PLS HELP!!!
Find the vertices of the image of △ABC under the transformation (x, y) ⟶ (x − 3, y + 1) followed by a dilation centered at the origin with scale factor 2.
Answers
The coordinates of the image of triangle ABC are A''(x, y) = (- 4, 2), B''(x, y) = (0, 0) and C''(x, y) = (2, 4).
How to determine the vertices of the image of a triangle
Triangles are generated by the location of three distinct points on Cartesian plane. In this problem we find the representation of a triangle, whose vertices are listed below:
A(x, y) = (1, 0), B(x, y) = (3, - 1), C(x, y) = (4, 1)
We need to apply the following rigid transformations:
Translation
(x, y) → (x - 3, y + 1)
Dilation centered at the origin with scale factor 2
(x, y) → (2 · x, 2 · y)
Now we proceed to determine the coordinates of the image:
Translation
A'(x, y) = (- 2, 1), B'(x, y) = (0, 0), C'(x, y) = (1, 2)
Dilation
A''(x, y) = (- 4, 2), B''(x, y) = (0, 0), C''(x, y) = (2, 4)
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Related Questions
SOMEONE PLEASE HELP...............
A plane that passes through three edges of a cube produces a triangular cross section as shown.
In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.
Answers
A cross section of a cube that is a regular hexagon can only be obtained if the plane passes through the cube at a 60-degree angle with respect to its edges. If a plane is placed in this manner, it will intersect six of the cube's edges at their midpoints, producing a regular hexagon cross section.
What are True Statements about a Plane that Pass Through a Cube?The plane that passes through three edges of a cube to produce a regular hexagonal cross section must intersect the edges of the cube at 60 degree angles. This can be achieved if the plane is aligned with the diagonal of one of the faces of the cube, passing through the opposite vertices of the face.
This configuration of the plane will result in a regular hexagonal cross section of the cube as each vertex of the hexagon will correspond to one of the vertices of the cube, and each side of the hexagon will intersect two edges of the cube at 60 degree angles.
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If M = {distinct letters in the word mathematics} and N = {distinct letters in the word nevertheless}, what is |M × N|?
|M × N| =
Answers
The value of the expression represented by |M × N| is 64
How to determine the value of |M × N|?from the question, we have the following parameters that can be used in our computation:
M = {distinct letters in the word mathematics} N = {distinct letters in the word nevertheless}Using the above as a guide, we have the following:
M = 8 i.e. {m, a, t, h, e, i, c, s}.
N = 8 i.e. {n, e, v, r, t, h, l, s}.
So, we have
|M × N| = 8 * 8
Evaluate
|M × N| = 64
Hence, the value of |M × N| is 64
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HELP ASAP TIMED!! hurry
Answers
Answer:
The solution is C. (x+8)² + (y-11)² = 4
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = -8
k = 11
r = 2
(x + 8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
The answer is C. (x+8)² + (y-11)² = 4
All numbers less than 17 and greater than or equal to -8. into SET BUILDER NOTATION!!
Answers
In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:
{x | -8 <= x < 17}
Explanation of set builder notation?
A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | }, where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.
In this case,
the set comprises of all figures higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint
-8 <= x < 17,where x is a real value. This predicts that x must exceed or equal to -8 and must be less than 17 to be a part of the set.
Thus, in set builder form, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows: {x | -8 <= x < 17}
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Conrad is reading a blue print to make a shed. On the blue print, the length of the shed is 12 inches and the ramp attached to the shed is 1 inch. He wants to convert the total length of the shed and ramp from inches to yards. Select all of the expressions which correctly show how to convert the length of the shed and ramp from inches to yards using the ratio 36 inches to 1 yard.
Answers
To convert inches to yards, we need to divide by 36, since 36 inches make 1 yard. Therefore, to convert the length of the shed and ramp from inches to yards, we can use the following expressions: (12 + 1) / 36 = 0.3611... yards, (12 / 36) + (1 / 36) = 0.3611... yards, 13 / 36 = 0.3611... yards
What are expressions?An expression in mathematics is a grouping of variables, numbers, and actions that can be evaluated to yield a value. A wide range of mathematical notions, from basic arithmetic computations to intricate algebraic formulas and beyond, are represented by expressions.
These components can be used to combine expressions in a wide range of different ways. For instance, we can construct straightforward arithmetic phrases such as "2 + 3" or "5 * 4" or more intricate algebraic expressions such as "3x2 + 2x + 1" or "sin(x) + cos(x)". In each instance, the expression denotes a mathematical idea that may be tested to provide a certain value.
Expressions play a significant role in mathematics and are utilized in a wide range of fields in science, engineering, and finance. By being aware of how expressions work, we can better understand and solve a wide variety of mathematical problems.
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a student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d= days, r= raffle tickets, and h= hours, what function can he use to calculate his earnings?
Answers
The function can be used to calculate his earnings, 15d + 0.25r + 2h
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
The function that the student can use to calculate his earnings is:
Earnings = 15d + 0.25r + 2h
where:
d = number of days worked
r = number of raffle tickets sold
h = number of hours worked at the game
The first term, 15d, represents the base pay of $15 per day worked.
The second term, 0.25r, represents the additional earnings of $0.25 per raffle ticket sold.
The third term, 2h, represents the additional earnings of $2 per hour worked at the game.
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Find the measure of the missing angles.
Answers
Answer:
F = 29
E= 151
D = 90
Step-by-step explanation:
For F:
The angle F is on a 180 degree angle with a degree next to it that is 151. To get the value F subtract 180-151 and you get 29.
For E: If F is 29 then the angle opposite of F is also 29. So again to find the measure of angle E, subtract 180 minus 29 and you get 151.
For D: D is also lying on a 180 degree angle. The angle next to it is 90. To get 180 add 90. 90 is the measure of angle d.
Answer:
d = 90°,e = 151°,f = 29°.-----------------------------------
Angle d is linear pair with a right angle, therefore:
d = 180° - 90°d = 90°Angle e is vertically opposite with 151° and therefore they are congruent:
e = 151°Angle f is adjacent with 151° and forming a linear pair, therefore:
f = 180° - 151°f = 29°Suppose you bought ares company 4 years ago at a price of $63.00 per share sold it at $71.50 per share. How much money die you make? $37750 $382.50 $387.50 $392.50
Answers
The amount you made per share is $8.50.
How to determine the amount you madeFrom the question, we have the following parameters that can be used in our computation:
Initial amount = $63.00
Final amount = $71.50
To calculate the profit made, we need to find the difference between the selling price and the buying price per share, and then multiply by the number of shares.
The difference in price per share is:
Difference = $71.50 - $63.00
Evaluate the difference
Difference = $8.50
Hence, the profit per share is $8.50.
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If sin t= 7/9, and t is in quadrant I, find the exact value of sin(2t) , cos(2t) , and tan(2t) algebraically without solving for t .
Answers
Step-by-step explanation:
we know :
sin(2t) = 2×sin(t)×cos(t)
cos(2t) = cos²(t) – sin²(t) = 2×cos²(t) – 1 = 1 – 2×sin²(t)
tan(t) = sin(t)/cos(t)
tan(2t) = sin(2t)/cos(2t) = (2×tan(t))/(1 – tan²(t))
sin²(t) + cos²(t) = 1
as t is in quadrant I, 2t must be in either quadrant I or II.
sin(t) = 7/9
sin²(t) = (7/9)² = 49/81
cos²(t) = 1 - sin²(t) = 1 - 49/81 = 81/81 - 49/81 = 32/81
cos(t) = sqrt(32)/9
sin(2t) = 2×sin(t)×cos(t) = 2×7/9 × sqrt(32)/9 =
= 14×sqrt(32)/81 ≈ 0.98
cos(2t) = cos²(t) - sin²(t) = 32/81 - 49/81 = -17/81 ≈
≈ -0.21
tan(2t) = sin(2t)/cos(2t) =
= 14×sqrt(32)/81 / -17/81 =
= 14×sqrt(32)/81 × -81/17 =
= -14×sqrt(32)/17 ≈ -4.66
NISSAN NP300 Special deal at 2007 price! R 221,180 (incl. VAT) Features • Dual airbags Power steering • Air-conditioning • Radio CD 3.3 Central locking Roof rack Roll bar and tonneau ber Side steps 3 year90 000km Service Plan • 3 year/100 000km Warranty NISSAN DataDot Anti theft Identification system NP300 Special Offers Months Interest Vehicle rate Price Deposit Click here to book your test drive *Residual Monthly instalments Total Payment R303 007 80 180 *Residual is an amount that must be paid at the end of the term after all the monthly payments have been made. 3.1 What is the cash price of the NISSAN NP 300? 3.2 If a person decide to pay for the vehicle in instalments, determine the number of years it will take to pay for the vehicle. Calculate the amount of the deposit needed. (2) (2) (3)
Answers
3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).
