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Lilit [14]
3 years ago
11

If b is the midpoint of AC, which of the following choices is the value of x?

Mathematics
1 answer:
katrin [286]3 years ago
8 0
If B is the midpoint of AC, that means that the distances from A to B and B to C are the same. The distance from A to B is 8x + 4, and the distance from B to C is 10x - 6, so we can set these two equivalent:

8x + 4 = 10x - 6

Solving for x:

4 = 2x - 6 (subtract 8x from both sides)
10 = 2x (add 6 to both sides)
5 = x (divide both sides by 2)

So, x = 5, which is the second option given.
You might be interested in
The function F(c)=log0.5x is decreasing true or false
nikitadnepr [17]

Answer:

  true

Step-by-step explanation:

We assume you intend your function to be ...

  F(x)=\log_{0.5}x

A logarithm with a base less than 1 is a decreasing curve. Here, the base appears to be 0.5, a value less than 1. Hence the curve is decreasing.

7 0
3 years ago
a student played a computer game 500 times and won 370 of these game. he then won the next "x" games and lost none. he has now w
a_sh-v [17]

So, this is a proportion problem. If we express 75% as a fraction (3/4ths), we have:

\frac{370+x}{500+x}=\frac{3}{4}

Since he won all of his games, we add the number won (x), to the number previously won and divide it by the total games played which is just the previous games played plus the number of current games played, so since he lost no games we still add x to the denominator as well. Solving this gives us:

4(370+x)=3(500+x) \implies\\ 1480+4x=1500+3x \implies \\ x=20

That x value is 20.

3 0
3 years ago
Val returned a bicycle while she was on vacation. She paid a flat rental fee of $55.00 plus $8.50 each day. The total cost was $
never [62]

Number of days Val rented the bicycle is 8

<h3><u>Solution:</u></h3>

Given that val paid a flat rental fee of $55.00 plus $8.50 each day

The total cost was $123

To find: number of days she rented the bicycle

Let "a" be the number of days she rented the bicycle

Rental fee = $55.00

Fee for one day = $ 8.50

So total cost is equal to rental fee and fee for "a" days

Total cost = rental fee + (number of days she rented the bicycle x Fee for one day)

123 = 55.00 + (a \times 8.50)

123 = 55 + 8.50a

123 - 55 = 8.50a

8.50a = 68

a = \frac{68}{8.50} = 8

Thus number of days she rented the bicycle is 8

4 0
3 years ago
how long will it take an investment of $300 to triple, if the interest rate is 3.5% per year, compounded continuously?
Rashid [163]

Answer:

31 years to triple the investment

Step-by-step explanation:

Initial investment = 300

Triple amount that is final amount = 300*3= 900

rate of interest = 3.5 % = 0.035

we need to find out number of years (t)

for compounded continuously we use formula

A= Pe^{rt}

A is the final amount

P is the initial amount

r is the rate of interest

t is the number of years

900 = 300e^{0.035*t}

Divide both sides by 300

3 =e^{0.035*t}

take 'ln' on both sides

ln(3) =ln(e^{0.035*t})

ln(3) = 0.035t ln(e)

ln(e)= 1

\frac{ln(3)}{0.035} = t

t= 31.3889

Round to nearest whole number

t= 31 years


4 0
3 years ago
Simplify x raised ^ 5 x - 2​
MaRussiya [10]
The property x^axb makes it x^a+b so x^5x-2 ,

Therefore x^-10 is final
5 0
3 years ago
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