What is 2/3 ÷ 1/8? <br> a. 3/16 <br> b. 5 1/3 <br> c. 1/12 <br> d. 3/11?

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%283%20%2B%20a%29%7D%7B3%7D%20%20%5Cleqslant%20%20%5Cfrac%7Bz%28a%20-%201%29%20%

Sindrei [870]

A= 15+z+ square root 17(z+15)/ z-2
z=2a^2/(a-1)^2 + 30a/(a-1)^2 - 15/(a-1)^2

6 0

3 years ago

Use the discriminant to determine what type of roots the equations will have, and categorize the equations according to their ro

topjm [15]

Step-by-step explanation:

The discriminant of the quadratic equation $ax^2+bx+c=0$ :

$\Delta=b^2-4ac$

If Δ < 0, then the equation has two complex roots $x=\dfrac{-b\pm\sqrt\Delta}{2a}$

If Δ = 0, then the equation has one repeated root $x=\dfrac{-b}{2a}[/tex If Δ > 0, then the equation has two discint roots [tex]x=\dfrac{-b\pm\sqrt\Delta}{2a}$

$1.\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\Delta=(-4)^2-4(1)(2)=16-8=8>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=2\sqrt2\\\\x=\dfrac{-(-4)\pm2\sqrt2}{2(1)}=\dfrac{4\pm2\sqrt2}{2}=2\pm\sqrt2\\\\==============================\\\\2.\ 5x^2-2x+3=0\\\\a=5,\ b=-2,\ c=3\\\\\Delta=(-2)^2-4(5)(3)=4-60=-56$

$3.\ 2x^2+x-6=0\\\\a=2,\ b=1,\ c=-6\\\\\Delta=1^2-4(2)(-6)=1+48=49>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt{49}=7\\\\x=\dfrac{-1\pm7}{(2)(2)}\\\\x_1=\dfrac{-8}{4}=-2,\ x_2=\dfrac{6}{4}=\dfrac{3}{2}\\\\==============================\\\\4.\ 13x^2-4=0\qquad\text{add 4 to both sides}\\\\13x^2=4\qquad\text{divide both sides by 13}\\\\x^2=\dfrac{4}{13}\to x=\pm\sqrt{\dfrac{4}{13}},\ \bold{two\ distinct\ roots}\\\\==============================$

$5.\ x^2-6x+16=0\\\\a=1,\ b=-6,\ c=16\\\\\Delta=(-6)^2-4(1)(16)=36-64=-28$

$7.\ 4x^2+11=0\qquad\text{subtract 11 from both sides}\\\\4x^2=-11\qquad\text{divide both sides by 4}\\\\x^2=-\dfrac{11}{4}\to x=\pm\sqrt{-\dfrac{11}{4}}\\\\x=\pm\dfrac{\sqrt{11}}{2}\ i,\ \bold{two\ complex\ roots}$

6 0

2 years ago

Read 2 more answers

amanda read 15 pages of her 150-page book in 2 hours. At this rate, how long will it take her to read the entire book?

irina [24]

20 hours. You find this by dividing 150 by 10 and then multiplying that by 2.

7 0

2 years ago

Read 2 more answers

Plz help im stuck

nignag [31]

Here you go I think lol

5 0

2 years ago

Sum of exterior angles in a equilateral triangle

poizon [28]

Answer:

In the case of the equilateral triangle, , the exterior angle, plus 60 equals 180. Subtracting 60 from both sides of this equation gives us a value of equal to 120. This means that the exterior angle of an equilateral triangle is equal to 120 degrees. The sum of all the exterior angles is always 360 degrees.

Step-by-step explanation:

8 0

2 years ago

What is 2/3 ÷ 1/8? a. 3/16 b. 5 1/3 c. 1/12 d. 3/11?