A. The graph shows four points on the line and the triangles resulting from sketching on the rise and run from one point to the next. Viewing the graph or R-value as a transversal to the rise and run segments, are the two pairs of corresponding angles along the transversal congruent? Explain.
B. What is the relationship between the two resulting triangles? Explain your answer.
C. Use the relationship from Part B to state the relationship between corresponding sides of the resulting triangles.
D. Use the properties of similar triangles to explain why the slope, or rise-to-run ratio, is constant between any two points on the line.
E. Use any two points to find the unit rate for this proportional relationship. Show your work.
Answers
Answer:
A. Yes
B. The triangles are similar
C. The corresponding sides are proportional
D. The slope of ΔABC = tanθ₁ = tanθ₂ = The slope pf ΔDEF, therefore, the slope of any two points on the line are congruent by similar triangles
E. The rate of proportionality = 2
Step-by-step explanation:
A. From the given graph, given that the angles are formed between the transversal and lines parallel to the R-value axis and the transversal and lines parallel to the thickness axis, the angle formed by the transversal and each parallel lines are corresponding angles and are therefore congruent
The tan of one of the angles on each triangle are
On the uppermost triangle, tanθ₁ = (9.42 - 3.14)/(3 - 1) = 3.14
On the other triangle, tanθ₂ =(25.12 - 12.56)/(8 - 4) = 3.14
tanθ₁ = tanθ₂
∴ θ₁ = θ₂
ΔABC and ΔDEF are right triangles, therefore, all the angles of ΔABC and ΔDEF are congruent
B. Given that the interior angles of the triangles formed by the line the graph are congruent, the triangles are similar by AA similarity postulate
C. Given that the triangles are similar, the length of the corresponding sides of the triangles are proportional
D. Given that the slope is the tangent of the angle between the line of the graph and the Thickness axis, and that the angle is the same for both triangles, (∠θ₁ and ∠θ₂) the slope or the rise-to-run ratio is constant for the two triangles and also for any two points on the line
E. The Unit of proportionality is found using any two points as follows;
Using points used to show the proportional relationship on triangle ΔABC are (8, 25.12) and (4, 12.56) and on triangle ΔDEF, the two points used to show proportional relationship are (3, 9.42), and (1, 3.14)
The ratio of the corresponding sides on ΔABC and ΔDEF are
[tex]\overline {AC}[/tex]/[tex]\overline {DF}[/tex] = (25.12 - 12.56)/(9.42 - 3.14) = 2
[tex]\overline {BC}[/tex]/[tex]\overline {EF}[/tex] = (8 - 4)/(3 - 1) = 2
Therefore, the unit rate of proportionality which is the scale factor = 2.
Related Questions
Jim and Carol recorded gas prices at five stations for their own towns in the table below. Gas Prices Name Station 1 Station 2 Station 3 Station 4 Station 5 Jim $3.45 $3.54 $3.71 $3.62 $3.49 Carol $3.89 $3.65 $3.39 $3.48 $3.49 Which person's town had the lower mean for gas prices and by about how much?
A Jim, by $0.02
B Carol, by $0.02
CJim, by $0.06
D. Carol, by $0.06
Answers
Writing a ratio as a percentage This year Jessica watched 40 movies. She thought that 16 of them were very good. Of the movies she watched, what percentage did she rate as very good?
Answers
The length of a rectangle is (x + 3) inches long, and the width is 3.4
inches. If the area is 15.3 square inches, which equation can be used to find
x? *
A. 3.4(x + 3) = 15.3
B 3.4x + 3 = 15.3
C. 3(x + 3.4) = 15.3
D. 3x + 3.4 = 15.3
Answers
Answer:
A)
Step-by-step explanation:
Solve the following quadratic equation for all values of xx in simplest form.
5(2x+1)^2+6=26 cant figure this out!!
Answers
Answer:
x=1/2 and x=-3/2
Step-by-step explanation:
5(2x+1)^2+6=26
5(2x+1)^2=20
(2x+1)^2=4
2x+1=±2
Now make two equations and solve both for x:
2x+1=2
2x=1
x1=1/2
2x+1=-2
2x=-3
x2=-3/2
PLEASE HELP I WILL MARK U AS BRAINLIST !!!!
The length of each of the legs of an isosceles triangle is represented by the expression 5x-2 inches. The length of the base of the isosceles triangle is represented by the expression 3x +1 inches. The perimeter of the isosceles triangle is 42 inches.
determine whether each equation represents the perimeter of the isosceles triangle , in inches .
select yes or no for each equation
A. 13x-2=42 yes or no
B. (10x-2)+(3x+1)=42 yes or no
C.2(5x-2)+2(3x+1)=42 yes or no
D.5x-2+3x+1+5x-2=42 yes or no
THERE CAN BE MORE THAN ONE ANSWER.
thank you
Answers
Answer:
A.NoAs,
5x - 2 + 5x - 2 + 3x + 1 = 13x - 3 = 42
But here,
13x - 2 which is not equal to 13x - 3
Hence, it's wrong.
