PLEASE HELP
Part A: Given the function g(x) = |x − 7|, describe the graph of the function, including the vertex, domain, and range. (5 points)
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Answers
Part A:
The required graph of the function is described.
The vertex of the function is (7,0)
The domain is : (-∝ , ∝) and
The range is : [0,∝), {yIy ≥ 0}
Part B:
The transformation which occurs from f(x) to h(x) is a vertical shift up to 2 units.
Define functions?Expressions separated by an equal sign are functions. Both dependent and independent variables are present.
Given Part A:
given the function is g(x) = I x - 7 I
hence from the function, vertex = (h,k)
h = 7 and k = 0
(h,k) = (7,0)
Find the domain by finding where the function is defined.
therefore, domain = (-∝ , ∝) , where {xIx ∈ R}
The range is the set of values that corresponds with the domain.
therefore, range = [0,∝), {yIy ≥ 0}
Part B:
given the parent function is: f(x) = |x|
which is transformed to h(x) = |x| + 2
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x axis or y axis, and if there is a vertical stretch.
Parent function = f(x) = |x|
Horizontal shift = none
Vertical shift = up 2 units.
Reflection about the x axis = none
hence from the function we can determine the vertex (h,k)
= (0,2)
Find the domain by finding where the function is defined.
therefore, domain = (-∝ , ∝) , where {xIx ∈ R}
The range is the set of values that corresponds with the domain.
therefore, range = [2,∝) , {yIy ≥ 2}
Hence, we get the required answers.
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Related Questions
. From a rectangular metal sheet of size 20 cm by 30 cm, a circular sheet as big as possible is cut. Find the area of the remaining sheet.
Answers
The area of the circle is given by the formula A = πr², where r is the radius. Substituting r = 10 cm, we get:
A = π(10 cm)²
A = 100π cm²
The area of the remaining sheet is equal to the area of the rectangle minus the area of the circle. The area of the rectangle is 20 cm × 30 cm = 600 cm². So, the area of the remaining sheet is:
600 cm² - 100π cm² ≈ 196.3 cm²
Therefore, the area of the remaining sheet is approximately 196.3 square centimeters.
The width of a rectangle measures (5v2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P = 2(11v + 5w) cm.
Explain about the perimeter of the rectangle?The perimeter of a rectangle is the length measured around the edge of the rectangle. Although a rectangle has two dimensions, its perimeter only has one and is expressed in linear distances like feet or meters.
The perimeter calculation can be used, for instance, to calculate that many ft of brick border are required overall if somehow the rectangle depicts a garden which needs a brick border.
The sum of the lengths of a rectangle's four sides is known as its perimeter.
Rectangle perimeter = 2L + 2W.
Length = (6v+7w)
width = (5v - 2w)
P = 2 (length + width)
P = 2(6v+7w + 5v - 2w)
On simplifying:
P = 2(11v + 5w)
Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P = 2(11v + 5w) cm.
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Compete question:
The width of a rectangle measures (5v - 2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The height after t seconds of a projectile that is launched upward with a velocity of 64 feet per second from the top of a 45 foot building is given by. When will the projectile attain a height of 85 feet?
Answers
The projectile will attain a height of 85 feet at approximately 0.775 seconds or 3.225 seconds.
Calculating the Time to reach a certain heightGiven that
Velocity = 64 feet per second --- v
Initial height = 45 feet --- h
The height function can be represented as
h(t) = -16t² + vt + h
So, we have
h(t) = -16t² + 64t + 45
where h is the height in feet and t is the time in seconds.
To find when the projectile will attain a height of 85 feet, we need to solve the equation for t
So, we have
-16t² + 64t + 45 = 85
-16t² + 64t - 40 = 0
Using a graphing tool, we have
t = 0.775 and t = 3.225
Therefore, the projectile will attain a height of 85 feet at approximately t = 0.775 seconds or t = 3.225 seconds.
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Peyton drew a right triangle with sides 5
cm, 12
cm, and 13
cm long. Carter drew a similar triangle to Peyton’s. Which of the following can be the measurements of Carter’s triangle?
Answers
Option B. The length of the hypotenuse of Carter's triangle is 13cm.
Since Carter's triangle is similar to Peyton's triangle, the ratio of corresponding side lengths will be the same. Let's use x to represent the length of the hypotenuse of Carter's triangle.
