We are learning about multiplying integers.
1. A hot air balloon is descending at a rate of 350m/min. How much higher was the balloon five minutes ago??
2. The sum of 2 integers is -1.Their product is -12. What are the integers??
How would i figure these out?? plz help :) thanks.
1. If it falls 350 meters for every minute that passes, that means it must have fallen 350*5= 1,750 meters after 5 minutes had passed. So the answer is 1,750 meters higher.
2. Just represent the unknown numbers with letters so you can solve for them. That's what algebra's all about. So we'll call the unknown numbers x and y.
We know that when you add them, you get -1, and when you multiply them, you get -12. So we have:
x+y=-1
x*y=-12
You can solve for y in terms of x in one equation and plug that in for the y in another equation to find what number x represents. Once we know x, we can easily find y using either equation. So:
SOLVE FOR y IN TERMS OF x
y=-x-1
PLUG IT INTO SECOND EQUATION
x*(-x-1)=-12
SOLVE FOR x:
-x^2-x=-12
-x^2-x+12
-(x+4)(x-3)
So x must be either -4 or 3
SOLVE FOR y:
We know that y is -x-1. We know that x is either -4 or 3. So:
-(-4)-1 = 3 = y
-(3)-4 = -4 = y
So y, too, can be either -4 or 3.
Therefore, the integers are -4 and 3, as their sum is -1 and their product is -12.
ths so much!! what would the two integers be for this one??
the sum = +2
the product = -12
and i gotta nother question :)
One amaze day, the outside temperature was cold. I mean, like -3 degrees celcius cold!!!! Then, later, the outisde temperature ended up THREE TIMES COLDER!!! I know, omg. SO what would the new temperature be?? :)
hello?????? plz help, thx :)
-3*3 is the same as 3*3 with a negative sign in front.
-3*3 = -9
So the new temperature would be -9 degrees Celsius.
the sum = +2
the product = -12
Use the same process I used for the second question. Remember to represent unknown numbers with letters and use algebra to solve them.
thanks sooo much i really apreciate it:)
To solve these problems, you need to understand the rules of multiplying integers and solving equations. Let's go through each question step-by-step:
1. A hot air balloon is descending at a rate of 350m/min. How much higher was the balloon five minutes ago?
To solve this, you need to find the total change in height. Since the balloon is descending, the change in height will be negative. To find the answer, you can multiply the rate of descent (-350m/min) by the number of minutes.
Formula: Change in Height = Rate of Descent x Time
In this case, we have: Change in Height = -350m/min x 5 min
By multiplying -350m/min by 5 min, you get -1750m. Therefore, the balloon was 1750 meters higher five minutes ago.
2. The sum of 2 integers is -1. Their product is -12. What are the integers?
To solve this, you need to set up a system of equations. Let's call the two integers x and y.
Given: x + y = -1 (sum of the two integers)
x * y = -12 (product of the two integers)
Now, you can solve this system of equations using different methods, such as substitution or elimination. Here, we'll use the substitution method.
From the first equation, we can express x in terms of y by rewriting it as x = -1 - y.
Substituting this value into the second equation, we get (-1 - y) * y = -12.
Expanding and rearranging, we have -y^2 - y - 12 = 0.
Now, you can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. By factoring, the equation can be rewritten as (y + 3)(y - 4) = 0.
By setting each factor to zero, we get y + 3 = 0 or y - 4 = 0.
From y + 3 = 0, we find y = -3. From y - 4 = 0, we find y = 4.
So the two integer solutions are: x = -1 - y, which gives x = -1 - (-3) = 2 when y = -3, and x = -1 - y, which gives x = -1 - 4 = -5 when y = 4.
Therefore, the two integers are 2 and -3, or -5 and 4.
In summary, to solve these multiplying integers problems:
1. Multiply the rate of change by the time to find the total change.
2. Set up a system of equations using the given information and solve for the unknowns using methods such as substitution, elimination, factoring, or the quadratic formula.