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3 years ago

Find the equation for the line that passes through the point (1,−4) and that is parallel to the line with the equation y=4.

Mathematics

1 answer:

diamong [38]3 years ago

6 0

Answer:

y = -4.

Step-by-step explanation:

The line with equation y = 4 is a horizontal line on the coordinate plane which passes through the y-axis at y = the point (0, 4).

The other line parallel to this must also be horizontal and , as it passes through the point (1 , -4), must also pass through the y-axis at ( 0, -4). The equation of this line is y = -4.

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The temperature of a mixture is decreasing by 5∘C every hour. When it was first mixed, its temperature was recorded at −20∘C.

Mandarinka [93]

Answer:

f(x)=−5x−20

Step-by-step explanation:

It's decreasing 5 degrees every hour, which is represented by -5x

You also have to take away the 20 (-20) from where it started.

So, f(x)=−5x−20

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3 years ago

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vfiekz [6]

Answer:

Option 4

Step-by-step explanation:

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3 years ago

The function y = f(x) is graphed below. What is the average rate of change of the

Yuliya22 [10]

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1 year ago

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a

STatiana [176]

Answer:

24761 mosquitoes

5.4 days

Step-by-step explanation:

Let the equation that shows the population of the mosquitoes after x days,

$A=P(1+r)^x$

Where,

P = Initial population,

r = rate of increasing per day,

Here, A = 1000, when x = 0,

$1000=P(1+r)^0\implies P = 1000$

A = 1900 when x = 1,

$1900 = P(1+r)^1\implies 1900 = 1000(1+r)\implies 1.9 = 1 + r\implies r = 0.9$

Thus, the required function that represents the population after x days,

$A=1900(1+0.9)^x=1900(1.9)^x$

If x = 4,

The number of mosquito after 4 days,

$A=1900(1.9)^4 = 24760.99\approx 24761$

If A = 60,000,

$60000 = 1900(1.9)^x$

$\frac{600}{19}=1.9^x$

Taking log both sides,

$\log(\frac{600}{19})=x\log 1.9$

$\implies x = \frac{\log(\frac{600}{19})}{\log 1.9}=5.378\approx 5.4$

Thus, there will 60,000 mosquitoes after 5 days.

6 0

2 years ago

What is the equation of the line that is parallel to y=2x+8yand goes through point (−4,1)?

vekshin1

y=2x+8 slope = 2

parallel to y=2x+8, so equation has same slope = 2
goes through point (−4,1)
then
y = mx+b
1 = 2(-4) + b
b = 9

so the equation
y = 2x + 9

7 0

2 years ago