Which transformation of a scalene triangle produces an image that is similar, but not congruent, to the original
2 answers:
You might be interested in
Answer:
9) y = -200x + 1200
11) slope = -2
15) $2,450
16) 9 days
Step-by-step explanation:
9) Given the two points from the graph:
Let (x₁, y₁) = (0, 1200)
(x₂, y₂) = (1, 1000)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = (1000 - 1200)/(1 - 0)
m = -200/1
m = -200
The slope of the line is -200.
Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis. Upon observing the graph, it shows that the line crosses at point (0, 1200). The y-coordinate of this ordered pair is the value of the y-intercept, b = 1200.
Therefore, the linear equation in slope-intercept form is y = -200x + 1200.
<h3>11) Given the points, (5, -18) and (-4, 0): </h3>Let (x₁, y₁) =(5, -18)
(x₂, y₂) = (-4, 0)
Substitute these values into the following <u>slope formula</u>:
m = (y₂ - y₁)/(x₂ - x₁)
Therefore, the slope of the line is -2.
<h3>15) Solve:</h3>Given the fixed fee of $200, and the $150 per hour after the initial meeting:
We can represent these in slope-intercept form:
y = 150x + 200
y = total cost for the Attorney's services
x = number of hours worked.
The y-intercept in this given problem is $200, which represents the flat fee charged for the initial meeting. While the slope in this equation is $150, which is the hourly rate that an Attorney charges his clients after the initial meeting.
If an Attorney works for 15 hours, then:
Let x = 15, and substitute its value into the equation to find the total cost:
y = 150x + 200
y = 150(15) + 200
y = 2,250 + 200
y = 2,450
Therefore, a client will pay a total of $2,450 for an Attorney's 15 hours of work.
<h3>16) Solve: </h3>Given the water level on a Lake of 165 inches after a rainstorm, and the water level's receding rate of 3 inches per day:
We can establish the following linear equation to model this given problem:
L = -3d + 165
Where:
L = represents the water level of the Lake
d = number of days that the water level recedes
In order to find the number of days it will take before the water level recedes to 84 inches:
Substitute the value of L = 84 into the equation:
L = -3d + 165
84 = -3d + 165
Subtract 165 from both sides:
84 - 165 = 3d + 165 - 165
-27 = -3d
Divide both sides by -3:
9 = d
Therefore, it will take 9 days for the water level to be at 84 inches.
Option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively. This can be obtained by knowing what similar triangles are and finding which sides are proportional.
<h3>Find the correct option:</h3>Similar triangles: If two triangles have proportional sides the are similar.
For example, if ΔABC and ΔDEF are similar then
∠ABC = ∠DEF and ∠ACB = ∠DFE
Then we can write that, ΔABC ~ ΔDEF
Here in this question,
Since A, Y, Z are midpoints of sides XW, VW, XV
XA = AW
WY = VY
XZ = VZ
To consider sides AY and XV we should take triangles ΔWAY and ΔWXV
(since A is the midpoint of WX)
(since Y is the midpoint of WV)
∠AWY = ∠XWV (reflexive property)
Therefore ΔWAY and ΔWXV are similar triangles
= 2
∠WAY = ∠WXV and ∠AYW = ∠XVW
Hence,
AY || XV option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively.
Learn more about similar triangle here:
#SPJ1
Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Analyze the diagram below and answer the question that follows. If Z, Y and A are midpoints of ΔVWX what is true about AY and XY?
A. AY || XV
B. 1/2 AY = XV
C. AY = XV
D. AY ≅ XV
