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3 years ago

- 3x + y = 3 2y = -3x - 12

Mathematics

1 answer:

Lynna [10]3 years ago

8 0

Answer:

x=-2, y=-3

Step-by-step explanation:

we can rearrange the questions to make it easier

y=3x+3

2y=-3x-12

if you add the two equations, you get

3y=0x-9

so y=-9/3 = -3

plug y into one of the equations

-3=3x+3

-6=3x

x=-2

and then check your work by plugging into the other equation:

2*-3=-3(-2)-12

-6=6-12

-6=-6

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Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ

sweet-ann [11.9K]

Answer:

x^2 +y^2 = 4y

Step-by-step explanation:

Using the usual translation relations, we have ...

r^2 = x^2+y^2

x = r·cos(θ)

y = r·sin(θ)

Substituting for sin(θ) the equation becomes ...

r = 4sin(θ)

r = 4(y/r)

r^2 = 4y

Then, substituting for r^2 we get ...

x^2 +y^2 = 4y . . . . . matches the first choice

8 0

3 years ago

The population (in millions) of a certain country t years after 1900 is given by the function p(t). There were 420 million in 19

gladu [14]

Answer:469 million

Step-by-step explanation:

Given

The population of a country at t=1900 is 420 million

and P'(t) is a constant therefore P(t) is a linear function of time

assuming P(t)=7t +c

at t=0 i.e. 1900 at starting Point P(t)=420 million

i.e.

$420=7\times 0+c$

$c=420 million$

Thus $at\ t=7\ year\ later\ i.e.\ 1907$

$P(t)=7\times 7+420=469 million$

Thus at 1907 Population is 469 million

P'(t)=7 indicates that growth rate of Population is constant equals to 7 billion

8 0

3 years ago

You drive your car 720 miles in 20 hours. What is your speed? (mph)

liberstina [14]

Answer:

Your average speed was 36.0 Miles per hour (mph)

Step-by-step explanation:

Divide -> 720 by 20

720/20=36.0

6 0

3 years ago

Read 2 more answers

A family drove 180 miles to disneyland. If they left at 10:30

luda_lava [24]

Average speed = Distance/ time

Distance = 180 mi

Time = time(final) - time(initial)

To find time will be easier if we translate am and pm into 24 h scale.

am will stay the same, so 10:30 am is 10:30. (initial)

pm will be turned (am time + 12), 3: 00 pm = 3:00 +12 =15:00 (final)

Time = time(final) - time(initial)= 15:00 - 10:30 = 14:60 - 10:30 =4h 30 min

4h + 30 min = 4h + 1/2 h= 4.5 h (time)

Average speed = Distance/ time = 180 mi / 4.5 h = 40 mi/h

Answer is 40 mi/h.

3 0

3 years ago

An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that th

Gwar [14]

Answer:

correct option is D.0.0019

Step-by-step explanation:

given data

journal reports p = 34%

random sample n = 225

yielded = 97

solution

we get here first Sample proportion that is

Sample proportion p1 = $\frac{97}{225}$ ...............1

Sample proportion p1 = 0.4311

and here Null hypothesis is

H0 = p ≤ 0.34 ........................2

and

for Alternate hypothesis is

Ha = p > 0.34 ..........................3

so we get here z statistics that is express as

z = $\frac{p1- p}{\sqrt{\frac{p(1-p)}{n}}}$ ....................4

put here value and we get

$z = \frac{0.4311-0.34}{\sqrt{\frac{0.34(1-0.34)}{225}}}$

solve it we get

z = 2.88468

so here p-value for a test will be

P (z > 2.88468)

P = 1 - P (z < 2.88468)

P = 0.001957

so correct option is D.0.0019

7 0

3 years ago