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3 years ago

13

Mark watches a movie that is 124 minutes long. He fell asleep 75% of the way through. How many minutes of the movie did Mark act

ually watch?

1 answer:

Ipatiy [6.2K]3 years ago

4 0

Answer:

He watch 31 minutes of the movie.

Step-by-step explanation:

75% of 124 minutes is 93 minutes. there is 25% left so 25% of 124 is 31

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Absolute Values Inequalitties<br><br>I x I + 3 > 4

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$| x | + 3 > 4\\
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If x = 10, find the value of:<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%7Bx%7D%5E%7B2%7D%28x%20-%205%29%20%7D%7B10x

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Answer:

$10$

Step-by-step explanation:

$\frac{2(10)^2(10-5)}{10(10)}$

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$\frac{2(100)(10-5)}{10(10)}$

Subtract 10 with 5.

$\frac{2(100)(5)}{10(10)}$

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How can you classify the results of operations on real numbers

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There are different levels of classification when it comes to numbers. The general classification is between real numbers and imaginary numbers. Imaginary numbers are those with 'i' in them which is equal to √-1. Next, real numbers can be classified as rational or irrational. Irrational numbers are those that can't be expressed into fractions. Lastly, rational numbers are classified into integers and fractions.

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3 years ago

If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

nikklg [1K]

The quadratic function given by:

$f(x)=a(x-h)^2+k, \ \ \ a\neq 0$

is in vertex form. The graph of $f$ is a parabola whose axis is the vertical line $x=h$ and whose vertex is the point $(h, k)$ . So:

To translate the graph of a function to the right, left, upward or downward we have:

$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating <em>11 units to the left:</em>

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating<em> 5 units down:</em>

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ <em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>

SECOND.

Translating <em>8 units to the right:</em>

$g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2$

Then translating<em> 1 unit down:</em>

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1$

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>

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dangina [55]

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