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3 years ago

5

Marna is playing a game where you score -5 points each time you guess the correct answer. The goal is to get the lowest score. T

o win the game, Marna must have a score less than -80 points. How many correct answers does Marna need to win the game? Write an inequality.

1 answer:

Mice21 [21]3 years ago

7 0

74 points she would have to answer.

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Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

<u>Answer</u><u> </u><u>Check</u>

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

<u>Answer</u>

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

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Answer:

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Step-by-step explanation:

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Our math team had m students last year, but this year it has already n students! By what percent did the number of students grow

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For this case we are going to assume the following:
m: whole number greater than zero.
n: integer greater than zero.
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the number of students did grow by:
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