Let's call the two numbers x and y. We can write a system of equations to describe the situation:
5x = 8y
x - y = 150
Let's solve the first equation for x:
x = 8y/5
Now we can use substitution to solve the system by plugging 8y/5 in for x in the second equation:
(8y/5) - y = 150
Simplify:
3y/5 = 150
3y = 750
y = 250
If y = 250, then x is:
x = 8(250)/5 = 400
The answer is 250 and 400.
Answer:
The system if equation that can be used to derive this are
6x + 4y = 69 AND
12x + y = 96
The price of a drink is $7.5
Step-by-step explanation:
The question here says that Taylor and Nora went to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks and 4 bags of popcorn Nora spends a total of $96.00 on 12 drinks and bag of popcorn.And we are now told to write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations,we should determine and state the price of a drink, to the nearest cent .
Now, Let's assume that the price of a drink is "X" and that of a bag of popcorn to be Y
The first person made a purchase which led to the equation
6x + 4y = 69______ equation 1
And the second person also made a purchase that lead to the equation
12x + y = 96_____ equation 2
We make y the subject of the formula in equation 2 and apply it in 1
Y = 96 - 12x
Now apply the above in equation 1
6x + 4y = 69
6x + 4(96 - 12x)= 69
6x + 384 - 48x = 69
42x = 384 - 69
X = 315/42
X = 7.5
Substitute x= 7.5 in equation 2
12x + y = 96
12(7.5) + y = 96
90 + y = 96
Y = 6
Therefore, the price of a drink is $7.5
Explanation
Step 1
We know that the general equation for a circle is
where
(h,k) is the center of the circel
and r is the radius
then, all we need to do is replace
Let
replace the values
therefore, the answer is
I hope this helps you
Answer:
He won 6 games and lost 24 games.
Answer:
System A has 4 real solutions.
System B has 0 real solutions.
System C has 2 real solutions
Step-by-step explanation:
System A:
x^2 + y^2 = 17 eq(1)
y = -1/2x eq(2)
Putting value of y in eq(1)
x^2 +(-1/2x)^2 = 17
x^2 + 1/4x^2 = 17
5x^2/4 -17 =0
Using quadratic formula:
a = 5/4, b =0 and c = -17
Finding value of y:
y = -1/2x
System A has 4 real solutions.
System B
y = x^2 -7x + 10 eq(1)
y = -6x + 5 eq(2)
Putting value of y of eq(2) in eq(1)
-6x + 5 = x^2 -7x + 10
=> x^2 -7x +6x +10 -5 = 0
x^2 -x +5 = 0
Using quadratic formula:
a= 1, b =-1 and c =5
Finding value of y:
y = -6x + 5
y = -6(\frac{1\pm\sqrt{19}i}{2})+5
Since terms containing i are complex numbers, so System B has no real solutions.
System B has 0 real solutions.
System C
y = -2x^2 + 9 eq(1)
8x - y = -17 eq(2)
Putting value of y in eq(2)
8x - (-2x^2+9) = -17
8x +2x^2-9 +17 = 0
2x^2 + 8x + 8 = 0
2x^2 +4x + 4x + 8 = 0
2x (x+2) +4 (x+2) = 0
(x+2)(2x+4) =0
x+2 = 0 and 2x + 4 =0
x = -2 and 2x = -4
x =-2 and x = -2
So, x = -2
Now, finding value of y:
8x - y = -17
8(-2) - y = -17
-16 -y = -17
-y = -17 + 16
-y = -1
y = 1
So, x= -2 and y = 1
System C has 2 real solutions