Answers
Answer:
ΔABC ~ ΔQPR by the Angle-Angle (AA) similarity theorem of two triangles
Step-by-step explanation:
The coordinates of the vertices are given as follows;
A = (1, 2), B =(9, 8), C = (1, 8)
P= (5, -3), Q = (-7, 6), R = (-7, -3)
The given dimensions of AB and PQ are 10, and 15 respectively
The, l lengths of the sides of triangles are found as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
For segment BC, we have;
B =(9, 8), C = (1, 8)
(x₁, y₁) = (9, 8), (x₂, y₂) = (1, 8), substituting gives;
Length BC = 8
For length CA, C = (1, 8) A = (1, 2)
(x₁, y₁) = (1, 8)
(x₂, y₂) = (1, 2)
The length found by substituting the values for (x₁, y₁), (x₂, y₂) in the length equation gives; Length CA = 6
Given that length CA² + BC² = 8² + 6² = 64 + 36 = 100 = BA², we have by Pythagoras theorem, we have ΔABC is a right triangle
Similarly, for ΔQPR, we have;
Length QR, Q = (-7, 6), R = (-7, -3) = 9
Length PR, P= (5, -3), R = (-7, -3) = 12
QR² + PR² = 9² + 12² = 225 = 15² = PQ²
∴ ΔQPR is a right triangle
By comparing the ratio of the sides, we have;
cos(θ) = PR/PQ = 12/15 = 4/5, θ = cos⁻¹(4/5) = 36.9°
∠RPQ = 36.9°
sin(θ) = QR/PQ = 9/15 = 3/5
Similarly in triangle ΔABC, we have;
cos(θ) = BC/AB = 8/10 = 4/5
∠CBA = 36.9°
Therefore, ∠CBA ≅ ∠RPQ = 36.9°
Also ∠PRQ ≅ ∠BCA = 90° (Angle opposite hypotenuse side of right triangle
Therefore, ΔABC and ΔQPR are similar triangles by the Angle-Angle (AA) similarity theorem of two triangles.
Related Questions
thing
Fill in the blank with the correct response.
The slope of the graph of y= 5x is
ao
Answers
Answer:
slope is 5
Step-by-step explanation:
y = 5x
This is in the form
y = mx+b where m is the slope and b is the y intercept
The slope is 5 and the y intercept is 0
In slope intercept form, y=mx+b, m is the slope. You can see that 5 is in the place of m, so the slope is 5
Factor x^4+xy^3+x^3+y^3 completely showing work.
Answers
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x^4+xy^3+x^3+y^3\\\\=x^3*x+x*y^3+x^3+y^3\\\\=x(x^3+y^3)+x^3+y^3\\\\\boxed{=(x+1)(x^3+y^3)}\\[/tex]
Thank you
85 POINTS! PLEASE HELP! Explain how to write an equation parallel to the equation y = 2x + 3 and the new line also includes the ordered pair (1,-2).
Answers
Answer:
[tex]\huge\boxed{\sf y = 2x -4}[/tex]
Step-by-step explanation:
The given equation is:
y = 2x + 3
Where Slope = m = 2 , Y-intercept = b = 3
Parallel lines have equal slopes
So, Slope of new line = m = 2
Now, Finding y-intercept:
Given Point = (x,y) = (1,-2)
So, x = 1 , y = -2
Putting m, x and y in standard form of equation to get b:
[tex]\sf y = mx+b[/tex]
[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]
Subtracting 2 to both sides
[tex]\sf b = -2-2\\[/tex]
b = -4
So, the standard form og equation for the new line is :
[tex]\sf y = mx+b[/tex]
[tex]\sf y = 2x -4[/tex]
Answer:
y = 2x - 4
Step-by-step explanation:
the problem is called (slope-intercept form)
the equation of the line is y = mx + b
the equation of a line is given as y = 2x + 3
slope = 2
b = y-intercept is where the line crosses the y-axis = 3
so point (x1, y1) = (1, -2)
by using the equation.
y = mx + b
-2 = 2 (1) + b
-2 -2 = b
therefore b = -4
writing the new equation using the slope intercept form
y = mx + b would be y = 2x + 4
so the equation parallel to the equation y = 2x + 3 is y = 2x - 4
Xian and his cousin Kai both collected stamps. Xian has 56 stamps, and Kai has 80 stamps. They boys recently joined different stamp-collecting clubs. Xian’s club will send him 12 new stamps per month. Kai’s club will send him 8 new stamps per month. after how many months will Xian and Kai have the same number of stamps? How many stamps will each have?
