Given the quadratic equation ax²-5b+4a=0, where a and b are constants has two real an equal roots,find a:b
Answers
Answer:
Therefore either a:b = 5:4 or a:b=-5:4
Step-by-step explanation:
ax²-5bx+4a=0
Since the quadratic equation has two real root.
Then b²-4ac>0
Here a= a , b= -5b and c=4a
∴(-5b)²-4.a.4a=0
⇔25b²=16a²
⇔5b=±4a
Therefore either a:b = 5:4 or a:b=-5:4
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Answers
-(sqrt(16)) is rational. It can be expressed as -4/1.
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Have a nice day!
2.876 is rational
-√16 is rational
3
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Please answer this math question!
Answers
(a): The original perimeter is 2(x+y), but the new one is 2(2x+2y). This is twice the original perimeter, so it is 18*2=36.
(b): The original area is xy, and the new one is (2x)(2y), or 4xy. This is four times the original area, or 20*4=80.
(c): As it's given that the side lengths are integers, the intended solution is most likely to divide by 2 in the perimeter to see that the sum of the side-lengths is 9 and their product is 20. Guessing/checking values for each side, we see that 4 and 5 work for the smaller rectangle. Multiplying by two, the larger one has lengths 8 and 10.
Alternatively, we set them to x and y and use the equations:
x+y=9
xy=20
Dividing by y, we see that x=20/y. Substituting, we have that y+20/y=9. Subtracting 9 and multiplying by y, we have:
y^2-9y=20
Factoring, we have (y-5)(y-4)=0. The solutions to this equation are 4 and 5, which result in x=5, y=4 or x=4, y=5 respectively. Thus, we see that 4 and 5 are the side-lengths. Note that this solution did not require the assumption that the side-lengths are integers!
Answers
-all their options are sandwiches, and they all cost 5 dollars.
-This means that they can buy 150/5=30 sandwiches. This will make them use the entire budget!
-I would suggest cutting the sandwiches in half, then everyone gets three halves!
and if you say r for roast beef and t for tuna, you can write:
r+t=30.
and you can distribute is freely as long as both are 0 or bigger and their sum is 30!
Answer:
D.The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
Step-by-step explanation:
Answers
Answer:
The value of x is 6
Step-by-step explanation:
we know that
If two angles are supplementary, then their sum is equal to 180 degrees
so
In this problem
m∠C+m∠E=180°
we have
m∠C=112°
m∠E=(3x+50)°
substitute and solve for x
112°+(3x+50)°=180°
3x+162=180
3x=180-162
3x=18
x=6
Answers
Then -3*-1=3
-3*0=0
-3*1=-3
-3*2=-6
The solution to the inequality is -1
Answers
The solution is 4.
The number of bratwursts, you can buy from $18 is 4.
What is inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
A bratwurst costs $4.50 at a softballgame.
And you have a total of $18 to spend.
Let n be the number of bratwursts, you can buy.
So, the inequality that represents the situation is,
4.5n ≤ 18
Divide the inequality by 4.5 into both sides,
we get,
n ≤ 18/4.5
n ≤ 4
n = 4.
Therefore, the number of bratwursts is 4.
To learn more about inequality;
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