The methods which can be used to prove that the two triangles are congruent are:
Prove all three sets of corresponding angles are congruent.
Prove all three sets of corresponding sides are congruent.
Option C and Option D are the correct answer.
What are corresponding angles?Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.
We have,
To prove that two triangles are congruent, we need to show that the corresponding sides and corresponding angles are congruent.
So,
Prove all three sets of corresponding angles are congruent.
Prove all three sets of corresponding sides are congruent.
These two methods can be used to prove that the two triangles are congruent.
Thus,
The methods which can be used to prove that the two triangles are congruent are:
Prove all three sets of corresponding angles are congruent.
Prove all three sets of corresponding sides are congruent.
Option C and Option D are the correct answer.
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Inverse & Composition of Functions
1. Find the inverse of f(x) = x² + 2
Answer: √x−2,−√x−2
Step-by-step explanation:
Christine gets $71 for working the weekend. She buys $53 in clothes and then
makes another $45 babysitting. How much does she have now?
Answer:
63 i think!
Step-by-step explanation:
71-53 is 18. 18+45 is 63!
Im so so so sorry if im wrong, have a nice day friend!: )
Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. Work out the probability that tina takes two blue counters in fraction.
Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. The probability that tina takes two blue counters in fraction is 15/72
What is the probability?Given parameters:
Bag A= 5 red + 3 blue
Bag B = 4 red + 5 blue
Hence,
Total counters in bag A = 5 +3 = 8
Total counters in bag B = 4 + 5 = 9
Now let determine the probability that she takes two blue counters
Probability = 3 /8 × 5 /9
Probability = 15 / 72
Therefore 15 / 72 is the probability that two blue was taken.
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URGENT!!!!!!!!!
Thank you to whoever solves it right!
Answer:
D
Step-by-step explanation:
The plane was at 24,000+ feet above the ground and then it ROSE (indicating an addition of feet to the original) 7,00+ feet.
Hope that helps
Plllsss help answer the question in the picture below!!!!!
The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.
What is the difference between standard deviation and histogram?It always displays the median and the middle 50% of the data. For data displayed in histograms, a similar spread measurement is helpful. The term for it is the standard deviation. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.
The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The sum of the bar heights is therefore one. Only discrete variables (right), where the histogram heights now total to unity, are suitable for relative frequency analysis.
A measurement of how far points deviate from the mean is the standard deviation. The first histogram includes fewer points that are close to the mean and more points that are distant from the mean (scores of 0, 1, 9, and 10). (scores of 4, 5 and 6). As a result, its standard deviation will be higher.
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Martin eats 3/8 of a pizza. Felix eats 2/5of a pizza of
same size. Who eats more pizza? How much more pizza
does he eat?
Hello! I need some help with this homework question, please? The question is posted in the image below. Q11
A one-to-one function means that there are no two elements in the domain of the function that corresponds to the same element in the range,
Mathematically since
[tex]\begin{gathered} x\text{ is the input or the domain, then} \\ f(x)\text{ is the output} \end{gathered}[/tex]A one-to-one follows that
[tex]\text{if }x_1\text{ and }x_2\text{ are two different inputs of a function }f,\text{ then }f(x_1)\neq f(x_2)[/tex]HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:Let r be the number of rides and g be the number of games.
2.50g + 4.00r = 52.50
r = 2g
Step-by-step explanation:
Answer:
lol no
Step-by-step explanation:
What is the completely simplified form of the expression 2(1 - 3x) - (5x + 1)?
A) -11x + 1
B) -8x + 1
C) -11x + 3
D) -8x + 3
Answer:
A
Step-by-step explanation:
2(1-3x)-(5x+1)
=2-6x-5x-1
=1-6x-5x
=1-11x/-11x+1
4. What is the value of x such that 5x + 2a > 2x-a?
a. x < -a
b. x > -a
C. x < a
d. x > a
Answer:
D: x > a
Step-by-step explanation:
We have 5x - 2a > 2x-a
We can rewrite this equation by subtracting 2x on both sides, which gives:
5x - 2x -2a > 2x - 2x - a,
so 3x - 2a > a
We now add 2a on both sides, which gives:
3x -2a + 2a > a + 2a, so 3x > 3a
We nog divide both sides by 3, which gives:
3x/3 > 3a/3, so x>a
The correct answer is D
13. The model represents an equation. 1 1 1 1 À AC X DOOD D0000 solue.) What value of x makes the equation true? 15.
Answer:
The equation is true when x = 2.25
Explanation:
On the left side of the equation, there are 3 triangles with value -x and 10 triangles with value 1. So, the expression for the left side of the equation is:
3*(-x) + 10*(1)
-3x + 10
For the right side, we have 5 triangles with value x and 8 triangles with value -1. So, the expression for the right side is:
5*x + 8*(-1)
5x - 8
Now, we can write the equation as:
-3x + 10 = 5x - 8
So, solving for x, we get:
-3x + 10 + 3x = 5x - 8 + 3x
10 = 8x - 8
10 + 8 = 8x - 8 + 8
18 = 8x
18/8 = x
2.25 = x
Therefore, the equation is true when x is equal to 2.25
Pls help me with this ill give brainlist
If 3 dogs eat 4 pounds of food per day, how many dogs eat 15 pounds of food?
