Triangle PQR has vertices P(3, 5), Q(-2, 6) and R(8, -1). Give the translation rule (x, y) → (x + 4, y – 5). What will Q’ (, ) be

Answers

Answer 1

Answer:

To find the image of point Q after applying the given translation rule, we need to apply the rule to the coordinates of point Q(-2, 6).

Using the translation rule (x, y) → (x + 4, y - 5), we can apply the rule to the coordinates of point Q:

Q' = (-2 + 4, 6 - 5)

= (2, 1)

Therefore, the image of point Q after the translation is Q'(2, 1).

Related Questions

The tree diagram shows the sample space of two-digit numbers that can be created using the digits 9,7,1, and 8.What is the probability of choosing a number from the sample space that contains both 7 and 8.

Answers

The probability of selecting a number that contains 7 and 8 is 1/8

Here, we have,

The tree diagram shows the sample space of two-digit numbers that can be created using the digits 9,7,1, and 8.

so, we get,

There are 16 samples given.

now, we have to find that the probability of choosing a number from the sample space that contains both 7 and 8.

here, the number of this event = 2

so, we get,

The probability of selecting a number that contains 7 and 8 is:

2/16 = 1/8

Hence, The probability of selecting a number that contains 7 and 8 is 1/8

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Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A ∪ B' ? Your Answer:

Answers

Consequently, there are 5 elements in A B'.

Given the following definitions:

U = {1, 2, 3, 4, 5, 6, 7}A = {1, 2, 4, 5}B = {1, 3, 5, 7}

The complement of a set B is the set of all elements that belong to the universal set U but not to B.

A’ = {x | x ∈ U and x ∉ A} = {3, 6, 7}B’ = {x | x ∈ U and x ∉ B} = {2, 4, 6}

The union of sets A and B is the set of all elements that belong to set A or set B, or both.

A ∪ B = {x | x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 7}A ∪ B'

= {x | x ∈ A or x ∈ B’}

= {1, 2, 4, 5, 6}

Therefore, the number of elements in A ∪ B' is 5.

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What’s the equation of the trig graph?

Answers

The equation for the trigonometric graph is:

y = 4 cos(x/2)

We have given is a graph with maximum point at 4 and minimum point at -4 with x intercepts are = -π, π, 3π, 5π, 7π, 9π, 11π.....

We need to identify the equation of the trigonometric graph.

To identify the equation of the given graph with maximum point at 4 and minimum point at -4, we can start by analyzing the characteristics of the cosine function.

The cosine function oscillates between 1 and -1 and has a period of 2π. The general form of the cosine function is:

y = A cos(Bx + C) + D

where A represents the amplitude, B represents the frequency (1/period), C represents the phase shift, and D represents the vertical shift.

Given that the maximum point is at 4 and the minimum point is at -4, we can determine the amplitude, A, to be 4.

y = 4 cos(Bx + C) + D

Next, let's consider the x-intercepts given as -π, π, 3π, 5π, 7π, 9π, 11π, and so on. The x-intercepts of the cosine function occur when the angle inside the cosine function, Bx + C, is equal to (2n + 1)π/2, where n is an integer.

We can start by analyzing the first x-intercept, which is -π. Setting Bx + C equal to -π, we have:

B(-π) + C = -π

Simplifying, we get:

B = -1 - C/π

Similarly, for the x-intercepts at π, 3π, 5π, 7π, 9π, 11π, and so on, we can write the following equations:

Bπ + C = π

B(3π) + C = π

B(5π) + C = π

B(7π) + C = π

B(9π) + C = π

B(11π) + C = π

Now, notice that these equations are satisfied when C is an odd multiple of π, and B = 1/2.

Therefore, we can conclude that:

C = (2n + 1)π

and

B = 1/2

Substituting these values into the equation, we have:

y = 4 cos((1/2)x + (2n + 1)π) + D

Finally, considering the vertical shift, we know that the maximum point is at 4 and the minimum point is at -4. Since the amplitude is 4, the vertical shift is the average of the maximum and minimum points, which is 0. Therefore, D = 0.

The final equation for the trigonometric graph is:

y = 4 cos(x/2)

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Answer(s):

[tex]\displaystyle y = 4sin\:(\frac{1}{2}x + \frac{\pi}{2}) \\ y = -4cos\:(\frac{1}{2}x \pm \pi) \\ y = 4cos\:\frac{1}{2}x[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{4\pi} \hookrightarrow \frac{2}{\frac{1}{2}}\pi \\ Amplitude \hookrightarrow 4[/tex]

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{4\pi} \hookrightarrow \frac{2}{\frac{1}{2}}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:\frac{1}{2}x,[/tex] in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \pi\:units[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \pi\:units,[/tex] which means the C-term will be negative; so, by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\pi} = \frac{-\frac{\pi}{2}}{\frac{1}{2}}.[/tex] So, the sine equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(\frac{1}{2}x + \frac{\pi}{2}).[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-2\pi, -4],[/tex] from there to [tex]\displaystyle [-6\pi, -4],[/tex] they are obviously [tex]\displaystyle 4\pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 4\pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, & the first aid station, F. The campground is 0.35 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular.

