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myrzilka [38]
3 years ago
5

A water tank holds 216 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 324 gallons but is leak

ing at a rate of 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same?
Mathematics
1 answer:
Tems11 [23]3 years ago
7 0

Answer:

54  

Step-by-step explanation:

216 - 3x = 324 -5x

subtract 216 from both sides

add 5x to both sides

divide both sides by 2x.

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30 Points!!
neonofarm [45]

Answer:

  multiply the left side of the constant vector by the inverse matrix

Step-by-step explanation:

The matrix equation ...

  AX = B

is solved by left-multiplying by the inverse of A:

  A⁻¹AX = A⁻¹B

  IX = A⁻¹B . . . . . the result of multiplying A⁻¹A is the identity matrix

  X = A⁻¹B . . . . . B needs to be multiplied by the inverse matrix

\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}-4&1\\3&2\end{array}\right]^{-1}\left[\begin{array}{c}9&7\end{array}\right]=\dfrac{1}{11}\left[\begin{array}{cc}-2&1\\3&4\end{array}\right]\left[\begin{array}{c}9&7\end{array}\right]=\left[\begin{array}{c}-1&5\end{array}\right]

4 0
3 years ago
Consider the graph of the linear function h(x) = –x + 5. Which could you change to move the graph down 3 units?
Yakvenalex [24]
I don't see a b or an m in this function, but generally, a linear function is of the form ax+b. The b in this equation (not sure if it is the same as your b), controls the shift of the function. Lower b by 3, the graph shifts down by 3.

So unless there is a minus sign before b, it has to be lowered by 3. (If there is a minus sign, it has to be increased by 3).
6 0
3 years ago
Read 2 more answers
What are all values of x for which the series shown converges? ​
adoni [48]

Answer:

One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:

Iaₙ₊₁I < IaₙI

This means that the absolute value of the terms must decrease as n increases.

Then we must have:

\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}}

We can write this as:

\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}} = \frac{(x -2)^n}{(n + 1)*3^n} * \frac{(x - 2)}{3}

If we assume that n is a really big number, then:

n + 1 ≈ 1

And we can write:

\frac{(x -2)^n}{n*3^n} > \frac{(x -2)^n}{(n)*3^n} * \frac{(x - 2)}{3}

Then we have the inequality

1 > (x - 2)/3

And remember that this must be in absolute value, then we will have that:

-1 < (x - 2)/3 < 1

-3 < x - 2 < 3

-3 + 2 < x < 3 + 2

-1 < x < 5

The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.

5 0
3 years ago
A circle has a diameter of 6 centimeters what is the approximate area of the circle​
KiRa [710]

Answer:

28.26 cm^{2}

Step-by-step explanation:

The radius is half of the diameter. 6/2 = 3, so the radius of this circle is 3 cm.

The formula for the area of a circle is: πr^{2}

Plugging 3 into the radius, we have:

3^{2} × π =

9 × π

We can round π to 3.14

9 × 3.14 = 28.26

7 0
3 years ago
Literal equations 2x-3y=8 solve for y
vichka [17]
2x-3y = 8

Add 3y on both sides

2x = 8 + 3y

Subtract 8 on both sides

3y = 2x - 8

Divide 3 on both sides

y= \frac{2}{3}x- \frac{8}{3}
4 0
4 years ago
Read 2 more answers
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