
We are given that BA is perpendicular to BD, so that must mean that <em>m∠ABD </em>is a right angle, or 90º. This means: (8x - 10) + (4x + 52) = 90º, since both of the angles add up to become a right angle. We have to solve for x in order to find <em>m∠CBD.</em>
<em />
<u>PART 1</u>
<em />
<em />
<em />
Equation: (8x - 10) + (4x + 52) = 90
Let's add the like values together first.



Let's subtract 42 from both sides of the equation to isolate the variable we are solving for, x. Our goal is to isolate it completely to get a value that is equal to x.


Divide both sides by 12 to get our final answer for x.

<u>PART 2</u>
<u></u>
Now that we have x, we simply plug it into our equation for <em>m∠CBD. </em>
<em />
<em />
<em />


Multiply 4 and add 52.


Answer:
in one minute they rake
leaves working together.
Step-by-step explanation:
If Maya rakes the leaves in x minutes, then, in one minute she rakes
leaves.
In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes
leaves.
Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: 
Now, to simplify this expression:

Thus, in one minute they rake
leaves.
Answer: The other player scored 10 points.
Step-by-step explanation:
Since we have given that
Number of players = 4
Number of scores each player score = 6
Total scores scored by 4 players would be

Total scores scored by a team = 34 points
So, the number of points scored by other player score is given by

Hence, the other player scored 10 points.
There are 13 green marbles in the bag.
Step-by-step explanation:
Total marbles = 18
Let,
Green marbles = x
Blue marbles = y
According to given statement;
The number of green marbles is 2 less than 3 times the number of blue marbles.
x = 3y-2 Eqn 1
x+y=18 Eqn 2
Putting value of x from Eqn 1 in Eqn 2;

Dividing both sides by 4

Putting y=5 in Eqn 1

There are 13 green marbles in the bag.
Keywords: linear equation, substitution method
Learn more about linear equations at:
#LearnwithBrainly