1. The fourth graph: D
2. The first graph: A
Answer:
y= -3/5x+5
Step-by-step explanation:
Answer:
24 1/6 - 19 5/12=
24 1/6÷12- 19 5/12÷12
24 2/2- 19 5/1= 5 3/1
3÷1= 3
5÷3= 3 1/2
Step-by-step explanation:
Step 1: Do the lcd and the number in between what you do is multiply the number next to it.
Step 2: Then subtract the mixed numbers and you get your answer.
Step 3: Divide 3 by 1
Step 4: Divide 3 by 5 and answer is 3 1/2
Answer:
m∠7 = 63 degrees
m∠8 = 117 degrees
m∠9 = 63 degrees
Step-by-step explanation:
When two lines intersect at a point, then they formed 2 pairs of vertically opposite angles and 4 pairs of linear angles
- The vertically opposite angles are equal in measures
- The linear angles have a sum of 180°
In the given figure
∵ There are two lines intersected at a point
∴ The angle of measure 117° and ∠8 are vertically opposite angles
∴ ∠7 and ∠9 are vertically opposite angles
∴ The angle of measure 117° and ∠7 are linear angles
∵ The vertically opposite angles are equal in measures
∴ The angle of measure 117° and ∠8 are equal in measures
∴ m∠8 = 117°
∵ The sum of the measures of the linear angles is 180°
∴ m∠7 + 117° = 180°
→ Subtract 118 from both sides
∵ m∠7 + 117 - 117 = 180 - 117
∴ m∠7 = 63°
∵ m∠7 = m∠9 ⇒ proved up
∴ m∠9 = 63°
The area of the triangle as a function of x is A = 3x^2/[2(x -5)] and the domain is x > 5
<h3>Write the area A of the triangle as a function of x</h3>
From the figure, we have the following points:
(0,y), (5,3), and (x,0)
Next, we calculate the slopes between the points.
This is calculated as follows:
- Slope between (0,y) and (5,3) = [y - 3]/[0 - 5] = [3 - y]/5
- Slope between (5,3) and (x,0) = [3 - 0]/[5 - x] = 3/[5 - x]
The slopes are equal.
So, we have:
[3 - y]/5 = 3/[5 - x]
Cross multiply
(3 - y)(5 -x) = 15
Divide by 5 - x
(3 - y) = 15/(5 -x)
This gives
y = 3 - 15/(5 -x)
This gives
y = [15- 3x - 15]/[5 - x]
Evaluate
y = 3x/(x - 5)
The area is calculated as:
Area = 1/2 * xy
So, we have:
Area = 1/2 * x * 3x/(x - 5)
Evaluate
Area = 3x^2/[2(x -5)]
Hence, the area of the triangle as a function of x is A = 3x^2/[2(x -5)]
<h3>
The domain of the function</h3>
We have:
A = 3x^2/[2(x -5)]
Set the denominator > 0
2(x - 5) > 0
Divide by 2
x - 5 > 0
Add 5 to the sides
x > 5
Hence, the domain is x > 5
Read more about domains at:
brainly.com/question/2428614
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