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2 years ago

13

How much water will be needed to completely fill a rectangular vase that has a length of 4 inches, a width of 4 inches, and a he

ight of 16 inches?

1 answer:

Free_Kalibri [48]2 years ago

3 0

Volume= length x width x height
4 x 4 x 16 = 256

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How old am I if 1,114 reduced by twice my age is 400?

Natasha_Volkova [10]

Answer:

13

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

What is the solution set of {x|x<-3} intersection {x|x>5}?

ziro4ka [17]

There’s no solution because x is less than 3 there is no way is greater than 5.

Hope this helps!

8 0

2 years ago

Find the product of all real values of r for which 1/2x=r-x/7

Dahasolnce [82]

Answer:

$r = \±\sqrt{14$

$Product = -14$

Step-by-step explanation:

Given

$\frac{1}{2x} = \frac{r - x}{7}$

Required

Find all product of real values that satisfy the equation

$\frac{1}{2x} = \frac{r - x}{7}$

Cross multiply:

$2x(r - x) = 7 * 1$

$2xr - 2x^2 = 7$

Subtract 7 from both sides

$2xr - 2x^2 -7= 7 -7$

$2xr - 2x^2 -7= 0$

Reorder

$- 2x^2+ 2xr -7= 0$

Multiply through by -1

$2x^2 - 2xr +7= 0$

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

$b^2 - 4ac = 0$

For a quadratic equation

$ax^2 + bx + c = 0$

By comparison with $2x^2 - 2xr +7= 0$

$a = 2$

$b = -2r$

$c =7$

Substitute these values in $b^2 - 4ac = 0$

$(-2r)^2 - 4 * 2 * 7 = 0$

$4r^2 - 56 = 0$

Add 56 to both sides

$4r^2 - 56 + 56= 0 + 56$

$4r^2 = 56$

Divide through by 4

$r^2 = 14$

Take square roots

$\sqrt{r^2} = \±\sqrt{14$

$r = \±\sqrt{14$

Hence, the possible values of r are:

$\sqrt{14$ or $-\sqrt{14$

and the product is:

$Product = \sqrt{14} * -\sqrt{14}$

$Product = -14$

8 0

2 years ago

The sum of consecutive integers 1,2,3,...,n is given by the formula 1/2n(n+1). How many consecutive integers, starting with 1, m

LuckyWell [14K]

1/2 * n * (n+1) = 1081

distribute

1/2 n^2 +1/2n -1081=0

factor out 1/2

1/2 (n^2 +n -2162) =0

multiply each side by 2

(n^2 +n -2162) =0

factor

(n-46) (n+47) =0

n=46, n=-47

n cannot be negative

n=46

Answer 46

7 0

2 years ago

Simplify the following expression:,3 + 5 (9+2n)

Rasek [7]

3 + 5(9+2n)
Distribute the 5 to the items in the parentheses
3 + 5(9+2n)
3 + 45 + 10n
Combine like terms
48 + 10n

6 0

2 years ago