How to find the domain and range of a function

Mathematics

1 answer:

MaRussiya [10]3 years ago

5 0

The domain are the x-values and the range are the y-values

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AB is a tangent. Find the length of the radius, r.

Lena [83]

Answer: 8

Step-by-step explanation:

Since AB is a tangent, angle CAB is a right angle. Thus, by the Pythagorean theorem, $r=\sqrt{17^{2}-15^{2}}=8$

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2 years ago

Find two numbers whose sum is 25 and the sum of whose reciprocals is 1/6

Katen [24]

Answer:

10 and 15

Step-by-step explanation:

Let 'x' and 'y' are the numbers we need to find.

x + y = 25 (two numbers whose sum is 25)

(1/x) + (1/y) = 1/6 (the sum of whose reciprocals is 1/6)

The solutions of the this system of equations are the numbers we need to find.

x = 25 - y

1/(25 - y) + 1/y = 1/6 multiply both sides by 6(25-y)y

6y + 6(25-y) = (25-y)y

6y + 150 - 6y = 25y - (y^2)

y^2 - 25y + 150 = 0 quadratic equation has 2 solutions

y1 = 15

y2 = 10

Thus we have :

First solution: for y = 15, x = 25 - 15 = 10

Second solution: for y = 10, x = 25 - 10 = 15

The first and the second solution are in fact the same one solution we are looking for: the two numbers are 10 and 15 (since the combination 10 and 15 is the same as 15 and 10).

5 0

3 years ago

Alton had $725 for Medicare, $3000 for state income tax, and $3100 for

ella [17]

Answer:

$\$6825$

Step-by-step explanation:

Amount deducted for Medicare = $725

Amount deducted for state income tax = $3000

Amount deducted for Social security = $3100

To find: Total amount deducted from Alton's pay for FICA last year

Solution:

Total amount deducted from Alton's pay for FICA last year = Amount deducted for Medicare + Amount deducted for state income tax + Amount deducted for Social security = $725+3000+3100$