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postnew [5]
3 years ago
15

Two perpendicular lines intersect at the origin. If the slope of the first line is -1/2, what is the equation of the second line

?
Mathematics
1 answer:
Dovator [93]3 years ago
5 0

bearing in mind that perpendicular lines have <u>negative reciprocal</u> slopes.

now, they both intersect at 0,0, namely they both pass through it, we know the slope of the first one, so

\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{2}{1}\implies 2}}

so, we're really looking for the equation of a line whose slope is 2, and runs through (0,0).

\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies 2 \\\\\\ \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-0=2(x-0)\implies y=2x

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JulijaS [17]

Answer:

(7, 3)

Step-by-step explanation:

(2+5, 6-3) = (7, 3)

4 0
3 years ago
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A rental agent claims that the mean monthly rent for apartments on the east side of town is less than $750. A random sample of 1
klio [65]

Answer:

Its statistically significant, that Mean monthly apartment rent in town east <  $ 750

Step-by-step explanation:

Null Hypothesis [H0] : Mean monthly apartment rent in town east = 750

Alternate Hypothesis [H1]: Mean monthly apartment rent in town east < 750

t = (x' - u) / (s / √n)

x' = sample mean = 737

u = population assumed mean = 750

s = standard deviation = 23

n = no. of units in sample

t = (737 - 750) / (23 / √18)  = -13 / 5.4212

= -2.39

t tabulated critical value : for one sided 0.05 significance level, at 17 degrees of freedom = -1.740

t calculated value, -2.39 < t tabulated critical value, - 1.740

We reject the null hypothesis, & state that its statistically significant, that Mean monthly apartment rent in town east < 750

3 0
2 years ago
The count of bacteria in a culture is 10 and doubles every 20 minutes. Find the population size after 11 hours. Can someone expl
RSB [31]

Since you asked how to solve this, I will put the answer at the bottom.

You might not think the same way as I but I think in steps.

<h3>(1) Calculate how many times the bacteria divide in eleven hours</h3>

The bacteria divide every 20 minutes, and will therefore divide three times every hour, 60/20 = 3.

If the bacteria grow for eleven hours, each bacterium will divide 3 times per hour × 11 hours = 33 times.

<h3>(2) Add the orginial size of bacteria into the equation</h3>

(This part is edited)

(orginial size)*2^number of divisions

10*2^{33\\}

=85899345920

7 0
2 years ago
PLEASE HELP ME WITH THIS I WILL GIVE BRAINLIEST
olga55 [171]

Answer:

The area of the large rectangle can be represented in two ways. Either the sum of each of the areas of the individual smaller rectangles, which is what the first equation represents, as its the base multiplied by the height (a) of each rectangle.

The second equation is a simplified version of the first one, and can be explained in three ways:

Each of the terms in the earlier equation had a common factor of a, which could be taken outside the parentheses.

or

Since the height is the same for each of the smaller rectangles, you can just multiply the height times the sum of the three smaller rectangle's widths

or

The width of the large rectangle is just the sum of each of the smaller widths, so the sum of those multiplied by a will give the area of the large rectangle.

Hope this helps!

5 0
2 years ago
A, B, and C are polynomials, where:
yan [13]

Answer:

Option A. 8x² - 25x + 7.

Step-by-step explanation:

The given polynomials are

A = 3x -4

B = x + 7

C = x² + 2

Now we have to find the simplest form of A² - (B + C)

A² = (3x - 4)² = 9x² + 16 -24 x

B + C = x + 7 + x² + 2 = x² + x + 9

Now A² - (B + C) = 9x² + 16 -24x -(x² + x + 9)

= 9x² -24x + 16 - x²- x - 9

= 8x² -25x + 7

Therefore Option A. 8x² - 25x + 7 is the answer.

7 0
2 years ago
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