The perimeter of the image of the triangle is approximately equal to 87 units.
How to determine the perimeter of the image of a triangle
In this problem we find the coordinates of the vertices of a triangle: A(x, y) = (- 4, 3), B(x, y) = (4, 3), C(x, y) = (- 4, - 6), of which we must determine the perimeter of its image, which is the result of a scale factor of 3. The perimeter is the sum of the lengths of the triangle. The length of each side of the image of the triangle can be found by Pythagorean theorem and definition of dilation:
l = √[(Δx)² + (Δy)²]
Where:
l - Side lengthΔx - Change in the x-direction.Δy - Change in the y-direction.And the perimeter of the image of the triangle is described below:
p = k · (AB + BC + AC)
Where k is the scale factor.
First, determine the lengths of sides AB, BC and AC:
Side AB
AB = √[[4 - (- 4)]² + (3 - 3)²]
AB = 8
Side BC
BC = √[(- 4 - 4)² + (- 6 - 3)²]
BC = √[(- 8)² + (- 9)²]
BC = √145
Side AC
AC = √[(- 4 - 4)² + (- 6 - 3)²]
AC = 9
Second, determine the perimeter of the image:
p = 3 · (8 + √145 + 9)
p = 3 · (17 + √145)
p = 51 + 3√145
p ≈ 87.125
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Consider the following expression: 3y+4+7x
Answer:3,4
Step-by-step explanation:
Prompt
Please number your responses to the questions as they are shown (1, 2a, and 2b).
A student in your class says the following.
"I'm having a hard time with this lesson, because the rules for rational exponents are so different than the rules for integer exponents."
1. Write a response to your classmate's comment. State whether you agree or disagree with the comment and why.
2. a. Choose one of the rules for rational exponents. Explain it to your classmate using complete sentences.
b. Create a problem and use it to show your classmate how your strategy works. Use complete sentences in your explanation.
A great place to start would be to look at one of the rules (maybe product or quotient) for rational exponents and for integer exponents and compare them. Explain the differences between the rules.
Answer:
Step-by-step explanation:
i ag
What type of variation does the following equation represent:
R = kst / v²
Direct
Joint and Inverse
Inverse
Direct and Inverse
Joint
The correct option is Joint variation, because there is not only diect variation or inverse variation.
What is variation in mathematics?
It gives the relationship between a set of variables with the other set of variables.
Consider the given equation.
R = kst / v²
In this question, details of variables is not given hence, consider k is constant and s, t, and v are variables.
Direct variation: When one variable is directly proportional to the other variable then the relation is known as direct variation.
Joint variation: When a variable depends directly or inversely on 2 or more than two variables then the variabtion is known as Joint variation.
Inverse: When a variable varies inversaly with respect to other variable then the the variation is known as inverse variation.
In the equation, there are 3 variables, R varies directly as s and t and varies inversely as [tex]v^2[/tex].
Hence, the correct option is Joint variation, because there is not only diect variation or inverse variation.
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Given: Line segment AC and line segment BD intersect at O.
Prove: ZAOB ZCOD
Since line segment AC and line segment BD intersect at O, ZAOB is supplementary to ZBOC and ZBOC is supplementary to
ZCOD by the linear pair theorem.
Which statement and reason best completes the proof?
ZCOD.
ZCOD.
By the congruent supplements theorem, ZAOB
By the substitution property of equality, ZAOB
By the congruent complements theorem, ZAOBZCOD.
By the subtraction property of equality, ZAOB ZCOD.
By the substitution property of equality, ∠AOB ≅ ∠COD. Then the correct option is B.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Given: Line segment AC and line segment BD intersect at O.
Prove: ∠AOB ≅ ∠COD
By the supplementary angles property, the equations are given as,
∠AOB + ∠BOC = 180° .....1
∠BOC + ∠COD = 180° ....2
By the substitution property of equality, ∠AOB ≅ ∠COD. Then the correct option is B.
