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1 year ago

Which of the following is a quadratic equation that has the roots x = 2 and x = −7? (4 points)

Mathematics

1 answer:

crimeas [40]1 year ago

8 0

Answer:

x^2 + 5x - 14

Step-by-step explanation:

We can assume that if there is 2 options for x, this is a quadratic equation that equals 0.

Therefore, we can put this into brackets as one bracket must equal 0.

(x - 2) (x + 7)

After this we expand, which is a process easier to search up

The answer is:

x^2 + 7x - 2x - 14

We can simplify this to:

x^2 + 5x - 14

x^2 represents x squared in case you were wondering

Therefore, the answer is:

x^2 + 5x - 14

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shutvik [7]

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Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = $\frac{1}{4}$

Step-by-step explanation:

Given that

3 white, 2 blue and 5 gray shirts are there.

To find:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?

Solution:

Here, total number of shirts = 3+2+5 = 10

First of all, let us learn about the formula of an event E:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}$

$P(First\ White) = \dfrac{3}{10}$

Now, this shirt is set aside.

So, total number of shirts left are 9 now.

$P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }$

So, the answer is:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = $\frac{1}{4}$

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