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3 years ago

13

Sarah swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Sarah swim in

the morning than in the evening?

1 answer:

ryzh [129]3 years ago

8 0

1/3 is the answer
Hope this is correct

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After how many audio books will both book clubs cost the same amount.

bulgar [2K]

Answer:

2 books

Step-by-step explanation:

10 + 5x = 16 + 2x

- 2x - 2x

10 + 3x = 16

-10 -10

3x = 6

/3 /3

<u>x = 2</u>

4 0

3 years ago

Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for

vivado [14]

Answer:

The equation to represent the rate of receding water level is L = 34 $(0.5)^{d}$ .

Step-by-step explanation:

Given as :

The initial level of water in river = 34 feet

The rate of receding water level = 0.5 foot per day

Or, The rate of percentage of receding water level = 50 % per day

Let the level of water after d days = L

Now,

The level of water after d days = initial level of water × ( $(1-\dfrac{\textrm Rate}{100})^{Time}$

I.e L = 34 × ( $(1-\dfrac{\textrm 50}{100})^{d}$

∴ L = 34 × $(0.5)^{d}$

Hence The equation to represent the rate of receding water level is L = 34 $(0.5)^{d}$ . Answer

5 0

3 years ago

A farm had 480 acres more wheat than corn. After the farmers collected 80% of the wheat and 25% of the corn, the area of the whe

SVEN [57.7K]

A farm had 480 acres more wheat than corn. Let use "W" to represent the Wheat and let use "C" to represent the corn. Hence, we have below:
W=C+480

The farmers collected 80% of the wheat and 25% of the corn and the area of the wheat is 300 acres less than the area of the corn:
W-0.8W=C-0.25C+300
0.2W=0.75C+300
We have two equations, two unknowns:
0.2(C+480)=0.75C+300
0.2C+96=0.75C+300
0.55C=294
C=534.55

6 0

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 $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .

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

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER. Find the values of

soldier1979 [14.2K]

Step-by-step explanation:

I am not sure this is a square.

this could be a rectangle.

to be safe, I am following that path.

in a rectangle opposite sides are of equal length.

that means

y - 1 = 2y - 7

y = 2y - 6

0 = y - 6

y = 6

3x - 4 = 3y - 13

3x - 4 = 3×6 - 13

3x - 4 = 18 - 13 = 5

3x = 9

x = 3

as it turns out, it is a square, so we could have used every side expression to be equal with every other side expression, but better safe than sorry ...

5 0

2 years ago