Answer:
A
Step-by-step explanation:
Answer:
Hotdog: $3.00
Hamburger: $4.00
Step-by-step explanation:
For the first time that Bob buys food, we can make an equation to find how much a single hotdog and a single hamburger costs, where:
x = cost of a hotdog
y = cost of a hamburger
He bought 2 hotdogs and 1 hamburger for $10, so the equation for his first time buying food is:
2x + y = 10
For the second time buying food, he bought 1 hotdog and 3 hamburgers for $15, so his equation would be:
x + 3y = 15
To find the value for x and y we need to solve this system of equations using the two equations we just came up with. We can do this multiple ways, but I'll be demonstrating the substitution method.
Using the second equation, we can solve for x by simply subtracting 3y from both sides:
x = 15 - 3y
We can then insert this value of x into the first equation so that way we are only dealing with one variable to solve - y:
2(15-3y) + y = 10
Distribute out the 2 into the paratheses, combine like terms, and then solve for y:
30 - 6y + y = 10
30 - 5y = 10
-5y = -20
y = 4
This means the cost for one hamburger is $4. But we still need to find the price of one hotdog, so we can insert this value of y into the equation we came up with earlier for x, and then solve for x:
x = 15 - 3y
x = 15 - 3(4)
x = 15 - 12
x = 3
So the price of one hotdog is $3 and the price of one hamburger is $4. Hope this helps.
The general equation for a circle,

, falls out of the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is always equal to the sum of the squares of its legs (you might have seen this fact written like

, where <em>a </em>and <em>b</em> are the legs of a right triangle and <em>c </em>is its hypotenuse. When we fix <em /><em>c</em> in place and let <em>a </em>and <em>b </em>vary (in a sense, at least; their values are still dependent on <em>c</em>), the shape swept out by all of those possible triangles is a circle - a shape defined by having all of its points equidistant from some center.
How do we modify this equation to shift the circle and change its radius, then? Well, if we want to change the radius, we simply have to change the hypotenuse of the triangle that's sweeping out the circle in the first place. The default for a circle is 1, but we're looking for a radius of 6, so our equation, in line with Pythagorus's, would look like

, or

.
Shifting the center of the circle is a bit of a longer story, but - at first counterintuitively - you can move a circle's center to the point (a,b) by altering the x and y portions of the equation to read:
Step-by-step explanation:
A. x²-x-10=0
is part of the solution process for solving this rational equation using the least common denominator
Answer:
The correct answer is 4.8 meters.
Step-by-step explanation:
Jamal stands on a dock 1.5 meters above the surface of the water.
A trout swims 4.8 meters below Jamal.
The trout must be swimming below the surface of water.
Therefore the distance below the surface of water where the trout is swimming is 4.8 - 1.5 = 3.5 meters.
But the vertical distance between Jamal and the trout is 4.8 meters only.