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2 years ago

What is the true solution to l n 20 + l n 5 = 2 l n x x = 5 x = 10 x = 50 x = 100

Mathematics

2 answers:

IgorLugansk [536]2 years ago

7 0

Answer: x = 10

Step-by-step explanation:ln20+ln5=2lnx

ln(20x5)=lnx^2

ln100=1nx^2

100=x^2

square root

x=10

Pani-rosa [81]2 years ago

3 0

Answer:

x = 10

Step-by-step explanation:

l n 20 + l n 5 = 2 l n x

ln (20×5) = ln x²

ln(100) = lnx²

100 = x²

x = +/- 10

Since logs of negative numebrs don't exist, we reject -10

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A study found that a driver’s reaction time A(x) to audio stimuli and his or her reaction time V(x) to visual stimuli (both in m

amid [387]

Answer:

The required inequality is $0.0001 x^2 - 0.089 x - 7$ .

Step-by-step explanation:

The given inequalities are

$A(x) = 0.0051x^2 - 0.319x + 15$

$V(x)= 0.005x^2 - 0.23x + 22$

where, x is the driver's age (in years), A(x) is driver’s reaction time to audio stimuli and V(x) is his or her reaction time to visual stimuli, 16 ≤ x ≤ 70.

We need to find an inequality that can be use to find the x-values for which A(x) is less than V(x).

$A(x)$

$0.0051x^2 - 0.319x + 15< 0.005x^2 - 0.23x + 22$

$0.0051x^2 - 0.319x + 15- 0.005x^2 + 0.23x- 22$

Combine like terms.

$0.0001 x^2 - 0.089 x - 7$

where, 16 ≤ x ≤ 70.

Therefore, the required inequality is $0.0001 x^2 - 0.089 x - 7$ .

5 0

2 years ago

Nakita rode her skateboard at an average speed of 8.8 feet per second for 0.2 miles. She wants to calculate how long it took her

timama [110]

Answer: $2\ minutes$

Step-by-step explanation:

We know that:

$d=rt$

Where "d" is distance, "r" is rate and "t" is time.

Solved for the time "t":

$t=\frac{d}{r}$

The first step is to convert the distance from miles to feet.

Since $1\ mile=5,280\ feet$ , we get:

$d=(0.2\ mi)(\frac{5,280\ ft}{1\ mi})\\\\d=1,056\ ft$

Knowing that:

$r=8.8\ \frac{ft}{s}$

We can substitute values into $t=\frac{d}{r}$ in order to find the time in seconds:

$t=\frac{1,056\ ft}{8.8\ \frac{ft}{s}}\\\\t=120\ s$

Since:

$1\ minute = 60\ seconds$

The time in minutes is:

$t=(120\ s)(\frac{1\ min}{60\ s})\\\\t=2\ min$

7 0

2 years ago

Solve for m:<br> -3(1 – 5m) = — 38 + 8m

Solnce55 [7]

Answer:

m = - 5

Step-by-step Explanation:

$-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}$

3 0

1 year ago

Read 2 more answers

The first three terms of a geometric sequence are shown below. x+3,-2x2-6x,4x3+12x2,.... What is the eighth term of the sequence

nika2105 [10]

So hmm is a geometric sequence, meaning, the next term is found by multiplying it by "something", namely the "common ratio"

now, if the next term is the product of the common ratio and the previous term, that means, if we divide the previous term by the next term, the quotient will then be the "common ratio", let's do that then

let's divide the 2nd term by the 1st term then

$\bf \cfrac{-2x^2-6x}{x+3}\implies \cfrac{-2x\underline{(x+3)}}{\underline{(x+3)}}\implies \boxed{-2x}\impliedby \textit{common ratio}\\\\
-----------------------------\\\\$

$\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{value of first term}\\
r=\textit{common ratio}\\
----------\\
a_1=x+3\\
n=8\\
r=-2x
\end{cases}
\\\\\\
a_8=(x+3)(-2x)^{8-1}\implies a_8=(x+3)(-2x)^7
\\\\\\
a_8=(x+3)(-2^7x^7)\implies a_8=(x+3)(-128x^7)
\\\\\\
a_8=-128x^8-384x^7$

8 0

2 years ago

Read 2 more answers

What is 2 divided 1 6/7 ? Please answer

Aliun [14]

If you would like to divide 2 by 1 6/7, you can do this using the following steps:

1 6/7 = 13/7

2 / 1 6/7 = 2 / 13/7 = 2/1 / 13/7 = 2/1 * 7/13 = 14/13 = 1 1/13

The correct result would be 1 1/13.

6 0

2 years ago