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Answer: By the congruent complements theorem
Step-by-step explanation: I took the test
Please answer ASAP
Dorothy is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
A Dorothy is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
Responses
Dorothy is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
Responses
Dorothy is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
Responses
Dorothy is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
Responses
Dorothy is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
Responses
A. slope of PQ = y2 - y1 / x2 - x1 = -1 - (-2)/1-5 = -1/4
B. Slope of QR = y2 - y1 / x2 - x1 = 7 - (-1) / 3 - 1 = 8/2 =4
C. Slope of PQ = y2 - y1 / x2 - x1 = 1 - 5 / -1 - (-2) = -4/1 = -4
D. slope of QR = y2 - y1 / x2 - x1 = 3 - 1 / 7 - (-1) = 2/8 = 1/4
The solution that correctly shows the slope calculation to enable Dorothy show that △PQR is a right triangle
C. Slope of PQ = (y₂ - y₁) / (x₂ - x₁) = (1 - 5) / (-1 - (-2)) = -4/1 = -4D. slope of QR = (y₂ - y₁) / (x₂ - x₁) = (3 - 1) / (7 - (-1)) = 2/8 = 1/4How to find slope of a lineRight triangles are triangles with have perpendicular relationships
The lines will be checked for perpendicularity by calculating the slopes, if any two slopes are negative reciprocals then they are perpendicular and the triangle is a right triangle
Using point PQ
m = (y₂ - y₁) / (x₂ - x₁)
m = (1 - 5) / (-1 - -2)
m = -4
Using point QR
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 1) / (7 - -1)
m = 2/8 = 1/4
Comparing the slopes shows that slopes calculated are negative reciprocals
-4 and 1/4
Therefore the triangle is a right triangle
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What's the domain of f(x)=log(5x+10)+3?
The domain of a function is the set of all possible input values that the function can take without breaking. In the case of f(x) = log(5x+10) + 3, the domain is all real numbers x such that 5x+10 is greater than 0. This is because the log function is not defined for values less than or equal to 0.
To find the domain of f(x), we need to solve the inequality 5x+10 > 0. We can do this by subtracting 10 from both sides of the inequality, which gives us 5x > -10. Dividing both sides by 5 gives us x > -2. Therefore, the domain of f(x) = log(5x+10) + 3 is all real numbers x such that x > -2.
There are 12 boys and 18 girls in Mr. Spano's
math class. If he randomly calls on three
students for answers to an assignment, what
s the probability that all three are girls?
Assume he does not call on the same
tudent more than once.
What are the zero(s) of the function f(x) = 5x² - 25x
————-
X
x = 5
O x = 0 and x = 5
O x = 0
O x = -5
Answer:
x=5
Step-by-step explanation:
Solve the equation by using the Square Root Property. (Enter your answers as a comma-separated list.)
x²
6
X=
= 24
Answer:
12 is the answer of this equation
multiply 2y (1/4y+ 3/4).
After multiplying the given expression, we are left with the following as our solution:
SOLUTION:
[tex]\frac{y^2}{2}+ \frac{3y}{2}[/tex]
Hope this helps!
Which expression is equivalent to square root 36/25 ? 6/25, 5/6
Answer: 6/25
Step-by-step explanation: To find the equivalent expression, we can use the property of square roots that says that the square root of the quotient of two numbers is the quotient of the square roots of the numbers. This property is given by the following equation: sqrt(a/b) = sqrt(a) / sqrt(b)
In this case, the expression we are trying to simplify is sqrt(36/25), which we can rewrite using the property of square roots as follows: sqrt(36/25) = sqrt(36) / sqrt(25)
Then, we can use the property of square roots that says that the square root of a perfect square is the number itself to simplify the expression as follows: sqrt(36/25) = 6 / sqrt(25)
Finally, we can use the property of square roots that says that the square root of a perfect square is the number itself to simplify the expression even further: sqrt(36/25) = 6 / 5
Therefore, the equivalent expression to sqrt(36/25) is 6/25. This means that the correct answer is 6/25, not 5/6.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the definition to the term it is describing.
