If x+ay=b, then y equals?

Question

1. If x+ay=b, then y equals??

2. If the measures of two complementary angles are in the ratio 1:5, the measure of the larger angle is?

3. For the set of data, 9,9,10,11,and 16, which one of the following statements is true??
a. mean < mode
b. mean = mode
c. median < mode
d. mean > median

Answer 1

1. x + ay = b
x + ay - x = b - x
ay = b - x
ay / a = (b - x) / a
==> y = (b - x)/a

2. Complementary angles means that the angles add up to 90 degrees. The ratio is 1:5. So let's let one angle be x. The other angle is 5x.
x + 5x = 90°
6x = 90°
x = 15.
They want the larger angle, so that's 5x = 5 * 15 =
==> 75°

3. Let's figure out the mean, median and mode.
Mean = average of all the numbers = sum them up and divide by the number of data there are. (9 + 9 + 10 + 11 + 16) / 5 = 55/5 = 11.
Median = the middle of the numbers when listed out in order. They give the numbers in order, the the median is 10.
Mode = the number that appears most in the set. In this case, it is 9.
Let's look at the four choices and use the process of elimination.
a) mean = 11, mode = 9. mean > mode, so a) is wrong.
b) mean = 11, mode = 9. mean > mode, so b) is wrong.
c) median = 10, mode = 9. median > mode, so c) is wrong.
d) mean = 11, median = 10. mean > median, so the correct answer is
==> d)

Answer 2

1)x+ay=b
Subtract x from both sides:
ay=b-x

Divide a from both sides:
y=(b-x)/a

2)x=the measure of the smaller angle
5x=the measure of the larger angle

x+5x=90
6x=90
x=15°
5(15)=75°

The measure of the larger angle is 75°.

3)9,9,10,11,16
Median:10
Mean:
(9+9+10+11+16)/5=
55/5=11
Mode:9
The true statement would be d) mean>median.

Answer 3

x + ay = b
ay = b - x
y = (b - x)/a

Complementary angles add up to 90 degrees.
Smaller angle = x
Larger angle = 5x
x + 5x = 90
6x = 90
x = 90/6 = 15
5x = 75

Mode is 9 because it occurs most often.
Mean is 11 because 55/5 = 11.
Median is 10 because it's in the middle of the ordered list.
D. Mean (11) is greater than median (10).

Answer 4

1. x + ay = b
ay = b - x
y = (b-x)/a

2. if the smaller is x, then x + 5x = 90
so x = 15, and the larger angle is 75 degrees

3. D

Answer 5

1. x + ay = b
First: subtract "x" from both sides:

x - x + ay = b - x
ay = b - x

Second: solve for "y" and keep it on one side > divide both sides by "a" >>>

ay/a = (b - x)/a
y = (b - x)/a

3. Mean - (add all the numbers and divide them by the quantity of numbers) > 55/5 = 11

Median- (the middle number; if there are two middle numbers, add them and divide them by 2) > 10

Mode - (a number repeated twice) > 9

*Now, you can choose the correct answer :-)

Answer 6

1. y=(b-x)/a

2. 90*5/6=75