Answer:
35 hotdogs
Step-by-step explanation:
You are running a concession stand at a basketball game. You are selling hotdogs and sodas.
Let the number of hot dogs be represented by x
The number of soda be represented by y
You sold a total of 87 hotdogs and sodas combined
x + y = 87
x = 87 - y
Each hotdog cost $1.50 and each soda cost $0.50. At the end of the night you made a total of $78.50.
Hence we have the equation:
$1.50 × x + $0.50 × y = $78.50
1.50x + 0.50y = 78.50
Substitute 87 - y for x
1.50(87 - y) + 0.50y = 78.50
130.5 - 1.50y + 0.50y = 78.50
Collect like terms
- 1.50y + 0.50y = 78.50 - 130.50
-1.00y = -52
y = -52/-1
y = 52 sodas
How many hotdogs did you sell?
Using the equation:
x = 87 - y
x = 87 - 52
x = 35 hotdogs
Hence, you sold 35 hotdogs
Answer:
650%
Step-by-step explanation:
First, you need to rewrite the expression into binomial form, so you are working with two terms (as you world with a quadratic):
(x²)²-3(x²)-4=0
Now, you can place the x²s into brackets as the coefficient is now 1:
(x² )(x² )
Next, find out two numbers that add together to give you -3 and multiply to give -4 (these are the leftover integers after removing the x²s). These two numbers are -4 and 1.
Place the -4 and 1 into the brackets:
(x²-4)(x²+1)=0
Notice that the x²-4 is a difference of two squares, so can be further factorised into (x+2)(x-2)
This leaves you with a final factorisation of:
(x+2)(x-2)(x²+1)=0
Now we handle each bracket individually to obtain our four solutions for x:
x+2=0
x=-2
x-2=0
x=2
x²+1=0
x²=1
x=<span>±1</span>
<u>Answer:</u>
Amount collected in 2012 = 3.49
and in 2013 = 3.35
<u>Explanation:</u>
Let x be the baggage fees collected in 2013 and
y be the baggage fees collected by airlines in 2012
From the given question we can obtain two equations as follows:
x + y = 6.84 $ - eq 1
and
y = 0.14 + x
as fees in 2012 exceeds that in 2013 by 0.14$
Now, solving these two equations by substitution,
we substitute y = 0.14 + x in eq 1
and solve for x,
which gives us x = 3.35 and
substituting this value in eq 1
we get y = 3.49
Answer:
2√137
Step-by-step explanation:
To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:
22² + 8² = c²
484 + 64 = c²
548 = c²
c = ± √548 = ± 2√137
c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.
