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2 years ago

7

What is the solution to the equation 1/4x-1/8=7/8+1/2x?

2 answers:

julia-pushkina [17]2 years ago

6 0

Answer:

x=-1/4

Step-by-step explanation:

1 / 4x-1/8 = 7/8 + 1 / 2x <=> 1/4x - 1/2x = 7/8+1/8 <=> 1/4x-2/4x = 1 <=> -1/4x = 1

<=> x= -1/4

NISA [10]2 years ago

4 0

Answer:

2.7 + 8x/8.2

Step-by-step explanation:

1/4x - 1/8 = 7/8 + 1/2x x/4 - 1/8 = 7/8 + x/2

8x + 4 (-1)/4.8 = 2.7 + 8x/8.2

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3 years ago

Please help me with these calculus bc questions

zhannawk [14.2K]

4. Compute the derivative.

$y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1$

Find when the gradient is 7.

$4x - 1 = 7 \implies 4x = 8 \implies x = 2$

Evaluate $y$ at this point.

$y = 2\cdot2^2-2-1 = 5$

The point we want is then (2, 5).

5. The curve crosses the $x$ -axis when $y=0$ . We have

$y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4$

Compute the derivative.

$y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}$

At the point we want, the gradient is

$\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}$

6. The curve crosses the $y$ -axis when $x=0$ . Compute the derivative.

$\dfrac{dy}{dx} = 3x^2 - 4x + 5$

When $x=0$ , the gradient is

$\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}$

7. Set $y=5$ and solve for $x$ . The curve and line meet when

$5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92$

Compute the derivative (for the curve) and evaluate it at these $x$ values.

$\dfrac{dy}{dx} = 4x + 7$

$\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}$

$\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}$

8. Compute the derivative.

$y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b$

The gradient is 8 when $x=2$ , so

$2a\cdot2 + b = 8 \implies 4a + b = 8$

and the gradient is -10 when $x=-1$ , so

$2a\cdot(-1) + b = -10 \implies -2a + b = -10$

Solve for $a$ and $b$ . Eliminating $b$ , we have

$(4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}$

so that

$4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}$ .

5 0

2 years ago

romeo ordered a bouquet of roses for his girlfriend. each rose cost $2.95. and the delivery charge was $8.50. if the total cost

LenaWriter [7]

Okay first you should subtract 8.50 from 61.60 because the delivery charge doesn't count. 61.60-8.50=53.1. now divide 53.1 by 2.95. 53.1÷2.95=18. Romeo ordered 18 roses for his girlfriend.

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3 years ago

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(03.02 MC)The number of pages that Ana, Hillary, Roger, and Juan can read in a day is shown below:

marusya05 [52]

Answer:

2564

Step-by-step explanation:

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3 years ago

a local park is in the shape of a square. a map of the local park is made with the scale 1 inch to 200 feet. if the park is show

vladimir2022 [97]

Answer:

600 ft per side

Step-by-step explanation:

1 in = 200 feet

12 in = 1 foot

12 in * 200 ft= 2400 ft

2400/4 = 600 ft per side

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3 years ago

Read 2 more answers