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4 years ago

Passing through the point (3,-2) and parallel to the line with the equation Y=1/3 x-7

Mathematics

1 answer:

umka21 [38]4 years ago

7 0

Answer:

y = $\frac{1}{3}$ x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

y = $\frac{1}{3}$ x - 7 ← is in slope- intercept form

with m = $\frac{1}{3}$

Parallel lines have equal slopes, thus

y = $\frac{1}{3}$ x + c ← is the partial equation

To find c substitute (3, - 2) into the partial equation

- 2 = 1 + c ⇒ c = - 2 - 1 = - 3

y = $\frac{1}{3}$ x - 3 ← equation of line

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Write each power as a product of factors 2^4 4^2 9^2 8^5 5^3 7^3

snow_lady [41]

 $2^{4}$ ⇒2×2×2×2⇒16
 $4^{2}$ ⇒4×4⇒16
 $9^{2}$ ⇒9×9⇒81
 $8^{5}$ ⇒8×8×8×8×8⇒32.768
 $5^{3}$ ⇒5×5×5⇒125
 $7^{3}$ ⇒7×7×7⇒343

5 0

3 years ago

Regina wrote an integer The opposite of her integer is -18

My name is Ann [436]

Answer: C

Step-by-step explanation: The opposite of a positive integer (18) is -18

Which also means its value is 18

Hope this helps!

4 0

3 years ago

I will give u brainlist

masha68 [24]

Answer:

the y intercept is (0,-4) or just -4

Step-by-step explanation:

5 0

3 years ago

Evaluate log25+log8 _log2

Lemur [1.5K]

Step-by-step explanation:

log 25 + log 8 = log (25 × 8) = log 200

log 200 - log 2 = log (200 ÷ 2) = log 100

logarithm base 10 of 100 is 2.

7 0

3 years ago

The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$

To convert billion to million you multiple by 1000

$P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year$

6 0

3 years ago