If the path from the park ranger station to the campground is 0.65 mile, determine and state, to the nearest
hundredth of a mile,
a. Find the length of PL

Answers

Whwn the line of sight from the park ranger station, P, to the lifeguard chair, L, the length of PL is 0.76 miles.

How to calculate the value

It should be noted that since the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F, then the path from the park ranger station to the lifeguard chair is the hypotenuse of a right triangle with legs of 0.35 miles and 0.65 miles.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Therefore, the length of PL is equal to:

= ✓(0.35² + 0.65²)

= 0.76 miles.

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HELP NEEDED PLEASEEE

Answers

b) -x

explanation: The Middle Term of a Binomial Expansion is the term that comes in the middle of the expansion of the binomial, given by the Binomial Theorem. If the power of expansion of the sum or difference of two terms is an even number, then there is only one middle term. Otherwise, there are two middle terms.

What does 5^6 x 4=
.
Zzzzzzzzzz

Answers

62,500. Have a good day!!

62,000. I think. I could be wrong

You pick 7 digits (0-9) at random without replacement, and write them in the order picked. What is the probability that you have written the first 7 digits of your phone number? Assume there are no repeats of digits in your phone number. Give your answer as a fraction.

Answers

The probability of writing the first 7 digits of your phone number is 1/604,800.

Given data ,

To determine the probability of writing the first 7 digits of your phone number, we need to consider the total number of possible outcomes and the favorable outcomes.

Total number of possible outcomes:

When picking 7 digits without replacement from the set of 10 digits (0-9), the total number of possible outcomes is given by 10P7 (permutations of 10 objects taken 7 at a time):

10P7 = 10! / (10 - 7)! = 10! / 3! = 10 * 9 * 8 * 7 * 6 * 5 * 4 = 604,800.

Favorable outcomes:

To have written the first 7 digits of your phone number, you need to pick those specific digits in the correct order. Since the phone number has no repeated digits, there is only one specific order that satisfies this condition.

Therefore, the number of favorable outcomes is 1.

Probability:

The probability is given by the ratio of favorable outcomes to total possible outcomes:

Probability = Favorable outcomes / Total possible outcomes

= 1 / 604,800.

Hence, the probability is 1/604,800.

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Choose the function whose graph is given by

Answers

The function whose graph is given include the following: D. y = cosx + 1.

How to plot the graph of a cosine function?

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = acos(x - h) + k

Where:

a represents the amplitude.h represents the horizontal shift.k represents the vertical shift.

By critically observing the graph of the given cosine function, we can reasonably infer and logically deduce that the parent cosine function y = cosx was vertically shifted (translated) upward by 1 unit, in order to produce the transformed cosine function as follows;

y = cosx

g(x) = y + 1

g(x) = cosx + 1

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cos2theta + sin2theta = 0, solve for theta

Answers

Answer:

The solution for the original equation is:

theta = n pi and theta = (2n + 1)^pi/2, Where n is an integer.

Step-by-step explanation:

Rewrite the equation:

cos(2theta) + (sin(2theta) = 0

Use the double-angle formulas:

2 cos(theta) sin(theta) + 2 sin(theta) cos(theta) = 0

Factor out the common term:

2 sin(theta) cos(theta)(1 + 1) = 0

Simplify:

4 sin(theta) cos(theta) = 0

Set each factor to Zero:

For sin(theta) = 0.theta = n pi, Where n is an integer.

For cos(theta) = 0.theta = (2n + 1)^pi / 2, Where n is an integer

Draw a conclusion:

The solution for the original equation is:

theta = n pi, and theta = (2n + 1)^pi / 2, Where n is an integer.

Hope this helps!

Please helpppp

Which answers describe the shape below? Check all that apply. I put the attachment below

Answers

The given shape is a quadrilateral and a trapezoid.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

A trapezoid is a quadrilateral with at least one pair of parallel sides.

In a trapezoid, the parallel sides are called the bases of the trapezoid.

The other two sides are called the legs of the trapezoid.

The given shape is not a parallelogram because only one pair of sides are parallel and other sides are not.

Hence, the given shape is a quadrilateral and a trapezoid.

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A
-2+
Which graph represents the
function y = tan x?
B
2T
2T
D
-2+1
21
4+
ㅠ
2T
2πT

Answers

The graph that represents the function y= tanx is Option A.

What is the description of the above function?

