Determine the rigid transformations that will map ΔABC to ΔXYZ.
a. Translate vertex B to vertex Z; reflect ΔABC across side AB.
b. Translate vertex X to vertex C; rotate ΔXYZ to align the sides and angles.
c. Reflect ΔABC across side AB; translate vertex C to vertex X.
d. Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Solution: The correct option is d, i.e., Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Explanation:
we know that the sum of angles of a triangle is always [tex]180^{\circ}[/tex]. In ΔXYZ,
[tex]\angle X +\angle Y +\angle Z=180^{\circ}[/tex]
[tex]35^{\circ} +\angle Y +47^{\circ}=180^{\circ}[/tex]
[tex]\angle Y +82^{\circ}=180^{\circ}[/tex]
[tex]\angle Y =98^{\circ}[/tex]
In both triangles it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A =\angle X=35^{\circ}[/tex] and [tex]\angle B =\angle Y=98^{\circ}[/tex].
By AAS rule of congruence ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having same angle and rotate the triangle to align the sides and angles.
Since vertex X and vertex A have same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.
Hence the correct option is d.
Answer: d
Step-by-step explanation:
Which of the following terms are like terms
A. 2a and 2x
B. 6xy and -16xy
C. X and x^2
D. 2x and 3xy
The length of a rectangle is 3 times the width. The difference between the length and the width is 8 feet. Determine the rectangle's length
The length of the rectangle will be 12 units.
What is a rectangle?
The rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of ractangle = 2( length + width).
Let say,
Length = l and width = w
Given,
length of a rectangle is 3 times the width
l = 3w
The difference between the length and the width is 8 feet
l - w = 8
By equation 1 and 2
3w - w = 8
2w = 8
w = 4
Substitute into equation 1
l = 3(4)
l = 12 units.
So the length of the rectangle will be 12 units.
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10 points!!!
Todd Gunderson went into a partnership with two of his friends. Manny and Jose, to share a route delivering newspapers. Manny owns 1/4 of the partnership, while Jose has a 1/5 interest. If the partnership's monthly revenue amounts to $765, how much of that is Todd's? Round to the nearest cent.
A company has determined that the number of items it sells varies inversely as the price of the item. If 20,000 items can be sold if the price is $9.50, how many items can be sold of the price is $8.75? Round your answer to the nearest whole number.
Find the probability when a couple has 6 children at at least one of them is a boy
The probability when a couple has 6 children at at least one of them is a boy is 63/64
First step
Probability of all 6 girls=(1/2)^6
Probability of all 6 girls = 1/64
Second step is to determine the probability at least one of them is a boy
Let at least one boy means not all girls
Hence:
P(all girls)+P(not all girls)=1
P(at least 1 boy)=1-P(all girls)
P(at least 1 boy)=1-1/64
P(at least 1 boy)=63/64
Inconclusion The probability when a couple has 6 children at at least one of them is a boy is 63/64
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Annie's cafe borrows $6100 at 6% for 290 days. Find the total amount that must be repaid after 290 days. (Use a 365 day year.)
General Idea:
The formula to find the Amount 'A' that need to be paid after ' t ' years for a Principal ' P ' with a annual rate of interest ' r ' is given below:
[tex] A= P(1+r \cdot t) [/tex]
Applying the concept:
Annie's cafe borrows $6100 at 6% for 290 days.
From the above statement we can conclude,...
[tex] P= \$6100\\ \\ r=6\%\\ \\ t=\frac{260}{365} [/tex]
Substituting the values of P, r and t in the formula, we get...
[tex] A=6100 \cdot (1+6 \% \cdot \frac{260}{365} )\\ \\ A=6100(1+\frac{6}{100} \cdot \frac{260}{365} )=6100(1+\frac{1560}{36500} ) \approx 6361 [/tex]
Conclusion:
The total amount that must be repaid after 290 days is approximately [tex] \$6361 [/tex]
Could you please help me out ?
A repairman charged $93.06. the price included 2 hours of labor and a $40 serive charge how much does the repaiman charge per hour for labor?
trapezoid: b1=3 m;b2 =4m A= 7 m2 What is the missing
dimension
Simplify 10/16 to lowest terms and find an equivalent fraction that has a denominator of 32?
