Angles <1 and <3 are proven to be congruent because they are both supplementary to the same angle <2, thus having the same measure as per the transitive property of equality.
When given that <1 and <2 are supplementary and that <2 and <3 are supplementary, we can prove that <1 is congruent to <3 through a series of logical steps. By definition, supplementary angles add up to 180 degrees. Therefore, if <1 and <2 are supplementary, we can write this as: m<1 + m<2 = 180 degrees (1). Similarly, if <2 and <3 are supplementary, that looks like: m<2 + m<3 = 180 degrees (2). By transposing m<2 from equation (1) to (2), we get m<1 = m<3, which implies that <1 is congruent to <3, as they have the same measure. This reflects the transitive property of equality where if a = b and b = c, then a = c. This conclusion demonstrates the Theorem 12, which states that if two angles are congruent to each other, their supplementary angles are also congruent.
A bus makes a stop at 2:30, letting off 14 people and letting on 5. The bus makes another stop ten minutes later to let off 4 more people. How does the number of people on the bus after the second stop compare to the number of people on the bus before the 2:30 stop?
2.135meters round to nearest hundredth on number line
2.135 meters rounded to the nearest hundredth is 2.14 meters. Decimal conversion for centimeters to meters involves moving the decimal two places to the left. A ruler measuring in millimeters allows for more precise measurement.
To round 2.135 meters to the nearest hundredth, you should look at the third digit after the decimal point, which is 5. Because the third digit is 5 or greater, you round the second digit up. Therefore, 2.135 meters rounded to the nearest hundredth is 2.14 meters when placed on a number line.
When considering decimal conversion from centimeters to meters, you need to move the decimal point two places to the left (e.g., 100 cm is equal to 1.00 meters). For precise measurements, it's important to have a ruler that can measure at least to the nearest tenths of a centimeter, which is also known as millimeters, so you can then estimate to the hundredths.
To round 2.135 meters to the nearest hundredth, we look at the digit in the hundredths place, which is 3 in this case. Since 3 is less than 5, we round down the digit in the tenths place. Therefore, the rounded value of 2.135 meters to the nearest hundredth is 2.13 meters.
On a number line, you can mark this value between 2.12 and 2.14, closer to 2.13.
siobhan rounds 99,498 to the nearest thousand and gets 100,00
The perimeter of a rectangle is 24 feet. The length is 3 feet less than twice the width. Which of the following systems would be used to solve this problem ???
The system of equations are 24 = 2(l + w) and l = 2w - 3 option third is correct.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
Let l be the length and w be the width of the rectangle
By the formula of perimeter:
24 = 2(l + w)
l = 2w - 3 (The length is 3 feet less than twice the width)
The system of equations:
24 = 2(l + w)
l = 2w - 3
Thus, the system of equations are 24 = 2(l + w) and l = 2w - 3 option third is correct.
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Which pair of points have equal X coordinates?
The points T and S will have the same abscissa, and the points Q and R have the same abscissa. Then the correct options are A and D.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The pair of points that have equal X coordinates that is abscissa will be
From the diagram, the coordinate of the points R, Q, S, and T will be
R ⇒ (-5, -7)
Q ⇒ (-5, 6)
S ⇒ (5, -6)
T ⇒ (4, 6)
The points Q and R have the same abscissa.
Then the correct options are A and D.
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Which is a better approximation of the square root of20, 4.5 or 4.47
Answer:
4.47
Step-by-step explanation:
Given : [tex]\sqrt{20}[/tex]
To Find : Which is a better approximation
Solution:
20 lies between two perfect squares i.e. 16 and 25
Square root of 16 = 4
Square root of 25 = 5
So, Square root of 20 must lie between 4 and 5
Using calculator
The [tex]\sqrt{20}=4.47[/tex]
Hence a better approximation of the square root of 20 is 4.47.
A local museum had a total of 38,267 visitors last year. The museum was open everyday except for four holidays. On average how many visitors did the museum have each day ?
peter bought 6 mangoes at $x each. He also bought a papaya for $5. Express the total cost of the fruits in terms of x.
Prime factorization of 92
How do I solve this and write it in scientific notation?
Express 0.18 as a fraction in simplest form
207 divided by 9 please I know might be easy but I'm bad at division someone help me by Friday this :D
math question down below
The quotient of two consecutive positive integers is 1.02. What is the sum of these two integers?
Plz help asap I need it badly
The sum of the two consecutive positive integers, approximated to be 51 and 52, is 103.