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and negative infinity, creating a wave- like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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someone please help me solve this

Answers

Answer:

161.67 square feet

Step-by-step explanation:

The explanation is attached below.

Area of rectangle = length * width

=> Area of ABIJ = (7 * 6)ft^2 = 42 ft^2

=> Area of IJHG = (5 * 7)ft^2 = 35 ft^2
=> Area of HGCD = (7.81 * 7)ft^2 = 54.67 ft^2

=> Area of triangle = (EIH) = JFG = 1/2 * Base * height

EIH = 1/2 * 6 * 5 = 15 ft^2

JFG = 1/2 * 6 * 5 = 15 ft^2

Total area = (42 + 35 + 54.67 + 15 + 15)ft^2 = 161.67 ft^2

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Every year, the value of a condominium in Singapore appreciates by 15% of its value in the previous year. If the value of the condominium was $899300 in 2020, find its value in 2020.

Answers

Answer:

To find the value of the condominium in 2020, we can work backward from the given information. Since we know that the value appreciates by 15% each year, we can calculate the value for the previous year using the formula:

Value in previous year = Value in current year / (1 + appreciation rate)

Let's calculate the value of the condominium in 2020:

Value in 2021 = $899,300 / (1 + 0.15) ≈ $781,521.74

Value in 2020 = Value in 2021 / (1 + 0.15) ≈ $781,521.74 / (1 + 0.15) ≈ $678,309.34

Therefore, the value of the condominium in 2020 is approximately $678,309.34.

Step-by-step explanation:

Please help with these two questions)l!!

Answers

The integral of xe^(7x) dx is equal to (1/7) xe^(7x) - (1/49) e^(7x) + C, where C is the constant of integration.

The integral of x cos(8x) dx is equal to (1/8) x sin(8x) + (1/64) * cos(8x) + C, where C is the constant of integration.

We have,

To solve the given integrals using integration by parts, we follow the formula:

∫u dv = uv - ∫v du

Let's solve each integral step by step:

∫xe^(7x) dx ; u = x, dv = e^(7x) dx

Taking the derivatives and integrals:

du = dx

v = ∫e^(7x) dx = (1/7) * e^(7x)

Applying the integration by parts formula:

∫xe^(7x) dx = uv - ∫v du

= x * (1/7) * e^(7x) - ∫(1/7) * e^(7x) dx

= (1/7) * xe^(7x) - (1/49) * e^(7x) + C

And,

∫x cos(8x) dx ; u = x, dv = cos(8x) dx

Taking the derivatives and integrals:

du = dx

v = ∫cos(8x) dx = (1/8) * sin(8x)

Applying the integration by parts formula:

∫x cos(8x) dx = uv - ∫v du

= x * (1/8) * sin(8x) - ∫(1/8) * sin(8x) dx

= (1/8) * x * sin(8x) + (1/64) * cos(8x) + C

Therefore,

The integral of xe^(7x) dx is equal to (1/7) xe^(7x) - (1/49) e^(7x) + C, where C is the constant of integration.

The integral of x cos(8x) dx is equal to (1/8) x sin(8x) + (1/64) * cos(8x) + C, where C is the constant of integration.

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...................................................................................................

Answers

Answer:

Among them 4/5 Is correct answer.

Answer:

3/4

Step-by-step explanation:

..,...............

Find the area of the isosceles trapezoid.
10 cm
9 cm
18 cm
OA.126 cm²
OB.91 cm²
OC. 252 cm²
OD. 63 cm2

Answers

Step-by-step explanation:

therefore, the correct option should be A.

a cylindrical brass pipe is 600cm in length. Its outside diameter is 10cm, and its inside radius is 4. what is the total surface area of the pipe including the internal surface area

Answers

The total surface area of the cylindrical brass pipe, including the internal surface area, is approximately 34183.08 cm².

How to calculate the surface area

The formula for the surface area of a cylinder includes the curved surface area (CSA) and the two circular base areas.

1. Outer Surface Area:

The curved surface area (CSA) of a cylinder is given by the formula: CSA = 2πrh, where r is the radius and h is the height.

Given:

Outer diameter = 10 cm

Outer radius (R) = 10 cm / 2 = 5 cm

Height (h) = 600 cm

Outer CSA = 2π(5)(600) = 6000π cm²

The circular base areas can be calculated using the formula: Base area = πr², where r is the radius.

Outer base area = π(5)² = 25π cm²

Therefore, the total outer surface area is the sum of the curved surface area and the two circular base areas:

Total outer surface area = Outer CSA + 2 * Outer base area = 6000π + 2 * 25π = 6050π cm²

2. Inner Surface Area:

The inner radius (r) is given as 4 cm. We can use the same formulas to calculate the inner surface area.

