Example

For what values of x is x2-36=5x true? 0 -9 and 4 04 and 9 4 and -9 09 and 4

ipn [44]

Answer:

x = - 4 and x = 9

Step-by-step explanation:

Given

x² - 36 = 5x ( subtract 5x from both sides )

x² - 5x - 36 = 0

Consider the factors of the constant term (- 36) which sum to give the coefficient of the x- term (- 5)

The factors are - 9 and + 4, since

- 9 × 4 = - 36 and - 9 + 4 = - 5, thus

(x - 9)(x + 4) = 0

Equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x + 4 = 0 ⇒ x = - 4

6 0

3 years ago

. If α and β are the roots of

Lostsunrise [7]

Answer:

$18x^2+85x+18 = 0$

Step-by-step explanation:

Given Equation is

=> $2x^2+7x-9=0$

Comparing it with $ax^2+bx+c = 0$ , we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = $-\frac{b}{a}$

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

Now, Finding the equation whose roots are:

α/β ,β/α

Sum of Roots = $\frac{\alpha }{\beta } + \frac{\beta }{\alpha }$

Sum of Roots = $\frac{\alpha^2+\beta^2 }{\alpha \beta }$

Sum of Roots = $\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }$

Sum of roots = $(\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}$

Sum of roots = $\frac{49}{4} + 9 /\frac{-9}{2}$

Sum of Roots = $\frac{49+36}{4} / \frac{-9}{2}$

Sum of roots = $\frac{85}{4} * \frac{2}{-9}$

Sum of roots = S = $-\frac{85}{18}$

Product of Roots = $\frac{\alpha }{\beta } \frac{\beta }{\alpha }$

Product of Roots = P = 1

The Quadratic Equation is:

=> $x^2-Sx+P = 0$

=> $x^2 - (-\frac{85}{18} )x+1 = 0$

=> $x^2 + \frac{85}{18}x + 1 = 0$

=> $18x^2+85x+18 = 0$

This is the required quadratic equation.

5 0

3 years ago

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25A) Find the length of a rectangular lot with a perimeter of 132 feet if the

Greeley [361]

Answer:

34.5 ft

Step-by-step explanation:

~Refer to the attachment for the solution.

5 0

3 years ago

I really need help with this, thank you!!!

Lyrx [107]

Answer:

6. 60°

7. 5.19559

8. 7.96011

Step-by-step explanation:

6. The sum of angles in a triangle is 180°, so the remaining angle is ...

180° -40° -80° = 60°

7. The lengths of sides are proportional to the sine of the opposite angle (Law of Sines).

a = c·sin(A)/sin(C) = 7·sin(40°)/sin(60°) ≈ 5.19559

8. Same explanation as 7.

b = c·sin(B)/sin(C) = 7·sin(80°)/sin(60°) ≈ 7.96011

3 0

3 years ago

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In the Treasure, Treasure! video game, players gain and lose points by finding and losing treasure. In Level 2, Leslie earned

USPshnik [31]

Answer:

. finding and losing treasure. In level 2, Leslie earned -22 points when a storm blew a treasure chest off her ship. Then, she earned 34 ... a storm blew a treasure chest off her ship. Then, she earned 34 points for finding more treasure on the deserted island. What is the overall change in Leslie's score during level 2? ansver.

Step-by-step explanation:

3 0

3 years ago

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