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Stells [14]
3 years ago
10

Find the solution to the given equation of the replacement set is [6, 9, 15, 16]. 6 + 2 x = 24

Mathematics
1 answer:
OLEGan [10]3 years ago
5 0
The answer to the question is 9
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1) Determine the discriminant of the 2nd degree equation below:
Aleksandr-060686 [28]

\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}

We have, Discriminant formula for finding roots:

\large{ \boxed{ \rm{x =  \frac{  - b \pm \:  \sqrt{ {b}^{2}  - 4ac} }{2a} }}}

Here,

  • x is the root of the equation.
  • a is the coefficient of x^2
  • b is the coefficient of x
  • c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

\large{ \rm{ \longrightarrow \: x =  \dfrac{ - 5\pm  \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}

\large{ \rm{ \longrightarrow \: x =  \dfrac{ - 5  \pm  \sqrt{25 - 24} }{2 \times 1} }}

\large{ \rm{ \longrightarrow \: x =  \dfrac{ - 5 \pm 1}{2} }}

So here,

\large{\boxed{ \rm{ \longrightarrow \: x =  - 2 \: or  - 3}}}

❒ p(x) = x^2 + 2x + 1 = 0

\large{ \rm{ \longrightarrow \: x =  \dfrac{  - 2 \pm  \sqrt{ {2}^{2}  - 4 \times 1 \times 1} }{2 \times 1} }}

\large{ \rm{ \longrightarrow \: x =  \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}

\large{ \rm{ \longrightarrow \: x =  \dfrac{ - 2 \pm 0}{2} }}

So here,

\large{\boxed{ \rm{ \longrightarrow \: x =  - 1 \: or \:  - 1}}}

❒ p(x) = x^2 - x - 20 = 0

\large{ \rm{ \longrightarrow \: x =  \dfrac{ - ( - 1) \pm  \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}

\large{ \rm{ \longrightarrow \: x =  \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}

\large{ \rm{ \longrightarrow \: x =  \dfrac{1 \pm 9}{2} }}

So here,

\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \:  - 4}}}

❒ p(x) = x^2 - 3x - 4 = 0

\large{ \rm{ \longrightarrow \: x =   \dfrac{  - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}

\large{ \rm{ \longrightarrow \: x =  \dfrac{3 \pm \sqrt{9  + 16} }{2 \times 1} }}

\large{ \rm{ \longrightarrow \: x =  \dfrac{3  \pm 5}{2} }}

So here,

\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \:  - 1}}}

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5 0
3 years ago
Read 2 more answers
30 points!!! Help me on 1. 2. 3.
BaLLatris [955]
I think 1 is to press C
8 0
3 years ago
Gavin drove 85 miles on 10 gallons of gas.How many miles can gavin drive on 25 gallons of gas?
bixtya [17]

Answer:

212.5 miles on 25 gallons.

Step-by-step explanation:

Set up a proportion

85 miles on 10 gallons

x miles on 25 gallons.

85/10 = x / 25                   Multiply both sides by 25

85*25 / 10 = x                   Simplify the left

2125 / 10 = x

x = 212.5 miles in 25 gallons.

6 0
3 years ago
Which of the following is not a rate?
IrinaK [193]

Answer:

Folding 6 loads

Step-by-step explanation:

5 0
3 years ago
HELP PLEASE!!!!!
Tasya [4]

Answer:

233 Times

Step-by-step explanation:

In a standard cube, there are 6 faces labelled 1 to 6.

Numbers less than 5=1,2,3,4

The probability of rolling a number less than 5 =4/6

Therefore, if the standard number cube is rolled 350 times.

Number of Expected Outcome Less than 5

=\dfrac{4}{6}X350

=233.33\\\approx 233$ (to the nearest integer)

We would roll a number less than 5 233 times.

6 0
3 years ago
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