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3 years ago

!!MATH GENIUSES HELP ME!!

Mathematics

1 answer:

seraphim [82]3 years ago

8 0

Answer:

Step-by-step explanation:

Let x be Bill’s scores.

Let y be Theo’s scores.

x + y = 90

x² = y

Solve for x in the second equation.

x = √y

Put x as √y in the first equation and solve for y.

√y + y = 90

√y = 90 - y

y = (90 - y)²

y = - y² - 180y - 8100

0 = -y² - 181y - 8100

0 = (-y+81)(y-100)

-y+81=0

y = 81

y - 100 = 0

y = 100

100 does not work if we plug in to check, so y is 81.

y = 81

Put y as 81 in the first equation and solve for x.

x + 81 = 90

x = 9

Bill scored 9 goals and Theo scored 81.

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If p is directly proportional to q, and p=9 when q=7.5, find q when p=24.

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<h3>Solution and Explanation:</h3>

If $p$ and $q$ are directly proportional, then they must have a common scalar.

To find $q$ we must first find its scalar. If we let $a$ be the scalar we can form the equation, $ap = q$ .

We are given the information that if $q = 7.5$ then $p = 9$ . We can use that in finding the scalar.

$a \times 9 = 7.5 \\ \frac{a \times 9}{9} = \frac{7.5}{9} \\ a = \frac{75}{90} \\ a = \frac{15}{18}$

Now we can solve for $q$ when $p = 24$ knowing that our scalar is $\frac{15}{18}\\$ .

$ap = q \\ \frac{15}{18} \times 24 = q \\ \frac{360}{18} = q \\ 20 = q$

<h3>Answer:</h3>

$q = 20$ when $p = 24$

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Given:

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