Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
<u>Given</u>:
Given that the two box plots summarize the ages of men and women during their first marriage over the course of one year.
We need to determine the sum of IQR of the top data set and the IQR of the bottom data set.
<u>IQR of the top data set:</u>
The IQR on the top represents the ages of women.
The IQR of the top data set is given by
Thus, the IQR of the top data set is 5.
<u>IQR of the bottom data set:</u>
The IQR on the bottom represents the ages of men.
The IQR of the bottom data set is given by
Thus, the IQR of the bottom data set is 6.
<u>Sum of the IQR:</u>
The sum of the IQR of top data set and the bottom data set is given by
Therefore, the sum of the IQR of top data set and the bottom data set is 11.
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To solve this problem, we should use a system of equations. In this example, we can construct two equations from the given equation letting the variable r represent the number of raspberries Diane has and b represent the number of blackberries Diane has.
r + b = 46 (the number of raspberries plus the number of blackberries is 46, the total number of berries)
b + 20 = r (there are 20 more raspberries than blackberries)
Our two equations are above. Because our second equation is already r in terms of b, we can substitute this value for r into our first equation, as modeled below:
r + b = 46
(b + 20) + b = 46
Now, to simplify, we should combine like terms on the left side of the equation.
2b + 20 = 46
Next, we should subtract 20 from both sides of the equation to get the variable term alone on the left side of the equation.
2b = 26
Finally, we should divide both sides of the equation by 2, in order to get rid of the coefficient on the variable b.
b = 13
Therefore, Diane has 13 blackberries (if you substitute in this value into the first equation, you can figure out that there are 33 raspberries in the bowl).
Hope this helps!
multiply 15430000 by 25%
25% = 0.25
15430000 x 0.25 = 3,857,500