B. NoAs,
5x - 2 + 5x - 2 + 3x + 1 = (10x - 4) + (3x + 1) = 42
But here,
(10x - 2) + (3x + 1) which is not equal to (10x - 4) + (3x + 1)
Hence, it's wrong.
C. NoAs,
5x - 2 + 5x - 2 + 3x + 1 = 2(5x - 2) + 3x + 1 = 42
But here,
2(5x-2)+2(3x+1) which is not equal to 2(5x - 2) + 3x + 1
Hence, it's wrong.
D. YesAs,
5x - 2 + 5x - 2 + 3x + 1 = 42
Also,
5x-2+3x+1+5x-2 equal to 5x-2+3x+1+5x-2
Hence, it's correct.
Answer:
A and D is right
Step-by-step explanation:
I did the quiz and use the answer and it was right
fill in the blank. 1/9 ? -4
A .>
B. <
C. =
Answers
Answer:
The answer is A.
Step-by-step explanation:
1/4 is greater than 0, since -4 is less than 0 1/4 is greater
Thomas wants to spend no more than $25.50 movies and CDs. If he buys a movie for $9.50 and the CDs cost $5.00, how many CDs can Thomas purchase?
Answers
Answer:
3
Step-by-step explanation:
25.5-9.5=16
16-15=1 (highest multiple of 5 that fits into 16)
He can buy 3 cds and he will have $1 left over
Find the mean. {21, 10, 27, 24, 15, 7, 19, 24, 31, 15, 11, 24}
Answers
Answer:
19 is your answer
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
The mean of a set of numbers is the sum divided by the number of terms.
How to Find the Mean:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Which statement describes the sequence defined by a Subscript n Baseline = StartFraction n squared minus 16 Over n cubed + 4 EndFraction? The sequence diverges. The sequence converges to 0. The sequence converges to 1. The sequence converges to ∞.
Answers
Calculating the limit as n goes to infinity, it is found that:
The sequence converges to 0.
------------------------------
The sequence is given by:
[tex]a_n = \sum_{n=0}^{\infty} f(n)[/tex]
In which
[tex]f(n) = \frac{n^2 - 16}{n^3 + 4}[/tex]
------------------------------
If the limit of f(n) as n goes to infinity is a value, it converges to this value.If the limit of f(n) as n goes to infinity is infinity, it diverges.------------------------------
The limit is:
[tex]\lim_{n \rightarrow \infty} f(n) = \lim_{n \rightarrow \infty} \frac{n^2 - 16}{n^3 + 4}[/tex]
Since it is a limit going to infinity, we consider just the terms with the highest exponents in the numerator and the denominator. Thus:
[tex]\lim_{n \rightarrow \infty} \frac{n^2 - 16}{n^3 + 4} = \lim_{n \rightarrow \infty} \frac{n^2}{n^3} = \lim_{n \rightarrow \infty} \frac{1}{n} = \frac{1}{\infty} = 0[/tex]
Thus: The sequence converges to 0.
A similar question is given at https://brainly.com/question/20553793
Answer: D The sequence converges to ∞.
Step-by-step explanation:
got it right 2022 edge
HELP ASAP FIRST PERSON WITH CORRECT ANSWER GETS BRAINLIEST
Which statements about the triangles are correct? Select two that apply.
A. Triangle P is similar to triangle Q.
B. Triangle P is a reflection and a translation of triangle Q.
C. Triangle P is not similar to triangle Q.
D. Triangle P is a reflection and dilation of triangle Q.
E. Triangle P is a translation and a dilation of triangle Q.
Answers
Help with this please!!
Answers
Answer:
the first answer
Step-by-step explanation:
well first ofc u have to graph both equations to be able to compare them and if u don't have a graphing calculator just search up Desmos graphing calculator it will help A LOT
Drag each rational number to the correct location on the table.
Identify the rational numbers as positive or negative.
Answers
Answer:
Step-by-step explanation:
Positive: -1/-3, -2/-2, +2/+3, -1/+3
the rest of them are negative
Answer:
Positive: 1+/+3 -2/-3 +2/+3 -1/-3 negative:-2/+3 +2/-3 -1/+3 +1/-3
Step-by-step explanation:
please help ill give brainliest answer!!
Answers
Answer:
Brainlyest answer plz
Answer:
IJ=77
Step-by-step explanation:
[tex]\frac{35}{20} =\frac{IJ}{44}[/tex]
[tex]20IJ=1540[/tex]
[tex]IJ=77[/tex]
50 POINTS WILL MARK BRAINLIEST find the area.
Answers
Answer:
43?