3.2. it would take approximately 6.67 years to pay off the vehicle through instalments.
A deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit
How The answer was obtained3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).
3.2 The given information does not explicitly state the number of years for the instalment plan, but it does provide the number of months (80) and the total payment amount (R303,007). Assuming a monthly payment plan, we can calculate the number of years as follows:
Number of years = Number of months / 12
Number of years = 80 / 12
Number of years ≈ 6.67 years
So it would take approximately 6.67 years to pay off the vehicle through instalments.
To calculate the deposit needed, we need to subtract the residual amount from the total cash price. From the given information, the total payment is R303,007 and the residual is R80,180, so:
Cash price = Total payment - Residual
Cash price = R303,007 - R80,180
Cash price = R222,827
So the cash price is slightly higher than the advertised price of R221,180, likely due to financing fees or interest. To determine the deposit needed, we can assume a specific percentage of the cash price that must be paid upfront. For example, if the deposit required is 10% of the cash price, then:
Deposit = 0.1 x Cash price
Deposit = 0.1 x R222,827
Deposit = R22,282.70
So a deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit.
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Which of the following graphs matches the equation y=-4x+3
Answers
The equation of line is y = -4x + 3 , where the slope is m = -4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -4x + 3 be equation (1)
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = -4
And , the y intercept is 3
The equation of line is plotted on the graph
Hence , the equation of line is y = -4x + 3
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The complete question is :
Which of the following graphs matches the equation y=-4x+3?
On a coordinate plane, a line goes through (0, 3)
On a coordinate plane, a line goes through (-2, 5) and (0, -3).
On a coordinate plane, a line goes through (0, 3) and (3, -1).
Which of the following angles is in the solution set of (see picture)
Answers
Angles are measured in degrees, with a full circle being 360°, and can be thought of as the amount of rotation that two straight lines or planes undergo.
What best define about angle?The class definition of angle changed from a collection of ambiguous expressions, such as “the measurement of all the sides,” “the place where lines meet,” and “the corner of a shape or anything,” to
The equation below can be set up to calculate this.
Tan(angle) = 80 ft / (200 ft – 4 ft)
Solving for the angle, we get:
angle = tan-1(80 ft / 196 ft (ca. 60 m))
angle = tan-1(0.408163265)
Angle = 36.87 degrees (to the nearest hundredth of a degree).
Therefore, The law of tangents indicates that the angle between the subject's eyes and the top of the structure is roughly 36.87 degrees.
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Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Answers
Answer:
(a) 24%
Step-by-step explanation:
You want the percentage of people in the Decades slice of a circle graph if it represents 96 people. The other slices represent 128, 72, 52, 24, and 28 people.
PercentThe fraction in the second category is the ratio of the number in that category to the total number. The percent is the fraction multiplied by 100%.
96/(128 +96 +72 +52 +24 +28) × 100% = 96/400 × 100% = 24%
The Decades slice of the circle would be 24%, choice A.
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You deposit $3000 in a savings account at Yorktown Bank, which has a
rate of 5%. Find the interest at the end of the first year.
Answers
Answer:
$150
Step-by-step explanation:
Interest = Principal x Rate x Time (in years)
I = 3000(.05)(1)
I = 150
Line A (y = 3x + 1) is transformed into
Line B (y=2x-7). Which best describes
the new slope and y-intercept?
The slope is[ ? ],
and the line is shifted[ ? ]
steeper
flatter
Answers
Answer:
The new slope is 2,
New y-intercept is - 7
Line is flatter since slope has reduced
Step-by-step explanation:
find the length of AB
Answers
Answer:
8.5 cm
Step-by-step explanation:
You want to know the length of AB in rectangle ABCD with perimeter 26 cm if BC = PQ, QR = 10 cm, and the area of rectangle PQRS is 45 cm².
PQThe area of rectangle PQRS is ...
Area = PQ·QR
45 cm² = PQ·(10 cm)
PQ = (45 cm²)/(10 cm) = 4.5 cm
ABThe perimeter of rectangle ABCD is ...
Perimeter = 2(AB +BC)
26 cm = 2(AB +4.5 cm) . . . . . . . . BC = PQ = 4.5 cm
13 cm = AB +4.5 cm . . . . . divide by 2
8.5 cm = AB . . . . . . . . subtract 4.5 cm
The length of AB is 8.5 cm.
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What is the completely factored form of 15a³bc³ – 6a²b²c³?
Answers
Answer:
The completely factored form of 15a³bc³ – 6a²b²c³ is 3a²bc³ × (5a - 2b).