Answer:
The lowest fraction for [tex]\frac{10}{16}[/tex] is [tex]\frac{5}{8}[/tex] and a equivalent fraction with denominator of 32 is [tex]\frac{20}{32}[/tex].
Step-by-step explanation:
First, to have the fraction to the lowest terms we will have to divide the numerator and denominator by 2, this is:
[tex]\frac{10/2}{16/2}=\frac{5}{8}[/tex]
As can be seen the expression couldn't be simplified more because there is no a common number that could divide the numerator and denominator.
Second, to have an equivalent fraction with 32 in the denominator we will have to multiply the denominator by 2 and of course the numerator, this is:
[tex]\frac{10*2}{16*2}=\frac{20}{32}[/tex]
The lowest fraction for [tex]\frac{10}{16}[/tex] is [tex]\frac{5}{8}[/tex] and a equivalent fraction with denominator of 32 is [tex]\frac{20}{32}[/tex].
To simplify 10/16 to lowest term, it becomes 5/8. An equivalent fraction of 5/8 with 32 as the denominator is 20/32.
Explanation:To simplify 10/16 to its lowest term, we have to find the greatest common divisor of 10 and 16, which is 2. Hence, when we divide both the numerator and the denominator by 2, we get 10/2 = 5 and 16/2 = 8. So, the fraction 10/16 simplified to its lowest term is 5/8.
Now, to find an equivalent fraction with 32 as the denominator, we need to multiply both the numerator and the denominator of 5/8 by the same number so as not to change the value of the fraction. Here, we multiply by 4 (since, 8*4 = 32) to get 5*4 = 20 on the numerator. Therefore, an equivalent fraction of 5/8 with 32 as the denominator is 20/32.
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when an aircraft takes off, it accelerates until it reaches its takeoff speed V. in doing so it uses up a distance R of the runway, where R is proportional to the square of the of the takeoff speed. if V is measured in miles per hour and R is measured in feet, then 0.1639 is the constant of proportionality. if an aircraft has a takeoff speed of about 215 miles per hour, how much runway does it need?
Lisa and Frank shared 1/3 pound of cherries equally what fractional part of a pound did each person receive?
Answer: 0.3333
Part A.
Molly wrote the following quotation to solve the problem: 2 . 1/3 = n.
Do you agree with Molly's equation? Support your answer with information from the problem.
Answer with explanation:
1)
If we divide 1/3 pounds equally among two people then each of them will get a share of:
[tex]\dfrac{1}{2}\times \dfrac{1}{3}\\\\=\dfrac{1}{6}\\\\=0.1666\ pounds[/tex]
Hence,the given answer that each will get 0.3333 pounds is incorrect.
2)
Molly wrote the following quotation to solve the problem: 2 . 1/3 = n.
This is an incorrect equation since this equation does not represent the half share of 1/3 pounds.
It represents the double amount of 1/3 pounds.
What is the GCF of 14x^2 and 4xy? A. 10x B. 28x^2y C. 2x2 D. 2x
What is the inverse of f(x) 3^sqrt x-4
The inverse of f(x) = ∛(x-4) is f(x)³ + 4.
What is inverse of function?The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.
Given:
We have the equation,
f(x) = ∛(x-4)
Let y = ∛(x-4)
In order to find the inverse function, we have to solve for y :
y = ∛(x-4)
y³ = (x-4)
x = y³ + 4
or, x = f(x)³ + 4
Therefore, f(x)³ + 4 is the inverse function.
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Which undefined term is needed to define an angle????
POINT WASNT AN OPTION ON MY TEST. THE ANSWER WAS PLANE. THE ANSWER CAN BE POINT, LINE, OR PLANE.
Answer:
Line
Step-by-step explanation:
A line is a undefined term used to define a angle. An angle is the corner that is created where two non-parallel lines meet/ intersect
There is 12/15 of a pizza left. How many 3/10 pieces can be made from the leftover pizza? Show work please!
