Answer:
7x2 + 14x = 0
x2 + 3x -5 = 0
x2 - x = 3x + 7
Step-by-step explanation:
A quadratic equation has the highest power of x to the second power. It must have x to the second power
7x2 + 14x = 0 quadratic
x3 - 3x2 + 1 = 0 not quadratic but cubic
5x - 7 = 0 not quadratic but linear
x2 + 3x -5 = 0 quadratic
x - 5 = 9x + 7 not quadratic but linear
x2 - x = 3x + 7 quadratic
Problem 9
r+h = 9
SA = 2*pi*r^2 + 2*pi*r*h = 54pi
2*pi*r^2 + 2*pi*r*h = 54pi
2pi*r(r + h) = 54pi
r(r+h) = 27
r(9) = 27
9r = 27
r = 27/9
r = 3
r+h = 9
h = 9-r
h = 9-3
h = 6
Answers: r = 3 and h = 6 are the radius and height respectively.
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Problem 10
d = diameter = 68 mm
r = radius = d/2 = 68/2 = 34 mm
SA = surface area of a sphere
SA = 4*pi*r^2
SA = 4*pi*34^2
SA = 4264pi
Answer: 4264pi square mm
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Problem 11
Plug V = 3000 into the sphere volume formula and isolate r.
V = (4/3)pi*r^3
3000 = (4/3)pi*r^3
(4/3)pi*r^3 = 3000
4pi*r^3 = 3*3000
4pi*r^3 = 9000
r^3 = 9000/(4pi)
r = cube root( 9000/(4pi) )
r = ( 9000/(4pi) )^(1/3)
r = 8.947002 approximately
Now we can determine the surface area of this sphere.
SA = 4pi*r^2
SA = 4*pi*( 8.947002 )^2
SA = 1005.923451
Answer: 1005.923451 square feet approximately
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Problem 12
We'll follow the same idea as problem 11, but in reverse.
SA = 4*pi*r^2
400pi = 4pi*r^2
r^2 = (400pi)/(4pi)
r^2 = 100
r = sqrt(100)
r = 10
Luckily we get a nice whole number for the radius r. Use it to find the volume.
V = (4/3)*pi*r^3
V = (4/3)*pi*10^3
V = (4000/3)pi
Answer: (4000/3)pi cubic inches exactly
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Problem 13
The diagram is missing. I don't have enough info to be able to answer.
Answer:
17.28in
Step-by-step explanation:
To find the area of a triangle, multiply the base by the perpendicular height (the length from the point opposite the base, to the base, which makes a 90-degree angle with the base), and half it:
7.2*4.8=34.56
34.56/2=17.28
<span>Their ratio bases off of 3:2. 3 representing the brother, 2 representing the sister.
I guess the way it works is that the brother is 1.5 times the sister's age, we can conclude that the sister's age can be represented by 'x' whereas the brother is represented as '1.5', together they ran a total of 300 yards, so we can use this to set up the problem:
</span>x + 1.5x = 300 - Now we add like terms:
2.5x = 300 - Divide.
<span>x = 120 - Of course upon adding that back in we just reroute back to only knowing how far they ran.
</span><span>The problem is this, we have no idea what the variable is to determine their ages, the ratio is 3:2, but... the only solutions I can think of are:
</span><span>If 10 yards = 1 Year of age(roughly) we have:
</span><span>18 = Brother
12 = Sister
If 20 yards = 1 Year of age(roughly) we have:
9 and 6.
</span><span>Regardless I can't say for certain what their ages are. :/</span>
