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Answer:

Step-by-step explanation:

If the object starts with a value [tex]V_0[/tex], and a annual percent of decay d, after a year the value will be

[tex]V_1 = V_0 * d[/tex]

after 2 years, taking now  [tex]V_1[/tex] as the starting value

[tex]V_2 = V_1 * d = V_0 * d * d [/tex]

[tex]V_2 = V_0 * d^2 [/tex]

and so on, after n years the value will be:

[tex]V_n = V_0 * d^n[/tex]

Now, in 1997 the value was $9500, in 2012 the value was $5000. Between 1997 and 2012 there are 15 years, so, our equation will be:

[tex] \$5000 = \$ 9500 * d^{15}[/tex]

Working it a little

[tex] \frac{\$5000}{\$ 9500} = d^{15}[/tex]

[tex] (\frac{\$5000}{\$ 9500})^{1/15} = d[/tex]

[tex] (0.5263})^{1/15} = d[/tex]

[tex] 0.9581 = d[/tex]

This mean that, after a year, the value will be at 95.81 %, this is, a decay rate of 4.19%.

Answer:

c

Step-by-step explanation:

Answer:

The area will increase by a factor of 4

Step-by-step explanation:

4 * 4 = 16

IT'S UP THERE STEVE (Like on family feud)

Answer:

x ≥ 0

Step-by-step explanation:

The function is graphed starting at 0 and going up the positive x-axis.

These are numbers that are greater than 0; thus the domain is greater than or equal to 0, or

x ≥ 0

The domain of the function is (d) x >= 0

From the graph, we have the following highlight:

Since 0 is inclusive, we make use of the greater than or equal to inequality

Hence, the domain of the function is (d) x >= 0

Read more about domain at:

https://brainly.com/question/10197594

Answer:

√74

Step-by-step explanation:

a^2 + b^2 = c^2

7^2 + 5^2 = c^2

49 + 25 = c^2

74 = c^2

√74 = √c^2

This is not enough information, sorry

For the first question please find the attached diagram.

As per the diagram, P is the upstream point and Q is the downstream point. The distance between P and Q is 22.5 miles.

Let the speed of the boat in the still waters of the lake be represented by S.

Then, when the boat travels upstream, the net speed of the boat will be (S-6) miles per hour because the river flows downstream and thus the speed of the boat will have to be subtracted from the speed of the river.

Now, we know that the relationship between the net speed, distance and time of travel is give as:

Distance = Net Speed x Time of travel

For the upstream ride of the board we know that Distance is 22.5 miles and Net Speed is (S-6). Therefore, the above equation will become:

[tex] 22.5=(S-6)\times T_{1} [/tex] where [tex] T_{1} [/tex] represents the time taken to travel upstream.

We can rearrange the above equation to be:

[tex] T_{1}=\frac{22.5 }{S-6} [/tex]......................(Equation 1)

By similar arguments we know that the downstream speed of the boat is S+6 and the distance travelled is the same and so the time taken to travel downstream (represented by [tex] T_{2} [/tex]) will be:

[tex] T_{2}=\frac{22.5}{S+6} [/tex]................(Equation 2)

Now, we know that the total time of travel should be 9 hours.

This means that: [tex] T_{1}+T_{2}=9 [/tex]............(Equation 3)

Plugging in the values of [tex] T_{1} [/tex] and [tex] T_{2} [/tex] from (Equation 1) and (Equation 2) into (Equation 3), we get:

[tex] \frac{22.5 }{S-6} +\frac{22.5 }{S+6}=9 [/tex]

Simplifying the above we will get a quadratic equation:

[tex] 9S^2-45S-54=0 [/tex]

The roots of this quadratic equation are:

[tex] S=-1 [/tex] and [tex] S=6 [/tex]

Since, speed cannot be negative, [tex] S=-1 [/tex] is out of consideration.

The speed of the boat in the lake is thus [tex] S=6 [/tex] miles per hour.

But we have a problem with S=6 too. The problem is that if S=6, then the boat will not be able to move upstream.

Let us solve problem 2

We are given that: [tex] \frac{x-2}{x+3}+\frac{10x}{x^2-9} [/tex]

We can rewrite it as:

[tex] \frac{x-2}{x+3}+\frac{10x}{(x-3)(x+3)} [/tex]

[tex] \frac{(x-3)(x-2)+10x}{(x-3)(x+3)} =\frac{x^2-5x+6+10x}{(x-3)(x+3)} [/tex]

Now, the numerator can be simplified as:

[tex] \frac{x^2+10x+6}{(x-3)(x+3)} =\frac{(x+3)(x+2)}{(x-3)(x+3)} =\frac{x+2}{x-3} [/tex]

Thus, our final simplified answer is:

[tex] \frac{x+2}{x-3} [/tex]

The restriction on the variable x is that it cannot be equal to either +3 or -3 as that would make the denominator of the original question equal to zero.

Thus, the restriction is [tex] x\neq \pm 3 [/tex]

Final answer:

To estimate the circumference of a circle with a diameter of 13 yards, use the formula C = π * d where π is approximated as 3.14. The estimated circumference is 40.82 yards.

Explanation:

To estimate the circumference of a circle that has a diameter of 13 yards, you can use the formula for the circumference of a circle, which is π times the diameter (C = π * d). The value of π (pi) can be rounded to 3.14 for convenience in calculation. Using this rounded value of π:

Circumference = 3.14 * 13 yards= 40.82 yards

Therefore, the estimated circumference of the circle is 40.82 yards.

Answer:

c is correct

Step-by-step explanation:

Answer:

the answer is 6 on algebra nation

Step-by-step explanation:

Answer:

2,750+2750=

2750 x 4+2750 x 2=

22,000

Step-by-step explanation:

Answer:

He now work 24 hours each week

Step-by-step explanation:

Dylan works 30 hours a week. His hours are decreased by 20%.

The number of work hours 30 is decreased by 20%

we need to find 20% of 30

[tex]30 \cdot \frac{20}{100} =6[/tex]

So number of hours should be decreased by 6

[tex]30-6= 24[/tex]

he now work 24 hours each week

Answer:

y²-2y+3

Step-by-step explanation:

We write the dividend, y³-y²+y+3, under the box and the divisor, y+1, to the left of the box.

We first divide y³ by y; this is y².  We write this above the box, over -y².  We multiply the divisor by y²:  

y²(y+1) = y³+y²

This goes under the divisor.  We then subtract:

(y³-y²)-(y³+y²) = -2y².  We then bring down the next term, y; this gives us -2y²+y.

We then divide -2y² by y; this is -2y.  This goes above the box beside the y² in the quotient.  We then multiply the divisor by -2y:

-2y(y+1) = -2y²-2y

We now subtract:

(-2y²+y)-(-2y²-2y) = 3y.  We bring down the last term, 3; this gives us 3y+3.  We divide 3y by y; this is 3.  This goes beside the -2y in the quotient.  We then multiply this by the divisor:

3(y+1) = 3y+3.  We then subtract:  (3y+3)-(3y+3) = 0

This makes the quotient y²-2y+3.