Using CPCTC, name the congruent parts of ΔABC & ΔQRS that are not labeled as congruent in the diagram.
A. AB=QR,BC=RS,
B.AC=QS,
C.AC=QS,BC=RS,
D. AB=QR,BC=RS,
Answers
Answer: A. AB=QR,BC=RS
Step-by-step explanation:
The congruence property of congruence triangle CPCTC says that the corresponding parts of congruent triangles are congruent.
From the given figure, we have
[tex]\angle{A}\cong\angle{Q}\\\angle{C}\cong\angle{S}[/tex]
[tex]\overline{AC}=\overline{QS}[/tex]
The other congruent parts in the triangle.
[tex]\overlien{AB}\cong\overlien{QR}[/tex] [∵ AB corresponds QR]
[tex]\\\\\overlien{BC}\cong\overlien{RS}[/tex] [∵BC corresponds RS]
Related Questions
which of the following is the sum of 3/18+2/18 reduced to lowest terms?
Answers
3/18 + 2/18 = 5/18
And it is in the simplest form.
a culture contains 1500 bacteria initially and doubles every 30 mins. a) find a function that models the number of bacteria at time t. b) find the number of bacteria after 2 hours. c) after how much time will there be 4000 bacteria ...?
Answers
Below are the answers:
a. An = Ao • 2^(t/30)
b. An = 1500 • 2^(60*2/30) or An = 24000
c. 4000 = 1500 • 2^(t/30)
or 4000/1500 = 2^(t/30)
or ln(40/15) = (t/30) ln(2)
or t = 30* ln(8/3) / ln(2)
or t ~ 42.45 min
A submarine's elevation changes -657 feet over a period of 6 minutes. If the submarine descended at a constant rate, what is the approximate elevation change per minute?
-130 feet
-90 feet
-120 feet
-110 feet
Answers
The approximate elevation change per minute for the submarine is -109.5 feet.
Explanation:To find the approximate elevation change per minute, we need to divide the total elevation change by the total time taken. The submarine's elevation changes by -657 feet over a period of 6 minutes. So, we divide -657 by 6 to get the approximate elevation change per minute.
-657 / 6 = -109.5 feet
Therefore, the approximate elevation change per minute is approximately -109.5 feet.
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Which best describes the sides of any trapezoid?
A.
All sides are the same length.
B.
Only one pair of sides is parallel.
C.
Both pairs of opposite sides are parallel.
Answers
Hope this helps!
The answer is: only one pair of sides is parallel a.k.a b
A new law requires that 12% of an individual's income be invested in the stock market. Your accounts show that you need to put $420 in the stock market this year. How much did you earn this year.
A $5,040 B $350 C $504** D $3,500
Answers
The problem can be solved by setting up the equation 0.12x = $420, where 'x' stands for your total income. Dividing both sides of the equation by 0.12 gives x = $3500 which is the total annual income. Thus, you earned $3,500 this year.
Explanation:To solve this mathematical problem, you can set up an equation that represents the problem context. You know that 12% of your whole year's income equals $420. So if 'x' represents your total income, the equation becomes 0.12x = $420. To solve for 'x' (your total income), you would divide both sides of the equation by 0.12.
So, x = $420 ÷ 0.12. When you perform this calculation, you'll find that 'x' equals $3,500. Therefore, you earned $3,500 this year.
The answer to the problem is D. $3,500.
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what does the 2 represent in 12.789
Answers
12.789
2 = (ones digit)
Hope this helps!
:)
Help! Need help!
1. Justin is considering two websites for downloading music.The costs are detailed here.
Website 1: a yearly fee of $30 and $1.50 for each download
Website 2: $2 for each download
What is a system of equations to represent the costs for one year?
Express your equations in the form of y=mx+by=mx+b where x is the number of downloads for the year and y is the total cost for the year.
