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3 years ago

Larry has 9 yards of fabric. He will use 2 yards to make each vest. How many vests

Mathematics

2 answers:

elena-14-01-66 [18.8K]3 years ago

8 0

Answer:

4 vests

Step-by-step explanation:

Larry has 9 yards of fabric, in which 2 are needed to make a vest.

Divide 9 with 2: 9/2 = 4.5

However, note that you cannot have half a vest, so you must round down.

4.5 becomes 4.

4 vests is the maximum Larry can make with 9 yards of fabric.

Sedbober [7]3 years ago

7 0

Answer:

9/2 or 4.5 vests

Step-by-step explanation:

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

Dahasolnce [82]

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$r = \±\sqrt{14$

$Product = -14$

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:

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

$Product = -14$

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