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3 years ago

A line goes through points (0, 3) and (6, 12). What would be the slope of this line's perpendicular bisector?

Mathematics

1 answer:

Leto [7]3 years ago

3 0

Answer:

the slope of the perpendicular bisector is -2/3

Step-by-step explanation:

The slope of the line joining the two points P1(0,3), P2(6,12) is given by

m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5

The slope m2 of a line perpendicular to the previous line is given by

m1*m2 = -1

solving

m2 = -1/m1 = -1/ (3/2) = -2/3

THerefore the slope of the perpendicular bisector is -2/3

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What can you do to get 2x alone on the equation? when finished, fill in the blanks and simplify the equation.

Tom [10]

Answer:

2x = 256

Step-by-step explanation:

Your problem → 82.5 + 8(0.25x) = 338.5

82.5+8(0.25x)=338.5

⇒-256+80.25x=0

⇒2x-256=0

⇒2x=256

⇒x=256/2

⇒x=128

4 0

2 years ago

A particular psychological test is used to measure need for achievement. The average test score for all university students in O

Angelina_Jolie [31]

Answer:

Only B and C are always true.

Step-by-step explanation:

To analyse which statements are always true, we go through the process of finding confidence intervals for sample means, from the start.

Confidence Interval = (Sample mean) ± (Margin of error)

From this expression, it is evident that the margin of error determines how wide the confidence interval would be.

Sample Mean = 110 (given)

Margin of Error = (Critical value) × (Standard deviation of the distribution of sample means)

Since no information about the population standard deviation is provided, the critical value is obtained using t-distribution.

The critical value usually varies at different confidence levels and degree of freedoms.

The higher the confidence level, the higher the critical value and the higher the margin of error leading to a wider range.

Hence, a confidence interval of 95% will have a higher critical value than a confidence interval of 90%. Hence, statement C is proved once that 'for n = 100, the 95% confidence interval will be wider than the 90% confidence interval'.

After obtaining the critical value, we then obtain the standard deviation of the distribution of sample means or simply the standard error of the mean. This is given as

σₓ = σ/√n

where σ = standard deviation; which isn't given. The standard deviation might be high enough to guarantee that the Margin of error is high too for the confidence interval to contain 115 or low enough to ensure that the Margin of error is very small and the confidence interval will not contain 115.

Or the sample size might be high enough to make the standard error of the mean to be eventually small and lead to a small margin of error and the condidence interval will not contain 115.

The point is, it isn't always sure that the resulting interval.would contain 115. So, statement A isn't always true.

Then from σₓ = σ/√n,

n = sample size, a large sample size means a more narrow confidence interval and a small sample size means a wider sample size. This proves statement C.

The 95% confidence interval for n = 100 will be more narrow than the 95% confidence interval for n = 50.

Hence, Only B and C are always true.

Hope this Helps!!!

5 0

3 years ago

Write the number named by the underlined digit in words.<br> 2.369<br> -

Liula [17]

Answer:

Nine thousandth

Step-by-step explanation:

Only the nine thousandth is underlined I think, therefore you did not have to write out the words for the numbers before it

4 0

3 years ago

Graph the following piecewise function on a separate piece of graph paper and upload your graph below.

Alecsey [184]

ANSWER

To graph the function

$f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x$

follow the steps below.

1. Find y- intercept by plugging in $x=0$ .

$x=0$ is on the interval, $-4\leq x$ , so we substitute in to

$f(x)=x+4$

$\Rightarrow f(0)=0+4$

$\Rightarrow f(0)=4$

Hence the y-intercept is $(0,4)$

2. Find x-intercept by setting $f(x)=0$

This implies that

$x+4=0,$ on $-4\leq x$

or

$2x-1=0$ on $3\leq x$

We now solve for $x$ on each interval,

$x=-4,$ on $-4\leq x$

or

$x=\frac{1}{2}$ on $3\leq x$

But observe that

$x=\frac{1}{2}$ does not belong to $3\leq x$

This means it can never be an intercept for this piece-wise function.

Hence our x-intercept is $(-4,0)$

3. Plotting the boundaries of the interval.

For $f(x)=x+4$ on $-4\leq x$

$f(-4)=-4+4$

$\Rightarrow f(-4)=0$ .

This point $(-4,0)$ coincides with the x-intercept.

$f(3)=3+4$

$f(3)=7$

So we have the point $(3,7)$ . But note that $x=3$ does not belong to this interval so we plot this point as a hole.

For $f(x)=2x-1$ on $3\leq x$

$f(3)=2(3)-1$

$\Rightarrow f(3)=5$

So we plot $(3,5)$

$f(6)=2(6)-1$

$\Rightarrow f(6)=11$

So we plot $(6,11)$ also as a hole.

Plotting all these points we can now graph the function,

$f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x$

See attachment for graph.

7 0

3 years ago

Read 2 more answers

Arner Home

alexandr1967 [171]

Answer:

The correct answer is

C. 23.1

Step-by-step explanation:

i think this is correct

5 0

4 years ago

Read 2 more answers