Answers
Answer:
After 4 months Xian will have 104 stamps,
But after three months Kai will also have 104 stamps
Step-by-step explanation:
Given the following venn diagram, choose the correct set for M
Answers
Answer:
M contains 3,4,7,9
M bar is 2 ,5 ,6 ,8
Step-by-step explanation:
The set for M is what is in the circle labeled M
M contains 3,4,7,9
The question in the picture asks for M bar which is what is not contained in M
M bar is 2 ,5 ,6 ,8
Quadratic and Ratios...
Answers
Answer:
x=0
Step-by-step explanation:
in the quadratic formula to only have one solution
[tex]b^{2} -4ac=0[/tex] for [tex]ax^2+bx+c=0[/tex]
so we have
[tex]ax^2+b=c[/tex]
[tex]ax^2+(b-c)=0[/tex]
if we insert in the formula we have
[tex]0^2-4(a)(b-c)=0\\\\-4ab+4ac=0\\\\4ac=4ab\\\\\frac{4ac}{4a} = \frac{4ab}{4a}\\\\c=b[/tex]
[tex]ax^2+b=c\\\\ax^2=b-b\\\\ax^2=0[/tex] since a≠0
[tex]\frac{ax^2}{a}=\frac{0}{a} \\\\x^2=0\\\\x=0[/tex]
in a 10 team league, each teams play every other team exactly twice. find the total number of games played in the league
Answers
Addition can be defined as the process of adding two numbers. The total number of games played in the league is 90.
What is Addition?Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.
Given that in a 10-team league, each team play every other team exactly twice. Therefore, the total number of games that will be played by the first team is 18, similarly, the number of games that will be played by the second team is 16.
Therefore, as mentioned above the series will continue with a common difference of -2 and will continue till 0. Thus, the total number of games played in the league is,
Total number of games = 18 + 16 + 14 + 12 + 10 + 8 + 6 + 4 + 2 = 90
Learn more about Addition:
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What is the y-intercept of the line that passes through the points (2, 5) and (3, 6)?
Answers
Answer:
(0, 3)
Step-by-step explanation:
First, find the slope using rise/run (y2 - y1) / (x2 - x1)
Plug in the points:
(6 - 5) / (3 - 2)
1/1 = 1
Now, we can plug in the slope and a point into the equation y = mx + b to find b (y-intercept)
y = 1x + b
5 = (1)(2) + b
5 = 2 + b
3 = b
= (0, 3)
. A salesman sold 300 bags of maize to a retailer at Kshs .2000 each .He was given a commission of 3%.The salesman allowed a discount of 0.2% on the maize sold. This discount was deducted from his commission. (a) Calculate (i) The discount allowed
Answers
Answer:
The discount allowed per bag is kshs 4
while the discount allowed on all the 300 bags is kshs 1,200
Step-by-step explanation:
Here, we are interested in calculating the discount allowed on the sales of the bag of maize.
From the question, we are told that the sales man allowed a discount of 0.2% on the maize sold.
Now, to find the amount of this, we proceed as follows;
What we simply need to do is to find 0.2% of the each of the price of the maize bags, and then we can proceed to find the total discount given on all maize bags sold.
