What is the Multiplicative Property?

Anna007 [38]

Using logarithmic laws: log(a) + log(b) = log(ab)

log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3

Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.

$4^{log_4 (x + 9)(x + 21)} = 4^{3}$
$(x + 9)(x + 21) = 64$
$x^{2} + 9x + 21x + 189 = 64$

Solving the quadratic we get:
$x^{2} + 30x + 125 = 0$
$(x + 5)(x + 25) = 0$

$x = -5, -25$

BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.

7 0

3 years ago

Every 150 miles is 1 inch there are 2160 miles how many inches are there

topjm [15]

Divide 2160 by 150 to get the answer. You should get a round number. If not, plz comment below.

8 0

3 years ago

Read 2 more answers

Problem Page A principal of $2100 is invested at 7.75% interest, compounded annually. How much will the investment be worth afte

just olya [345]

Answer:

After 12 years the investment will be worth $5145.

Step-by-step explanation:

The formula used for compounded interest is:

A = P(1+r/n)^nt

where,

A = future value

P = Principal Amount

r = interest rate

n = no of times interest is compounded

t = time

In the question given:

A=?

P = $2100

r = 7.75% or 0.0775

n = 1

t= 12

A= 2100*(1+0.0775/1)^1*12

A= 2100 *(1+0.0775)^12

A= 2100 *(1.0775)^12

A= 2100 * 2.45

A= 5145

So, after 12 years the investment will be worth $5145.

6 0

3 years ago

A college entrance exam company determined that a score of 2222 on the mathematics portion of the exam suggests that a student i

kolbaska11 [484]

Answer:

Yes, Students are scoring above 2222 on the math portion of the exam.

Step-by-step explanation:

We are given that a college entrance exam company determined that a score of 2222 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics i.e., population mean is 22.

Null Hypothesis, $H_0$ : $\mu$ = 22 {Students are scoring equal to 2222 on the math portion of the exam}

Alternate Hypothesis, $H_0$ : $\mu$ > 22 {Students are scoring above 2222 on the math portion of the exam}

Also, a random sample of 150 students who completed this core set of courses results in a mean math score of 22.7 on the college entrance exam with a standard deviation of 3.93 i.e.;

Sample mean, $Xbar$ = 22.7 and Sample standard deviation, s = 3.93

The Test statistics is given by;

Z = $\frac{Xbar -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

Test Statistics = $\frac{22.7 -22}{\frac{3.93}{\sqrt{150} } }$ ~ $t_1_4_9$

= 2.1815

Since, we are not given with the significance level, so we assume it to be 5%. At 5% significance level t table gives critical value of 1.6578 at 149 degree of freedom. Since our test statistics is more than the critical value so we reject null hypothesis as our test statistics fall in the rejection region.

Therefore, we conclude that Students are scoring above 2222 on the math portion of the exam.

7 0

3 years ago

Which of the following pairs of functions are inverses of each other?

yan [13]

The answer is c hopefully it helps

3 0

3 years ago