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3 years ago

8

In their last game, the school football team scored an equal number of points in each of the first three quarters, then 14points

in the fourth quarter. If they scored 44 points in all, how many points did they score in the first quarter?

1 answer:

Ksenya-84 [330]3 years ago

7 0

Answer:

10 points

Step-by-step explanation:

Points scored in each of the first 3 quarter = x

Total points scored in the first 3 quarter = x + x + x

= 3x

Points scored in the fourth quarter = 14

Total points scored = 44 point

Total points scored = Total points scored in the first 3 quarter + Points scored in the fourth quarter

44 = 3x + 14

Subtract 14 from both sides

44 = 3x + 14

44 - 14 = 3x + 14 - 14

30 = 3x

Divide both sides by 3

x = 30/3

= 10

x = 10 points

Points scored in each of the first 3 quarter = x = 10 points

The school football team scored 10 points points in the first quarter

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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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Step-by-step explanation:

Given

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Required

Find all product of real values that satisfy the equation

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Cross multiply:

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

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Subtract 7 from both sides

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

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

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

$a = 2$

$b = -2r$

$c =7$

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

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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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3 years ago