The discount on each bag of maize would be;
0.2% of kshs 2000
That would be;
0.2/100 * 2,000 = 400/100 = kshs 4
Since there are 300 bags, the total amount of discount allowed is 300 * kshs 4 = kshs 1,200
The graphic below shows a protractor, which is used to measure angles. What is the level of accuracy of this measurement tool? its a projractor
Answers
Step-by-step explanation:
A protractor is a handheld to use in measuring angles. It is most cases made up of plastic or glass materials, and can accurately measure angles of circles up to 180°.
However, when measuring straight lengths, a ruler or tape has better measuring accuracy than the protector.
What is the difference between sin^-1 and sin?
Answers
Answer:
Step-by-step explanation:
sin of angle x is the trig ratio sine of x.
sin-1 x is the angle whose sine is x.
sin-1 x can also be written as arcsin x.
According to the number line, which statement MUST be true? A) A > 1 B) B > 4 C) C < 4 D) D < 0
Answers
Answer:
The anwser is C) C < 4
......... .
WILL GIVE BRAINLIEST
Question 8(Multiple Choice Worth 1 points) (06.04 LC) Choose the correct product of (6x − 2)(6x + 2). A.36x2 + 4 B.36x2 − 24x + 4 C. 36x2 + 24x + 4 D. 36x2 − 4
Answers
Answer:
D) 36x²-4
Step-by-step explanation:
36x²+12x-12x-4
36x²-4
[tex](6x - 2)(6x + 2) \\ = {(6x)}^{2} - {(2)}^{2} \\ = {36x}^{2} - 4[/tex]
Answer:
D.
[tex] {36x}^{2} - 4[/tex]
Hope you could understand.
If you have any query, feel free to ask.
simplify 3/7
into a whole number
Answers
Answer:
You can't because it's not a "full fraction" like 7/7. The best you can do is turn that into a decimal like 0.43
Step-by-step explanation:
ast week, the Vargas family drove 30 miles in their car and 15 miles in their truck. The letter m stands for the total number of miles they drove. Which equation can you use to find m?
Answers
Answer:
m = 30 + 15
Step-by-step explanation:
The distance traveled by the Vargas family in their car is 30 miles while the distance traveled when using their truck is 15 miles. To get the total distance traveled, we need to add the distance traveled by the truck and the distance traveled by the car. Since m stands for the total number of miles they drove, the equation needed to find the total distance traveled (m) is given as:
m = 30 + 15
m = 45 miles
For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.989. Using alph=0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Correlation Coefficient (r) = 0.989
alph=0.05
Number of observations (n) = 8
determine if there is a linear correlation between chest size and weight.
Yes, there exists a linear relationship between chest size and weight as the value of the correlation Coefficient exceeds the critical value.
What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
To determine the the proportion of variation in weight that can be explained by the linear regression line between weight and chest size, we need to obtain the Coefficient of determination(r^2) of the model.
r^2 = square of the correlation Coefficient
r^2 = 0.989^2 = 0.978121
Hence, about 0.978 (97.8%) of the variation in weight can be explained by the linear relationship between weight and chest size.
please helppp ill give brainliest the question is attached below
Answers
Answer: It is false, the diameter is not 16 m.
Step-by-step explanation:
P 4m are 8 m are 32 m away. The diameter= 32 m.
(I hope its rights!!!)
WILL CHOOSE BRAINLIEST Let Events A & B be described as follows: P(A) = watching a movie P(B) = going out to dinner The probability that a person will watch a movie is 62% and the probability of going out to dinner is 46%. The probability of watching a movie and going out to dinner is 28.52% Are watching a movie and going out to dinner independent events? Group of answer choices No, because the P(A)P(B) ≠ P(A and B). Yes, because the P(A)P(B) = P(A and B). No, because the P(A) + P(B) ≠ P(A and B). Yes, because the P(A) + P(B) is greater than 100%.
