Let h(x)=|2x|-4. Find h(x) when x = -7.<br> a)-10<br> b) 10<br> c) -13<br> d) 13<br> Plzzz

What is the true solution to 3 in 2 + in 8 = 2 in (4x)

The first step for solving this equation is to determine the defined range.
3㏑(2) + ㏑(8) = 2㏑(4x), x > 0
Write the number 8 in exponential form.
3㏑(2) + ㏑(2³) = 2㏑(4x)
Using ㏑( $a^{x}$ ) = x × ㏑(a),, transform the expression.
3㏑(2) + 3㏑(2) = 2㏑(4x)
Now collect the like terms on the left side of the equation.
6㏑(2) = 2㏑(4x)
Switch the sides of the equation.
2㏑(4x) = 6㏑(2)
Using x × ㏑(a) = ㏑( $a^{x}$ ),, transform the expression on the left side of the equation.
㏑((4x)²) = 6㏑(2)
Using x × ㏑(a) = ㏑( $a^{x}$ ),, transform the expression on the right side of the equation.
㏑((4x)²) = ㏑( $2^{6}$ )
Since the bases of the logarithms are the same,, you need to set the arguments equal.
(4x)² = $2^{6}$
Take the square root of both sides of the equation and remember to use both the positive and negative roots.
4x = +/- 8
Now separate the equation into 2 possible cases.
4x = 8
4x = -8
Solve the top equation for x.
x = 2
Solve the bottom equation for x.
x = 2
, x > 0
x = -2
Lastly,, check if the solution is in the defined range to find your final answer.
x = 2
This means that the correct answer to your question is x = 2.
Let me know if you have any further questions
:)

5 0

3 years ago

Read 2 more answers

Emily spent 1/2 of her money at the grocery store.Then, she spent 1/2 of what was left at the bakery. Next, at the music store,

Artist 52 [7]

I believe the answer is $48 because 6 * 2 is 12 and 12 * 2 is 24 and 24 * 2 is 48, thus 48$. Please feel free to check my work, though.

4 0

3 years ago

25.

bulgar [2K]

Using the slope concept, it is found that the angle between the ladder and the floor will be of 33.69º.

<h3>What is a slope?</h3>

The slope is given by the <u>vertical change divided by the horizontal change</u>, and it's also the tangent of the angle of depression.

In this problem, we have that:

The angle is of 45º.

The vertical distance is the height of h.

The horizontal distance is of 3m.

Hence:

tan(45º) = h/3.

1 = h/3.

h = 3 m.

If the ladder slides 1 m down, the height will be of 2m, hence the angle will be given as follows:

$\tan{\theta} = \frac{2}{3}$

$\theta = \arctan{\left(\frac{2}{3}\right)}$

$\theta = 33.69^\circ$

More can be learned about the slope concept at brainly.com/question/18090623

#SPJ1

8 0

2 years ago

4(2x−3)=4(2x)−4(3) what is the proptery

Nikitich [7]

9514 1404 393

Answer:

distributive property

Step-by-step explanation:

The <em>distributive property</em> of multiplication over addition lets you expand the product in the manner shown.

4 0

3 years ago

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the

EastWind [94]

Answer:

a) $\hat p=\frac{471}{1024}=0.460$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

b) The 99% confidence interval would be given by (0.429;0.491)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

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

Data given and notation

n=1024 represent the random sample taken

X=471 represent the people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

$\hat p=\frac{471}{1024}=0.460$ estimated proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

p= population proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

Part a

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.