We know that the ratio of the lengths of the hypotenuse and the shorter leg of Peyton's triangle is 13:5. So, the ratio of the lengths of the hypotenuse and the shorter leg of Carter's triangle must also be 13:5.
Thus, we have x/5 = 13/5, which simplifies to x = 13.
Therefore, the length of the hypotenuse of Carter's triangle is 13cm.
Therefore, the only possible length for Carter's hypotenuse is 13cm, and the correct answer is A.
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Peyton drew a right triangle with sides 5cm, 12cm, and 13cm long. Carter drew a similar triangle to Peyton’s. Which of the following can be the measurements of Carter’s triangle?
A. 15cm
B. 13cm
C. 11cm
D. 10cm
According to the National Student Clearinghouse Research Center, women now comprise 60% of enrollment in universities. What is the probability in a random sample of 55 university students that more than 35 are women? Round your answer to 3 decimal places.
Answers
The probability that more than 35 students are women in a random sample of 55 university students is 0.256.
What is binomial distribution?The binomial distribution is a probability distribution that expresses the number of successes in a finite number of independent trials when the chance of success is constant and there are only two potential results (success or failure). Since a known chance of success for each trial is known, we may use it to determine the likelihood of a certain number of successes (or failures) in a set number of trials.
Given that p = 60% = 0.6, n = 55.
Using normal approximation we have:
SD = sqrt(np(1-p))
= sqrt(55 x 0.60 x 0.40) = 3.05
The z-score is:
z = (X - np) / SD)
z = (35 - (0.4)(0.6)) / 3.05
z = 11.39 = 0.256.
Hence, the probability that more than 35 students are women in a random sample of 55 university students is 0.256.
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What is 2-2x5+7 hurry!!!!!!!!!!!!
Answers
Answer: 15 / fifteen
Step-by-step explanation:
2*5 = 10 - 2 = 8 + 7 = 15
The value of the given expression is -1.
What is PEDMAS rule?PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
The given numerical expression is 2-2×5+7.
Here, first multiply 2 and 5, that is
2-10+7
Next add 2 and 7, that is
9-10
Finally subtract 9 and 10, that is
9-10= -1
Therefore, the value of the given expression is -1.
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A salesman gets paid an annual salary of $35,000 plus he makes $75 for each sale. If this salesman made $46,700, how many sales did he make?
Answers
Answer: 156
Step-by-step explanation:
Annual Salary = $35, 000
Subtract anual salary from 46, 700. ---> 46,700-35,000= 11,700
One sale = $75
To find out how many sales, divide the remaining 11,700 by 75.
11,700/75= 156
156 sales.
Name the minor arc and find it’s measure. Then name the major arc and find it’s measure.
Answers
The minor arc in the given diagram as required to be determined is; arc TU and it's measure is; 116°.
The major arc in the given diagram as required to be determined is; arc TVU and it's measure is; 244°.
What are the measures of the minor and major arcs in the diagram?It follows from the task content that the minor and major arcs are to be named and their measures determined as required.
The minor arc in a circle is usually subtended by an angle less than 180° while the major arc is subtended by an angle greater than 180°.
Ultimately, the minor arc is; arc TU and it's measure is; 116° while the major arc is; arc TVU and it's measure is; 244°.
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A Small Monster collector is visiting the Knightrola region, bringing 30 Small Monster Containment Devices with them. The devices are highly reliable and can effectively be assumed to always work. How many different types of Small Monsters can the collector capture under the following conditions? a. The collector has access to Grass, Space Electric Scooter, Mask, Citrus, and Rubber Duck type Small Monsters 7 types b. The above, and intends to capture at least one of each of those types c. Both of the above, and intends to capture at least five Space types d. All of the above and intends to capture at most four Electric Scooter types e. All of the above, and intends to capture at most three Rubber Duck type
Answers
The different types of Small Monsters combinations can the collector capture under that collector .lunder the following conditions are a) 593775 ; b) 100947 ; c) 27132 ; d) 30752 ; e) 26334.
For these questions as we are dealing with combination and repetition, we will be using the rule nC(r-1) where n = the number of total items and r = the number of ways we can choose.
