Triangle ABC is rotated 180º using the origin as the center of rotation. On a coordinate plane, triangle A B C has points (negative 4, negative 3), (negative 5, negative 2), (negative 3, negative 2). Triangle A prime B prime C prime has points (4, 3), (5, 2), (3, 2). Which sequence of transformations will produce the same result? a translation up 4 and then a reflection over the y-axis a translation up 4 and then a translation right 6 a reflection over the x-axis and then a reflection over the y-axis a translation right 6 and then a reflection over the x-axis

The radius of the semicircle that will make the rectangular region a maximum is 40 feet.

The physical fitness room consists of a rectangular region with a semicircle at each end, and the perimeter of the room is a 200ft running track. To maximize the rectangular region, you need to find the radius of the semicircle.

Let the radius of the semicircle be r and the length and width of the rectangle be L and W, respectively. Since there are two semicircles, the total length of their circumferences is equal to the full circle with radius r. Therefore, the perimeter of the room can be expressed as:

Perimeter = L + 2W + πr = 200

To maximize the rectangular area (A = L * W), we should express either L or W in terms of r and use calculus to find the maximum. Let's express W in terms of r:

W = (200 - L - πr) / 2

Now, we can find the area:

A = L * W = L * (200 - L - πr) / 2

To find the maximum area, take the derivative of A with respect to L and set it to zero:

dA/dL = (200 - 2L - πr) / 2 = 0

Solve for L:

L = (200 - πr) / 2

Since L is the length of the rectangle, it must equal the diameter of the semicircles (2r):

2r = (200 - πr) / 2

Solve for r:

4r = 200 - πr
5r = 200
r = 40 ft

Thus, the radius of the semicircle that will make the rectangular region a maximum is 40 feet.

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Answer:

Step-by-step explanation:

If they are vertical angles, they are equal.

5x - 24 = 3x + 24                      Add 24 to both sides

5x -24 +24 = 3x + 24 + 24       Combine

5x =   3x + 48                           Subtract 3x

5x - 3x = 3x-3x + 48                Combine

2x = 48                                    Divide by 2                                

x = 24

<A =5*24 - 24

<A = 96

Answer: x= 24

Step-by-step explanation: (5x-24)+(3x+24)=180 and when you solve this equation you get 24. Hopes this helps love u ❤️

Answer: 9

Step-by-step explanation: We know how many boys there are (6) and girls (54). But we need to fill out all of the possible ratios of boys to girls.

To do that, we divide 54 by 6.

54 / 6 = 9

Answer: a=-0.75

Step-by-step explanation:

14a - (2a +9)=2/3 (12a-18)​

14a - 2a -9=2/3 * 6(2a-3)​

12a-9=2*6/3 (2a-3)​

12a-9=2*2(2a-3)​

12a-9=4(2a-3)​

12a-9=8a-12

4a-9=-12

4a=-3

a=-3/4

a=-0.75

Answer:

Is there a type of equation your looking for or do you want the straight up answer?

Step-by-step explanation:

Answer:

(1, 7)

Step-by-step explanation:

y = 3x + 4

y = 6x + 1

6x + 1 = 3x + 4 ⇒ x = 1

y = 3(1) + 4 = 7

(1, 7)

Answer:

(1, 7)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

y = 3x + 4

y = 6x + 1

Step 2: Solve for x

Step 3: Solve for y

Answer:180.1 feet

Step-by-step explanation:

Using tan to find the answer; Opposite/Adjacent = 62/x

tan19=62/x

xtan19=62 (cross multiply)

xtan19/tan19=62/tan19 (Divide each side by tan19)

x=62/tan19=180.0611=180.1 feet

The initial value problem is:

\(y(t) = -\frac{1}{12}e^{-3t} + \frac{1}{4}e^{t} -\frac{1}{4}e^{-t}\)

This is the solution to the differential equation \(y" + 2v' - 3y = e^{-t}\) with the initial conditions y(0) = v'(0) = 0.

To solve the given initial value problem, we can follow these steps:

The characteristic equation corresponding to the given differential equation is:

Solving for r, we get:

The general solution to the homogeneous equation\(y" + 2v' - 3y = 0\) is given by:

The particular solution, we can use the method of undetermined coefficients. Since the forcing function e^{-t} is an exponential function with the same form as the homogeneous solution e^{-3t}, we can assume a particular solution of the form:

Taking the first and second derivatives of \(y_p(t)\), we get:

Substituting these into the differential equation, we get:

Simplifying, we get:

The general solution to the differential equation is:

The values of c1 and c2, we can use the initial conditions y(0) = v'(0) = 0. Substituting these into the general solution and simplifying, we get:

Solving these equations simultaneously, we get:

We first find the characteristic equation by substituting y(t) = e^{rt} into the homogeneous differential equation, where y(t) is the solution to the homogeneous equation and r is a constant. This leads to the characteristic equation r^2 + 2r - 3 = 0. The roots of this equation give us the homogeneous solution to the differential equation.

