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2 years ago

Solve the quadratic equations

Mathematics

1 answer:

Alexxx [7]2 years ago

6 0

Answer:

for quadratic equation 1

y^2-10y+21=0

Step-by-step explanation:

y^2-7y-3y+21=0

y(y-7)-3(y-7)=0

(y-7)(y-3)=0

y-7=0,y-3=0

y=7,y=3

y=(3,7)

for quadratic equation 2

16p^2-8p+1=0

16p^2-4p-4p+1=0

4p(4p-1)-1(4p-1)=0

(4p-1)twice=0

4p-1=0,4p-1=0

4p=1

p=1/4 twice

for quadratic equation 3

x^2-400=0

x^2=400

x=√400

x=20

for quadratic equation 4

-16m^2-8m-1=0

multiply the equation by -

16m^2+8m+1=0

16m^2+4m+4m+1=0

4m(4m+1)1(4m+1)=0

4m+1=0 twice

m=-1/4 twice

for quadratic equation 5

-3n^2+75=0

divide both side by -3

-3n^2/-3=-75/-3

n^2=25

n=√25

n=5

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Can someone help me with this?

jekas [21]

Answer:

$\huge\purple{ x^2 +(y+2)^2 = 4}$

Step-by-step explanation:

Circle is centred at (0, -2)

-> h = 0 & k = - 2

radius of the circle (r) = y-coordinate of the center = - 2

Equation of circle in standard form is given as:

$(x-h)^2 +(y-k)^2 = r^2$

Plugging the values of h, k and r in the above equation, we find:

$(x-0)^2 +[y-(-2)]^2 = (-2)^2$

$\implies\huge\orange{ x^2 +(y+2)^2 = 4}$

This is the required equation of circle.

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2 years ago

The radius of one sphere is twice as great as the radius of a second sphere. Find the ratio of their volumes.

Juliette [100K]

The ratio of the radii is 2:1, so the ratio of their surface areas is 4:1. The area of a sphere is defined by 4 * pi * r^2 

So if the radius of the first sphere is 2r, then it would be (2r)^2 = 4r^2 

The rest is the same. So the ratio of their surface areas would be 

4 * pi * 4r^2 divided by 
4 * pi * r^2 

or 4.

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3 years ago

32.28 in expanded form

igor_vitrenko [27]

Step-by-step explanation:

expanded form is adding each place value together with zeros replacing all other spots

32.28

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3 years ago

If the distance traveled is (4s3 - 6s² + 4s + 14) miles and the rate is (s + 1) mph, write an expression, in hours, for the time

BartSMP [9]

The equation for time is URM:

$time = \frac{distance}{speed \: (rate)}$

$t(s) = \frac{4s {}^{3} - 6s {}^{2} + 4s + 14}{s + 1} = \frac{2(s + 1)(2s {}^{2} - 5s + 7) }{s + 1} \\ t(s) = 2(2s {}^{2} - 5s + 7) \\ t(s) = 4s {}^{2} - 10s + 14$

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1 year ago

A biologist is researching the population density of antelopes near a watering hole. The biologist counts 32 antelopes within a

Setler [38]

Answer:

=0.3 per km²

Step-by-step explanation:

Population density is the population per uni area.

Area=πr² Where A is area and r is the radius of the circle.

A=3.14×34

=106.76km²

Population density = Population/Area

=32 antelopes/106.76 km²

=0.3 per km²

The population of antelopes within the given radius is 0.3 per km²

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3 years ago