Website 1:
Website 2:
2. Is the system of equations is consistent, consistent and coincident, or inconsistent?
y=4x−4y=−4x+4
a. consistent b. consistent and coincident c. inconsistent
Answers
website 2 : y = 2x + 0...or just y = 2x
=======================
y = 4x - 4
y = -4x + 4
4x - 4 = -4x + 4
4x + 4x = 4 + 4
8x = 8
x = 1
y = 4x - 4
y = 4(1) - 4
y = 4 - 4
y = 0
so this is a consistent system because it has one solution (1,0)
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
Answers
y be the speed of bicyclist B (heading south)
since A is 5km/hr faster than B
x = y + 5 -----equation 1
time = 9 to 10:45 = 1.75hours since the distance is 47.25km then,
x(1.75) + y(1.75) = 47.25 ---equation 2
substitute equation 1 to 2 (y+5)(1.75) + 1.75y
= 47.25 1.75y +8.75 + 1.75y
= 47.25 3.5y
= 47.25 - 8.75 3.5y
= 38.5
y = 11km/hr
substitute to equation 1
x = y + 5 x
= 11 + 5 x
= 16km/hr
The speed of Bicyclist A (heading north) is 16 km/h.
The speed of Bicyclist B (heading south) is 11 km/h.
Given:
- Let x be the speed of bicyclist A (heading north).
- Let y be the speed of bicyclist B (heading south).
- Bicyclist A is 5 km/h faster than Bicyclist B, so [tex]\(x = y + 5\)[/tex] (Equation 1).
- Time from 9:00 to 10:45 is 1.75 hours.
- The total distance covered by both bicyclists during this time is 47.25 km.
From the equation for time and distance, we have:
[tex]\[ x \times 1.75 + y \times 1.75 = 47.25 \][/tex]
Substituting Equation 1 into this equation:
[tex]\[ (y + 5) \times 1.75 + y \times 1.75 = 47.25 \]\[ 1.75y + 8.75 + 1.75y = 47.25 \]\[ 3.5y + 8.75 = 47.25 \]\[ 3.5y = 38.5 \]\[ y = \frac{38.5}{3.5} \]\[ y = 11 \text{ km/h} \][/tex]
Substituting the value of y back into Equation 1:
[tex]\[ x = 11 + 5 \]\[ x = 16 \text{ km/h} \][/tex]
Thus, the correct answer is:
- The speed of Bicyclist A (heading north) is 16 km/h.
- The speed of Bicyclist B (heading south) is 11 km/h.
Question :
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
What are odd numbers 1-35?
Answers
Is that what you meant.
A triangle has side lengths of 12 cm, 35 cm, and 37 cm. Classify it as acute, obtuse, or right.
acute
obtuse
right
Answers
the answer is so easy
it is acute
There are 132 people seated in the school auditorium for an assembly. There are 6 rows in the auditorium, each with the same number of seats. If the auditorium is completely filled, how many seats are there in each row?
Answers
Explanation:
132÷6=22
Hope it helps!
Which expression is equivalent to 3(x + 4y)?
6x + 16y
3x + 12y
8x + 24y
x + 4y
Answers
3x + 12y is the answer.
kenya picked 18 flowers from her garden. If 3/5 of flowers in her garden remain unpicked, how many flowers are still in her garden?
Answers
Make a mapping diagram for the relation.
{(–2, 2), (–1, –4), (0, –3), (2, 5)}
Answers
IT is dependant on what x equals We plug in our x-value such as 1 into an equation and then we get our y-value. SO basically we start off with an x-value and then land up with a y-value
SO for example we have an equation:
y=3x-4 Let x=3 ---> y=3(3)-4=5
So our y-value is 5 WE are doing the same thing with that mapping picture. ON the left hand side is all the x-values and the right hand side is all the y-values once it has been plugged "some" equatio which is unknown to us
Now we know that a paired coordinate has the form (x,y) where the first value in the bracket is the x-coordinate and the second value is the y-coordinate. The paired coordinate basically tells us that when x is this value y is that value
Jay earns $5.90 per hour working at the ice cream parlor after school. He needs at least $236 for a stereo system. Choose the inequality that describes how many hours Jay must work to buy the stereo system.
Answers
What is 10 to the power of 3?
