Answer:
4x^2 + 9x + 4 = 0
Using the quadratic formula:
x = [-9 +- sqrt(81 - (-64)] / 2 * 4
x = [-9 +- sqrt (145)] / 8
So, the solution is your second answer:
negative 9 plus or minus the square root of 145 divided by 8.
If the q is: are 4z2-22 and 4 equivalent expressions, the answer is No.
4z2-22=4
8z-22 is not equal to 4
If you are looking for value of z, then:
8z-22=4
8z=4+22
8z=26
z=26/8
z=13/4
In case in which z=13/4, than expression
4z2-22 would be equivalent to 4.
Hope this helped.
Answers:
- team one = 162
- team two = 108
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Explanation:
The ratio 3:2 scales up to 3x:2x for some positive whole number x.
This tells us that the first team has 3x people and the second team has 2x people. We'll subtract 12 from the first team and add 12 to the second team to represent 12 people moving.
- 3x becomes 3x-12
- 2x becomes 2x+12
The new team counts 3x-12 and 2x+12 represent team 1 and team 2. Those expressions are in the new proportion 5:4.
This means....
(team 1 new count)/(team 2 new count) = 5/4
(3x-12)/(2x+12) = 5/4
4(3x-12) = 5(2x+12)
12x-48 = 10x+60
12x-10x = 60+48
2x = 108
x = 108/2
x = 54
From this, we then can say:
- team 1 original count = 3x = 3*54 = 162
- team 2 original count = 2x = 2*54 = 108
The two subtotals add to 162+108 = 270 players overall.
If we were to subtract 12 from team 1, and add 12 to team 2, then,
- team 1 new count = 162-12 = 150
- team 2 new count = 108+12 = 120
The ratio 150:120 then reduces to 5:4 when we divide both parts by the GCF 30. This helps confirm we have the correct answer.
Answer:
(x-9)^2 +(y-12)^2 = 225
Step-by-step explanation:
First find the length of the radius
If is the distance from the center to the point
d = sqrt( (x2-x1)^2 + (y2-y1)^2 )
= sqrt( (0-9)^2 + (0-12)^2)
= sqrt ( 81+144)
= sqrt(225)
= 15
The equation for a circle is
( x-h) ^2+ (y-k)^2 = r^2
(x-9)^2 +(y-12)^2 = 15^2
(x-9)^2 +(y-12)^2 = 225
