(02.05 MC)
Two similar triangles are shown on the coordinate grid:
Which set of transformations has been performed on triangle ABC to form triangle A'B'C'?
Dilation by a scale factor of 4 followed by reflection about the x-axis
Dilation by a scale factor of 2 followed by reflection about the x-axis
Dilation by a scale factor of 4 followed by reflection about the y-axis
Dilation by a scale factor of 2 followed by reflection about the y-axis
Answers
Answer:
Dilation by a scale factor of 2 followed by reflection about the x-axis
Step-by-step explanation:
To answer it and view it properly let's do it by parts.
1) A closer look at the Triangle ABC shows us the coordinate points A(-2,-1) B(0,0) and C(1,-3).
2) Reflection across the x-axis gives us this triangle: A'(-2,1) B'(0,0) and C'(1,3). Notice that all y-coordinates have an opposite sign. This is a natural characteristic of a Reflection: an opposed sign of one Coordinate.
3) Finally, To Dilate a Triangle is to transform it so that it gets bigger than its original size.
If we compare the triangle with points A''(-4,2) B"(0,0) and C"(2,6) to A'(-2,1) B'(0,0) C'(1,3). Each coordinate is multiplied by 2.
Dilation by a scale factor of 2 followed by reflection about the x-axis
Related Questions
he time spent dancing (minutes) and the amount of calories burned can be modeled by the equation c = 5.5t. Which table of values matches the equation and includes only viable solutions? Image for option 1 Image for option 2 Image for option 3
Answers
Answer:
0 0
5 27.5
10 55
15 82.5
Step-by-step explanation:
Why is world population distribution uneven what factors contribute to this uneven distribution?
Answers
If angle A measures 57 degrees and angle C is adjacent to angle A, what is the measure of angle C if the two angles are complementary?
Answers
90-57=33
complementary angles mean that together, the angles add up to equal 90 degrees
Lena will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs an additional $0.50 per mile driven. The second plan has no initial fee but costs $0.70 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same
Answers
50 = 0.70m - 0.50m
50 = 0.20m
50 / 0.20 = m
250 = m......the plans will cost the same at 250 miles <==
50 + 0.50(250) = 50 + 125 = 175
0.70(250) = 175
and they would both cost $ 175 <==
The two plans cost the same when Lena drives 250 miles, resulting in a cost of $175 for both plans, as per the given linear equation.
A linear equation is a mathematical expression that represents a straight line relationship between variables, typically in the form of ax + b = 0.
The two plans cost the same when the amount of driving satisfies the equation:
50 + 0.50x = 0.70x
Where:
50 represents the initial fee for the first plan,
0.50x represents the cost per mile for the first plan, and
0.70x represents the cost per mile for the second plan.
Now, let's solve for x:
50 + 0.50x = 0.70x
Subtract 0.50x from both sides:
50 = 0.20x
Now, divide both sides by 0.20:
x = 50 / 0.20
x = 250
So, the two plans cost the same when Lena drives 250 miles. To find the cost at this point, plug x = 250 into either plan:
For the first plan:
Cost = 50 (initial fee) + 0.50 (cost per mile) * 250
Cost = $50 + $125
Cost = $175
For the second plan:
Cost = 0.70 (cost per mile) * 250
Cost = $0.70 * $250
Cost = $175
So, when Lena drives 250 miles, both plans cost $175.
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What is the area of the polygon given below?
Answers
(4*7)+(13*9)+(6*6)=181
Answer:
181 square units
Step-by-step explanation:
What is the process that you need to follow in order to prove a circle?
Answers
Line segment
a.a series of points that extend in two directions without end plane
b.two lines that intersect at 90° angles perpendicular lines
c.lines that lie in the same plane and do not intersect line
d.a flat surface that extends infinitely and has no thickness parallel lines
e.part of a line that has two endpoints
Answers
Point A and Point B are two points on Line L
The line between point A and point B that is also a part of Line L is called line segment
The correct definition of a line segment is given by the option e)
Line segment is a part of a line that has two end points
The relationship between feet and inches is described by the equation y = 12x, where x = a given length in feet and y = the equivalent length in inches. If a table is 7.25 feet long, what is its length in inches? A. 84 inches B. 87 inches C. 81 inches D. 90 inches
Answers
The length of the table in inches is 87 inches.