Answers
solve for x
5(2x - 1) = 6
A)x=1/10
B)X=11/10
C)X=1/2
Answers
Find the least residue of 7^5 mod 50 without using a calculator.
so far I have 7=7 mod 50 7^5 = 7^5 mod 50 7^2 = 49 7^3=343 since 7^2=(-1)mod50 and 7^3=(-43)mod50 it follows that 7^6=7^2 * 7^3 = (-1)(-43) = 43 feel like this is wrong though could somebody please explain where I have made an error?
Answers
7^2 = 49 = -1 (mod 50)
7^3 = 7^2*7 = (-1)*7 = -7 (mod 50)
7^4 = (7^2)*(7^2) = (-1)*(-1) = 1 (mod 50)
7^5 = (7^4)*7 = 1*7 = 7 (mod 50)
So 7^5 = 7 (mod 50)
In other words, if we divided 7^5 over 50, the remainder would be 7. We don't need to worry about the quotient.
Is the number 53 a prime number or a composite number
Answers
Answer:
It's prime:)
Step-by-step explanation:
The number of private investigators is expected to increase from 52,000 in 2006 to 61,000 in 2016. If there are 648,982 police officers in 2006, how many police officers must there be in 2016 to have a greater percent increase than that of private investigators?
Answers
p = ( 61,000 * 100 ) : 52,000 = 117.30769 %
The percent of increase of the number of private investigators is 17.30769 %.
The number of police officers in 2006 is 648,982
648,982 x 1.1730769 = 761,305.79
Answer:
In 2016 must be at least 761,306 police officers
To have a greater percent increase than private investigators between 2006 to 2016, there must be approximately 760,945 police officers in 2016. This is found by applying the formula for percentage increase and adjusting it to find the required final number.
Explanation:The percent increase of private investigators from 2006 to 2016 is found by subtracting the initial number from the final number, then dividing by the initial number and multiplying by 100%. This formula gives us (61000 - 52000) / 52000 * 100 = 17.3%, rounded to the nearest tenth of a percent.
To have a greater increase in police officers than that of private investigators, the percent increase must be more than 17.3%. To find the required number of police officers in 2016, we first express 17.3% as a decimal, which is 0.173. Then we use the formula for percentage increase, which is (final number - initial number) / initial number = percentage increase. By rearranging the formula, we get the required final number = (initial number * percentage increase) + initial number. Substituting the given figures, we have (648982 * 0.173) + 648982 = 760945, rounded to the nearest whole number.
Therefore, there must be approximately 760,945 police officers in 2016 to have a greater percent increase than that of the private investigators.
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What is 1 5/6 + 1/2 ?
a.
14/6
b.
17/12
c.
17/6
d.
25/12
Answers
convert to improper fraction
1 and 5/6=1+5/6=6/6+5/6=11/6
1/2 and 11/6
2 times 3=6
1/2 times 3/3=3/6
1/2+11/6=3/6+11/6=(4+11)/6=14/6
answer is A
70 is 25% of what number
Answers
70=?.25%
70=?.25/100
70=?.1/4
?=280
Wren bought a baseball card last year for $2.25. this year the price dropped to $.45. what was the percent of decrease in the price of the card?
a. 80%
b. 400%
c. 500%
d. 120%
Answers
80%
I hope this helps! :)
Answer:
a. 80%
Step-by-step explanation:
The percent of decrease can be calculated as:
[tex]Percentage Decrease = \frac{Initial price - Final Price}{ Initial Price}*100 [/tex]
Then, replacing initial price for $2.25 and final price for $.45 we get:
[tex]Percentage Decrease = \frac{2.25 - 0.45}{2.25} *100[/tex]
percentage of decrease = 80%
Finally the percentage of decrease in the price of the card is 80%
equation for line parallel to 2x-3y+6=0, with the same y intercept
Answers
the equation of a line that is paralell to the line with the SAME y intercept is the same line
so the answer is 2x-3y+6=0 or any other form of that like 2x-3y=-6, or y=2/3x+2
In algebra, why do you think that you are given many problems to solve that aren't really "real life" problems? For example, "Twice the sum of a number and 5 is 24. Find the number." ...?
