A: 2x + 8y = 5 B: x + 9y = 10 To solve this system of equations by elimination, what could you multiply equation B by if you wan
1 answer:
You might be interested in
<h3>Answer: 12</h3>
==============================================================
Explanation:
The two integers multiply to 36, so,
ab = 36
which solves to
a = 36/b
Then we want to add the numbers such that we get the smallest possible result.
a+b = (36/b)+b
So we want (36/b)+b to be as small as possible.
Let's say we replace b with x and we consider this function
f(x) = (36/x) + x
The goal is to find when f(x) is smallest, ie, we want to minimize the function.
If we were to graph out the function, we get the curve shown below.
To make things easier, we'll only focus on positive values of x.
The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.
So the input x = 6 leads to the smallest output f(x) = 12.
This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.
In short, a = 6 and b = 6.
----------------------
As a check,
a*b = 6*6 = 36
a+b = 6+6 = 12
We can make a table of various values to help confirm that 12 is the smallest sum.
Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.
Answer:
The least number of stamps required is
Step-by-step explanation:
Let the number of cent stamps be
and
cent stamps be
We have
The minimum number is obtained when more cent stamps are used
Here cannot be greater than
since
Substitute
Not possible since is not a fraction
Substitute
Not possible since is not a fraction
Substitute
Possible
Hence minimum number of stamps is
The length of the ramp is 61 feet.
<h3>What is the length of the ramp?</h3>In order to determine the length of the ramp, Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
√11² + 60²
√121 + 3600
√3721
= 61 feet
Please find attached the image of the ramp. To learn more about Pythagoras theorem, please check: brainly.com/question/14580675
Answer:
x=5
y=4
Step-by-step explanation:
Step 1:
Let us solve for <em>x</em> using the equation by <u>isolating terms containing the variable</u>:
Great! <em>x</em> is 5... let's find <em>y</em>.
Step 2:
Since we know the value of <em>x</em>, we can use what we know to find <em>y</em> using the <u>other equation</u>:
<em>Given that x=5, we can </em><u><em>replace</em></u><em> x with 5</em>.
<em>I hope this helps! Let me know if you have any questions :)</em>