Explanation:To solve this problem, you can use the equation y = 12x to convert the length from feet to inches. Given that the table is 7.25 feet long, you can substitute x = 7.25 into the equation to find y.
y = 12(7.25) = 87
Therefore, the length of the table in inches is 87 inches.
Find the difference.
Correct and best explained answer gets brainliest.
Answers
(-3x^4-9x^3-4x^2-4)-(5x^3-7x^2+6)
= -3x^4-9x^3-4x^2-4-(5x^3-7x^2+6)
= -3x^4-9x^3-4x^2-4-5x^3+7x^2-6
=-3x^4-14x^3+3x^2-10
hence, option D is the answer.
HOPE IT HELPED :D ☺☺
A party was organised for thirty people at which they could have either a hamburger or a pizza. if there were five times as many hamburgers as pizzas, calculate the number of each\
Answers
b + p = 30
5p = b
5p + p = 30
6p = 30
p = 30/6
p = 5 <== 5 pizzas
b + p = 30
b + 5 = 30
b = 30 - 5
b = 25 <== 25 burgers
There are 5 pizza and 25 hamburgers.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A party was organized for thirty people.
And, There were five times as many hamburgers as pizzas.
Now,
Let number of pizza = x
Then, Number of hamburgers = 5x
So, We get;
⇒ x + 5x = 30
⇒ 6x = 30
⇒ x = 5
Thus, Number of pizza = x
= 5
Then, Number of hamburgers = 5x
= 5 × 5 = 25
Therefore, There are 5 pizza and 25 hamburgers.
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An __________ is used to indicate the repeating part of a repeating decimal.
Answers
Luisa knit a rectangular scarf that measures 4 feet by 1 foot. She wants to use the remaining 6 square feet of fabric to create a border around the scarf.
Which equation can she use to find the required width of the border x?
Answers
To solve this problem, let us recall that the formula for Area of a rectangle is:
A = l * w
Where,
l = length of one side = 4 ft
w = width of one side = 1 ft
Therefore the original area is:
Ao = 4 ft * 1 ft
Ao = 4 ft^2
Since each border would be increased by x, therefore the new l and w would be:
l = 4 + 2x
w = 1 + 2x
The new area becomes:
A = (4 + 2x) (1 + 2x)
The difference of the two would be the area of the remaining scarf:
A – Ao = 6 square ft
(4 + 2x) (1 + 2x) – 4 = 6 ---> 1
(4 + 2x) (1 + 2x) = 10 ---> 2
The equation to use can be equation 1 or equation 2.
HELP!! QAQ
Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).
An visual of the function would be really appreciated. Thanks!
Answers
Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martin’s account and let c represent the amount of money in cary’s account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y–4 martin: 200(0.05)y cary: 200(0.05)y–4 martin: 200(1.05)y cary: 200(1.05)y–4
Answers
year interest balance
1 200 * 5% 200(1.05)
2 200(1.05) * 5% 200(1.05)^2
3 200(1.05)^2*5% 200(1.05)^3
y 200(1.05)^y
=> m = 200 (1.05)^y
four years later, cary deposits $200 in an account earning the same interest.