One of the major differences between line segment, line and ray is the number of the endpoints, or no endpoint in either. Thus the definition of the terms are:
line segment - part of a line that is bounded on both ends by an endpointline - a set of points that extends infinitely in two opposite directionsray - part of a line that has an endpoint and extends infinitely only in one direction.A given set of lines can be differentiated by the major differences among them which could either be in length or a line segment, line or ray. All these are parts of a line but have their individual differences as a means of identification.
Thus, the required definition of terms that would complete the pairs given in the question are:
line segment - part of a line that is bounded on both ends by an endpoint line - a set of points that extends infinitely in two opposite directions ray - part of a line that has an endpoint and extends infinitely only in one directionLearn more about the differences among line, line segment and ray at https://brainly.com/question/14447004
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Select whether the pair of lines is parallel, perpendicular, or neither. y−4=3(x+5), y+3=−13(x+1)
Answer:
neither
Step-by-step explanation:
parallel lines will have the same number next to the x
perpendicular lines will have the negative reciprocal number next to the x
(for example 2 and -1/2 are negative reciprocals)
y−4=3(x+5)
parenthesis first
y−4=3x+15
y=3x+19
y+3= −13(x+1)
y+3= −13x−13
y= −13x−16
3x and −13x are neither the same nor negative reciprocals of each other so
the answer is neither
HELP PLEASE
Krystal bought 9 pounds of ground beef. She saved $8.37 by using a coupon. How much did she save per pound of ground beef?
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
9 pounds = $8.37
1 pound = $0.98
The amount saved per pound is $0.98
What is a unit rate?Unit rate is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Krystal bought 9 pounds of ground beef. She saved $8.37 by using a coupon.
This means,
9 pounds = $8.37
Divide both sides by 9.
1 pounds = 8.37/9
1 pounds = $0.93
Thus,
The amount saved per pound is $0.98
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does anyone know this?
Answer:
10
Step-by-step explanation:
subtract 14 from 24 or 24 from 14
Two bicycle trails were developed in a new housing development. One trail is
3 1/2 miles long. The other trail is 3/4 as long. How long is the second trail?
The length of the second trial will be equal to 2(⁵/₈) miles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.
The length of the second trial will be calculated as,
Length = 3/4 x ( 3¹/₂ )
Length = 2(⁵/₈)
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shawn sells 36 vehicles in 4 weeks. brett sell 56 vehicles in 7 weeks. who sells more vehicles per week?
The person who sells more vehicles per week between Shawn and Brett is Shawn who sells 9 vehicles sold per week.
How to find who sells more per week?In order to determine who sells more vehicles per week between Shawn and Brett, find the unit of cars sold per week.
Shawn:
Number of vehicles sold = 36Number of weeks = 4Number of vehicles sold per week = Number of vehicles sold / Number of weeks
= 36/4
= 9 vehicles sold per week
Brett:
Number of vehicles sold = 56Number of weeks = 7Number of vehicles sold per week = Number of vehicles sold / Number of weeks
= 56/7
= 8 vehicles sold per week
In conclusion, Shawn sold more vehicles per week.
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Find the equation for the line that passes through the point (−1,4), and that is parallel to the line with the equation y−5=34(x−2)
In point-slope form, the equation of the parallel line to y − 5 = 3/4(x − 2) is: y - 4 = 3/4(x + 1).
What is the Equation of Parallel Lines?If two lines are parallel their equation, written in point-slope form y - b = m(x - a), will have the same value of m, which is the same slope.
The slope of the line with the equation y - 5 = 3/4(x - 2), is 3/4. This means that the line that passes through the point (−1, 4), and that is parallel to the line with the equation y − 5 = 3/4(x − 2), will have the same slope, m = 3/4.