We have provide that Small Monster collector is visiting the Knightrola region, bringing 30 Small Monster Containment Devices with them. We have to determine the different types of Small Monsters can the collector capture under the following conditions :
a) Here n = 30,
Number of monstor access by him = 7 {Grass, Space Electric Scooter, Mask, Citrus, and Rubber Duck}
So, different types of Small Monsters can the collector capture = ³⁰C₇₋₁ = ³⁰C₆
= 593775
b) Here, he captures at least one of each of those 7 places. So, we have to distribute 23 ( 30 -7) among 7 places
= ²³C₆ = 100947
c) Here provided that atleast one to all plus atleast five Space types captured, so we have to distribute 30 - 11 = 19 devices among 7 places, = ¹⁹C₆ = 27132
d) All above conditions plus at most four Electric Scooter types captured, so ³⁰⁻¹¹C₅ + ³⁰⁻¹²C₅+ ³⁰⁻¹³C₅ + ³⁰⁻¹⁴ C₅
= 30752
e) All of the above and capture at most three Rubber Duck type, First, we will subtract the combination where we capture n = 20-3 (at most 3 rubber ducks) from the combination we have so ³⁰⁻¹⁴C₅ + ³⁰⁻¹⁵C₅ + ³⁰⁻¹⁶C₅ = 26334. Hence, required value is 26334.
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A company finds that if it charges 2 dollars for a cell phone, it can expect to sell 1,000 - 2x phones. The company uses the function
defined by r(x)=(1,000-2x) to model the expected revenue, in dollars, from selling cell phones at a dollars each.
1. Use graphing technology to graph the function r.
2. What do the z-intercepts mean in this situation?
3. Is 0≤x≤ 600 an appropriate domain for the function 7? Explain your reasoning.
4. At what price should the company sell their phones to get the maximum revenue? Explain your reasoning.
Answers
The z-intercept is at 500, the domain of the function is all non-negative real numbers, or [0, ∞) and the maximum revenue is 500
What does the z-intercepts interpret in this situation?1. The graph of the function is attached below;
2. The z-intercept is where the graph intersects the x-axis, which occurs when the revenue is 0. In this situation, the z-intercept represents the maximum price that the company can charge for the cell phone and still expect to sell some units. So, the z-intercept is $500, meaning if the company charges more than $500, it will not sell any cell phones and its revenue will be 0.
3. No, 0≤x≤ 600 is not an appropriate domain for the function. The company can charge any price, not just prices between 0 and 600 dollars. The domain of the function should be all non-negative real numbers, or [0, ∞).
4. The maximum revenue occurs at the point where the slope of the function changes from negative to positive, which is the vertex of the parabola. In this case, the function r(x) is a linear function, so there is no vertex. The maximum revenue occurs at the endpoint of the domain, which is x=500, since the company cannot charge more than $500 without reducing the number of phones sold to 0. Therefore, the company should charge $500 to get the maximum revenue.
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Find the measure of XY.
Y
●
74°
N
X
Answers
Check the picture below.
I need help with these 3 questions.
Answers
a. The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.
What is the statistics
b.the pressure to build to its highest point (75/264).
c. Sample statistic's value is 0.2835.
d. Estimate's standard error is 0.0255.
e. Its highest level, the 95% confidence interval, is (0.2326, 0.3344).
A subfield of mathematics called statistics is concerned with the gathering, examination, interpretation, presentation, and arrangement of data.
Several disciplines, including business, economics, sociology, psychology, epidemiology, and public health, employ it. Statistic uses a variety of techniques to gather and analyse data to better understand.
(A) The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.
(b) The sample statistic, given as p, is the percentage of subjects that allowed the pressure to build to its highest point (75/264).
(c) The sample statistic's value is 0.2835.
(d) The estimate's standard error is 0.0255.
(e) For the percentage of people who would permit the pressure to reach its highest level, the 95% confidence interval is (0.2326, 0.3344).
Therefore, Overall, the findings of this study indicate that a significant majority of high school pupils will tolerate pressures up to 300 mmHg without ever complaining about the discomfort. The range of values inside the 95% confidence.
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Write an equation for a linear function whose graph has the given characteristics. Horizontal, passes through (9, −45)
Answers
Answer:
y = -45
Step-by-step explanation:
y=mx+b
because the graph is horizontal m = 0
y=0x+b --> y=b
next sub in points
y=b (9,-45)
-45=b
therefore equation is y=-45
the recipe for ellie fruit drink included 1 1/4 quarts of cranberry juice 2 2/3 quarts of apple juice and 5/8 of a quart of lemonade. The recipe makes enough for 4 people. Ellie needs to make enough fruit drink for 20 people . How much of each ingredient does she need?
