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3 years ago

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Mathematics

1 answer:

mars1129 [50]3 years ago

6 0

The answer to ur problem is -5.20

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Find the equation of a line that is perpendicular to y = 3x – 5 and passes through the point (1, -3).

Svetradugi [14.3K]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

$\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y = \stackrel{\stackrel{m}{\downarrow }}{3}x-5$

well then therefore

$\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}$

so we're really looking for the equation of a line with slope of -1/3 and that passes through (1, -3 )

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-\cfrac{1}{3}}(x-\stackrel{x_1}{1})\implies y+3=-\cfrac{1}{3}x+\cfrac{1}{3} \\\\\\ y=-\cfrac{1}{3}x+\cfrac{1}{3}-3\implies y=-\cfrac{1}{3}x-\cfrac{8}{3}$

6 0

2 years ago

In recent commercials Toyota claimed that 80% of its vehicles sold in the past 20 years are still on the road. You work for an a

Anvisha [2.4K]

Answer:

Step-by-step explanation:

We have to perform one sample proportion test. To do so we have to proceed through following steps.

(1) We have to collect data about vehicle sales in last 20 years.

(2) Using random number table or random number generator or otherwise we have to select sample of vehicles from the list of sale. In this step, we have to keep an eye on the fact that sample is to be selected from all years (all of 20). Using stratified random sampling by dividing vehicles sold over different years is an effective way to do so. That means, we may divide vehicles sold into 20 homogeneous strata over 20 years and select sample from each strata.

(3) After selecting sample of vehicles we have to communicate to corresponding vehicle owners to gather information about that particular vehicle.

(4) We have to note number of vehicles which are still on the road.

Suppose, we have selected n vehicles as sample and after communicating we found that \tiny r of those are still on the road.

We have to test for null hypothesis $H_0:p=0.80$

against the alternative hypothesis $H_1 \neq 0.80$

Our test statistic is given

$z=\frac{\hat p - p_0}{\sqrt{p_0(1-p_0)/n} }$

here,

$\hat p =\frac{r}{n}$

$p_0 =0.80$

$z=\frac{r/n-0.80\sqrt{n} }{0.40} \\\\=2.5(\frac{r}{n} -0.8)\sqrt{n}$

We then calculate corresponding p-value.

We reject our null hypothesis if $\text{p-value}$ , level of significance.

According to our obtained p-value and level of significance we proceed to certain conclusion.

8 0

3 years ago

A triangular pyramid and its net are shown. Rain uses Calculations below to conclude that the surface area of a triangular pyram

Harman [31]

Answer:

Rain is correct, calculates correctly, 238.5 square inches

Step-by-step explanation:

The given triangular pyramid is shown with the dimensions.

The surface area of the triangular pyramid is given by :

$A=\frac{1}{2}\left(a \times b\right) + 3\left(\frac{1}{2}\times b\times s\right)$

$A=\frac{1}{2}\left(10 \times 8.7\right) + 3\left(\frac{1}{2}\times 10\times 13\right)$

$A=43.5+(3\times 65)$

$A=43.5+195$

$A=238.5 \ \text{inche}^2$

Therefore, the surface area of the triangular pyramid is = 238.5 square inches.

5 0

3 years ago

Find the quotient. ( − 2 ) ÷ 9 − 2 9 18 -18

Airida [17]

Answer:

I don´t know and i don´t want you to get it wrong so i think it is..

Step-by-step explanation:

-18 is probably the answer

Hope this helps!! lol

6 0

3 years ago

The diagram shows a straight line ABCD.

Nady [450]

Answer:

B (0, 285 ) , C (380, 0 )

Step-by-step explanation:

the first step is to obtain the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = A(- 260, 480 ) and (x₂, y₂ ) = D (620, - 180 )

m = $\frac{-180-480}{620-(-260)}$ = $\frac{-660}{620+260}$ = $\frac{-660}{880}$ = - $\frac{66}{88}$ = - 0.75 , then

y = - 0.75x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equatio

using (620, - 180 ) , then

- 180 = - 465 + c ⇒ c = - 180 + 465 = 285

So y- intercept is B (0, 285 )

y = - 0.75x + 285 ← equation of line

to find the x- intercept , let y = 0 in the equation and solve for x

0 = - 0.75 + 285 ( subtract 285 from both sides )

- 285 = - 0.75x ( divide both sides by - 0.75 )

380 = x

x- intercept is C (380, 0 )

4 0

2 years ago

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