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Maru [420]
3 years ago
13

A rectangle has an area of 30 square units and a perimeter of 34 meters.what are the dimensions of this rectangle

Mathematics
1 answer:
enyata [817]3 years ago
7 0
P=2L+2W
A=WL

Therefore, if P=34, and A=30, then let us find the factors of 30 that could give a sum of half of the perimeter which is 34. Therefore:

P=2*15+2*2
A=15*2

P=34
A=30

Therefore, the dimensions of this rectangle are 15 and 2.
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Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id
Thepotemich [5.8K]

\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

Explanation

\frac{1}{a+bi}=c+di

Step 1

multiplicate by the conjugate

\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}

notice that

\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\  \end{gathered}\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

I hope this helsp you

6 0
1 year ago
The cost of a taxi ride is represented by the function c(m)=2m+4, where m is the number of miles traveled. What is the cost per
galina1969 [7]

Answer:

cost per mile = $2.

Step-by-step explanation:

Given the cost function, c(m) = 2m + 4,

Where the m represents the number of miles traveled, and $2 is the cost per mile of the cab. The $4 represents the flat rate, a set fee, or the initial value.

Therefore, the cost per mile of the cab is $2.  

3 0
3 years ago
Need help with cross multiplying
saw5 [17]
So to solve for this, we need to set up proportional fractions, which I will help show you how to do.
First, if we are given an amount out of a total, we need to put it over x (if we are looking for the total). It looks like this:
12/x, 12 being the given number and x being the total.
If we are given the total but are looking for an amount, put the total at the bottom of the fraction (aka the denominator). It looks like this: x/16, 16 being the total amount and x being the amount out of the total.
We have a total of 40 test problems, so we can put our total at the bottom, x/40.
X is the amount of questions answered correctly (we are looking for x in the question).
We have answered 80% correct, so put 80% over 100 (100 being the total). It should look like this: 80/100.
Now we have our two fractions: x/40 & 80/100.
Set these up as an equation.
x/40 = 80/100.
Now this is where things may get tricky if you don't pay attention.
Multiply the numerator (the top number of a fraction) of x/40 by the denominator (the bottom number of a fraction) of 80/100.
Your product equation should look like this:
x times 100. This will give is 100x. Leave it at that.
Now, multiply the denominator of x/40 (the bottom number of the fraction) by the numerator (the top number of a fraction) of 80/100. It should look like this:
80 x 40. This will give us 3200.
Now set up our products as an equation.
100x = 3200.
To solve for x, divide both sides by 100.
3200/100 = 32.
x = 32.
I hope this helps and has taught you something!
4 0
3 years ago
How do i simplify (3/5 - 1) / 1 2/3?
Tpy6a [65]
I hope this helps you

4 0
3 years ago
The prism below is made of cubes which measure 1/4 of an inch on one side. What is volume
choli [55]
Volume of cube=side length cubed

1/4^3=0.015625in^3
4 0
4 years ago
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