Answers
Answer:
25/4 quarts of cranberry juice
40/3 quarts of apple juice
25/8 quarts of lemonade
Step-by-step explanation:
just multiply everything by 5
:)
can you solve this question?
f'(7)=?
instantaneous rate of change=?
Answers
(a) f'(7) = 9. The derivative of the function f(x) evaluated at x=7, is 9.
(b) The instantaneous rate of change of y with respect to x at x = 7 is 9.
What is the derivative of the function?
Given that the tangent line to the graph of y = f(x) at point (7, 56) has the equation y = 9x - 7, we can use the slope-intercept form of the equation of a line to find the slope of the tangent line.
The slope of the tangent line is 9. This is also equal to the derivative of the function f(x) evaluated at x=7, which gives us the answer to part (a).
The instantaneous rate of change of y with respect to x at x = 7 is also given by the derivative of the function at x=7. Therefore, the answer to part (b) is also f'(7) = 9.
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Can someone please help me with this? find the value of x and write answer in simplest radical form. I understand the concept but I don’t know how to differentiate each side to find out if it’s sin, cos, or tan. Please explain how you got the answer.
Answers
The value of x is 5√3
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
The longest sides is the hypotenuse and the side opposite the acute angle is the opposite, the other side is adjascent.
Sin(tetha) = opp/ hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
therefore Tan 60 = x/5
√3 = x/5
x = 5√3
therefore the value of x is 5√3
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bobby is painting a figure on a banner for a homecoming parade. the figure he is painting consists of an isosceles triangle, a rectangle, and a semicircle, as shown how do i sovle it
Answers
Using the perimeter formula, the total length of sparkling lights he can add to the banner is 40.56ft.
Define perimeter?The perimeter of a shape is its whole length. It is any border or outline's length that defines a two-dimensional geometric shape. Different figures may have the same perimeter depending on their sizes.
The same wire can be used to create a square if each of its four sides is the same length.
Here in the question,
We have to find the perimeter of the whole figure.
Now the total perimeter =
Sum of sides of the triangle + sum of sides of quadrilateral and the sum of the circumference of the semi-circle.
Perimeter = 10 + 5 + 3 + 10 + πr
= 28 + 3.14 × 8/2
= 28 + 12.56
= 40.56ft.
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The complete question is:
Bobby is creating a banner for the homecoming parade. The banner consists of an isosceles triangle, a rectangle, and a semicircle. He wants to add sparkling lights around the trim of the banner.
What is the total length of sparkling lights he can add to the banner?
Find the shaded area
Answers
Answer:
21.5 m^2
Step-by-step explanation:
Area of circle A = πr^2 = 3.14(10/2)^2 = 78.5
Area of square A = 10^2 = 100
Area of shaded area: 100 - 78.5 = 21.5 m^2
Martha Martha and Steven are in the same math class. The box plot shows the number of minutes that Martha and Steven spent studying for their final exam each day for a week. Steven 0 5 10 Study Time 15 20 Number of Hours 25 30 35 Which statement is best supported by the information in the box plots? 2 of 9 A 07:34
Answers
Answer:
Based on the given information in the box plots, the statement that is best supported is that Steven spent more time studying than Martha did during the week for their math final exam. This can be inferred because the top line of Steven's box plot is higher than the top line of Martha's box plot, indicating that Steven spent more time studying than Martha in the given time period. Additionally, Steven's whisker extends higher than Martha's whisker, further supporting the idea that Steven studied for a longer period of time than Martha.
Eight times a number, x, is one-third the sum of the number and two. Which answer represents this situation? Responses 8x=13x+2 8 x equals 1 third x plus 2 8x=13(x+2) 8 x equals 1 third open parentheses x plus 2 close parentheses 8x+13(x+2) 8 x plus 1 third open parentheses x plus 2 close parentheses 8x+13x+2
Answers
The problem can be translated into an equation as follows: 8x = (1/3)(x+2)
the answer that represents this situation is: 8x = (1/3)(x+2)
Simplifying the right side of the equation:
8x = (1/3)x + (2/3)
Multiplying both sides of the equation by 3 to eliminate the fraction:
24x = x + 2
Subtracting x from both sides of the equation:
23x = 2
Dividing both sides of the equation by 23:
x = 2/23
Therefore, the answer that represents this situation is:
8x = (1/3)(x+2)
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Determine the length of side AB and BC in triangle ABC.
AB=9.68,BC=7.04
AB=8.8,BC=6.4
AB=9.152,BC=6.656
AB=7.92,BC=5.76
Answers
In triangle ABC, the values of AB and BC are 9.68 and 7.04 respectively i.e. A.
What is a triangle's definition?
A triangle is a geometric form that has three straight sides and three angles. It is a fundamental geometric form that is frequently utilised in mathematics, science, and everyday life.
Triangles are distinguished by three sides and three angles. The sum of each triangle's three angles is always 180 degrees. Triangles are classified according to the length of their sides and the measurement of their angles.
Now,
As given ΔDEF ≈ΔABC
that means ratio of all sides will be equal
i.e. AB/DE=BC/EF=AC/DF
then AB/8.8=6.71/6.1
AB=1.1*8.8
AB=9.68
and BC/6.4=6.71/6.1
BC=1.1*6.4
BC=7.04
Hence,
the values of AB and BC are 9.68 and 7.04 respectively.
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In the circle below, suppose and . Find the following.
Answers
The missing values in the figure are solved to be
angle KLI = 111
angle LIJ = 129 degrees
How to find the missing anglesThe missing angles are solved using the inscribed angle theorem and the knowledge of cyclic quadrilateral
arc KLI = 138 degrees = 2 * angle KJI (inscribed angle theorem)
angle KJI = 138 / 2
angle KJI = 69 degrees
angle KLI + angle KJI = 180 degrees (cyclic quadrilateral property)
where angle KJI = 69
angle KLI = 180 - 69
angle KLI = 111 degrees
angle LIJ + angle LKJ = 180 degrees (cyclic quadrilateral property)
angle LKJ = 51 degrees (given)
angle LIJ = 180 - 51
angle LIJ = 129 degrees
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Eric has 4 pounds of blueberries to make into pies. How many pies can Eric make if each pie needs the given amount of blueberries?
Answers
Draw the image of traingel ABC under a dilation whose center is p and scale factor is 1/2
Answers
A graph of the image of ABC under a dilation whose center is P and scale factor is 1/2 is shown in the image below.
What is dilation?In Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape.
In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/2 centered at P.
Based on the image (see attachment), we can logically deduce that each vertex is 1/2 times as far from center P as the original vertex and each segment is 1/2 times as long as the original:
Side length A'C' = 8.2/2 = 4.1
Side length A'B' = 5.7/2 = 2.85
Side length B'C' = 12.2/3 = 6.1
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Tammy must run more than 63 miles total to reach your fitness goals. She has already ran 31 miles and runs for miles per day which of the following inequalities could be used to solve for X the number of days Tammy still needs to run to reach your fitness goals.
Answers
Answer:
[tex]31+4x > 63[/tex]
To reach her fitness goal, she needs to run for more than 8 days.
Step-by-step explanation:
She has already run 31 miles and runs 4 miles per day:
This means that after x days, the distance she will have run is:
[tex]D(x)=31+4x[/tex]
Tammy must run more than 63 miles total to reach her fitness goals.
This means that:
[tex]D(x) > 63[/tex]
[tex]31+4x > 63[/tex]
The inequality is:
[tex]31+4x > 63[/tex]
Solution:
[tex]4x > 32[/tex]
[tex]x > \dfrac{32}{4}[/tex]
[tex]x > 8[/tex]
To reach her fitness goal, she needs to run for more than 8 days.
A circle is shown. 2 radii with length 8 inches are drawn. A line connects the radii points on the circle to form a triangle. The angle between the 2 radii is 90 degrees. The area between the triangle and the outline of the circle is shaded.
What is the area of the shaded portion of the circle?
(16π – 32) in2
(16π – 8) in2
(64π – 32) in2
(64π – 8) in
Answers
The Area οf the shaded pοrtiοn is given by (16 π -32) inch², the cοrrect οptiοn is A.
What is a CircIe?A circIe is a rοund shaped figure whοse aII pοints Iie in οne pIane and the distance between the center οf the circIe and aII the pοints οn the circIe is cοnstant.
The area οf the shaded pοrtiοn is equaI tο the difference οf the area οf the arc and Area οf the TriangIe.
Area οf an Arc =(θ /360) × π r²
Area = (90/360) × π × (8)²
Area οf the arc = 16 π in²
Area οf the triangIe = (1/2) × base × height
Area οf the triangIe = (1/2) × 8 × 8 = 32 in²
Area οf the shaded pοrtiοn = (16 π -32) inch²
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Where are the vertices of triangle A’B’C’ located? Show your work or explain your steps. (4points)
Answers
The vertices of ∆A′B′C′ are A′(-6, 5), B′(-6, 8), and C′(-10, 5) upon the application of the translation rule.
What is the translation rule in geometry?
In geometry, a translation is a transformation that moves every point of a figure the same distance in the same direction. In the case of a triangle, a translation rule describes how to move each vertex of the triangle to a new location to create a new triangle with the same size and shape, but in a different position.
A translation rule for a triangle is given by a pair of numbers (a, b), which indicate the amount of horizontal and vertical movement of the vertices. Specifically, the rule is given by the formula:
(x, y) → (x + a, y + b)
This formula means that we move every point in the triangle a unit to the right or left (depending on the sign of a) and b units up or down (depending on the sign of b).
The translation rule (x, y) → (x − 3, y + 4) means that we move every point in the original triangle left by 3 units and up by 4 units. So, the translation is described as a leftward shift of 3 units and an upward shift of 4 units.
To find the vertices of ∆A′B′C′, we apply the translation rule to each vertex of ∆ABC:
Vertex A: (x, y) → (x - 3, y + 4)
(-3, 1) → (-3 - 3, 1 + 4) = (-6, 5)
So, vertex A of ∆A′B′C′ is located at (-6, 5).
Vertex B: (x, y) → (x - 3, y + 4)
(-3, 4) → (-3 - 3, 4 + 4) = (-6, 8)
So, vertex B of ∆A′B′C′ is located at (-6, 8).
Vertex C: (x, y) → (x - 3, y + 4)
(-7, 1) → (-7 - 3, 1 + 4) = (-10, 5)
So, vertex C of ∆A′B′C′ is located at (-10, 5).
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The complete question is as follows:
Find the extract value of x
Answers
Answer:
25 + 5√29
Step-by-step explanation:
(I added a photo below)
First, let's find BC using the Pythagorean theorem (from ∆BCD):
[tex] {bc}^{2} = {25}^{2} + {10}^{2} = 625 + 100 = 725[/tex]
[tex]725 > 0[/tex]
[tex]bc = \sqrt{725} =5 \sqrt{29} [/tex]
Then we see, that AB = 25 + x
So, now we can find AC:
[tex] {ac}^{2} = ({25 - x})^{2} - ({5 \sqrt{29} })^{2} = 625 - 50x + {x}^{2} - 25 \times 29 = 625 - 50x + {x}^{2} - 725 [/tex]
Now we have a quadratic equation:
[tex] {x}^{2} - 50x - 100 = 0[/tex]
[tex]d = {b}^{2} - 4 \times a \times c = ({ - 50})^{2} - 4 \times 1 \times ( - 100) = 2500 + 400 = 2900 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{50 - 10 \sqrt{29} }{2} = 25 - 5 \sqrt{29} [/tex]
This is a negative number and we cannot use it, since x has to be a natural number
[tex]x2 = \frac{ - b + \sqrt{d} }{2 a} = \frac{50 + 5 \sqrt{29} }{2} = 25 + 5 \sqrt{29} [/tex]
A point R (-5, 6) is reflected across X axis to obtain point S, write the coordinates of S.
Answers
This is because a reflection across the x axis retains the same x value and the why value flips
determine whether the proportion is true or false 16miles/18quarts=24miles/27quarts
Answers
To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:
16 miles / 18 quarts = 24 miles / 27 quarts
Cross-multiplying, we get:
16 miles * 27 quarts = 18 quarts * 24 miles
432 milesquarts = 432 milesquarts
The equation holds, so the proportion is true.
The proportion is true .
To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:
16 miles / 18 quarts = 24 miles / 27 quarts
Cross-multiplying, we get:
16 miles * 27 quarts = 18 quarts * 24 miles
432 milesquarts = 432 milesquarts
Proportion can be checked by simplifying the ratios given,
16miles/18quarts=24miles/27quarts
Simplifying further,
8miles/9squarts = 8miles / 9squarts .
The equation holds, so the proportion is true.
Know more about proportions,
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