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2 years ago

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the total of housemates in my house is x. a housemate is not there. Stay some people y If 12-x = (y+3) nuggets in the pan are co

oked for housemates y, and distributed equally to all how many nuggets would 'one' y get?

1 answer:

mart [117]2 years ago

8 0

Answer:

because of the gravity of the earth

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Figure ABCD has vertices A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2). What is the area of Figure ABCD? 5 square units 20 square u

Sladkaya [172]

Answer:

The area of Figure ABCD is 25 square units

Step-by-step explanation:

we have

A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2)

step 1

Plot the figure

using a graphing tool

The figure is a trapezoid

see the attached figure

step 2

Find the area of the trapezoid

The area of the trapezoid is equal to

$A=\frac{1}{2}[AD+BC]AB$

we have

$AD=2-(-2)=4\ units$ ---> difference in the y-coordinates

$BC=2-(-4)=6\ units$ ---> difference in the y-coordinates

$AB=2-(-3)=5\ units$ ---> difference in the x-coordinates

substitute

$A=\frac{1}{2}[4+6]5$

$A=25\ units^{2}$

3 0

2 years ago

Consider the following function. f(x) = 2x3 + 9x2 − 24x (a) Find the critical numbers of f. (Enter your answers as a comma-separ

viktelen [127]

Answer:

(a) The critical number of $f(x)$ are $x=-4, 1$

(b)

Increasing for $(-\infty, -4)$
Decreasing for $(-4, 1)$
Increasing for $(1, \infty)$

(c)

relative maximum $(-4, 112)$
relative minimum $(1, -13)$

Step-by-step explanation:

(a) The critical numbers of a function are given by finding the roots of the first derivative of the function or the values where the first derivative does not exist. Since the function is a polynomial, its domain and the domain of its derivatives is $(-\infty, \infty)$ . Thus:

$\frac{df(x)}{dx} = \frac{d(2x^3+9x^2-24x)}{dx} =6 x^2+18x -24\\6 x^2+18x -24=0\\\boxed{x=-4, x=1}$

(b)

A function $f(x)$ defined on an interval is monotone increasing on $(a, b)$ if for every $x_1, x_2 \in (a, b): x_1$ implies $f(x_1)$

A function $f(x)$ defined on an interval is monotone decreasing on $(a, b)$ if for every $x_1, x_2 \in (a, b): x_1$ implies $f(x_1)>f(x_2)$

Combining the domain $(-\infty, \infty)$ with the critical numbers we have the intervals $(-\infty, -4)$ , $(-4, 1)$ and $(1, \infty)$ . Note that any of the points are included, in the case of the infinity it is by definition and the critical number are never included because the function monotony is not defined in the critical points, i.e. it is not monotone increasing or decreasing. Now, let's check for the monotony in each interval, for this, we check for the sign of the first derivative in each interval. Evaluating in each interval the first derivative (one point is enough), we obtain the monotony of the function to be:

Increasing for $(-\infty, -4)$
Decreasing for $(-4, 1)$
Increasing for $(1, \infty)$

(c) From the values obtained in (a) so the relative extremum are the points $(-4, 112)$ and $(1, -13)$ . The $y$ -values are found by evaluating the critical numbers in the original function. Since the first derivative decreases after passing through $x=-4$ and increases after passing through the point $x=1$ we have:

relative maximum $(-4, 112)$
relative minimum $(1, -13)$

3 0

3 years ago

Which number produces

Dvinal [7]

Answer:

A is the answer.

Step-by-step explanation:

A fraction plus a fraction is equal to a fraction. An irrational number cannot be expressed as a fraction.

0.3333333 even though it looks like an irrational number it is actually: 1/3

3/5 is already a fraction so adding it with another fraction will NOT equal an irrational number (decimal)

-0.75 is equal to -3/4 (75/100 => 3/4). Same thing that applies above.

However, Pi cannot be expressed as a fraction exactly. You can round up like 3.14. However it is not the full number. So 3.141592654....+(3/4) is not going to add up perfectly into a fraction.

In short, a fraction is a rational number. Rational + Rational = Rational. Irrational + Rational = Irrational.

3 0

2 years ago

Read 2 more answers

How would you write 8^5 as a multiplication expression? A. 8 × 5 B. 8 × 8 × 8 × 8 × 8 C. 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5

Neporo4naja [7]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

<u>if </u><u>we </u><u>ever </u><u>face </u><u>a </u><u>number </u><u>written </u><u>in </u><u>the </u><u>form </u><u>of </u> $\underline{x^{n}}$ <u>where </u><u>x </u><u>denotes </u><u>the </u><u>base </u><u>and </u><u>n </u><u>denotes </u><u>the </u><u>exponent</u><u> </u><u>or </u><u>power </u><u>,</u><u> </u><u>we </u><u>can </u><u>expand </u><u>it </u><u>in </u><u>the </u><u>following</u><u> </u><u>way </u><u>-</u>

$x^{n} = x \times x \times x \times.... x ( upto\: " n " \: times )$

therefore ,

$8 {}^{5} = 8 \times 8 \times 8 \times 8 \times 8$

option ( B )

hope helpful -,-

4 0

2 years ago

Read 2 more answers

What is 0.75*0.75*0.75*0.75*0.75 written as a power

laiz [17]

Oof I think it's 0.75^5 I hope it right heh :)

8 0

2 years ago