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3 years ago

Graph the line with slope 2 passing through the point (-2,3).

Mathematics

2 answers:

NemiM [27]3 years ago

7 0

Find the equation using y=mx+b and what you're given in the question.
3=2(-2)+b
3=-4+b
3+4=b
7=b
The equation is y=2x+7
Hope this helps!

Dafna1 [17]3 years ago

4 0

(-2,3) with a slope of 2. You could find another point with the rise over run rule.
(-2,3) rises by 2 making it (-2,5) then it runs 1 making it (-1,5)
Your new coordinate should be (-1,5)
Now you can make a line using the coordinates of (-2,3) and (-1,5)

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If the fuel tank in Jim's car holds 14 gallons of fuel, define a formula to determine the number of gallons of fuel in Jim's fue

salantis [7]

Considering that the car does 50 miles per gallon, the linear function for the number of gallons of fuel in Jim's fuel tank, n, in terms of the number of miles x that Jim has driven since filling his tank is given by:

$y = -0.02x + 14$

<h3>What is a linear function?</h3>

A linear function is modeled by:

$y = mx + b$

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

In this problem:

Jim's car holds 14 gallons of fuel, hence $b = 14$ .

Considering it does 50 miles per gallon, and the amount in the tank will decrease, the slope is $m = -\frac{1}{50} = -0.02$ .

Hence, the function is:

$y = -0.02x + 14$

You can learn more about linear functions at brainly.com/question/25898120

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2 years ago

Digby wants to determine how many calories are in his bag of chips. Which calorimeter should he use?

KiRa [710]

Answer:

b. bomb calorimeter

Step-by-step explanation:

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3 years ago

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The variance of a stock's returns can be calculated as the:

Tamiku [17]

Answer:

The correct option is b.

Step-by-step explanation:

The formula for standard deviation is

$\sigma^2=\frac{\sum {(x-\overline{x})^2}}{n}$

where, $\overline{x}$ is mean of the data and n is number of observation.

The variance of a stock's returns can be calculated by the above formula.

Variance of stock's returns is the average value of squared deviations from the mean.

Therefore the correct option is b.

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3 years ago

The quotient of (x^3+3x^2-4x-12)/(x^2+5x+6)

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Answer: The quotient is (x-2).

Step-by-step explanation:

Since we have given that

$f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}$

Now, we have to find the quotient of the above expression.

So, here we go:

$Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)$

Now, we will divide the above simplest form with g(x):

$\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2$

Hence, the quotient is (x-2).

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