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3 years ago

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Tanya is printing a report. There are 96 sheets of paper in the printer, and the number of sheets p left after t minutes of prin

ting is given by the function p(t)=96-8t

1 answer:

AleksandrR [38]3 years ago

4 0

Answer:

$0 = -8t + 96\\\\\Rightarrow\ 8t=96\\\\\Rightarrow\ t=\dfrac{96}{8}\\\\=12$

<h3>Hence, it will take 12 minutes by the printer to use all 96 sheets of paper.</h3>

Step-by-step explanation:

Given :

Tanya is printing a report.

There are 96 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function

$p(t) = -96 - 8t$

When all the 96 sheets printed , then the number of sheets will left to print =0

Substitute p(t)=0 in the given function, to find the value of t, we get

$0 = -8t + 96\\\\\Rightarrow\ 8t=96\\\\\Rightarrow\ t=\dfrac{96}{8}\\\\=12$

<h3>Hence, it will take 12 minutes by the printer to use all 96 sheets of paper.</h3>

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The sums of the measures of the angles of a triangle is 180. Write and solve an equation to find the missing measure in the figu

torisob [31]

60 + 35 + n = 180 <<< equation
60 + 35 =95
180 - 95 = 85
n = 85 <<< solution
Hope this helped ;)

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3 years ago

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options.

Nady [450]

Answer:

Domain is all real numbers.

The range is $\{y|y\le 6\}$

The function is increasing over $(-\infty,-2)$ .

The function is decreasing over $(-2,\infty)$

The function has a positive y-intercept.

-----------------This is a guess if I had interpreted your choices correctly:

Second option: The range is $\{y|y\le 6\}$

Third option: The function is increasing over $(-\infty,-2)$ .

Last option: The function has a positive y-intercept.

I can't really read some of your choices. So you can read my above and determine which is false. If you have a question about any of what I said above please let me know.

Note: I guess those 0's are suppose to be infinities? I hopefully your function is $f(x)=-x^2-4x+2$ .

Step-by-step explanation:

$f(x)=-x^2-4x+2$ is a polynomial function which mean it has domain of all real numbers. All this sentence is really saying is that there exists a number for any value you input into $-x^2-4x+2$ .

Now since the is a quadratic then it is a parabola. We know it is a quadratic because it is comparable to $ax^2+bx+c$ , $a \neq 0$ .

This means the graph sort of looks like a U or an upside down U.

It is U, when $a>0$ .

It is upside down U, when $a$ .

So here we have $a=-1$ so $a$ which means the parabola is an upside down U.

Let's look at the range. We know the vertex is either the highest point (if $a$ ) or the lowest point (if $a>0$ ).

The vertex here will be the highest point, again since $a$ .

The vertex's x-coordinate can be found by evaluating $\frac{-b}{2a}$ :

$\frac{-(-4)}{2(-1)}=\frac{4}{-2}=-2$ .

So the y-coordinate can be found by evaluate $-x^2-4x+2$ for $x=-2$ :

$-(-2)^2-4(-2)+2$

$-(4)+8+2$

$4+2$

$6$

So the highest y-coordinate is 6. The range is therefore $(-\infty,6]$ .

If you picture the upside down U in your mind and you know the graph is symmetrical about x=-2.

Then you know the parabola is increasing on $(-\infty,-2)$ and decreasing on $(-2,\infty)$ .

So let's look at the intevals they have:

So on $(-\infty,-2)$ the function is increasing.

Looking on $(-4,\infty)$ the function is increasing on (-4,-2) but decreasing on the rest of that given interval.

The function's y-intercept can be found by putting 0 in for $x$ :

$-(0)^2-4(0)+2$

$-0-0+2$

$0+2$

$2$

The y-intercept is positive since 2>0.

8 0

3 years ago

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damaskus [11]

Answer:

Hey man, I don't really know how to do these problems following those exact steps, but these are the steps i used to solve it:

Step-by-step explanation:

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3 years ago

Simplify the expression: 6 + 8j - 9j + -5j - 3

dangina [55]

So first you’ll combine the J’s.
8j - 9j = 1j
+ -5j
Which will be -4j.
That makes: 6 + -4j - 3
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Which makes 3 + -4j
That’s the answer!

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4 years ago

Which expression is equivalent to 144 Superscript three-halves? 216 1,728 RootIndex 3 StartRoot 12 EndRoot RootIndex 3 StartRoot

Afina-wow [57]

Question:

Which expression is equivalent to 144^(3/2)

Answer:

1728

Step-by-step explanation:

The options are not well presented. However, this is the solution to the question.

Given:

144^(3/2)

Required:

Find Equivalent.

We start my making use of the following law of logarithm.

A^(m/n) = (A^m)^1/n

So,

144^(3/2) = (144³)^½

Another law of indices is that

A^½ = √A

So,

144^(3/2) = (144³)^½ = √(144³)

144³ can be expanded as 144 * 144 * 144.

This gives

144^(3/2) = √(144 * 144 * 144)

The square root can then be splitted to

144^(3/2) = √144 * √144 * √144

144^(3/2) = 12 * 12 * 12

144^(3/2) = 1728.

Hence, the equivalent of 144^(3/2) is 1728

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3 years ago

Read 2 more answers