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3 years ago

Please explain to me how to get the answer! I know it’s 1/16 but I don’t know how to get it. See picture below!

Mathematics

1 answer:

barxatty [35]3 years ago

8 0

Answer:

Step-by-step explanation:

4³/ 4^5

64 / 1024

= 1/16

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Science 8th grade 10 pts

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Answer:

Photosynthesis depends on the carbon dioxide released during cellular respiration.

Step-by-step explanation:

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3 years ago

Write the equation of the line in fully simplified slope-intercept form.

fiasKO [112]

$y = -\frac{1}{2}x - 1$

Step-by-step explanation:

Let's pick two points on the line: $P_1(-4, 1)$ and $P_2(2, -2).$ Let's calculate the slope of this line using these points:

$m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-2 - 1}{2 - (-4)} = -\dfrac{1}{2}$

With this value of the slope, we can write the general slope-intercept form of the equation as

$y = -\frac{1}{2}x + b$

To solve for the y-intercept b, let's use either P1 or P2. I'm going to use P2:

$-2 = -\frac{1}{2}(2) + b \Rightarrow b = -1$

Therefore, the slope-intercept form of the equation is

$y = -\frac{1}{2}x - 1$

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2 years ago

What is 119,000,003 in two forms

ratelena [41]

One hundred thousand, nineteen million,three.

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3 years ago

Read 2 more answers

In a G.P the difference between the 1st and 5th term is 150, and the difference between the

liubo4ka [24]

Answer:

Either $\displaystyle \frac{-1522}{\sqrt{41}}$ (approximately $-238$ ) or $\displaystyle \frac{1522}{\sqrt{41}}$ (approximately $238$ .)

Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

$a$ ,
$a\cdot r$ ,
$a \cdot r^2$ ,
$a \cdot r^3$ ,
$a \cdot r^4$ .

First equation:

$a\, r^4 - a = 150$ .

Second equation:

$a\, r^3 - a\, r = 48$ .

Rewrite and simplify the first equation.

$\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}$ .

Therefore, the first equation becomes:

$a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150$ ..

Similarly, rewrite and simplify the second equation:

$\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}$ .

Therefore, the second equation becomes:

$a\, r\, \left(r^2 - 1\right) = 48$ .

Take the quotient between these two equations:

$\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}$ .

Simplify and solve for $r$ :

$\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}$ .

$8\, r^2 - 25\, r + 8 = 0$ .

Either $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ or $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ .

Assume that $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}$ .

Similarly, assume that $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .