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3 years ago

6

Roxanne's car used 4.8 gallons of gasoline to drive 124 miles. If Roxanne has 180 more miles to go, which is closest to the addi

tional number of gallons of gasoline the car will use to complete the trip?

1 answer:

Reika [66]3 years ago

3 0

She would use 6 i believe

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The number of paper clips that crystal has is 42 divided by the number of paper clips that gayle has. If gayle has 11 more paper

Rom4ik [11]

Answer:

• Gayle: 14

• Crystal: 3

Step-by-step explanation:

Let g represent the number of paperclips Gayle has. Then 42/g is the number Crystal has. The relationship between the two numbers is said to be ...

g - (42/g) = 11

Multiplying by g gives ...

g^2 -42 = 11g

g^2 -11g -42 = 0 . . . . subtract 11 g to put into standard form

To factor this, you are looking for two factors of -42 that sum to -11.

-42 = -42·1 = -21·2 = -14·3 = -7·6

You can see that -14 and 3 sum to -11, so the factoring is ...

(g -14)(g +3) = 0

g = 14 . . . . . . . . . . makes the product zero. (The g=-3 solution is extraneous.)

Gayle has 14 paperclips and Crystal has 3.

8 0

2 years ago

Integrala x la a treia ori ln la a doua dx va rog

Studentka2010 [4]

I don't speak Romanian, but the closest translation for this suggests you're trying to compute

$\displaystyle \int x^3 \ln(x)^2 \, dx$

Integrate by parts:

$\displaystyle \int x^3 \ln(x)^2 \, dx = uv - \int v \, du$

where

u = ln(x)² ⇒ du = 2 ln(x)/x dx

dv = x³ dx ⇒ v = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \int x^3 \ln(x) \, dx$

Integrate by parts again:

$\displaystyle \int x^3 \ln(x) \, dx = u'v' - \int v' du'$

where

u' = ln(x) ⇒ du' = dx/x

dv' = x³ dx ⇒ v' = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x) \, dx = \frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx$

So, we have

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \left(\frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx \right)$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \int x^3 \, dx$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \left(\frac14 x^4\right) + C$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac1{32} x^4 + C$

$\boxed{\displaystyle \int x^3 \ln(x)^2 \, dx = \frac1{32} x^4 \left(8\ln(x)^2 - 4\ln(x) + 1\right) + C}$

3 0

1 year ago

Xelga [282]

Answer:

$y = \dfrac{1}{2}x-4$

Step-by-step explanation:

<h2>Equation of line in slope y-intercept form:</h2>

$\sf slope = m =\dfrac{1}{2}\\\\Point (2, -3) ; x_1 = 2 \ \& y_1 = -3\\\\\boxed{\bf y - y_1 =m(x -x_1)}$

$\sf y - [-3] = \dfrac{1}{2}(x - 2)\\\\y + 3 = \dfrac{1}{2}x - 2*\dfrac{1}{2}\\\\y + 3 = \dfrac{1}{2}x-1\\\\$

$\sf y = \dfrac{1}{2}x - 1 - 3\\\\ y =\dfrac{1}{2}x-4$

6 0

1 year ago

Find the greatest common factor of 15x^2 y^3 and -20x^3 yz.

katrin [286]

The answer is 5x^2y. The lowest exponent would be the GCF for each term if it has one

8 0

2 years ago

Read 2 more answers

On Monday 475 students went on a trip to the zoo. All 9 buses were filled and 7 students had to traveled in car . How many stude

KIM [24]

Answer:

52 students were in each bus

Step-by-step explanation:

475-7=468÷9=52 so 52

7 0

3 years ago