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3 years ago

12 more than the difference of half a number and 3 is 45. Plz answer

Mathematics

1 answer:

son4ous [18]3 years ago

7 0

Answer:

x=18

Step-by-step explanation:

the result of 12 added to the difference of half a number and 3 is 45.

that looks something like this

$12+\frac{1}{2}x= 45$

which can be solved as such

$\frac{1}{1} x+(12-3)=45\\\frac{1}{2}x+9=45\\\frac{1}{2}x=45-9\\ \frac{1}{2}x=36\\\frac{2}{1}*\frac{1}{2}x=36*\frac{2}{1} \\ x=36*2\\x=72$

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write an equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)

dimaraw [331]

The equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is $y - 3 = \frac{-7x}{2}+ \frac{21}{4}$

<h3>Solution:</h3>

Given that we have to write equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)

Let us first find the slope of given line AB

The slope "m" of the line is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here the given points are A(-2,2) and B(5,4)

$\text {Here } x_{1}=-2 ; y_{1}=2 ; x_{2}=5 ; y_{2}=4$

$m=\frac{4-2}{5-(-2)}=\frac{2}{7}$

Thus the slope of line with given points is $\frac{2}{7}$

We know that product of slopes of given line and slope of line perpendicular to given line is always -1

$\begin{array}{l}{\text {slope of given line } \times \text { slope of perpendicular bisector }=-1} \\\\ {\frac{2}{7} \times \text { slope of perpendicular bisector }=-1} \\ \\{\text {slope of perpendicular bisector }=\frac{-7}{2}}\end{array}$

The perpendicular bisector will run through the midpoint of the given points

So let us find the midpoint of A(-2,2) and B(5,4)

The midpoint formula for given two points is given as:

$\text {For two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right), \text { midpoint } \mathrm{m}(x, y) \text { is given as }$

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Substituting the given points A(-2,2) and B(5,4)

$m(x, y)=\left(\frac{-2+5}{2}, \frac{2+4}{2}\right)=\left(\frac{3}{2}, 3\right)$

Now let us find the equation of perpendicular bisector in point slope form

The perpendicular bisector passes through points (3/2, 3) and slope -7/2

The point slope form is given as:

$y - y_1 = m(x - x_1)$

$\text { Substitute } \mathrm{m}=\frac{-7}{2} \text { and }\left(x_{1}, y_{1}\right)=\left(\frac{3}{2}, 3\right)$

$y - 3 = \frac{-7}{2}(x - \frac{3}{2})\\\\y - 3 = \frac{-7x}{2}+ \frac{21}{4}$

Thus the equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is found out

7 0

4 years ago

In politics, marketing, etc. We often want to estimate a percentage or proportion p. One calculation in statistical polling is t

inessss [21]

Answer: |p-72% |≤ 4%

Step-by-step explanation:

Let p be the population proportion.

The absolute inequality about p using an absolute value inequality.:

$|p-\hat{p}| \leq E$ , where E = margin of error, $\hat{p}$ = sample proportion

Given: A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .

|p-72% |≤ 4%

⇒ 72% - 4% ≤ p ≤ 72% +4%

⇒ 68% ≤ p ≤ 76%.

i.e. p is most likely to be between 68% and 76% (.

6 0

3 years ago

Find the indicated side of the triangle a= I'll mark you brainliest for the correct answer

saul85 [17]

Answer:

$a = 17 \sqrt{2}$

Step-by-step explanation:

$\sin \: 45 \degree = \frac{17}{a} \\ \frac{1}{ \sqrt{2} } = \frac{17}{a} \\ a = 17 \sqrt{2} \\$

3 0

4 years ago

The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week that is

Hatshy [7]

Answer:

A. Normal

B. 30.1, 32.9

C. 95, 5

Step-by-step explanation:

A. The sampling distribution follows a normal distribution

Given that the sample size is large, we have that the sample distribution follows a normal distribution according to the central limit theorem

B. The 95% confidence interval is given as follows;

$CI=\bar{x}\pm z \times \dfrac{s}{\sqrt{n}}$

The number of residents in the study, n = 120 residents

The sample mean, $\overline x$ = 31.5 pounds

The standard deviation, s = 7.8 pounds

The z-value for 95% confidence level, z = 1.96

Therefore, we get;

C.I. = 31.5 ± 1.96 × 7.8/√(120)

The 95% C.I. ≈ 30.1 ≤ $\overline x$ ≤ 32.9

Therefore, we have that with 95% confidence, the population mean number of pounds per person per week is between 30.1 and 32.9

C. Therefore, according to the central limit theorem, about 95 percent of the groups of 120 will contain the true population mean number of pounds of trash generated per person per week and about 5 percent will not contain the true population mean number of pounds of trash generated per person per week.

8 0

3 years ago

(12x - 2y + 3/5) - (1/4 - 8x + 6y)

Neko [114]

Answer:

20x-8y+ 7/20

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers