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3 years ago

What is the solution of log4(2x-6)=2

Mathematics

1 answer:

Flauer [41]3 years ago

3 0

Answer: $x=11$

Step-by-step explanation:

Remembert that, by definition:

$log_b(x)=y$ → $b^y=x$

Then, you can rewrite $log_4(2x-6)=2$ in exponential form:

$4^2=2x-6$

Now you can solve for the variable "x":

Add 6 to both sides of the equation:

$4^2+6=2x-6+6$

$22=2x$

And finally you must divide both sides of the equation by 2, then:

$\frac{22}{2}=\frac{2x}{2}\\\\x=11$

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A triangle has the vertices A(-7, 8), B(1, -7), and C(7,6). After a dilation, the vertices of the image are A(-28, 32).

steposvetlana [31]

Answer: the answer is A.4

Step-by-step explanation:

Dilation in this context is the transformation is an object into a larger one.

ABC is transformed to A'B'C'

To get the scale factor, we divide the coordinates of A'B'C' by ABC

i.e

A'/A = -28/-7, 32/8 = 4

B'/B = 4/1, -28/-7 = 4

C'/C = 28/7, 24/6 = 4

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3 years ago

The manager of the motor pool wants to know if it costs more to maintain cars that are driven more often. Data are gathered on e

Liula [17]

Answer:

b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost

Step-by-step explanation:

The p-value for the slope estimate show us how strong is the certainty that there are a linear relationship between both variables. In this case, the p-value for the slopes shows if there is a significant relationship between the number of miles driven and the maintenance cost.

If we have a high p-value like 0.7 we can said that there is no certainty in the linear relationship. it means that there's no statistically significant linear relationship between the number of miles driven and the maintenance cost.

5 0

2 years ago

Gas prices are up 30% since last year when they were $4.35, how much is gas now?

Anestetic [448]

Answer:

$5.66/gal

Step-by-step explanation:

To calculate the current price of gas, multiply $4.35/gal by (1 + 0.30), or by 1.30:

1.30($4.35/gal) = $5.66/gal

7 0

2 years ago

In a random sample of 45 newborn babies, what is the probability that 40% or fewer of the sample are boys. (Use 3 decimal places

erastova [34]

Answer:

$z= \frac{p- \mu_p}{\sigma_p}$

And the z score for 0.4 is

$z = \frac{0.4-0.4}{\sigma_p} = 0$

And then the probability desired would be:

$P(p$

Step-by-step explanation:

The normal approximation for this case is satisfied since the value for p is near to 0.5 and the sample size is large enough, and we have:

$np = 45*0.4= 18 >10$

$n(1-p) = 45*0.6= 27 >10$

For this case we can assume that the population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Where:

$\mu_{p}= \hat p = 0.4$

$\sigma_p = \sqrt{\frac{p(1-p)}(n} =\sqrt{\frac{0.4(1-0.4)}(45}= 0.0703$

And we want to find this probability:

$P(p$

And we can use the z score formula given by:

$z= \frac{p- \mu_p}{\sigma_p}$

And the z score for 0.4 is

$z = \frac{0.4-0.4}{\sigma_p} = 0$

And then the probability desired would be:

$P(p$

7 0

3 years ago

Read 2 more answers

CASEY HAS A BACKYARD THAT IS A 50-BY-50 FOOT SQUARE. SHE TURNED OVER AN IRREGULARLY-SHAPED PLOT OF SOIL TO PLAN A GARDEN. TO FIN

ser-zykov [4K]

Given the description of the irregular garden, the area will be given by:
Area=(regular points)+1/2(irregular points)
regular points=1500
irregular points=420
thus
Area=1500+1/2(420)
Area=1500+210
Area=1710 ft²

5 0

2 years ago

Read 2 more answers