How many 1/3 pieces can be made from 2 pizzas, we know it is 6 and it is arrived by dividing 2 by 1/3 or multiplying by its reciprocal 3/1.
Hence to find how many 3/10 pieces can be made from 12/15 pizza, we have to divide 12/15 by 3/10 or multiplying by its reciprocal 10/3, i.e.
12/15 times 10/3= 8/3 or 2 2/3
What does that mean? This means that while 2 three-tenths pieces can be made, 2/3of 3/10 i.e. 2/3×3/10=2/10=1/5 or one-fifth of pizza will be left out.
So the answer is 2 three-tenths pieces can be made, and one-fifth pizza will be left out.
Answer: it would be 2 3/10 pieces will be left over
Find the new amount given the original amount and the percent amount 810 songs; 130% increase
Help!!!!!!!!!!!!!!!!!!!!!!!
please ty
c:
Janice makes 4 pizzas for dinner. There are 5 people to eat dinner. How much will each person get to eat?
Use the following figure to answer the question. 1 and 4 are _____ angles. corresponding vertical supplementary adjacent
Answer:
vertical angles
Step-by-step explanation:
We need to identify ∠1 and ∠4 are which type of pair of angles .
Since we are given the options :
1, correspoding angles: Corresponding Angles
When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles.
2. vertical angles : The angles opposite each other when two lines cross. They are always equal.Vertical" refers to the vertex (where they cross), NOT up/down
3. supplementary angles : Two Angles are Supplementary when they add up to 180 degrees
4. adjacent angles:Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.
Thus according to definitions ∠1 and ∠4 are vertical angles
In △DEF, DE = 5 and m∠F=55. Find FE.
The gandhara region is the home of many portrayals of ____.
if the parent function is square root of x, describe the translation of this function square root x+7
The function [tex] y=\sqrt{x} [/tex] sits with its starting point at the origin. The function [tex] y=\sqrt{(x-h)}+k [/tex] is translated h units to the left or right and k units up or down. Since our radicand, the value under the square root sign, is x+7, putting that into our standard form it would be x-(-7) because minus a negative is a positive. So we move the parent graph to the left (-7 moves to the left) 7 units. There is no number k so our function is not moving up or down. Only to the left 7.
What is the area of this figure?
Enter your answer in the box.
PLEASE HELP ASAP!!! IF CORRECT YOU WILL GET 10 POINTS AND MARKED AS BRAINLIEST AS SOON AS I CAN!!!
Try this solution:
1. The final formula for the area of the figure is: A=A₁+A₂, where A₁ - the area of the square (its side is 18m) and A₂ - area of the triangle (the base is (8+18)m., height is 16 m.)
2. Using all the data in the formula above:
A=18*18+0.5*16*(8+18)=324+8*26=324+208=532 m².
answer: 532
If P(x) = 0.25, find the complement
The low temperature in Leroy’s town one day was -4. The difference between the high temperature and the low temperature that day was 6. The equation h-(-4)=6 can be used to find h, the high temperature in the town that day in degrees Fahrenheit. What was the high temperature in the town that day, in degrees Fahrenheit?
A rectangular garden is 6 feet long and 4 feet wide. A second rectangular garden has dimensions that are double the dimensions of the first garden. What is the percent of change in perimeter from the first garden to the second garden? The perimeter increases % from the first garden to the second garden.
Answer:
100%
Step-by-step explanation:
When the dimensions double, the perimeter doubles.
The percent change can be found from ...
percent change = ((new value)/(old value) -1) × 100%
Filling in your values, you have ...
percent change = ((2×(old perimeter))/(old perimeter) -1) × 100%
= (2 - 1) × 100%
= 100%
The perimeter increases by 100% from the first garden to the second.
After 5 months, the number of subscribers to a newspaper was 5,730. After 7 months, the number of subscribers to the newspaper was 6,022. Which equation models the number of newspaper subscribers y after x months? y = –146x – 5,000 y = 146x + 5,000 y = 146x – 5,000 y = –146x + 5,000
The can of wood stain is twice as wide but half as tall as the can of paint. What is true about the areas of their labels?
Answer:
Astain = Apaint
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Step-by-step explanation: