(a) Coordinates:
A (0, 0)
B (3, 2)
C (9, 6)
Triangle A to B has a change of +3 in x values, but Triangle B to C has a change of +6 values so each triangle doesn’t have the same changes in x values.
Triangle A to B has a change of +2 in y values, Triangle B to C has a change of +4 values so each triangle doesn’t have same change in values.
Triangle A to B change in y over change in x = 2/3, Triangle B to C change in y over change in x = 4/6, both have decimal values of 0.66. Therefore, each triangles has the same ratio of change in y over change in x.
Answer:
t = 31s
Step-by-step explanation:
................
1/2 = 3/6
5 gallons of water changed it to 5/6, so that would mean 2/6 would be 5 gallons worth.
5 x 3 = 15.
Hope this helps.
Answer:
Step-by-step explanation:
The exponential function and the natural log are inverse functions:
e^ln(x) = x
Using both sides of your given equation as exponents for e, we have ...
e^(ln(3x)) = e^5
From the above, we know that ...
e^(ln(3x)) = 3x
so we can substitute that into the preceding equation to get ...
3x = e^5
Swapping sides of the equal sign gives an equation that matches choice B:
e^5 = 3x
If Lines AC and ED intersect at point B, then ∠ABD and ∠EBC are vertically opposite angles
The point where two lines meet is known as an angle.
If line Lines AC and ED intersect at point B, then ∠ABD and ∠EBC will be vertically opposite to each other (They will be equal).
To show that the are equal
Given the angles
m∠ABD = 5x - 5
m∠EBC = 3x + 15
m∠ABD = m∠EBC (vertical angles)
5x - 5 = 3x + 15
5x - 3x = 15 + 5
2x = 20
x = 10
Substitute x = 10 into m∠ABD and m∠EBC
m∠ABD = 5x - 5
m∠ABD = 5(10)-5
m∠ABD = 50 - 5
m∠ABD = 45
Get m∠EBC
m∠EBC = 3x+15
m∠EBC = 3(10)+15
m∠EBC = 30+15
m∠EBC = 45 degrees
We can see that both angles are equal. Hence we can also conclude that they are vertically opposite angles
Learn more here: brainly.com/question/23466343