Find the values for x and y.

Mathematics

1 answer:

vivado [14]3 years ago

8 0

Both sides need to equal 180 (The side with the 90 degrees measurement and the side with equations). So first subtract 180 from 90
$180 - 90$
to get the measurement of 5x and you get 90 but we aren't done yet since we need to find x so now we need to divide 5 by 90
$90 \div 5 = 18$
and we get 18 which is X.
$x = 18$
Now we need to find the measurement of Y. Now both angles on that side together equals 180 so we need this equation.
$5(y + 11) + 4y - 10 = 180$
First, distribute 5(y + 11)
$5 \times y \\ 5 \times 11$
Then you get this equation :
$5y + 55 + 4y - 10 = 180$
Now, add the two equations together
$5y + 55 + 4y - 10$
and you get this equation

$9y + 45 = 180$
Now subtract 45 from both sides
$9y + 45 - 45 = 180 - 45$
and divide by 9 on both sides
$9y \div 9 = 135 \div 9$
and you get your answer
$y = 15$

So
$x = 18$
and
$y = 15$

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A college is currently accepting students that are both in-state and out-of-state. They plan to accept three times as many in-st

ziro4ka [17]

Answer:

0 < x ≤ 100 and 0 < y ≤ 300

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW;

college is currently accepting students that are both in-state and out-of-state. They plan to accept three times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.

0 < x ≤ 100 and 0 < y ≤ 300

x > 0 and y > 0

0 < x ≤ 100 and y > 300

0 < x and y < 100

SOLUTION

they only have space to accept 100 out-of-state students,which means that the Maximum number of out-of-state students that can be accepted is 100

Then x= 100(Maximum number of out-of-state students that can be accepted)

They plan to accept three times as many in-state students as out-of-state which means that

Y = 3x(Maximum number of in-state students)

Then we can deduced that the numbee out-of-state students that can be accepted can lyes between the range of 0 and 100 which means from interval 0 to 100

Which can be written as 0 < x ≤ 100

But we need to know the interval for the Maximum number of in-state students(Y), to do that we need to multiply the equation above by 3 since Y = 3x

0 < x ≤ 100

3× 0 = 0

3× X = X

3× 100= 300

Then 0 < 3x≤ 300

But we know that Y = 3x then substitute into last equation

We have

0 < y ≤ 300

ThenBthe constraints to represent the incoming students at the college is

0 < x ≤ 100 and 0 < y ≤ 300