year interest balance
5 200 * 5% 200(1.05)
6 200(1.05) * 5% 200(1.05)^2
7 200(1.05)^2*5% 200(1.05)^3
y 200(1.05)^(y-4)
=> c = 200(1.05)^ (y-4)
Answer:
Martin: 200(1.05)^y
Cary: 200(1.05)^(y–4)
Answer:
d then d again
Step-by-step explanation:
what is the final step to solving the inequality -2(5-4x)<6x-4
Answers
[tex]-2(5-4x) \ \textless \ 6x - 4 \\ -10+8x \ \textless \ 6x -4 \\ -6+8x \ \textless \ 6x \\ -6 \ \textless \ -2x \\ 3 \ \textgreater \ x [/tex]
Answer:
x< 3
Step-by-step explanation:
-2(5-4x)<6x-4
multiply -2 inside the parenthesis
-2 * 5 = -10
-2 * -4x= 8x
-2(5-4x)<6x-4
-10 + 8x < 6x -4
To solve for x we need 'x' on the left hand side
Subtract 6x from both sides
-10 + 8x -6x< 6x -6x -4
-10 +2x < -4
Add 10 on both sides
-10 +10 +2x < -4+10
2x < 6
divide by 2 on both sides
x< 3
what is the x-intercept of the graph of the function f(x)=x2-16x+64?
Answers
Answer:
x-intercept: (8,0)
Step-by-step explanation:
Given: [tex]f(x)=x^2-16x+64[/tex]
For x-intercept, Put y=0 and solve for x.
x-intercept: It is a point where y-coordinate zero.
[tex]x^2-16x+64=0[/tex]
[tex]x^2-8x-8x+64=0[/tex]
[tex](x-8)(x-8)=0[/tex]
Equate each factor to 0 and solve for x
x-8 = 0 , x-8 = 0
x=8,8
x-intercept: (8,0)
Hence, The x-intercept is 8.
The x-intercept of the function is 8
The equation of the function is given as:
[tex]f(x) = x^2 - 16x + 64[/tex]
Expand the equation
[tex]f(x) = x^2 - 8x - 8x + 64[/tex]
Factorize the above equation
[tex]f(x) = x(x - 8) - 8(x -8)[/tex]
Factor out x - 8
[tex]f(x) = (x - 8) (x -8)[/tex]
Set f(x) to 0, to calculate the x-intercept
[tex](x - 8) (x -8)=0[/tex]
Rewrite as:
[tex](x - 8)^2=0[/tex]
Take the square roots of both sides
[tex]x - 8=0[/tex]
Solve for x
[tex]x = 8[/tex]
Hence, the x-intercept of the function is 8
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Using Newton’s cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?
A.130
B.109.16
C.109.76
D.71.35
E.60
Answers
ln(T-Ts) = ln(T0-Ts) - kt
where
T is the final temperature
T0 is the initial temperature
Ts is the temperature of the surroundings
t is the time
k is a constant
Substituting the values:
ln(T-70) = ln(200-70) - (0.6)(2)
T = 109.16°F
The answer is B.
Jessica purchased items worth $41.23 at the local
grocery store. The cashier made a mistake while
ringing up her items, and Jessica ended up paying
$50.23. How many extra dollars did she pay?
Answers
50.23 - 41.23 = 9 <== she paid 9 extra dollars
Your goal is to save at least $240.00 over the next 4 week. How much money must you save each week in order to meet that goal? Write and solve an inequality
Answers
So at least $60/week (notice the = sign, because it at at least, and not 'more than')
The solution is x ≥ $ 60
The value of the inequality equation is x ≥ 60
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Let the minimum money per week to be saved be = x
The number of weeks = 4
The goal is to save at least $240.00 over the next 4 week
So , substituting the values in the equation , we get
x ≥ 240 / number of weeks
x ≥ 240 / 4
On simplifying the equation , we get
x ≥ 60
Therefore , the value of A is x ≥ 60 and should save a minimum of $ 60 per week
Hence , the inequality equation is x ≥ 60
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The product of the roots of 8x² - 2x = 1 is:
Answers
Answer:
[tex]\text{Product of its zeros = }\frac{-1}{8}[/tex]
Step-by-step explanation:
The quadratic equation is given to be : 8x² - 2x = 1
We need to find the product of its zeros
First finding the number of zeros :
⇒ 8x² - 2x - 1 = 0
⇒ 8x² - 4x + 2x - 1 = 0
⇒ (4x + 1)(2x - 1) = 0
[tex]\implies x = \frac{-1}{4}\:\:and\:\: x = \frac{1}{2}[/tex]
[tex]\text{Product of its zeros = }\frac{-1}{4}\times\frac{1}{2}=\frac{-1}{8}[/tex]
A regular pyramid has a height of 12 cm in a square base if the volume of the pier mid is 236 cm³ how many centimeters are in the length of one side of its base?