If the quotient of two consecutive positive integers is 1.02, it indicates a very small difference between the two integers.
However, since integers cannot have fractional parts, the quotient cannot be exactly 1.02. If we assume the quotient is approximately 1.02, it means the two consecutive integers are very close to each other.
Let's solve it:
Let's denote the smaller integer as x, then the larger one would be x + 1.
So, we have:
[tex]\[\frac{x}{x + 1} \approx 1.02\][/tex]
Now, we can cross multiply:
[tex]\[x \approx 1.02(x + 1)\][/tex]
[tex]\[x \approx 1.02x + 1.02\][/tex]
Subtract 1.02x from both sides:
[tex]\[0.02x \approx 1.02\][/tex]
Now, divide both sides by 0.02:
[tex]\[x \approx \frac{1.02}{0.02}\][/tex]
[tex]\[x \approx 51\][/tex]
So, one integer is approximately 51. The next consecutive integer would then be 52.
The sum of these two integers is 51 + 52 = 103.
Thus, the sum of the two consecutive positive integers is approximately [tex]\(\boxed{103}\).[/tex]
Which of the following equations has the same solution as m - (-62) = 45?
x + 25 = 8
25 - x = 8
120 - x = 13
120 + x = 13
A number has 2 tens and 15 ones write the number in words
The revenue from selling x shirts is r(x) = 11x.
The cost of buying x shirts is c(x) = 6x + 20.
The profit from selling x shirts is p(x) = r(x) – c(x).
What is p(x)?
MULTIPLE CHOICE:
A. p(x) = 17x + 20
B. p(x) = 17x – 20
C. p(x) = 5x + 20
D. p(x) = 5x – 20
Give me an example of a decimal that is irrational...then show me the ratio.
Assume that a balloon is spherical shaped. If you have a. Balloon with a radius of 3 cm, what's the volume?
What’s 67/100 in simplest form
Figure ABCD is a parallelogram with point C (3, −2). Figure ABCD is rotated 90° counterclockwise to form figure A′B′C′D′. What coordinate would be the output for point C'?
Answer: (2,3) C’
Step-by-step explanation:
I took the test and got it right
Find the LCM of 6 and 12
If the probability of rain is 0.87, what is the probability of NO rain?
There were 340,000 cattle placed on feed. Write an equivalent ratio that could be used to find how many of these cattle were between 700 and 799 pounds. How many of the 340,000 cattle placed on feed were between 700 and 799 pounds?
There were 340,000 cattle placed on feed
How many of the 340,000 cattle placed on feed were between 700 and 799 pounds?
Given the fraction of total cattle for 700 - 799 pounds is 2/5
Let x be the number of cattle between 700 - 799 pounds
We make a proportion using the fraction
[tex]\frac{2}{5} = \frac{x}{340,000}[/tex]
Cross multiply it and solve for x
340000* 2 = 5x
680000 = 5x
Divide by 5 on both sides
So x= 136,000
There were 136,000 cattle between 700 and 799 pounds
Can someone plz help me with this math problem.
3x-4/4 = 5x+2 solve it
What is the relationship between 9.125×10−3 and 9.125×102 ? Select from the drop-down menus to correctly complete the statement. 9.125×10−3 is times than 9.125×102 .
is it 100
9.125×10² is 100000 times the [tex]9.125\times10^{-3}[/tex].
We need to find what is the relationship between [tex]9.125\times10^{-3}[/tex] and 9.125×10².
What is scientific notation?The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.
9.125×10² can be written as [tex]9.125\times10^{-3+5}=9.125\times10^{-3}\times10^{5}[/tex]
= [tex]9.125\times10^{-3+5}=9.125\times10^{-3}\times100000[/tex]
Therefore, 9.125×10² is 100000 times the [tex]9.125\times10^{-3}[/tex].
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how is the subtraction of integers related to the addition of integers?
The table shows the record monthly high and low temperatures for a city in Alaska.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
High(F) 56 57 56 72 82 92 84 85 73 64 62 53
Low(F) -35 -38 -24 -15 1 29 34 31 19 -6 -21 -36
a. Find the range of temperatures for each month.
b. What are the all-time high and low temperatures?
c. What is the range of the temperatures in part (b)?
Answer:
it is 40 f to -3 f
Step-by-step explanation:
so i just subtracted and got 3 supposedly. than ad another 37 and got 40 so it is 40 f to - 3 f
A giraffe can run up to 46.93 feet per second. How far could a giraffe run in 1.8 seconds? Justify your answer.