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nlexa [21]
3 years ago
8

Quadratic formula 2x²+9x-4=0

Mathematics
2 answers:
posledela3 years ago
5 0
2x^2+9x-4=0\ \ \ \ /:2\\\\x^2+\frac{9}{2}x-2=0\\\\x^2+2x\cdot\frac{9}{4}+(\frac{9}{4})^2-(\frac{9}{4})^2=2\\\\(x+\frac{9}{4})^2-\frac{81}{16}=2\\\\(x+\frac{9}{4})^2=\frac{32}{16}+\frac{81}{16}\\\\(x+\frac{9}{4})^2=\frac{113}{16}\iff x+\frac{9}{4}=-\sqrt\frac{113}{16}\ \vee\ x+\frac{9}{4}=\sqrt\frac{113}{16}\\\\x=-\frac{9}{4}-\frac{\sqrt{113}}{4}\ \vee\ x=-\frac{9}{4}+\frac{\sqrt{113}}{4}\\\\x=-\frac{9+\sqrt{113}}{4}\ \vee\ x=-\frac{9-\sqrt{113}}{4}
blondinia [14]3 years ago
4 0
2x^2+9x-4=0 \\ \\a=2 , b =9 , \ c=- 4 \\ \\\Delta = b^{2}-4ac = 9^{2}-4*2* (- 4)= 81+32 =113 \\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{-9- \sqrt{113}}{4} \\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} = \frac{-9+\sqrt{113}}{4}


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Step-by-step explanation:

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andre [41]

Answer:

x ≥ 1  (how to graph is listed below)

Step-by-step explanation:

To find where we need to plot the line, we first need to solve the inequality for x:

-2x - 3 ≤ -5

(Add three to both sides)

-2x ≤ -2

(Divide both sides by -2, but we can't forget that whenever we multiple or divide by a negative number, the sign flips!)

x ≥ 1

To graph this on the number line, you would put a dot on the 1 and fill it in completely (you fill in the dot for a "___ and equal to" sign.     ex. ≥, ≤)

Then you would make an arrow from the dot to the right on the number line (this is because x must be greater than or equal to 1, so it must be facing in that direction)

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baherus [9]

Answer:

\sqrt{34}

Step-by-step explanation:

Calculate the distance using the distance formula

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with (x₁, y₁ ) = A(- 2, 5) and (x₂, y₂ ) = B(3, 8)

d = \sqrt{(3+2)^2+(8-5)^2}

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It took sandy two hours to jog 13 miles. She ran 7 1/2 miles in one hour. How far did she run during the second hour
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Sandy ran 5 ½ during the second hour.

  • Total amount Sandy used to jog for 2 hours = 13 miles
  • Amount Sandy used to run in the 1st hour = 7 ½
<h2>Further Explanation</h2>

Therefore the amount Sandy used to run in the 2nd hour = Total amount Sandy used to jog for 2 hours – Amount Sandy used to run in the 1st hour

= 13 – 7 ½ (and can be expressed as 7 + ½)

= 13 – (7 + ½)

= 13 – 7 – ½

= 6 – ½ (otherwise expressed as 6/1 – 1/2)

= (6 x 2) – (1 x 1) / 2

= (12) – (1) / 2

= 12 – 1 / 2

= 11/2

= 5 ½

Hence, Sandy ran 5 ½ miles during the second hour.

Based on the above expression, it is observed that there is an element of fractions in the math problem. Also, BODMAS was clearly used to derive the solution to the given question.

Recall, 13 – (7 + ½). The mathematical signs, (–) and (+) were multiplied; one of mathematics rule states that – x + = –; thus 13 – 7 – ½

Notably, fractions deal with denominators and numerators; and in these questions, with the help of BODMAS, they (6/1 – 1/2) were used to factor each other out to derive the final answer 5 ½.

LEARN MORE:

  • Numbers: brainly.com/question/2906770
  • mixed numbers brainly.com/question/12853142
  • fraction brainly.com/question/6201432

KEYWORDS:

  • bodmas
  • fractions
  • mathematical sign
  • denominators
  • numerators
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