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Nana76 [90]
3 years ago
5

Which of the following expressions are equivalent to 6-3?

Mathematics
1 answer:
Zigmanuir [339]3 years ago
4 0

Answer:

1/216 and 1/6 raised to the 3 power.

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Use the graph to answer F(-3)=
Virty [35]

Answer:

  f(-3) = 1

Step-by-step explanation:

The only point with an x-coordinate of -3 has a y-coordinate of 1. That is the value of the function f(x) for x=-3.

  f(-3) = 1

7 0
3 years ago
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At a local store, bananas cost 0.54 per pound , apples cost 2.19 per pound , and oranges cost 1.55 per pound . Aaron bought 3 po
Alex777 [14]

$0.54 x 2.6 =$1.404  

$1.28 x 3.1=$3.968  

$1.404 rounds to $1.40

$3.968 rounds to $4

$4 = $ 1.40 = $5.40  

:)

8 0
3 years ago
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A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of m
posledela

Answer:

Check the attached document for the solutions, cheers

Step-by-step explanation:

Download docx
7 0
3 years ago
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.

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}.

4 0
3 years ago
Jane works as a tutor for $14 an hour and as a waitress for $11 an hour. This month, she worked a combined total of 93 hours at
daser333 [38]

Answer:

3t + 1,023

Step-by-step explanation:

The computation is shown below:

As a tutor it is $14 per hour

As a waitress it is $11 per hour

Total number of hours worked is 93

Now let us assume the number of hours worked as a tutor is t

So as a waiter is 93 - t

Now the equation is

= $14(t) + $11(93 - t)

= 14t + 1,023 - 11t

= 3t + 1,023

3 0
3 years ago
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