Answer:
[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]
Step-by-step explanation:
[tex]15a^{3} bc^{3} - 6a^{2} b^{2} c^{3}[/tex]
[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]
what is the slope of this line?
Answers
Answer: -1/2
Step-by-step explanation: Down 1 over 2
Which of the following is not an exponential function?
A y = 5x
By = 5x - 1
© y=5x-1
Dy = 3.5x
Answers
The correct answer would be an option (C) y = 5x - 1 is not an exponential function.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
As per option (A), we have
y = 5ˣ
This is an exponential function.
As per option (B), we have
y = 5ˣ - 1
This is an exponential function.
As per option (C), we have
y = 5x - 1
This is not an exponential function because it is a linear function.
As per option (D), we have
D. y = 3.5ˣ
This is an exponential function.
Thus, the correct answer would be an option (C) y = 5x - 1
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The complete question would be as:
Which of the following is not an exponential function?
A. y = 5ˣ
B. y = 5ˣ - 1
C. y = 5x - 1
D. y = 3.5ˣ
Tony’s yearly pay is $8,320 rounded it is $8,300. Tony’s monthly car insurance 1/30 of his rounded yearly pay. Can he afford it. Explain why or why not
Answers
Tony m,ay or may not afford the car insurance
How to determine if Tony can afford the car insurance or notFrom the question, we have the following parameters that can be used in our computation:
Yearly pay = $8300 (approximated)
Insurance = 1/30 of his rounded yearly pay
Using the above as a guide, we have the following:
Insurance= 1/30 * $8300
Evaluate
Insurance= $276.7
Additional information about Tony's expenses and financial situation are needed to determine if he can afford the monthly car insurance or not.
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Quadrilateral ABCD has the following angle measures:
m∠A = ?°, m∠B = 97°, m∠C = 47°, m∠D = 90°
What is m∠A?
306°
234°
126°
54°
PLEASE HELP!
Answers
Answer:
126
Step-by-step explanation:
360-97-47-90=126
so 126
Answer: C) 126
Step-by-step explanation: first, you need to use this equation...
m∠A + m∠B + m∠C + m∠D = 360°
=> m∠A + 97° + 47° + 90° = 360° add all of the numbers...
=> m∠A + 234° = 360° subtract both sides by 234
=> m∠A = 360°- 234°
=> m∠A = 126°
Hope you've understood...
keeps saying ive gotten it wrong yet its an easy question.. help me? (probability)
Answers
Answer:
Pole Vault, Discus, 200m, Long Jump
Step-by-step explanation:
Once putting them all as decimals can’t you just sort it our from there? From what I can see, your answers are incorrect, but they might have reset.
A company that makes golf balls needs to ship bags of balls that contain 690 balls, plus or minus 6 balls. Write an absolute value inequality that expresses the acceptable number of balls in each bag.
Answers
Word Problems
1. The sum of 21 and three times a number is 60. What is that number?
2. Three times the difference between a number and three is equal to four times the number.
That is that number?
3. The sum of three consecutive integers is 48. Once you find them, answer this question: What
is > times the 3m as minus z times the 1St ?
4. Twice the smallest of three consecutive odd integers is seven more than the largest. What is the middle number?
5. The length of a rectangle is 3 cm more than the width. The perimeter is 22 cm. What is the
AREA of this rectangle? Note: A = (L)(W)
6. The perimeter of a triangle is 43 in. Side b is 3 times the length of side a. Side c is 1 more than twice the length of side a. What is the SUM of sides a and b?
Answers
In the word problems given above, the results are:
The number is 13.The number is 12.The consecutive integers are 15, 16, 17. The answer to the question is 19.The middle number is 9.The width is 4 cm and the length is 7 cm. The area of the rectangle is 28 sq cm.The sum of sides a and b is 28 in. (a=7 in, b= 21 in, c= 15 in)What is the rationale for the above response?1) Let's call the number we're looking for "x". According to the problem, "three times a number" is the same as 60 minus 21, which is 39. So we can write the equation:
3x + 21 = 60
Subtract 21 from both sides:
3x = 39
Divide by 3:
x = 13
Therefore, the number we're looking for is 13.
2)
Let's call the number we're looking for "x" again. According to the problem, "three times the difference between a number and three" is the same as "four times the number". So we can write the equation:
3(x - 3) = 4x
Simplify:
3x - 9 = 4x
Subtract 3x from both sides:
-9 = x
Therefore, the number we're looking for is -9.