Answers
Algebra problems may not seem like 'real-life' problems, but they help build a deeper understanding of mathematical concepts.
Explanation:Often, in algebra, you are given problems that may not seem like 'real-life' problems because they are designed to emphasize understanding the underlying concepts rather than simply executing a mathematical recipe. These problems aim to build a more meaningful understanding of the content by focusing on what the numbers represent and how they relate to each other. For example, in the problem 'Twice the sum of a number and 5 is 24. Find the number,' you can practice solving by setting up an equation and using algebraic manipulation to find the number.
Which of the binomial is a factor of this trinomial x2-7x-44?
Answers
x^2-7x-44
x -11
x +4
(x-11)(x+4)
A side of the square is 4t. the area of the square is 400. what is the value of t?
Answers
The value of the variable 't' will be 5.
What is the area of the square?All the sides of a square are congruent. Let a be the side length of the square. Then the area of the square is the square of the side length of the square.
Then the area of the square will be
Area of the square = a² square units
A side of the square is 4t. the area of the square is 400. Then the value of the variable 't' will be
400 = (4t)²
(4t)² - 20² = 0
(4t - 20)(4t + 20) = 0
t = -5, 5
Thus, the value of the variable 't' will be 5.
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What is the surface area of this design
Answers
hope it helps
Answer:
[tex]384\ in^{2} \\[/tex]
Step-by-step explanation:
Hello
according to the graph the figure is a cube, which has 6 square faces of 8 inches each side,the total area will be equal to the area of one of these faces multiplied by 6
Area of a square=side* side
Area of square= 8 in * 8 in
[tex]Area = 64\ in^{2} \\[/tex]
Now, the total area is
[tex]Tarea=6*64\ in^{2} \\Tarea=384\ in^{2}[/tex]
1 in= 1 inch = 2.54 cm
have a fantastic day
Simplify each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither. Explain your answers.
(a)6x + 2(2x – 3) = 24 + 9x
(b)25 – 4x = 3(5 – x) + 10 – x
(c)4(x + 2) = 2x + 7 + 2(x – 10)
Answers
6x + 2(2x - 3) = 24 + 9x
6x + 2 * 2x + 2 * (-3) = 24 + 9x
6x + 4x - 6 = 24 + 9x
10x - 6 = 24 + 9x
10x - 9x = 24 + 6
x = 30
b) The answer is infinity solutions, identity
25 – 4x = 3(5 – x) + 10 – x
25 - 4x = 3 * 5 - 3 * x + 10 - x
25 - 4x = 15 - 3x + 10 - x
25 - 4x = 25 - 4x
4x - 4x = 25 - 25
0x = 0
x can be any number, so an infinite number of solution
c) The answer is no solution, contradiction
4(x + 2) = 2x + 7 + 2(x – 10)
4 * x + 4 * 2 = 2x + 7 + 2 * x - 2 * 10
4x + 8 = 2x + 7 + 2x - 20
4x + 8 = 4x - 13
4x - 4x = - 8 - 13
0 = -13
this is contradiction
A basketball team averages 98 points in its first three games.How many points must it score in the next game in order to have 100 point average overall?
Answers
The basketball team must score 106 points in the next game to have a 100-point average overall.
To determine how many points the basketball team must score in the next game to have a 100-point average overall, we need to consider the total points scored in the first three games and the desired average.
The team has already played three games and has an average of 98 points. To find the total points scored in these three games, we multiply the average by the number of games:
Total points in the first three games = 98 points/game * 3 games = 294 points.
To have a 100-point average overall, the team needs to score a total of 100 points per game multiplied by the total number of games played, including the next game.
Let's represent the number of points needed in the next game as "x."
(294 points + x points) / (3 games + 1 game) = 100 points/game.
Simplifying the equation:
(294 + x) / 4 = 100.
Cross-multiplying and solving for "x":
294 + x = 400.
x = 400 - 294.
x = 106.
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