We use the method of undetermined coefficients to find the particular solution. We assume a particular solution of the form y_p(t) = Ae^{-t}, where A is a constant to be determined. We then substitute this into the differential equation and solve for A.

We combine the homogeneous and particular solutions to obtain the general solution. We use the initial conditions to find the values of the constants c1 and c2.

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The probability of A and B occurring simultaneously (P(A ∩ B)) is c. 0.00.

In this scenario, A and B are stated to be mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa.

Given that P(A) = 0.4 and P(B) = 0.5, we can deduce that the probability of A occurring is 0.4 and the probability of B occurring is 0.5. Since A and B are mutually exclusive, their intersection (A ∩ B) would be an empty set, meaning no outcomes can be shared between the two events. Therefore, the probability of A and B occurring simultaneously, P(A ∩ B), would be 0.

To further clarify, let's consider an example: Suppose event A represents flipping a coin and getting heads, and event B represents flipping the same coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, the intersection of events A and B would be empty. Therefore, the probability of getting both heads and tails in the same coin flip is 0.

In this case, since events A and B are mutually exclusive, the probability of their intersection, P(A ∩ B), is 0.

Therefore, the correct answer is: c. 0.00

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Answer:the first one

Step-by-step explanation:

Answer:

To solve this problem, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Since the lines a and b intersect at point D, we can form two triangles: ADB and CDB. We can label the angles as shown in the figure below.

A

/ \

/   \

/     \

/       \

/         \

/           \

B-----------D-----------C

(5z + 8)°   (4z + 20)°

In triangle ADB, we have:

(5z + 8) + (4z + 20) + z = 180

Simplifying and solving for z, we get:

10z + 28 = 180

10z = 152

z = 15.2

Therefore, the value of z is 15.2 degrees.

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Hz (Hertz) is a unit of frequency, which measures the number of events or occurrences of a certain phenomenon per second. In this case, the tape timer creates 28 dots per second, which means that the frequency of dot creation is 28 Hz.

To find the time interval between 3 successive dots, we need to calculate the time it takes for the tape timer to create 3 dots. This can be done by dividing the total time by the number of dots created.

Since the tape timer creates 28 dots per second, the time interval between 3 dots can be calculated as follows:

Time interval = 1 second / 28 dots = 1/28 seconds

So, the time interval between 3 successive dots created by the tape timer is 1/28 seconds, which is the amount of time that elapses between the creation of each dot.

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The y-intercept and the horizontal asymptote of g(x) = 7ˣ + 2 is (a) (0, 3) ; y = 2

The equation of the function is given as

g(x) = 7ˣ + 2

To calculate the y-intercept, we set x = 0

So, we have

g(0) = 7⁰ + 2

Evaluate the exponent

g(0) = 1 + 2

Evaluate the sum

g(0) = 3

So, we have

(x, y) = (0, 3)

The equation of the function is given as

g(x) = 7ˣ + 2

To calculate the horizontal asymptote, we set 7ˣ

So, we have

y = 0 + 2

Evaluate the sum

y = 2

Hence, the solution is (a) (0, 3) ; y = 2

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The required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.

Asymptote is the line on the curve that does not intersect the curve but passes as near to the maximum and minimum of the graph.

Here,
The y-intercept of the given function is evaluated as put the x coordinate to zero,
So,
g(0) = 1 + 2
g(0) = 3

Now, the horizontal asymptote is a line that passes near to the line but does not intersect with the curve,
So,
Terminating the x compositon of the function 7ˣ = 0 the rest will be the horizontal asymptote,
y = 7ˣ + 2
y =  0 + 2
y = 2

Thus,  the required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.

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Step-by-step explanation:

OR

The simplified expression of -15r + 3(2s - 4r) is 3(-9r + 2s)

The expression can be simplified as follows:

-15r + 3(2s - 4r)

open the brackets

-15r + 6s - 12r

let's combine the like terms

-15r - 12r + 6s

Therefore,

-15r - 12r + 6s

-27r + 6s

-27r + 6s = 3(-9r + 2s)

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Answer:

The answer is 1 1/4 or a.

Step-by-step explanation:

Basicallly percents are based of 100% so there is a 100% which would be a whole then there is only 25% and if you take 4 quarters and each quarter is 25 cents and there is 4 quarters in a whole that would be 1/4. You add the 1 whole and the 1/4 to get 1 1/4.

Hope this helps, tried to explain it in the best way I can.

Answer:

Area = 867 meters

Step-by-step explanation:

You have a rectangle. This means opposite sides are equal. If you set these expressions equal to each other, you will get two equations with two unknowns, x and y. Next, solve the system of equations to find x and y. Then, use the values to find the length and width of the rectangle. Last, multiply length × width to find the area.

The distance from lake b to camp is 310 km and the direction of lake b to camp is 57° S of W.

Distance is a numerical value. The length between the two points is measured by distance. The face or position of an object or person can be said by direction.

There are four cardinal directions which are the main four compass directions. The four directions are North, East, West and South. North-East, North-West, South-East and South-West also come under directions.

As per the question,

With a scale of unit 1, the vector from the base camp to the lake to the vector connecting lakes a and b is graphically represented.

Therefore, 310 km is the distance from the lake b to base camp and 57.0° south of west is the direction of the plane.

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Answer:

  B' = (18, -16)

Step-by-step explanation:

Dilating means to stretch or shrink a figure. The scale factor tells us how much we are stretching or shrinking. The scale factor is 2, so the coordinates are multiplied by 2.

There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Answer:

32= 2×2×2×2×2=2 power 5

Answer:

\(2^{-5}\)

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

Given

\(\frac{1}{32}\)

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

= \(2^{-5}\)

B OR D IT WAS confusing.

Step-by-step explanation:

I tried different equations multiple ways I'm pretty sure I did it wrong

Answer:

Here, hope that answers your question

The function g tells us the amount of remaining water.

The variable x gives us how much time has passed.

Given g(840) = 0,

We can see that the variable x is 840 and the functional value of g is 0.

This means at after 840 minutes the amount of water in the pool will be zero.

Looking at the choices, the correct answer is >>>

The excel statement to estimate the test average of these 4 grades is -

An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.

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The student's errors are (41)² or (√41)² instead of 41, similarly,  (29)² or (√29)² instead of 29.

The correct equation in standard form of the ellipse x²/b² + y²/a² = 1.

The standard equation of an ellipse is x² a² + y² b² = 1.

x² a² + y² b² = 1. this equation defines an ellipse centered at the origin.

If a > b , a > b , the ellipse is stretched further in the horizontal direction, and if b > a , b > a , the ellipse is stretched further in the vertical direction

A student claims that an equation of the ellipse shown is x²/41 + y²/29 = 1.

The standard equation of an ellipse is x² a² + y² b² = 1.

If we divide by a² * b²,

The final equation is

x²/b² + y²/a² = 1.

If compare with  x²/41 + y²/29 = 1.

We find that,

So, the student's errors are (41)² or (√41)² instead of 41, similarly,  (29)² or (√29)² instead of 29.

Therefore, the correct equation in standard form of the ellipse x²/b² + y²/a² = 1.

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Answer:

D

Step-by-step explanation:

There are 2 triangles on the sides. On the bottom we have one rectangle, than we have the tilted rectangle, and the straight rectangle.

The answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5).

A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function defined by

s(t) = -16t² + 800t + 600.

To find out

(a) From what height was the projectile fired

Given height functions: s(t) = -16t² + 800t + 600

Now,

\(s^{'}(t)\) - -32t+800

(b) Now, to find the time it will attain maximum height,

\(s^{'}(t)\) = 0

-32t = -800

t = 25 seconds

(c) The maximum height it will reach

= \(-16*(25)^{2} + 800*25+600\)

= -10000+20000+600

= 10,600 feet

(d) Between what two times (in seconds, to the nearest tenth) will it be more than 5000 ft above the ground

By putting x = 3

\(P(3) = 4*(3)^{3}-50 * (3)^{2}-8*3+6\)

= 108-90-24+6

= 114-114

= 0

Therefore x = 3 is a zero of P(x)

(e) How long to the nearest tenth of a second will the projectile be in the air

Now, factoring,

\(f(x) = x^{3}+3x^{2} -13x-15\\ \\= x^{3}+x^{2} +2x^{2}+2x-15x-15\\ \\ = (x+1)(x^{2} +5x-3x-15)\\\\= (x+1)(x(x+5)-3(x+5))\\\\=(x+1)(x-3)(x+5)\)

Hence the answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5)

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