zach has akready baked cakes, and he can bake 1 cake with each additional stick of butter he buys, how many additional sticks of
1 answer:
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Step-by-step explanation:
1. making the equation:
shoes = x
shirts = y
175 = x + 3y
x = 4y
2. graph it (I'm using desmos)
the green line is for 175 = x + 3y and the purple one is for x = 4y
3. find the price
x = 4y
175 = 4y + 3y
175 = 7y
y = 175/7 = $25
price of the shirt = $25
x = 4y = 4*25 = $100
price of a pair of shoes = $100
Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
Answer: 3.217 & 12.434
Step-by-step explanation:
If we use <em>w</em> to represent the width, the length will be 6 more than 2 times w.
Hence, the length is .
The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.
We can also substitute 40 in for A as it's given in the question.
Distributing <em>w</em> by multiplying it by both terms in the parentheses, we get
We can make the equation simpler by dividing both sides by 2.
Subtracting both sides by 20 will make the left-hand side 0.
Now that we have put this <em>quadratic equation</em> into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.
For reference, the quadratic formula is
In this case, a is 1, b is 3, and c is -20.
Substituting, we get
Since the second solution results in a negative number, it cannot be the length of w.
The width/breadth of the rectangle is 3.217 cm.
To calculate the length, let's substitute the width into the expression for the length:
The length of this rectangle is 12.434 cm.