The solution to the system of equations is x = 8, y = 4.
<h3>
How to write the system of equations?</h3>
First, let's define our variables as x and y.
"the sum of two numbers is twelve" is written as:
x + y = 12
"two times the first number minus three times the second number is four" is written as:
2x - 3y = 4
Then the system of equations is:
x + y = 12
2x - 3y = 4
<h3>How to solve it?</h3>
First, we isolate one of the variables in one equation, I will isolate x on the first one to get:
x = 12 - y
Now we replace this on the other equation, so we get:
2*(12 - y) - 3y = 4
Now we can solve this for y.
24 - 2y - 3y = 4
24 - 5y = 4
24 - 4 = 5y
20/5 = y = 4
Now we know the value of y, and:
x = 12 - y = 12 - 4 = 8
Then the solution of the system is:
x = 8, y = 4.
If you want to learn more about systems of equations, you can read:
brainly.com/question/13729904
Answer:
There are 36 blueberries and 12 Strawberries! I hope this helps you out. :)
Step-by-step explanation:
Hi, so I have a really easy way for you to do this and understand! :)
Basically, you can just add the two numbers in the ratio together and divide that from the bigger total. For example, 9+3=12 and 48/12 is 4. Then you can just multiply each beginning ratio by four and you have your answer: 9*4=36 and 3*4 equals 12. An what does 12+36 equal? 48.
You have the correct answer. Nice work. If you need to see the steps, then see below
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First we need to find the midpoint of H and I
The x coordinates of the two points are -4 and 2. They add to -4+2 = -2 and then cut that in half to get -1
Do the same for the y coordinates: 2+4 = 6 which cuts in half to get 3
So the midpoint of H and I is (-1,3). The perpendicular bisector will go through this midpoint
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Now we must find the slope of segment HI
H = (-4,2) = (x1,y1)
I = (2,4) = (x2,y2)
m = (y2 - y1)/(x2 - x1)
m = (4 - 2)/(2 - (-4))
m = (4 - 2)/(2 + 4)
m = 2/6
m = 1/3
Flip the fraction to get 1/3 ---> 3/1 = 3
Then flip the sign: +3 ----> -3
So the slope of the perpendicular bisector is -3
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Use m = -3 which is the slope we found
and (x,y) = (-1,3), which is the midpoint found earlier
to get the following
y = mx+b
3 = -3*(-1)+b
3 = 3+b
3-3 = 3+b-3
0 = b
b = 0
So if m = -3 and b = 0, then y = mx+b turns into y = -3x+0 and it simplifies to y = -3x
So that confirms you have the right answer. I've also used GeoGebra to help confirm the answer (see attached)
Answer:
18
Step-by-step explanation:
since there are 9 liters and three days, you double the amount of days to get 6, so you do the same to the amount of liter she makes. so 18 liters of jam
The diagonals of a kite meet at a right angle.