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Debora [2.8K]
3 years ago
10

On your family trip, you used 9 gallons of gas. If the odometer readings before and after your trip were 74,233 and 74,545, resp

ectively, how many miles per gallon did you average? Round your answer to the nearest whole number.
Mathematics
1 answer:
sveta [45]3 years ago
6 0

Find the number of miles driven by subtracting the odometer readings:

74545 - 74233 = 312 miles driven.

Divide miles driven by gallons of gas used:

312 / 9 = 34.66 = 35 miles per gallon.

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Vladimir79 [104]

Answer:

y = 0.55 or 5 / 9

Step-by-step explanation:

here's the solution :-

=》y + 7 = 19y - 3

=》7 + 3 = 19y - y

=》18y = 10

=》y = 10 ÷ 18

=》y = 5 ÷ 9

=》y = 0.55

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2 years ago
Dolve for theta. С 13 4 o o A B Your answer​
ANTONII [103]

Answer:

θ ≈ 17.1°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan θ = \frac{opposite}{adjacent} = \frac{BC}{AC} = \frac{4}{13} , then

θ = tan^{-1} (\frac{4}{13} ) ≈ 17.1° ( to the nearest tenth )

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3 years ago
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KATRIN_1 [288]

Ok

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6 0
3 years ago
Read 2 more answers
Help. <br>Please its urgent show workings.<br>​
laiz [17]

Answer:

see explanation

Step-by-step explanation:

There are 2 possible approaches to differentiating these.

Expand the factors and differentiate term by term, or

Use the product rule for differentiation.

I feel they are looking for use of product rule.

Given

y = f(x). g(x) , then

\frac{dy}{dx} = f(x).g'(x) + g(x).f'(x) ← product rule

(a)

y = (2x - 1)(x + 4)²

f(x) = 2x - 1 ⇒ f'(x) = 2

g(x) = (x + 4)²

g'(x) = 2(x + 4) × \frac{d}{dx} (x + 4) ← chain rule

       = 2(x + 4) × 1

        = 2(x + 4)

Then

\frac{dy}{dx} = (2x - 1). 2(x + 4) + (x + 4)². 2

    = 2(2x - 1)(x + 4) + 2(x + 4)² ← factor out 2(x + 4) from each term

    = 2(x + 4) (2x - 1 + x + 4)

    = 2(x + 4)(3x + 3) ← factor out 3

    = 6(x + 4)(x + 1)

--------------------------------------------------------------------------

(b)

y =  x(x² - 1)³

f(x) = x ⇒ f'(x) = 1

g(x) = (x² - 1)³

g'(x) = 3(x² - 1)² × \frac{d}{dx} (x² - 1) ← chain rule

        = 3(x² - 1)² × 2x

        = 6x(x² - 1)²

Then

\frac{dy}{dx} = x. 6x(x² - 1)² + (x² - 1)³. 1

    = 6x²(x² - 1)² + (x² - 1)³ ← factor out (x² - 1)²

    = (x² - 1)² (6x² + x² - 1)

     = (x² - 1)²(7x² - 1)

----------------------------------------------------------------------

(c)

y = (x² - 1)(x³ + 1)

f(x) = x² - 1 ⇒ f'(x) = 2x

g(x) = (x³ + 1) ⇒ g'(x) = 3x²

Then

\frac{dy}{dx} = (x² - 1). 3x² + (x³ + 1), 2x

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   = x[3x(x² - 1) + 2(x³ + 1) ]

   = x(3x³ - 3x + 2x³ + 2)

   = x(5x³ - 3x + 2) ← distribute

    = 5x^{4} - 3x² + 2x

--------------------------------------------------------------------

(d)

y = 3x³(x² + 4)²

f(x) = 3x³ ⇒ f'(x) = 9x²

g(x) = (x² + 4)²

g'(x) = 2(x² + 4) × \frac{d}{dx}(x² + 4) ← chain rule

       = 2(x² + 4) × 2x

       = 4x(x² + 4)

Then

\frac{dy}{dx} = 3x³. 4x(x² + 4) + (x² + 4)². 9x²

    = 12x^{4}(x² + 4) + 9x²(x² + 4)² ← factor out 3x²(x² + 4)

    = 3x²(x² + 4) [ 4x² + 3(x² + 4) ]

    = 3x²(x² + 4)(4x² + 3x² + 12)

    = 3x²(x² + 4)(7x² + 12)

5 0
2 years ago
Write the expanded form for this expression <br><br> -1/2(y - x)
grin007 [14]

Answer:  =-1/2x+-1/2y

Step-by-step explanation:

5 0
2 years ago
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