To write the equation of the line that is parallel to y - 5 = 3/4(x - 2), in point-slope form, substitute m = 3/4 and (a, b) = (-1, 4) into y - b = m(x - a):
y - 4 = 3/4(x - (-1))
y - 4 = 3/4(x + 1)
The equation of the line that is parallel to y − 5 = 3/4(x − 2) is therefore expressed in point-slope form as: y - 4 = 3/4(x + 1).
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Find the inverse of this question
HELPPP
19. You earn $7 per hour at a fast-food restaurant. You earned a total of
$161 last week. How many hours (h) did you work last week?
On Saturday, Pam spent 1 hour and 15 minutes working on a puzzle. On Sunday, she spent 48 minutes on the puzzle. How many seconds did Pam work on the puzzle in all?
900 seconds
2,880 seconds
3,600 seconds
7,380 seconds
I’m giving 20 points
Pam worked on puzzle for 7380 seconds.
What is unit conversion?Conversion of unit is a multi-step process which involves multiplication or division by a numerical factor. In it one unit of the quantity is changed to another unit of same quantity.
Given,
Pam spent 1 hour and 15 minutes on puzzle, on Saturday.
She spent 48 minutes on puzzle on Sunday.
Total time spent on puzzle by Pam
= 1 hour 15 minutes + 48 minutes
∵ 1 hour = 60 minutes
Total time spend in minutes
= 60+15+48
= 123 minutes
now, 1 minute = 60 seconds
Total time spend in seconds
= 123 × 60
= 7380 seconds.
Hence, 7380 seconds is the total time spend by Pam on the puzzle.
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Write the domain as an inequality. Write the range as an inequality
The Domain and Range are −2 ≤ x ≤ ∞ & 0 ≤ y ≤ ∞ respectively.
What are the Domain and Range?
Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values or range.
Domain:
The x-value at the farthest left point is at x = −2. Now continue tracing the graph until you get to the point that is the farthest to the right. The x-value at this point is at ∞. There are no breaks in the graph going from left to right which means it’s continuous from -2 to ∞.
Domain: [-2, ∞][−2, ∞] also written as −2 ≤ x ≤ ∞
Range:
Look at the furthest point down on the graph or the bottom of the graph. The y-value at this point is y=0. Now, look at how far up the graph goes or the top of the graph. This is when x = ∞, but now we’re finding the range so we need to look at the yy-value of this point which is at y = 0. There are no breaks in the graph going from down to up which means it’s continuous.
Range: [0, ∞][0, ∞] also written as 0 ≤ y ≤ ∞.
Hence, the Domain and Range are −2 ≤ x ≤ ∞ & 0 ≤ y ≤ ∞ respectively.
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What is the mean absolute deviation of these numbers 76, 70, 66, 80, 72, 67, 78, 69
The mean absolute deviation of the given values would be = 4.3125
What is mean absolute deviation?The mean absolute deviation in statistics is defined as the average distance between each data point and the mean and this gives us an idea about the variability in the dataset.
To calculate the mean absolute deviation the following is carried out:
Calculate the mean of the given data:76, 70, 66, 80, 72, 67, 78, 69 = 578/ 8 = 72.25
Calculate the distance between each data point and the mean.76-72.25 = 3.75
70-72.25 = 2.25
66-72.25 = 6.25
80-72.25 = 7.75
72-72.25 = 0.25
67-72.25 = 5.25
78-72.25 = 5.75
69-72.25 = 3.25
The distance should be added together;3.75+2.25+6.25+7.75+0.25+5.25+5.75+3.25 = 34.5
The divide the sum with the number of dataset ;= 34.5/8
= 4.3125
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Consider the polynomial shown
p(x)=2x^4-8x^3+6
The zeroes for the given polynomial will be 1 and 3.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial is, p(x)=2x⁴-8x³+6
[tex]=2x^4-8x^3+6 \\\\ =2\left(x^4-4x^3+3\right) \\\\ =2\left(x-1\right)\left(x^3-3x^2-3x-3\right) \\\\ 2(x-1)+x^2(x-3)-3(x-3) \\\\ x =1 \\\\ x = 3[/tex]
Thus, the zeroes for the given polynomial will be 1 and 3.
