Six years ago, Lucia’s age was 1/3 the age she will be in 6 years. How old is Lucia now? Enter an integer.

If B is the midpoint of AC, AB=x+6 and AC=5x-6, then what is BC?

nikklg [1K]

If B is the midpoint of AC, then AB=BC. It is also BC=AC-AB

AB = x + 6

AC = 5x - 6

BC = (5x - 6) - (x + 6)

We can kinda use distributive property, like this:

BC = 5x - 6 -x - 6

Combine like terms:

BC = 4x - 12

To verify, we can add AB and BC to see if their sum is equal to AC.

(x + 6) + (4x - 12) = 5x - 6

If we are correct, this equation will be true.

x + 6 + 4x - 12 = 5x - 6

Combine like terms:

6 + 5x - 12 = 5x - 6

5x - 6 = 5x - 6

It's correct!

BC = 4x - 12. Final Answer.

Let me know if you have any questions about this! :)

7 0

2 years ago

PLEASE HELP! Economics

pashok25 [27]

Answer: b

Step-by-step explanation:

if u stop imports then u have money

4 0

2 years ago

Read 2 more answers

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by ℎ = −16푡 ଶ+103푡+5 w

Liono4ka [1.6K]

Question:

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by h(t)=-16t^2+80t+5, where t is measured in seconds. Write an equation to determine how long it will take for the ball to reach the ground.

Answer:

$t = 5.0625$

Step-by-step explanation:

Given

$h(t)=-16t^2+80t+5$

Required

Find t when the ball hits the ground

This implies that h(t) = 0

So, we have:

$0=-16t^2+80t+5$

Reorder

$-16t^2+80t+5 = 0$

Using quadratic formula, we have:

$t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

Where

$a = -16$ $b =80$ $c = 5$

So, we have:

$t = \frac{-80\±\sqrt{80^2 - 4*-16*5}}{2*-16}$

$t = \frac{-80\±\sqrt{6400 +320}}{-32}$

$t = \frac{-80\±\sqrt{6720}}{-32}$

$t = \frac{-80\±82.0}{-32}$

This gives:

$t = \frac{-80+82.0}{-32}$ or $t = \frac{-80-82.0}{-32}$

$t = \frac{2}{-32}$ or $t = \frac{-162}{-32}$

$t = -\frac{2}{32}$ or $t = \frac{162}{32}$

But time can not be negative.

So, we have:

$t = \frac{162}{32}$

$t = 5.0625$

Hence, time to hit the ground is 5.0625 seconds

3 0

2 years ago

I recently got a bad grade on a test. How can I make sure I don't make silly mistakes when I hardly have time to double check?

Nataliya [291]

Make sure you study, and if necessary, do some practice problems. Then, check to make sure you are right, and if not, find out why, and correct your mistakes.

4 0

3 years ago

Principle=$745 rate= 9% time= 4years

Dennis_Churaev [7]

Based on a yearly rate (which is the norm) I give you my answer ..

Your principle is at 745$
Annual Rate 9%

For the first year your principle will grow by 67.05 $ if untouched (9%) up to 812.05 $

2nd year .. 9% of the 812.05 $ is 73.0845 $ .. So by the 2nd year you reach 885.1345 $

3rd year .. 79.662105 $ .. Total 964.796605 $

4th year .. 86.83169445 $ .. Final 4 Years Total 1051.62829945 $

4 0

3 years ago