Answers
Answer:
Yes, because the P(A)P(B) = P(A and B)
Step-by-step explanation:
Independent Events are events that occurs simultaneously i.e they occur at the same time. This means that the occurrence of one does not affect the other. If A and B are two events, for the to be independent then;
P(A and) = P(A)P(B)
Given: P(A) = watching a movie = 62% = 0.62
P(B) = going out to dinner = 46% = 0.46
The probability of watching a movie and going out to dinner will be
P(A and B)
P(A and B) = 0.62×0.46
P(A and B) = 0.2852
P(A and B) = 28.52%
Since the probability of watching a movie and going out to dinner is 28.52% which tallies with the question, hence it can be concluded that watching a movie and going out to dinner are independent events.
What will be the effect on the graph of y = |x| if x is replaced with -x?
A. a vertical shift
B. no change
C. a reflection over the x-axis
D. a horizontal shift of 1 unit to the left
Answers
The vertical lines on each side of the x mean it is the absolute value of x.
Replacing x with -x would make no change on the graph, because the absolute value is always a positive number.
The answer is B.
There will be no change on the graph of y = |x| if x is replaced with -x. Option B is correct.
What is a function?
A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The vertical lines on each side of the x mean it is the absolute value of x. Replacing x with -x would make no change on the graph because the absolute value is always a positive number.
Therefore, there will be no change on the graph of y = |x| if x is replaced with -x. Option B is correct.
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33. Find the area of the parallelogram above?
Answers
Answer:
120
Step 1: Value of triangle's sides
First, we need to find out the height of the parallelogram, since the equation to find the area is b * h. To find the height, we must use the Pythagorean Theorem to find the sides of the triangle on the right. Since the base is 15 cm, we know that the top is also 15 cm, so we subtract 9 from 15 to get 6. One of the sides of the triangle is 6, and the hypotenuse (longest side of the triangle) is 10.
Step 2: Pythagorean Theorem
[tex]a^2+b^2=c^2[/tex]. This is the equation we always use if we want to find the sides of a right triangle. Here, a = 6 and c = 10. In the formula, a and c needs to be squared to find b.
[tex]10^2 (10*10)=100\\6^2 (6*6)=36\\\\c^2=100\\a^2=36[/tex]
Now, we have to subtract c^2 from a^2 to get b^2.
[tex]100-36=b^2\\100-36=64\\b^2=64[/tex]
Finally, we find the square of 64 and that is 8.
8 is our height.
Step 3: Finding the area
This last step is really simple. to find the area of this parallelogram, we just have to multiply the height (8) by the base (15).
[tex]8*15=120\\Area=120[/tex]
Our area is 120.
Answer:
120
Step-by-step explanation:
at first you need to calculate h Using the Pythagorean relation
10
[tex]10 { }^{2} = 6 {}^{2} + x {}^{2} [/tex]
[tex] x {}^{2} = 100 - 36 = 64[/tex]
[tex]x = 8 = h[/tex]
area=
[tex]8 \times 15 = 120[/tex]
help plz I think the first one is correct but I'm not sure
Answers
The left side 10x+25 is the cost expression for Black Diamond, while the right hand side 5x+50 is for Bunny Hill. The x is the number of hours.
Which statement is true about the solutions to x^2 - 1 = 24
A. There are two distinct irrational solutions.
B. There are two distinct rational solutions
C. There is only one rational solution
D. There is only one irrational solution
Answers
Answer:
B. There are two distinct rational solutions
Step-by-step explanation:
x^2 -1 = 24
Add 1 to each side
x^2 -1+1 = 24+1
x^2 = 25
Take the square root of each side
sqrt(x^2) = ±sqrt(25)
x = ±5
Answer:
B.
Step-by-step explanation:
x^2 - 1 = 24
x^2 = 25
Taking the square root of both sides:
x = -5, 5.
2 distinct rational solutions.
what is 0.7619047619 as a fraction?
Answers
Answer:
7619047619
10000000000
Step-by-step explanation:
Yeah big numbers:
To write 0.7619047619 as a fraction you have to write 0.7619047619 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.7619047619 = 0.7619047619/1 =
7.619047619/10 = 76.19047619/100 =
761.9047619/1000 = 7619.047619/10000 =
76190.47619/100000 = 761904.7619/1000000 =
7619047.619/10000000 = 76190476.19/100000000 = 761904761.9/1000000000 = 7619047619/10000000000
Hope this helps, have a good day :)
(brainliest would be appreciated?)