The question is incomplete the complete question is"Consider the polynomial p(x)=2x⁴-8x³+6
a. Graph p(x)=2x⁴-8x³+6, and find the real zero of polynomial p.
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Which of the following sets of numbers could represent the three sides of a triangle? \{13,20,35\}{13,20,35} \{11,24,35\}{11,24,35} \{11,24,32\}{11,24,32} \{10,20,31\}{10,20,31}
The correct sets of numbers which represent the three sides of a triangle will be;
⇒ { 11, 24, 32 }
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The sides of a triangle are shown.
Now,
We know that;
The sum of two sides of triangle is greater than the third side.
Hence, We get;
First option;
⇒ [ 13, 20, 35 ]
Cleary, 13 + 20 = 33 < 35
Thus, It is not possible.
Second option;
⇒ [ 11, 24, 35 ]
Cleary, 11 + 24 = 35 = 35
Thus, It is not possible.
Third option;
⇒ [ 11, 24, 32 ]
Cleary, 11 + 24 = 35 > 32
Thus, It is possible.
Therefore, The correct sets of numbers which represent the three sides of a triangle will be;
⇒ { 11, 24, 32 }
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y=-9x+3 complete ordered pairs
Answer:
I think its (0,3), (1,-6), (2,-15)
Step-by-step explanation:
5. Principal: $850
Compound Interest Rate: 5%
Time: 8 years
Answer:
34000
Step-by-step explanation:
you would do 8x5 witch is 40 o now 40x850 is 34000
Tanya had solar panels installed on her house. The graph
below shows the change in temperature of the solar panels
over time.
Temperature (°F)
160
140
120
100
80
60
40
20
0
Solar Panel
Temperature
10 20 30 40 50 60
Time (seconds)
What is the rate of change in the temperature, in degrees
Fahrenheit per second, during the first 45 seconds?
POSSIBLE POINTS: 2
✪
M
10
ED
C
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The rate of change in the temperature during the first 45 seconds is
3.67 degrees Fahrenheit per second
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The following coordinates from the graph as,
(15, 80) and (45, 130)
15 and 45 are the seconds.
80 and 130 are the temperatures.
Now,
The rate of change in the temperature during the first 45 seconds.
= (130 - 80) / (45 - 15)
= 50/30
= 5/3
= 3.67 degrees Fahrenheit per second
Thus,
The rate of change in the temperature during the first 45 seconds is
3.67 degrees Fahrenheit per second
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In a lottery daily game, a player picks four number from 0 to 9 (without repetition). How many different choices does the player have?
a) If order matters?
B)If order did not matter?
A fish descends 4 meters per minute for 2 minutes. Then it ascends 3 meters per minute for 3 minutes. What is the total distance, in meters, the fish traveled?
The fish's total distance traveled is 17 meters in 5 minutes based on multiplication and addition operations.
How is the total distance traveled determined?The total distance the fish traveled can be determined using mathematical operations, especially multiplication and addition.
We know that distance is the product of speed and time, i.e. d = st, where s is speed, t is time, and d is distance.
In this situation, we separately find the distance the fish traveled during its descent and ascent by multiplying time and speed.
The results are added to obtain the total distance the fish traveled for both activities.
The fish's descent speed = 4 meters per minute (MPM)
The total time for the descent = 2
The total distance for the descent = 8 miles (4 x 2)
The fish's ascent speed = 3 meters per minute (MPM)
The total time during ascent = 3 minutes
The total distance for the ascent = 9 miles (3 x 3)
The total distance the fish traveled for descent and ascent = 17 meters (8 + 9)
Thus, we can mathematically conclude that the fish traveled 17 meters.
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