Step-by-step explanation:
the equation of the line that is perpendicular to the line with equation y=-2x-1 and passes through the point (1, -2) is?
Answers
Answer:
[tex]y=\frac{1}{2} x-\frac{5}{2}[/tex]
Step-by-step explanation:
Hi there!
Note that:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals of each other (ex. 3 and -1/3, 5/6 and -6/5, etc.)1) Determine the slope (m)
When we look at the given line, [tex]y=-2x-1[/tex], we can identify that -2 is in the place of m, the slope of the line. Because perpendicular lines are negative reciprocals of each other, we know that a line perpendicular to this would have a slope of [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{1}{2} x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{2} x+b[/tex]
Plug in the given point (1,-2)
[tex]-2=\frac{1}{2}(1)+b\\-2=\frac{1}{2}+b[/tex]
Subtract 1/2 from both sides
[tex]-2-\frac{1}{2}=\frac{1}{2}+b-\frac{1}{2}\\-\frac{5}{2} = b[/tex]
Therefore, the y-intercept of the line is [tex]-\frac{5}{2}[/tex]. Plug this back into [tex]y=\frac{1}{2} x+b[/tex]
[tex]y=\frac{1}{2} x-\frac{5}{2}[/tex]
I hope this helps!
Which expression represents a rational number?
Please help right now!!!
Answers
Answer:
A
Step-by-step explanation:
Every integer is a rational number; a whole number. The square root of 49 equals 7, which is the only outcome giving an integer as an answer.
Is (5.7) a solution for the following system of equations?
y=2x-3
y=x+2
Answers
Answer: yes y=2x-3, y=x+2 : y=7, x=5
volume of a cone is 48 pi cubic inches the cone has a height of 36 inches Mark finding the radius of the cone complete his work
Answers
Answer:
c or take the square root of both sides
a or 2 inches
Step-by-step explanation:
Which of the following is true about the expression v3 • V12?
Answers
Answer:
I think is B.
Step-by-step explanation:
hope its help
Answer:
Option B
Step-by-step explanation:
Find the volume of the cone in the attached image.
Answers
PLEASE help me ASAP with this QUETION!!!!!!!!!!
Answers
Answer:help with what
Step-by-step explanation:
You need to say
Whats LN? *with picture*
Answers
Answer:
LN = 15 in
Step-by-step explanation:
We can say that arc PL plus arc LM is equal to arc PM:
arcPL + arcLM = arcPM
We can substitute what we have:
10 + 14 = arcPM
arcPM = 24.
Since both arcPM and arcLN equal 24, we can say they are congruent.
In circles, congruent arcs create congruent chords, so, we can say PM = LN.
Since PM is 15, LN = 15 in
helpppp which one is it
Answers
Answer:
12ft
Step-by-step explanation:
This is a right triangle with a 45° angle so the other angle is also 45° so this is a right isosceles triangle. so, height=base=7ft
5+7=12ft
The graph shows the relationship between the number of weeks and the number of hours spent on the computer. What rule relates the number of weeks to the number of hours of computer time?
Answers
Answer: multiply the number of weeks by 3 or A ( if in assessment guide book)
Step-by-step explanation: just look at the point where its between 2 and 4
During a trip, a driver travelled a distance of 80km at an average speed of 60km/hr.He then changed his speed and travelled the remaining 20km of his journey at 30km/hr. What was the drivers average speed for the entire journey?
Show all working!!
Answers
Answer:
50 km/hr
Step-by-step explanation:
D = RT
Time for first part of trip = 80/60 = 4/3 hr.
Time for second part of trip = 20/30 = 2/3 hr.
total time for entire trip = 4/3 + 2/3 = 6/3 = 2 hr.
Total distance = 100 km
Average rate of speed for entire trip = 100/2 = 50 km/hr
hello please help i’ll give brainliest
Answers
(C) Find the arithmetic mean of given data
12, 10, 15, 14, 16, 25, 18, 22
Answers
Answer: Mean- 16.5
Step-by-step explanation:
The cost price of an article is $40 and the profit is 20 per cent of the cost price.
What is the selling price of the article?
Answers
40x0.20=8
40-8=32
What is the range of the following parabola? (5 points)
Answers
Answer:
D
Step-by-step explanation:
Range is all the possible Y values in a graph
we can see that the graph will never reach a y value greater than three but will go to negative infinity
This means that answer is D (the y value will always be less than or equal to 3)
Sanjay sold 2/5 of his mangoes. What percentage of his mangoes did he remain with?
Answers
Answer:
60%
Step-by-step explanation:
3/5 left x 100 = 60%
Answer:
60%
Step-by-step explanation:
1/5 = 20%
20% x 3 = 60%