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3 years ago

Find the area of the shape

Mathematics

1 answer:

nydimaria [60]3 years ago

8 0

Answer: 3 pie symbol

Step-by-step explanation:

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Use the discriminant to predict the nature of the solutions to the equation 4x-3x²=10. Then, solve the equation.

AleksandrR [38]

Answer:

Two imaginary solutions:

x₁= $\frac{2}{3} -\frac{1}{3} i\sqrt{26}$

x₂ = $\frac{2}{3} +\frac{1}{3} i\sqrt{26}$

Step-by-step explanation:

When we are given a quadratic equation of the form ax² +bx + c = 0, the discriminant is given by the formula b² - 4ac.

The discriminant gives us information on how the solutions of the equations will be.

If the discriminant is zero, the equation will have only one solution and it will be real
If the discriminant is greater than zero, then the equation will have two solutions and they both will be real.
If the discriminant is less than zero, then the equation will have two imaginary solutions (in the complex numbers)

So now we will work with the equation given: 4x - 3x² = 10

First we will order the terms to make it look like a quadratic equation ax²+bx + c = 0

So:

4x - 3x² = 10

-3x² + 4x - 10 = 0 will be our equation

with this information we have that a = -3 b = 4 c = -10

And we will find the discriminant: $b^{2} -4ac = 4^{2} -4(-3)(-10) = 16-120=-104$

Therefore our discriminant is less than zero and we know that our equation will have two solutions in the complex numbers.

To proceed to solve the equation we will use the general formula

x₁= (-b+√b²-4ac)/2a

so x₁ = $\frac{-4+\sqrt{-104} }{2(-3)} \\\frac{-4+\sqrt{-104} }{-6}\\\frac{-4+2\sqrt{-26} }{-6} \\\frac{-4+2i\sqrt{26} }{-6} \\\frac{2}{3} -\frac{1}{3} i\sqrt{26}$

The second solution x₂ = (-b-√b²-4ac)/2a

so x₂= $\frac{-4-\sqrt{-104} }{2(-3)} \\\frac{-4-\sqrt{-104} }{-6}\\\frac{-4-2\sqrt{-26} }{-6} \\\frac{-4-2i\sqrt{26} }{-6} \\\frac{2}{3} +\frac{1}{3} i\sqrt{26}$

These are our two solutions in the imaginary numbers.

7 0

3 years ago

In rhombus ABCD, AB = 13 and AC = 25. Find the area of the rhombus to the nearest tenth.

const2013 [10]

Area=lengthxwidth
=25x13
=325

5 0

3 years ago

John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel. Write an equation to determine the total

suter [353]

Answer: the equation is 1/3p-3=114

The novel has a total of 351 pages

Step-by-step explanation:

6 0

3 years ago

i need help asa!! . f(x) = 4x + 6 g(x) = 2x + 10 At what input would both functions produce the same output?

adelina 88 [10]

x = 2

solve 4x + 6 = 2x + 10

subtract 2x from both sides

2x + 6 = 10

subtract 6 from both sides

2x = 10 - 6 = 4

divide both sides by 2

x = $\frac{4}{2}$ = 2

as a check f(2) =(4 × 2 )+ 6 = 14 and g(2) =( 2× 2) + 10 = 14

3 0

3 years ago

Based on the smiths bbq report based

Mila [183]

Answer:

what? is there suppoused to be a image

Step-by-step explanation:

6 0

3 years ago