11 dogs will eat 15 pounds of food.
According to the question,
We have the following information:
3 dogs eat 4 pounds.
We have to find how many dogs will eat 15 pounds.
We have the following expression:
4 pounds = 3 dogs
We can treat dog as a non-living object or a product.
So, we can find the parts devoted to 1 pound:
1 pound = 3/4
Now, we have to find the same for 15 pounds:
15 pounds = (3/4)*15
15 pounds = 11.25
Now, note that the number of dogs can not be in points. So, we will round it off to form a whole number.
So, 15 pounds = 11 dogs
Hence, 15 pounds of food is enough for 11 dogs.
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A rectangular room is 4 meters longer than it is wide, and its perimeter is 24 meters. Find the dimension of the room.The length is : meters and the width is meters.
We are given the following information
Perimeter of the rectangular room = 24 meters
The rectangular room is 4 meters longer than it is wide.
Let L be the length and W be the width of the rectangular room.
[tex]L=4+W[/tex]The perimeter of a rectangular shape is given by
[tex]P=2(L+W)[/tex]Substitute P = 24 and L = 4 + W into the above equation
[tex]\begin{gathered} P=2(L+W) \\ 24=2(4+W+W) \\ 24=2(4+2W) \\ 24=8+4W \\ 24-8=4W \\ 16=4W \\ \frac{16}{4}=W \\ W=4\;m \end{gathered}[/tex]So, the width of the rectangular room is 4 meters.
[tex]\begin{gathered} L=4+W \\ L=4+4 \\ L=8\;m \end{gathered}[/tex]So, the length of the rectangular room is 8 meters.
Length = 8 meters
Width = 4 meters
Example Problem:
Suppose that perimeter is 1055 meters.
The length is 45 meters longer than the width of the rectangle.
[tex]L=45+W[/tex]Now, substitute P = 1055 and L = 45 + W into the equation for the perimeter of the rectangle.
[tex]\begin{gathered} P=2(L+W) \\ 1055=2(45+W+W) \\ 1055=2(45+2W) \\ 1055=90+4W \\ 1055-90=4W \\ 965=4W \\ W=\frac{965}{4} \\ W=241.25\;m \end{gathered}[/tex]So, the width of the rectangle is 241.25 meters.
[tex]\begin{gathered} L=45+W \\ L=45+241.25 \\ L=286.25\;m \end{gathered}[/tex]So, the length of the rectangle is 286.25 meters
Find the value of x in the diagram. ΔPQR ~ ΔSTU
find the ratio of the boxes and the circles there are 7 boxes and 10 circles
The ratio of boxes to the circles is 7: 10
2) A toy store is having a sale on puzzles. For each puzzle, Naomi buys she
gets 75% off of a second puzzle. The original price of each puzzle is
$16.50. Naomi bought 4 puzzles. How much did she spend?
Naomi bought 4 puzzles and she spend total $21.91
What is percentage?The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.
Given that : A toy store is having a sale on puzzles. For each puzzle, Naomi buys she gets 75% off of a second puzzle. The original price of each puzzle is $16.50. Naomi bought 4 puzzles
Naomi first puzzle price is $16.50
she get 75% off on as second puzzle
=[tex]16.50(\frac{75}{100} )[/tex]
=12.375
=16.50 - 12.375
= 4.125
So , second puzzle price is 4.124
=[tex]4.125(\frac{75}{100} )[/tex]
=3.09
= 4.125 - 3.09
=1.03
So , third puzzle price is 1.03
=[tex]1.03(\frac{75}{100} )[/tex]
=0.7725
=0.2575
So ,fourth puzzle price is 16.50+4.124+1.03+ 0.2575
=21.91
Total naomi spend 0.2575
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The amount of vinegar that melody used for a recipe can be written as a whole number which could be the amount of vinegar that Melody used?A. -3.75 tspB. 1.5 tspC. 2 1/3 tspD. 12/3
Given:
The amount of vinegar that melody used for a recipe can be written as a whole number.
So, we will check the options to find which one represents a whole number
The whole number does not contain numbers after the decimal point and also the denominator will be 1
So, the answer is option D) 12/3 = 4
45.6 divided by 0.03
Answer:
1,520
Step-by-step explanation:
all the odd numbers from 51 to 5001 are written what is the total number of digits used
Answer:
9404 digits
Step-by-step explanation:
The numbers written:
51, 53, 55, 57, 59, . . . 97, 99 [5*5=25 numbers; 50 digits]
101, 103, 105, . . . 997, 999 [9*50=450 numbers; 1350 digits]
1001, 1003, 1005, . . . 4997, 4999, 5001 [40*50+1=2001 numbers; 8004 digits]
Total:
50 + 1350 + 8004 = 9404 digits
Can you please explain? I have the other options also.