If F(x) = x - 7 and G(x) = x3, what is G(F(x))
Answers
[tex]g(f(x))=(x-7)^3=x^3 - 21 x^2 + 147 x - 343[/tex]
Which graph represents a function?
Answers
Answer:
The first one is the only function
Step-by-step explanation:
You cannot have points on the same y gridline
If it is a function is has to pass the pencil test
Answer:
[tex]\boxed{Graph A.}[/tex]
Step-by-step explanation:
Hey there!
Well graph A is correct because if you do the vertical line test which decides is the graph is a function or not you can see that all the graph expect A have the vertical line go through 2 points.
Hope this helps :)
At a frisbee-throwing competition, one contestant threw a frisbee 113.47 meters.
Round the distance to the nearest meter.
Answers
Answer:
113 meters
Step-by-step explanation:
113.47 rounded to the nearest meter is 113.
The distance of frisbee to the nearest meter will be equal to 113 meters.
What is a round of numbers?An integer containing one or more "0"s at the end in a specific base is said to be round. In this way, 590 is more rounded than 592 but less rounded than 600.
A round number is frequently understood to stand for a value or values close to the nominal value expressed in both formal and informal language.
The distance to the nearest meter will be given as below:-
113.47 meters. = 113 meters.
Therefore, the distance of the frisbee to the nearest meter will be equal to 113 meters.
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If the geometric mean of a and 120 is 60, find the value of a.
Answers
Answer:
The answer is option 4.
Step-by-step explanation:
Given that the mean formula is total score/number of score. So we can assume that total score is (a+120), number of score is 2 and the mean value is 60. Then you have to find the value of a :
[tex] \frac{a + 120}{2} = 60[/tex]
[tex]a + 120 = 60 \times 2[/tex]
[tex]a + 120 = 120[/tex]
[tex]a = 120 - 120[/tex]
[tex]a = 0[/tex]
[tex] \text{ Geometric mean of two numbers } a \text{ and } b , \text{ where } a,b>0 \text{ is given by } G= \sqrt{ab}[/tex]
[tex] \sqrt{a\cdot120}=60 [/tex]
[tex] \implies 60 \cdot 2 \cdot a=60\cdot 60 \qquad \text{Squaring both sides} [/tex]
[tex] \implies a =30 [/tex]
Gene is playing a game with a bag of marbles. 3 of the marbles are blue, 4 are green, and 7 are yellow. See below for awarded prizes. $2 green $0.5 yellow $4 blue What is the expected cost (or payout for Gene's game?
Answers
Answer:
$23.5Step-by-step explanation:
Gene is playing a game with a bag of marbles. If 3 of the marbles are blue, 4 are green, and 7 are yellow and awarded prices for the marbles are $2 green $0.5 yellow $4 blue, the expected payout for Gens game is expressed as shown;
If a blue marble costs $4, 3 blue marbles will cost 3*$4 = $12
If a green marble costs $2, 4 green marbles will cost 4*$2 = $8.0
If a yellow marble costs $0.5, 7 yellow marbles will cost 7*$0.5 = $3.5
Total payout for Gene's game will be the equivalent to $12+ $8 + $3.5 = $23.5.
Hence Gene expected cost will be $21.5
Please answer these 3 questions for 70 points 1 thanks 5 stars and brainiest
Answers
Answer:
Step-by-step explanation:
Problem 14: Mean 5.5, Range: 5.8
Problem 15: question #1 4, mode: 63
Probelm 16: Median 63, Range: 8.3
Answer:
14: Mean is 5.5 Hours
Range is 7.9 Hours
15: 4 Numbers
Mode is 6.3
16: Median is 6.3
Range is 8.3
Step-by-step explanation:
(I'll edit in the explanations momentarily)
7(x+1)=21 solve for x
Answers
7x + 7 = 21
7x = 14
x = 2