Answers
now, is a square pyramid, like the picture below, so the base is just a square, so B = length * width, thus
[tex]\bf B=length\cdot width\quad \begin{cases} length=x\\ width=x\\ B=59 \end{cases}\implies B=x\cdot x\implies B=x^2 \\\\\\ 59=x^2\implies \sqrt{59}=x[/tex]
A mother gives birth to a 9 pound baby. every 4 months, the baby gained 2 pounds. if x is the age of the baby in months, then y is the weight of the baby in pounds. find an equation of a line in the form y = mx + b that describes the baby's weight.
Answers
slope = (11 - 9) / ( 4 - 0) = 2/4 = 0.5
at x = 0, it is said that the weight of the baby is 9 lbs so the value of b would be 9.
The equation of the line would be y = 0.5x + 9
Final answer:
The equation of the line that represents the baby's weight as it grows is y = 0.5x + 9, where x is the age of the baby in months, and y is the weight of the baby in pounds.
Explanation:
The student is looking for an equation of a line that represents the weight of a baby as it grows. This situation can be described using a linear equation in the form of y = mx + b, where y represents the weight of the baby in pounds, x represents the age of the baby in months, m is the rate at which the baby gains weight, and b is the initial weight of the baby at birth.
Given that the baby weighs 9 pounds at birth, we have our b value as 9. It is also given that the baby gains 2 pounds every 4 months, which can be converted to a monthly weight gain of ½ pound per month (since 2 pounds ÷ 4 months = ½ pound per month). Consequently, the value of m is ½ or 0.5.
Using these values, the equation of the line that describes the baby's weight over time can be written as:
y = 0.5x + 9
This equation indicates that the baby's weight (y) is 9 pounds at birth (when x = 0) and increases by 0.5 pounds each month.
Joel and Melinda provide the following proofs for vertical angles to be equal:
Joel's proof: angle 2 + angle 3=180° (t is a straight line)
angle 1 + angle 2 = 180° (PQ is a straight line)
Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality)
Hence, angle 1 = angle 3 (Subtraction Property of Equality)
Melinda's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°
Therefore, angle 1 + angle 4 = 180° (t is a straight line)
Hence, angle 4 = angle 2 (Transitive Property of Equality)
Which statement is correct?
A Joels is correct
B Melindas is correct
C Both Melinda and joels is correct
D Neither is correct
Answers
Let's discuss Joel's first. It is clear from the picture than line t and line PQ are straight lines. So the first two statements are true. Transitive property is illustrated as, if a=b and c=b, then a=c. Since angles 1+2 and angles 2+3 are each equal to 180, then these sum of angles are then equal. Subtraction property of equality is illustrated as, if a-c=d and b-c=d, then a=b. Hence,it applies. The proof is correct.
For Melinda's solution, the logic is missing after the statement: Therefore, angle 1 + angle 4 = 180° (t is a straight line). There must be additional proofs before she could use the transitive property of equality.
Therefore, the answer is letter A.
The answer is A! I just did it and gotit right
If f(x)=square root of x+12 and g(x)=2square root of x, what is the value of (f – g)(144)? –84
–60
0
48
Answers
g(x)=2√x
(f-g)(x)=f(x)-g(x)
(f-g)(144)=f(144)-g(144)=
(√144)+12-(2√144)=
12+12-2(12)=
24-24=
0
result is 0
g(x) = 2√x
(f – g)(144) = √(144)+12 - 2√144
(f – g)(144) = 12 +12 - 2(12)
(f – g)(144) = 24 - 24
(f – g)(144) = 0
Use the form of the definition of the integral given in theorem 4 to evaluate the integral x^3-3x^2
Answers
[tex]= \int{x^{3}}\,dx - \int{3x^{2}}\,dx[/tex]
[tex]= \frac{1}{4}x^{4} - \frac{3}{3}x^{3} + C[/tex]
[tex]= \frac{1}{4}x^{4} - x^{3} + C[/tex]
GUYS HELP PLEASE URGENT!!!!!!
