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3 years ago

14

Working alone ryan can dig a 10ft by 10ft hole in five hours. castel can dig the same hole in six hours how long would it take t

hem to dig the hole if they worked together

1 answer:

Inessa [10]3 years ago

7 0

<span>Ryan rate = 1/5 job/hr
Castel rate = 1/6 job/hr
Together rate = 1/x job/hr

Equation:

1/5 + 1/6 = 1/x
6x + 5x = 30
11x = 30

x = 2 8/11 hr = 2 hr (8/11)60 = 2hr 47 minutes (time to do the job together)</span>

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Solve: x2 − x − 6/x2 = x − 6/2x + 2x + 12/x After multiplying each side of the equation by the LCD and simplifying, the resultin

Vesna [10]

The resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

According to the given question.

We have an equation

$\frac{x^{2}-x-6 }{x^{2} } = \frac{x-6}{2x} +\frac{2x+12}{x}$

So, to find the resulting equation of the above equation we need to simplify.

First we will take LCD

$\frac{x^{2} -x - 6 }{x^{2} } = \frac{x -6+2(2x + 12)}{2x}$

$\implies \frac{x^{2}-x-6 }{x^{2} } =\frac{x-6+4x+24}{2x}$

$\implies \frac{x^{2}-x-6 }{x^{2} } = \frac{5x +18}{2x}$

Multiply both the sides by x.

$\frac{x^{2}-x-6 }{x} = \frac{5x+18}{2}$

Again multiply both the sides by x

$2x^{2} -2x-12 = 5x^{2} +18x$

$\implies 5x^{2} -2x^{2} +18x +2x +12 = 0$

$\implies 3x^{2} + 18x+2x + 12 = 0$

Factorize the above equation

⇒3x(x+6)+2(x+6) = 0

⇒(3x + 2)(x+6) = 0

⇒ x = -2/3 or x = -6

Hence, the resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

Find out more information about equation here:

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1 year ago

The population of a county is growing at a rate of 9% per year, compounded continuously. How many years will it take for the pop

torisob [31]

Answer:

$t=15.4\ years$

Step-by-step explanation:

The exponential growth function compounded continuously is equal to

$A=P(e)^{rt}$

where

A is the final population

P is the initial population

r is the rate of growth in decimal

t is Number of years

e is the mathematical constant number

we have

$A=4x\\P=x\\ r=9\%=9/100=0.09$

substitute in the function above

$4x=x(e)^{0.09t}$

simplify

$4=(e)^{0.09t}$

Take natural log of both sides

$ln(4)=ln[(e)^{0.09t}]$

$ln(4)=0.09t(ln(e))$

$ln(e)=1$

$ln(4)=0.09t$

$t=ln(4)/0.09$

$t=15.4\ years$

8 0

3 years ago

John runs 15 miles in 3 hours how many miles can john runs per hour

Effectus [21]

Answer:25

Evan has a summer job to pick berries on a farm.

• He earns

$

2.0$2.00 every

15

15 minutes that he picks strawberries.

• He earns

$

2.40

$2.40 for every

15

15 minutes that he picks blueberries.

• He picked strawberries for an hour and blueberries for

45

45 minutes.

How much money did Evan earn?

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

The functions f and g are graphed in the same rectangular coordinate system, shown to the right. If g is obtained from f through

german

The first thing we notice is that the function is reflected. So we can start by reflecting it with respect to the x-axis.

We do this by adding a negative sign in the function:

$\begin{gathered} f_0(x)=x^2 \\ f_1(x)=-f_0(x)=-x^2 \end{gathered}$

Now, we have the function reflected, but in the wrong position. We can track its position by the vertex. It was originally at (0,0) and remains at (0,0) after the reflection.

But the final function have its vertex at (-5,0), so we have to translate the function 5 units to the left. we do this by adding 5 to the x in the function:

$f_2(x)=f_1(x+5)=-(x+5)^2$

Now, to check if there isn't any dilatation, we can check on other point in the graph to see if it checks out.

In the blue graph, we see the point (-3,-4), so let's input x = -3 and see if it checks out:

$f_2(-3)=-(-3+5)^2=-(2)^2=-4$

We got y = -4, so it checks out.

Thus, the answer is:

$g(x)=-(x+5)^2$

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1 year ago

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2 years ago