellipse will be parallel to the slanted direction of the plane, while the minor axis will be perpendicular to it.

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Answer:

x=2/3

Step-by-step explanation:

25-(3x+5)=2(x+8)+x

25-3x-5=2x+16+x

20-3x=3x+16

20-3x-3x=16

20-6x=16

6x=20-16

6x=4x=4/6

simplify

x=2/3

Answer:

x=2/3

Step-by-step explanation:

Answer:

66.99 cm³

Step-by-step explanation:

V=πr²h /3

V = (3.14)(2)²(16)/3 = 66.99 cm³

Answer:

8x.

Step-by-step explanation:

coordinates: (3,10) (5,26)

use slope formula (y2 - y1/x2-x1)

26-10/5-3

16/2

= 8

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Given

The current figure is in quadrant II.

Explanation

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

Solution

Therefore, the figure reflected on the x-axis would be in quadrant III.

Answer:

24 ft^2

Step-by-step explanation:

The small aquarium:

1 * 3 * 2 = 6 ft^2

The large aquarium

(1 + 1) * (3 + 2) * (2 + 1)

2 * 5 * 3 = 30 ft^2

Difference between the larger aquarium and the smaller aquarium:

30 - 6, or 24.

This means that the answer to this question is a, 24 ft^2

Answer:

Angelica’s house is 7.81 miles from the gas station

Step-by-step explanation:

By pythogorean theorem, AG² = AP² + GP²

A (4,3), G(10,8), P(10,3)

Since AP lies along the x axis, the distance is calculated using the x coordinates of A and P

AP = 10 - 4 = 6

GP lies along the y axis, so the distance is calculated using the y coordinates of G and P

GP = 8 - 3 = 5

AG² = 6² + 5²

= 36 + 25

AG² = 61

AG = √61

AG = 7.81

Answer:

2x+3y=5

hope this helps if its wrong tell me and I'll fix it thank you!.