All categories

2 years ago

What is the solution to this rational equation? 24/x-8=4

Mathematics

1 answer:

Annette [7]2 years ago

4 0

Answer:

24/x-8 = 4

Multiplying both the sides with x-8

24 = (x-8)*4

24 = 4x - 32

24 + 32 = 4x

56 = 4x

56/4 = X

14= X

You might be interested in

If 1 yard = 3 feet and 1 mile = 5,280 feet, how many yards are there in 2 miles?

dsp73

Answer:

h7g8g8g8bibkjb8hucfymiohvtgiee

3 0

4 years ago

Read 2 more answers

No Need to show work.

jok3333 [9.3K]

Answer:

Step-by-step explanation:

3 0

3 years ago

PLEASE HELP!!!! The question is in the picture.

oee [108]

2 and 3 are both 58 as well. For 4 do 180-58 because a straight line is 180 degrees.

8 0

4 years ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

4 years ago

a ball is dropped from the height of 64 feet. its height can be modeled by the function h(t)=-16t^2+64, where t is the time in s

puteri [66]

Answer:

It takes 1.323 seconds for the ball to fall by 36 feet

Step-by-step explanation:

The height of the ball dropped from a height of 64 ft is modeled by the equation:

h(t) = -16t² + 64 where t is the time in seconds.

To find the time it takes to fall 36 ft, we substitute h(t) too be 36 ft and then solve the resulting quadratic function.

Substituting h(t) to be 36 ft:

36 = -16t² + 64

multiply through by -1

-36 = 16t² - 64

add 36 to both sides

16t² -64 + 36 = -36 + 36

16t² - 28 = 0

add 28 to both sides

16t² - 28 + 28 = 0 +28

16t² = 28

Divide both sides by 28

16t²/16 = 28/16

t² = 1.75

Find squre root of both sides

√t² = √1.75

t = 1.323 seconds

It takes 1.323 seconds for the ball to fall by 36 feet

5 0

3 years ago