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Marina CMI [18]

3 years ago

5

What is the estimate to 8,244?

1 answer:

Yuri [45]3 years ago

5 0

To the nearest tenth: 8240
To the nearest hundred: 8200
To the nearest thousand: 8000

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Solve the following equations.<br> log2(x^2 − 16) − log^2(x − 4) = 1

Alenkasestr [34]

Answer:

$x=\frac{4*(2+e)}{e-2}$

Step-by-step explanation:

Let's rewrite the left side keeping in mind the next propierties:

$log(\frac{1}{x} )=-log(x)$

$log(x*y)=log(x)+log(y)$

Therefore:

$log(2*(x^{2} -16))+log(\frac{1}{(x-4)^{2} })=1\\ log(\frac{2*(x^{2} -16)}{(x-4)^{2}})=1$

Now, cancel logarithms by taking exp of both sides:

$e^{log(\frac{2*(x^{2} -16)}{(x-4)^{2}})} =e^{1} \\\frac{2*(x^{2} -16)}{(x-4)^{2}}=e$

Multiply both sides by $(x-4)^{2}$ and using distributive propierty:

$2x^{2} -32=16e-8ex+ex^{2}$

Substract $16e-8ex+ex^{2}$ from both sides and factoring:

$-(x-4)*(-8-4e-2x+ex)=0$

Multiply both sides by -1:

$(x-4)*(-8-4e-2x+ex)=0$

Split into two equations:

$x-4=0\hspace{3}or\hspace{3}-8-4e-2x+ex=0$

Solving for $x-4=0$

Add 4 to both sides:

$x=4$

Solving for $-8-4e-2x+ex=0$

Collect in terms of x and add $4e+8$ to both sides:

$x(e-2)=4e+8$

Divide both sides by e-2:

$x=\frac{4*(2+e)}{e-2}$

The solutions are:

$x=4\hspace{3}or\hspace{3}x=\frac{4*(2+e)}{e-2}$

If we evaluate x=4 in the original equation:

$log(0)-log(0)=1$

This is an absurd because log (x) is undefined for $x\leq 0$

If we evaluate $x=\frac{4*(2+e)}{e-2}$ in the original equation:

$log(2*((\frac{4e+8}{e-2})^2-16))-log((\frac{4e+8}{e-2}-4)^2)=1$

Which is correct, therefore the solution is:

$x=\frac{4*(2+e)}{e-2}$

6 0

3 years ago

Please help me no uncool answers

Lyrx [107]

Answer:

$a_{n} =n-4$

Step-by-step explanation:

With every number following, you just keep subtracting 4 from the previous number

6 0

2 years ago

A particle is moving on a straight line with velocity

Lena [83]

$v = {t}^{2} - 6t + 5$

t=2

$v = {2}^{2} - 6 \times 2 + 5 = - 3$

7 0

3 years ago

What are the intercepts of the line?

Mama L [17]

The answer is D. <span>x-intercept: 8; y-intercept: 2
i hope this helps u out!</span>

8 0

3 years ago

Read 2 more answers

Find the equation for the line that passes through the point (5,-3), and that is perpendicular to the line with the equation y-1

8090 [49]

Answer:

y+3=-4(x-5)

Explanation:

Part A

Given the line:

$y-1=\frac{1}{4}(x-2)$

We want to find the equation of a perpendicular line that passes through the point (5,-3),

First, determine the slope of the perpendicular line.

Comparing the given line with the slope-point form:

$\begin{gathered} y-y_1=m(x-x_1) \\ \implies\text{Slope},m=\frac{1}{4} \end{gathered}$

By definition, two lines are perpendicular if the product of their slopes is -1.

Let the slope of the perpendicular line = n

$\begin{gathered} \implies\frac{1}{4}n=-1 \\ n=-4 \end{gathered}$

Thus, using a slope of -4 and a point (5,-3), we find the equation of the line.

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-4(x-5) \\ y+3=-4(x-5) \end{gathered}$

The equation of the perpendicular line in the slope-point form is:

$y+3=-4(x-5)$

Part B

In order to graph the line, first, find two points on the line.

When x=0

$\begin{gathered} y+3=-4(0-5) \\ y+3=20 \\ y=20-3=17 \\ \implies(0,17) \end{gathered}$

When y=1

$\begin{gathered} 1+3=-4(x-5) \\ 4=-4(x-5) \\ \frac{4}{-4}=x-5 \\ -1=x-5 \\ x=5-1=4 \\ \implies(4,1) \end{gathered}$

Join the points (0,17) and (4,1) as shown in the graph below:

3 0

1 year ago