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Natali5045456 [20]
2 years ago
8

What are the solutions for 2x+7 is less than or equal to 3x-5

Mathematics
1 answer:
solmaris [256]2 years ago
5 0

Answer:

x≥2 2/5 or x≥ 2.4 or [2.4,∞)

Step-by-step explanation:

2x+7≤3x-5

7+5≤3x+2x

12≤5x

x≥12/5 or x≥2 2/5 or x≥2.4

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Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your
bonufazy [111]

Answer:

Using the rule of 72, the doubling time is 9.35 years.

The exact answer is that the doubling time is 8.89 years.

Step-by-step explanation:

By the rule of 72, we have that the doubling time D is given by:

D = \frac{72}{Interest Rate}

The interest rate is in %.

In our exercise, the interest rate is 7.7%. So, by the rule of 72:

D = \frac{72}{7.7} = 9.35.

Exact answer:

The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).

The compound interest formula is given by:

A = P(1 + \frac{r}{n})^{nt}

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

A = 2P

r = 0.077

There are 52 weeks in a year, so n = 52

A = P(1 + \frac{r}{n})^{nt}

2P = P(1 + \frac{0.077}{52})^{52t}

2 = (1.0015)^{52t}

Now, we apply the following log propriety:

\log_{a} a^{n} = n

So:

\log_{1.0015}(1.0015)^{52t} = \log_{1.0015} 2

52t = 462.44

t = \frac{462.44}{52}

t = 8.89

The exact answer is that the doubling time is 8.89 years.

6 0
3 years ago
Help ASAP show work please thanksss!!!!
Llana [10]

Answer:

\displaystyle log_\frac{1}{2}(64)=-6

Step-by-step explanation:

<u>Properties of Logarithms</u>

We'll recall below the basic properties of logarithms:

log_b(1) = 0

Logarithm of the base:

log_b(b) = 1

Product rule:

log_b(xy) = log_b(x) + log_b(y)

Division rule:

\displaystyle log_b(\frac{x}{y}) = log_b(x) - log_b(y)

Power rule:

log_b(x^n) = n\cdot log_b(x)

Change of base:

\displaystyle log_b(x) = \frac{ log_a(x)}{log_a(b)}

Simplifying logarithms often requires the application of one or more of the above properties.

Simplify

\displaystyle log_\frac{1}{2}(64)

Factoring 64=2^6.

\displaystyle log_\frac{1}{2}(64)=\displaystyle log_\frac{1}{2}(2^6)

Applying the power rule:

\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}(2)

Since

\displaystyle 2=(1/2)^{-1}

\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}((1/2)^{-1})

Applying the power rule:

\displaystyle log_\frac{1}{2}(64)=-6\cdot log_\frac{1}{2}(\frac{1}{2})

Applying the logarithm of the base:

\mathbf{\displaystyle log_\frac{1}{2}(64)=-6}

5 0
2 years ago
A die is rolled, what is the probability of getting an even number or a 3?
ruslelena [56]

Hello!

possibility : 2,3,4,6

4/6 = 2/3

Good luck!

7 0
2 years ago
Help please, this is a math question. &lt;3
AfilCa [17]
Parenthesis first
11+4=15
division second
15/3=5
what is the square root of 64? 8!
8x5=40
Answer is 40
6 0
2 years ago
Read 2 more answers
My noob has 36 apples he puts 29 in a bag how much he has now
SCORPION-xisa [38]

Answer: He has 7 at the moment, technically, if he still has the bag, he still has all 36

Step-by-step explanation:

8 0
2 years ago
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