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3 years ago

What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?

1 answer:

6 0

$2x^2+16x-9=0\ \ \ |+9\\\\2x^2+16x=9\ \ \ |:2\\\\x^2+8x=4.5\\\\x^2+2x\cdot4=4.5\ \ \ |+4^2\\\\\underbrace{x^2+2x\cdot4+4^2}_{(a+b)^2=a^2+2ab+b^2}=4.5+4^2\\\\(x+4)^2=20.5\to x+4=\pm\sqrt{20.5}\\\\x+4=-\sqrt{\dfrac{205}{10}}\ \vee\ x+4=\sqrt{\dfrac{205}{10}}\\\\x+4=-\sqrt{\dfrac{2050}{100}}\ \vee\ x+4=\sqrt{\dfrac{2050}{10}}\\\\x+4=-\dfrac{\sqrt{25\cdot82}}{10}\ \vee\ x+4=\dfrac{\sqrt{25\cdot82}}{10}\\\\x=\dfrac{-40-5\sqrt{82}}{10}\ \vee\ x=\dfrac{-40+5\sqrt{82}}{10}$

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Help me do 1/6+1/4 make sure the demonator is the same

Alik [6]

<h2><u>Answer: </u></h2><h2> $\boxed{\boxed{\sf\frac{5}{12}=0.416666667}}$ </h2><h2></h2><h2><u>Solution Steps: </u></h2>

______________________________

$6,4=12$

<em> - We do this because in order to add these, they must have the same denominator. So you must find the LCF, (Least Common Factor) of 6 and 4.</em>

<em />

<h3>2.) Convert the fractions to have the same denominator: </h3>

$\frac{1}{6}=\frac{2}{12}$

$\frac{1}{4}=\frac{3}{12}$

<em> - </em> $\frac{1}{6}$ <em> changes to </em> $\frac{2}{12}$ <em> by multiplying the numerator and denominator by 2. And </em> $\frac{1}{4}$ <em> changes to </em> $\frac{3}{12}$ <em> because you multiply the numerator and denominator by 3. </em>

<h3>3.) Add the numerators: </h3>

$2+3=5$

<em> - Since both fractions have the same denominator all you have to do is add the numerators together. </em>

<em />

______________________________

7 0

3 years ago

Find the circumference and area of a circle with a diameter of 12 cm. (Use the approximation of 3.14 for )

MArishka [77]

Answer:

37.68 for circumference

Step-by-step explanation:

You find the circumference by doing 3.14 x diameter

6 0

3 years ago

Read 2 more answers

15) You are buying balloons and cupcakes for your friend's

inysia [295]

Answer:

variable is number of balloons

b = balloons

b+10 = cupcakes

85 = 2b + 5b + 50 = 7b + 50

Step-by-step explanation:

#cupcakes = 10 + b #balloons

total cost $85 = ($2 x b) + $5 x (b + 10)

balloons cupcakes

85 = 2b + 5b + 50 combine terms and subtract 50 from both sides of =

35 = 7b then divide both sides by 7

5 balloons

15 cupcakes

5 0

3 years ago

A 4.2 kg object hangs at one end of a rope that is attached to a support on a railroad boxcar. When the car accelerates to the r

Firlakuza [10]

Answer:

5.21 m/s²

Step-by-step explanation:

Data provided in the question:

Mass of the hanging object = 4.2 kg

Angle made by the rope with vertical = 28°

Acceleration of gravity = 9.8 m/s²

Now,

let the tension in the rope be 'T'

Thus,

The vertical component of the tension = Tcos(28°)

The horizontal component of the tension = Tsin(28°)

Thus,

For the equilibrium

Net force in vertical direction

Tcos (28) = mg [as Fynet = 0] ..............(1)

and,

Net Horizontal force

Tsin(28°) = ma [as the acceleration of the boxcar is what is causing the object to make the angle] ....................(2)

Now, 2 divided by 1

tan(28°) = $\frac{mg}{ma}$

a = g[tan(28°)]

a = 9.8 × tan(28°)

a = 5.21 m/s²

6 0

4 years ago

What is the equation of a line that contains the points (0,8) and (8,8)

Aleonysh [2.5K]

Answer: y=8

Step-by-step explanation:

The equation for a line is y=mx+b

m represents slope and b is the y intercept

8 is our y intercept, and this is how high or down the line will go, in this case it is 8 because of (0,8) because x is equal to 0

lets find the slope using: y2-y1 / x2-x1

and we are given (0,8) and (8,8)

0: x1

8: y1

8: x2

8:y2

simply plug in

8-8 / 8-0

0/8

= 0

so 0 is our slope

so:

y=0x+8 or y=8

you can also check this by going onto desmos.com/calculator or by using a graphing calculator like a ti-89 and see that both will go through the line of (0,8) and (8,8)

3 0

3 years ago