Use Pythagorean Theorem to solve for the

1 answer:

6 0

Pythagorean theorem is all about squaring the numbers. the equation is a^2+b^2=c^2
when you know two sides of the triangle, you fill in those spaces. they hypotenuse is ALWAYS ‘c’

to figure this problem out you put
a as 4
keep b as b since you don’t know what it is
c as 6

4 squared=16
6 squared=36

16+b^2=36
36-16=20
square root of 20 is 4.47

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Ninety six passengers rode a train. Tickets for regular coach seats are $114. Tickets for sleeper car seats are $295. The receip

MrRa [10]

C = amount of folks buying coach tickets
s = amount fo folks buying sleeper car tickets

we know the train had a total of 96 passengers, so, whatever "c" and "s" are
c + s = 96

we know all tickets sold for all 96 passengers was 19994, so, if "c" folks rode coach, each ticket is 114, thus 114*c is how much money was from couch, or 114c

if "s" folks rode the sleeper car, we know each ticket is 295 each, so 295*s is how much money was from the sleeper car

we also know, the total for all tickets is 19994

thus 114c + 295s = 19994

thus $\bf \begin{cases}
c+s=96\implies \boxed{s}=96-c\\
114c+295s = 19994\\
----------\\
114c+295\left( \boxed{96-c} \right)=19994
\end{cases}$

solve for "s", to see how many folks rode coach

what about the sleeper car? well, s = 96 - c

5 0

3 years ago

A rectangular deck has an area of 320 ft squared. The length of the deck is 4 feet longer than the width. Find the dimensions of

AnnyKZ [126]

So, the area of a rectangle is LxW. For this rectangle, LxW=320. We also know that the length is 4 feet longer than the width, that is L=W+4. With some substitution, we get(W+4)W=320. Simplify to get W^2+4w=320. Now the fun part! When we complete the square, we'll end up with (W+___)^2, right? So, let's take half of 4, which is 2, and square it. That's 4. Add that 4 to what we already have:W^2+4W+4. But remember, what we do to one side of an equation we must do to the other side. So we really have W^2+4W+4=320+4.We simplify and get W^2+4W+4=324. Factor the left side of the equation and get(W+2)^2=324. When we take the square root of both sides of the equation we getW+2=18, so W=16, which means the length (4 ft longer) is 20 ft. Do you have questions about the completing the square part? In a trinomial, the coefficient in the x term is the sum of the two factors and the constant term is the product. So, in the completing the square, you have the sum of a number added to itself or 2 times that factor. That's why we take half of it. Then, we square it to get the constant term. Square completed. But don't forget to keep the balance in the equation by also adding the constant term to the other side.

3 0

3 years ago

I went to the grocery store the other day and there were no price tags on anything! I bought 3 loaves of bread and 1 milk jug an

Lostsunrise [7]

To solve this problem, set up and solve a system of equations. The variables b and m will represent a bread loaf and milk jug, respectively:

$\left \{ {{3b + m = 9} \atop {b + 2m =5.5}} \right.$

I would solve using substitution. Take one of the equations and set it equal to one of the variables, for example:

$3b + m =9 \\ m = 9 -3b$

Now, plug this into the other equation for m and solve for b:

$b + 2m =5.5 \\ b + 2(9-3b)= 5.5 \\ b + 18 - 6b = 5.5 \\ -5b + 18 = 5.5 \\ -5b = -12.5 \\ b = 2.5$

We now know that a loaf of bread costs $2.50. Plug this value in for b in the first equation and solve for m:

$3b + m = 9 \\ 3(2.5) + m = 9 \\ 7.5+m = 9 \\ m = 1.5$

One jug of milk costs $1.50 and one loaf of bread costs $2.50.

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3 years ago

Find the length of the variable w

miss Akunina [59]

Answer:

w = 3

Step-by-step explanation:

Δ BDE and Δ BAC are similar, then the ratios of corresponding sides are equal, that is

$\frac{BD}{BA}$ = $\frac{DE}{AC}$ , substitute values