Given
[tex]f(x)=\frac{1}{3}\lvert x+4\rvert-4[/tex]The graph
A cylinder with a radius of 1 yd and a height of 2 yd
determine the domain of each function yx-3x=3y-1
Domain of the given function yx-3x=3y-1 is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3}.
What is a domain?The dependent variable and the independent variable are the two types of variables used to define a function.
The domain of a function is a set of all possible values of x which is an independent variable. For example The domains of function f(x)=x² can be all real numbers.
Despite x=0, the domain of g(x)=1/x can contain any real number.
The input values to a function are referred to as domains, while the output values are referred to as the range. The data flow is as follows:
Domain → Function → Range
We are aware that the value of x is the function's domain. Therefore, the domain is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3} for the provided function.
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following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed
Points which would fall on the line produced by the point-slope form equation y - 3=1/2(x - 7) when graphed are as follow:
c. (1,0)
d. (3, 1)
As given,
Equation of given line
y - 3=1/2(x - 7)
Points which would fall on the line produced by the point-slope form:
a.(0,1)
x=0
y-3=1/2(0-7)
⇒ y=-1/2
b.(1,-1)
x=1
y-3=1/2(1-7)
⇒y=0
c.(1,0)
x=1
y-3=1/2(1-7)
⇒y=0
Required point
d.(3,1)
x=3
y-3=1/2(3-7)
⇒y=1
Required point
Therefore, points which would fall on line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed are as follow:
c. (1,0)
d. (3, 1)
The complete question is :
Which of the following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed?
a. (0,1) b. ( 1,-1) c. (1,0) d. (3,1)
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Bill owns land but has no access to water so he has to pay for well water from Jim.
Jim charges him $8 per month plus $0.80 per gallon.
During any given summer month, his water bill costs between $48 and $72.
Write and solve a compound inequality to determine how much water Bill is using.
Justin places a bet on the giants to win the superbowl. the odds are 2:3. a) Are the giants expected to win? why or why not?b) Find P(Giants win)=
To convert the odds to a probability, we can divide the odds by one plus the odds.
then, in this case we have the following:
[tex]\begin{gathered} \text{odds:} \\ 2\colon3=\frac{2}{3} \\ \Rightarrow1+\frac{2}{3}=\frac{5}{3} \end{gathered}[/tex]then, we have that the probability is:
[tex]\frac{\frac{2}{3}}{\frac{5}{3}}=\frac{2\cdot3}{5\cdot3}=\frac{2}{5}[/tex]thus, the probability that the Giants will win the superbowl is 2/5=0.4=40%
As we can see, we cannot expect for sure that the giants will win
two trains travel at a constant speed. Train a travels 1400 miles in 5 hours and train b travels 2100 miles in 7 hours. Which train travels faster?
Given that events A and B are independent with P(A)=0.85 and P(B) = 0.3,determine the value of P(A|B), rounding to the nearest thousandth, if necessary.
The Solution.
Given that
[tex]\begin{gathered} P(A)=0.85 \\ P(B)=0.3 \end{gathered}[/tex]The conditional probability P(A/B) is given as
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]But for independent events, we have that
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence, it follows that
[tex]\begin{gathered} P(A|B)=\frac{P(A)\times P(B)}{P(B)}=P(A)=0.85\approx0.850 \\ \text{though the nearest thousandth is not necessary.} \end{gathered}[/tex]Therefore, the correct answer is 0.85 ( 0.850 if you consider it necessary)
Tickets of a program at college cost $4 for general admission or $3 with a student ID. If 181 people paid to see a performance and$616 was collected, how many of each type of ticket were sold?In a program at college tickets ?were sold for general admission and?tickets were sold with a student ID.
Tickets were sold for a program at a college .It cost $4 for general admission or $3 with a student ID.
Let
number of people that used student ID = x
number of people that used the general admission cost = y
[tex]x\text{ + y = 181}[/tex][tex]3x\text{ + 4y = 616}[/tex][tex]\begin{gathered} x+y\text{ = 181} \\ 3x+4y=616 \\ x=181-y \\ 3(181-y)+4y\text{ = 616} \\ 543-3y+4y=616 \\ y=616-543 \\ y=73 \\ x+73=181 \\ x=181-73 \\ x=108 \end{gathered}[/tex]108 used the student ID ticket while 73 used the general admission ticket .
The proportion of a population with a characteristic of interest is p = 0.37. What is the standard deviation of the sampling distribution when the sample size is 1,600?
The standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 is equal to 0.0121.
What is a sample proportion?A sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.
Mathematically, sample proportion can be calculated by using this formula:
[tex]\hat{p} = \frac{x}{n}[/tex]
Where:
x represent the number of individuals with a specified characteristic.n represent the total number of individuals in a sample.In Mathematics, the standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 can be calculated by using this formula:
Standard deviation (SD) = √(p(1 - p)/n)
Substituting the given parameters into the formula, we have;
Standard deviation (SD) = √(0.37(1 - 0.37)/1,600)
Standard deviation (SD) = √(0.37(0.63)/1,600)
Standard deviation (SD) = √(0.2331)/1,600)
Standard deviation (SD) = √0.0001457
Standard deviation (SD) = 0.0121.
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