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3 years ago

Which is an equation of the line through (-1, -4) and parallel to 3x+y=5

Mathematics

1 answer:

kherson [118]3 years ago

7 0

Answer:

Step-by-step explanation:

3x + y = 5 {subtract 3x from both sides}

y = -3x + 5 ← slope-intercept form

y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂

{Two lines are parallel if their slopes are equal}

y = -3x + 5 ⇒ m₁ = -3 ⇒ m₂ = -3

(-1, -4) ⇒ x₁ = -1, y₁ = -4

The point-slope form:

y - (-4) = -3(x - (-1))

y + 4 = -3(x + 1)

y + 4 = -3x - 3 {subtact 4 from both sides}

<h3><u>y = -3x - 7 </u><u> ← slope-intercept form</u></h3>

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Mary bath 14 gallons of gasoline at $1.19 a gallon and 3 gallons of oil at $2.25 per gallon how much did she spend?

BigorU [14]

Mary bought 14 gallons of gasoline at $1.19 a gallon and 3 gallons of oil at $2.25 per gallon how much did she spend?

To find how much Mary spent, simply multiply the total cost per gallon with the total amount of gallons spent.

Let's start off with: Mary bought 14 gallons of gasoline at $1.19 a gallon

Gallons bought x price per gallon = total amount of money spent on the gallons

14 (gallons) x $1.19 (per gallon) = $16.66 (total cost of 14 gallons)

Next step, Mary buys 3 gallons of oil at $2.25 per gallon, we do the exact same steps above.

Gallons bought x price per gallon = total amount of money spent on the gallons

3 (gallons) x $2.25 (per gallon) = $6.75 (total cost of 3 gallons)

Now, be sure to remember those 2 number (I've bolded it for you so you could see how to get it and where it is if you need to go back and look at the problem)

Now, we want to find the total amount in dollars Mary had spent on gasoline. Simply add the two total cost of gallons (14 gallons + 3 gallons solution)

Remember the bolded parts? Those come in handy right about now: simply add them together.

$16.66 (total cost of 14 gallons) + $6.75 (total cost of 3 gallons) = $23.41 (total amount of money Mary spent on gasoline)

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3 years ago

Read 2 more answers

PLEASE HELP IN MATH MADDD POINTS

lions [1.4K]

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3 years ago

PRE CALC, help please

suter [353]

Answer:

<h2>option C is correct ...</h2>

Step-by-step explanation:

<h2>Because, x= -1 and x =3 are the solution of function.....</h2>

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3 years ago

Read 2 more answers

In order to evaluate 7 sec(θ) dθ, multiply the integrand by sec(θ) + tan(θ) sec(θ) + tan(θ) . 7 sec(θ) dθ = 7 sec(θ) sec(θ) + ta

Maurinko [17]

Answer:

$\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c$

Step-by-step explanation:

The question is not properly formatted. However, the integral of $\int {7 \sec(\theta) } \, d\theta$ is as follows:

$\int {7 \sec(\theta) } \, d\theta$

Remove constant 7 out of the integrand

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) } \, d\theta$

Multiply by 1

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * 1} \, d\theta$

Express 1 as: $\frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}$

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta$

Expand

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta$

Let

$u = \sec(\theta) + \tan(\theta)$

Differentiate

$\frac{du}{d\theta} = \sec(\theta)\tan(\theta) + sec^2(\theta)$

Make $d\theta$ the subject

$d\theta = \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}$

So, we have:

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{u}} \,* \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}$

Cancel out $\sec(\theta)\tan(\theta) + sec^2(\theta)$

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{1}{u}} \,du}}$

Integrate

$\int {7 \sec(\theta) } \, d\theta = 7\ln(u) + c$

Recall that: $u = \sec(\theta) + \tan(\theta)$

$\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c$

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3 years ago

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Artemon [7]

Answer:

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3 years ago