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2 years ago

11

Which of the following equations represents a line that is perpendicular to

1 answer:

Andreyy892 years ago

8 0

Answer:

$\large\boxed{y=\dfrac{1}{2}x}$

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================$

$\text{We have the equation:}\ y=-2x+4\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{We have the equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinate of the point (4, 2) to the equation:}\\\\2=\dfrac{1}{2}(4)+b\\\\2=2+b\qquad\text{subtract 2 from both sides}\\\\0=b\to b=0.\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x$

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3 years ago

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A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the number of shoppers is 10

Marta_Voda [28]

Answer:

1138

Step-by-step explanation:

From the information given:

We can represent it perfectly in an exponential form:

$m = p(q)^x$

where;

p = initial value = 120

q = base of the exponential form

q = 1 + r

here; r = rate in decimal = 10% = 0.1

Then q can now be = 1 + 0.1 = 1.1

Replacing it into the exponential form, we get:

$m = 120(1.1)^x$

where;

x = number of days and m = number of shoppers

Thus:

For the first day:

$m = 120(1.1)^x$

m = 120

For the second day:

$m = 120(1.1)^1$

m = 132

For the third day:

$m = 120(1.1)^2$

m = 145.2

For the fourth day

$m = 120(1.1)^3$

m = 159.72

For the fifth-day

$m = 120(1.1)^4$

m = 175.692

For the sixth-day

$m = 120(1.1)^5$

m = 193.2612

For the seventh-day

$m = 120(1.1)^6$

m = 212.58732

Thus; the total numbers of shoppers for the first 7 days is:

$= 120+ 132 + 145.2 + 159.72 + 175.692+193.2612+212.58732$

= 1138.46052

≅ 1138

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2 years ago

I need help with this problem

kolbaska11 [484]

It’s 20 I believe. All together it should be 160 so you add 118 and 22 to get 140. Then subtract that from 160 and you get 20.

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2 years ago

Find the product of the solutions

irina1246 [14]

Answer:

A. -41/15.

Step-by-step explanation:

15x^2 + 23x - 41 = 0

Product of the roots of ax^2 + bx + c = c/a.

Thus the product of the roots of this equation = -41/15.

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2 years ago