A newborn baby weighs 3.136x10^3 units. Which unit of measure was used? grams ounces pounds tons
Answers
its grams because it cant be pounds because a baby isnt 3000 pounds, thats is just crazy!
The unit 'gram' will used to measure the weight of newborn baby in this case.
Unit conversion:
Conversion of units is the conversion between different units of measurements for the same quantity.
1 pound = 0.454kilogram1 kg = 1000 g1 ton = 1000 kg1 ounce = 0.0283 kgAccording to the given question we have,
Weight of the new born baby = [tex]3.136[/tex] × [tex]10^{3}[/tex] = 3136
From the unit conversion,
3136 pound = 1,423.744kg
3136 gram = 3136/1000 = 3.136gram
3136 ton = 3136000 kg
3136 ounce =88.7488 kg
The range of weight of new born baby in kg is 3 to 4.
Hence, only 3136 gram is possible .So, the unit 'gram' will used to measure the weight of newborn baby in this case.
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Two trains leave stations 306 miles apart at the same time and travel toward each other. one train travels at 75 miles per hour while the other travels at 95 miles per hour. how long will it take for the two trains to meet?
Answers
they will meet in 306/170 = 1.8 hours or 1 hour 48 minutes.
Answer: It will take 1.8 hours for the two trains to meet.
Step-by-step explanation:
Since we have given that
Speed of one train = 75 mph
Speed of other train = 95 mph
Since they travel towards each other.
so, Relative speed = 75+95 = 170 mph
Distance between them = 306 miles
We need to find the time taken:
So, it becomes,
[tex]time=\dfrac{Distance}{Speed}\\\\Time=\dfrac{306}{170}\\\\Time=1.8\ hours[/tex]
Hence, it will take 1.8 hours for the two trains to meet.
What is the difference of 28y - 16y
Answers
28y - 16y = 12y
So, 12y is the answer.
Which classifications apply to the polygon? Check all that apply.
convex
concave
regular
hexagon
octagon
Answers
Answer: Concave and Hexagon.
Step-by-step explanation: In the given figure we have one angle is greater than 180 degrees.
A polygon has an angle between 180 to 360 is called a concave polygon.
Therefor given polygon is a concave polygon.
Also the given polygon has six sides.
A polygon with six sides is a hexagon.
Therefore, correct options are Concave and Hexagon.The classifications that apply to the polygon are concave and hexagon.
What is a polygon?
A polygon is a shape with at least three straight sides and angles. A regular polygon has at sides and angles of the same length and size. A convex polygon is a shape in which all of its vertices point in the outward direction. A concave polygon is a shape in which all of its vertices point in the outward direction. A hexagon is a polygon with eight sides.
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A forensic detective is called to the scene of a murder at 2 am. When she checks the temperature of the body, she sees that it is 80 degrees Fahrenheit. The temperature of the room in which the body is found is 65 degrees. If the detective uses Newton's law of cooling, what will she say is the time of death? T(t)=Ta+(To-Ta)e^(-0.1947t).
Thank you to anyone who helps! :)
Answers
[tex]T(t)=T_{a}+(T_{0}-T_{a})e^{-0.1947t}[/tex]
where
T(t) = temperature of the body after t hours, 80 °F
[tex]T_{a}[/tex] = ambient temperature, 65 °F
[tex]T_{0}[/tex] = normal body temperature, assumed to be 98.6 °F
The elapsed time since death is obtained from
[tex]65+(98.6-65)e^{-0.1947t|} = 80[/tex]
[tex]33.6e^{-0.1957t}=15[/tex]
[tex]-0.1947t=ln \frac{15}{33.6} [/tex]
[tex]t= \frac{ln(15/33.6)}{-0.1947} =4.142[/tex]
4.142 hours before 2 am is 9:52 pm (the previous day) approximately.
Answer: 9:52 pm the previous day.