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3 years ago

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Two sisters have decided to watch all the episodes of a popular TV show on DVD. Eva has already watched 9 episodes and will cont

inue to watch the show at a rate of 3 episodes per day. Kate, who hasn't yet seen the show, will start watching 4 episodes per day. Once the two sisters get to the point where they have watched the same number of episodes, they plan to finish the series together. How many episodes will each sister have watched at that point? How long will that take?

1 answer:

sergejj [24]3 years ago

6 0

Answer:

Step-by-step explanation:

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How many solutions does this equation have?<br><br> –10q = –10q − 7

Salsk061 [2.6K]

Answer:

None (no solutions)

Step-by-step explanation:

-10q=-10q-7 (add 10q to both sides to get the costant 7 by itself)

-10q+10q=-10q+10q-7

0=-7 ( zero will never equal -7 hence there are no solutions to this equation)

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3 years ago

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Leno4ka [110]

Answer:

$x=10$

Step-by-step explanation:

we know that

If the lines m and n are parallel

then

$130\° = (8x+50)\°$ ----> by corresponding angles

solve for x

$8x=130-50\\8x=80\\x=10$

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3 years ago

A parabola has an x-intercept of -1, a y-intercept of -3, and a minimum of -4 at x = 1.

torisob [31]

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^{2}+k$

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(1,-4)

substitute

$y=a(x-1)^{2}-4$

we have

An x-intercept of (-1,0)

substitute and solve for a

$0=a(-1-1)^{2}-4$

$0=4a-4$

$4a=4$

$a=1$

The equation is

$y=(x-1)^{2}-4$

<u><em>Verify the y-intercept</em></u>

For x=0

$y=(0-1)^{2}-4$

$y=-3$

The y-intercept is the point (0,-3) -----> is correct

using a graphing tool

see the attached figure

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4 years ago

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sveticcg [70]

Answer:

x = 24.8

Step-by-step explanation:

2x + 12.8 + 117.6 = 180

Then solve.

2x + 130.4 = 180

2x = 4.6

x = 24.8

7 0

3 years ago

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Solve each quadratic equation by completing the square. Give exact answers--no decimals.

denis-greek [22]

Answer:

$x_1 = \frac{3}{2} + \frac{1}{2}(\sqrt{47})i\\\\x_2 = \frac{3}{2} - \frac{1}{2}(\sqrt{47})i\\\\$

Step-by-step explanation:

In this problem we have the equation of the following quadratic equation and we want to solve it using the method of square completion:

$x ^ 2 -3x +14 = 0$

The steps are shown below:

For any equation of the form: $ax ^ 2 + bx + c = 0$

1. If the coefficient a is different from 1, then take a as a common factor.

In this case $a = 1$ .

Then we go directly to step 2

2. Take the coefficient b that accompanies the variable x. In this case the coefficient is -3. Then, divide by 2 and the result squared it.

We have:

$\frac{-3}{2} = -\frac{3}{2}\\\\(-\frac{3}{2}) ^ 2 = (\frac{9}{4})$

3. Add the term obtained in the previous step on both sides of equality:

$x ^ 2 -3x + (\frac{9}{4}) = -14 + (\frac{9}{4})$

4. Factor the resulting expression, and you will get:

$(x -\frac{3}{2}) ^ 2 = -(\frac{47}{4})$

Now solve the equation:

Note that the term $(x -\frac{3}{2}) ^ 2$ is always > 0 therefore it can not be equal to $-(\frac{47}{4})$

The equation has no solution in real numbers.

In the same way we can find the complex roots:

$(x -\frac{3}{2}) ^ 2 = -(\frac{47}{4})\\\\x -\frac{3}{2} = \±\sqrt{-(\frac{47}{4})}\\\\x = \frac{3}{2} \±\frac{1}{2}\sqrt{-47}\\\\x = \frac{3}{2} \±\frac{1}{2}(\sqrt{47})i\\\\x_1 = \frac{3}{2} + \frac{1}{2}(\sqrt{47})i\\\\x_2 = \frac{3}{2} - \frac{1}{2}(\sqrt{47})i\\\\$

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3 years ago

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