3)
Let's call the first of the three consecutive integers "x". The next two would be x+1 and x+2. According to the problem, their sum is 48, so we can write the equation: x + (x+1) + (x+2) = 48
Simplify:
3x + 3 = 48
Subtract 3 from both sides:
3x = 45
Divide by 3:
x = 15
So the three consecutive integers are 15, 16, and 17. To answer the second part of the question, we can substitute these values into the given expression:
3m - z(1st) = 3(16) - 15(15) = 48 - 225 = -177
4)
Let's call the smallest of the three consecutive odd integers "x". The next two would be x+2 and x+4. According to the problem, twice the smallest is seven more than the largest, so we can write the equation:
2x = (x+4) + 7
Simplify:
2x = x + 11
Subtract x from both sides:
x = 11
So the three consecutive odd integers are 11, 13, and 15. The middle number is 13.
5)
Let's call the width of the rectangle "w". According to the problem, the length is 3 cm more than the width, so the length is w + 3. The perimeter is the sum of all four sides, which is:
P = 2w + 2(w + 3) = 4w + 6
We know that the perimeter is 22 cm, so we can write the equation:
4w + 6 = 22
Subtract 6 from both sides:
4w = 16
Divide by 4:
w = 4
So the width is 4 cm, and the length is 7 cm (since it's 3 cm more than the width). To find the area, we use the formula:
A = (L)(W) = (7)(4) = 28 square cm
6)
Let's denote the length of side a as x. Then we know that side b is 3 times the length of side a, or 3x, and side c is 1 more than twice the length of side a, or 2x+1.
Since the perimeter of the triangle is 43 inches, we can write the equation:
a + b + c = 43
Substituting in our expressions for b and c, we get:
x + 3x + 2x + 1 = 43
Simplifying the left-hand side, we get:
6x + 1 = 43
Subtracting 1 from both sides, we get:
6x = 42
Dividing both sides by 6, we get:
x = 7
thus:
a = 7
b= 3x = 21; na d
c = 2x + 1 = 14+1
c = 15
Thus the sum of sides a and b =
21 + 7
= 28
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determine an equation of the line drawn on the right. The shapes under the line are squares
Answers
Answer:57.6^3
thats t
Solve for x, please!! I really need help!!
Answers
Answer:
x = 13
Step-by-step explanation:
You want to find x when one half of the diagonal of a parallelogram is 80 and the other half is 6x+2.
DiagonalsThe diagonals of a parallelogram bisect each other, so point Y is the midpoint of each. That means ...
VY = YX
80 = 6x +2 . . . . . substitute the given values
78 = 6x . . . . . . . subtract 2
13 = x . . . . . . . . divide by 6
The value of x is 13.
If n = 200 and (p-hat) = 0.45, construct a 90% confidence interval.
Give your answers to three decimals
__ < p < __
Answers
Answer:
0.392 < p < 0.508
Step-by-step explanation:
[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.45\pm 1.645\sqrt{\frac{0.45(1-0.45)}{200}}\\\\CI_{90\%}\approx0.45\pm0.058\\\\CI_{90\%}=\{0.392,0.508\}[/tex]
Thus, we are 90% confident that the true population proportion [tex]\hat{p}[/tex] is between 0.392 and 0.508, assuming conditions are met.
What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning
Answers
The approximate angle of elevation if Brendan looks up at the tower is 20.03°
What is an elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
We know that, sinθ = opposite/hypotenuse
Here, sinx° = 50/146
sinx° =0.34246575342
x = sin⁻¹(0.34246575342)
x = 20.0271724581
x = 20.03°
Therefore, the approximate angle of elevation if Brendan looks up at the tower is 20.03°
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"Your question is incomplete, probably the complete question/missing part is:"
Amelia and Brendon are both on the ground looking at The top of a tower point D. Amelia is at point A and Brendan is at point B.
What is the approximate angle of elevation in Brendan looks up at the tower explain your reasoning.
last month maria hiked a total of 90 miles on two trails a 5 mile mountain trail and a 10 mile canal trail let x represent the number of times maria hiked the mountain trail and let y represent the number of times maria hiked the canal trail. which equation can be used to find the number of times maria hiked each trail
Answers
Answer:
5x + 10y = 90
Step-by-step explanation:
x represents the mountain trail which she walked 5 miles
y represents the canal trail which she walked 10 miles
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answers
Answer: 39%
Step-by-step explanation:
using calculator
1 seat = 0.058%
1700 - 1037 = 663 seats are taken.
0.058% x 663 seats = 39%