Inner CSA = 2π(4)(600) = 4800π cm²

Inner base area = π(4)² = 16π cm²

Total inner surface area = Inner CSA + 2 * Inner base area = 4800π + 2 * 16π = 4832π cm²

Total surface area = Total outer surface area + Total inner surface area = 6050π + 4832π = 10882π cm²

To find the numerical value, we can use the approximation π ≈ 3.14:

Total surface area ≈ 10882 * 3.14 = 34183.08 cm²

Therefore, the total surface area of the cylindrical brass pipe, including the internal surface area, is approximately 34183.08 cm².

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Today, interest rates on 1-year T-bonds yield 1.8%, interest rates on 2-year T-bonds yield 2.6%, and interest rates on 3-year T-bonds yield 3.7%.

A.) If the pure expectations theory is correct, what is the yield on 1-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.

B.) If the pure expectations theory is correct, what is the yield on 2-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.

C. If the pure expectations theory is correct, what is the yield on 1-year T-bonds two years from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.

Answers

The yield on 1-year T-bonds one year from now, based on the pure expectations Theory, is approximately 0.0349 or 3.49%. the yield on 2-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0443 or 4.43%.the yield on 1-year T-bonds two years from now, based on the pure expectations theory, is 5%.

The pure expectations theory, which suggests that the yield on a bond for a particular period is determined by the market's expectation of future interest rates. The theory assumes that investors are indifferent between investing in shorter-term bonds and rolling over their investments or investing in longer-term bonds.

A.) To calculate the yield on 1-year T-bonds one year from now, we need to find the geometric average of the current yield on 1-year T-bonds and the expected yield on 1-year T-bonds two years from now. Let's assume the current yield on 1-year T-bonds is 3% and the expected yield on 1-year T-bonds two years from now is 4%.

Using the geometric average formula, we can calculate the yield as follows:

Yield = sqrt((1 + Current Yield) * (1 + Expected Yield)) - 1

= sqrt((1 + 0.03) * (1 + 0.04)) - 1

= sqrt(1.03 * 1.04) - 1

≈ sqrt(1.0712) - 1

≈ 0.0349

Therefore, the yield on 1-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0349 or 3.49%.

B.) To calculate the yield on 2-year T-bonds one year from now, we need to find the geometric average of the current yield on 2-year T-bonds and the expected yield on 2-year T-bonds two years from now. Let's assume the current yield on 2-year T-bonds is 4% and the expected yield on 2-year T-bonds two years from now is 5%.

Using the geometric average formula, we can calculate the yield as follows:

Yield = sqrt((1 + Current Yield) * (1 + Expected Yield)) - 1

= sqrt((1 + 0.04) * (1 + 0.05)) - 1

= sqrt(1.04 * 1.05) - 1

≈ sqrt(1.092) - 1

≈ 0.0443

Therefore, the yield on 2-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0443 or 4.43%.

C.) To calculate the yield on 1-year T-bonds two years from now, we need to find the expected yield on 1-year T-bonds two years from now. Let's assume the expected yield on 1-year T-bonds two years from now is 5%.

The yield on 1-year T-bonds two years from now, based on the pure expectations theory, is equal to the expected yield, which is 5%.

Therefore, the yield on 1-year T-bonds two years from now, based on the pure expectations theory, is 5%.

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Question 2: Solve each of the equations below (a) x² + 6x +8=0 (d) y² + 3y -4 = 0 (g) y² - 10y + 25 = 0 (1) y² +10y + 24 = 0 (m) y² - 13y +22=0 (p) x² - 11x + 18 = 0 (s) m²-m-56=0 (v) x²-38x+72 = 0 (y) g²-12g-64 = 0 (b) x² + 7x + 12 = 0 (e) x² - 2x - 8 = 0 (h) y² - 4y - 45 = 0 (k) x² + 9x + 18 = 0 (n) x² + x - 12 = 0 (q) y² - 14y +48 = 0 (t) y² + 22y + 96 = 0 (w) x² + 14x-51=0 (z) y² + 22y + 121 = 0 (c) y² + 7y + 10 = 0 (f) m²-7m+12=0 (1) x²-x-56=0 (1) x² + 23x+22=0 (0) m²-6m-27 = 0 (r) x² - 15x+56= 0 (u) k²-18k-88=0 (x) y² + 32y + 240 = 0

Answers

Answer:

(a) x² + 6x + 8 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = 6, and c = 8

Substituting the values, we get:

x = (-6 ± sqrt(6² - 4(1)(8))) / 2(1)

x = (-6 ± sqrt(36 - 32)) / 2

x = (-6 ± sqrt(4)) / 2

x = (-6 ± 2) / 2

x = -4 or -2

Therefore, the solutions are x = -4 or x = -2.

(b) x² + 7x + 12 = 0