Answer:
3/4*10/1=7.5
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Answer: Yes (5, 50) is a solution
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Explanation:
The point (5, 50) means x = 5 and y = 50 pair up together.
Plug those values into the first equation and simplify both sides as much as possible. This is so we have one number on each side.
y = 5x+25
50 = 5*5+25
50 = 25+25
50 = 50
Because we ended up with a true statement at the end, this makes the original equation y = 5x+25 to be true when (x,y) = (5,50).
In other words, the first equation has been confirmed.
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Repeat those steps for the second equation
y = 3x+35
50 = 3*5+35
50 = 15+35
50 = 50
We get another true statement, and we've confirmed the second equation.
Both equations are true when (x,y) = (5, 50)
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This fully confirms that (5, 50) is indeed a solution to this system.
It turns out it's the only solution. Visually we can verify this by looking at the graph. The two lines intersect at one location and it is (5, 50).
See below.
For this case, the first thing we must do is define variables.
We have then:
t: the time in minutes
k: the number of kilometers
The relationship between both variables is direct.
Therefore, the function is:
Where, "c" is a constant of proportionality.
To determine "c" we use the following data:
After running for 18 minutes, she completes 2 kilometers.
Substituting values:
Clearing c we have:
Then, the equation is given by:
Answer:
An equation that can be used to represent k, the number of kilometers Julissa runs in t minutes is:
Answer:
-4
Step-by-step explanation:
x³ + cx + 4 divided by x + 2 has a remainder of 4, so:
(x³ + cx + 4) / (x + 2) = ax² + bx + d + 4 / (x + 2)
Multiply both sides by x + 2:
x³ + cx + 4 = (ax² + bx + d) (x + 2) + 4
Distribute:
x³ + cx + 4 = ax²(x + 2) + bx(x + 2) + d(x + 2) + 4
x³ + cx + 4 = ax³ + 2ax² + bx² + 2bx + dx + 2d + 4
x³ + cx + 4 = ax³ + (2a + b)x² + (2b + d)x + 2d + 4
Match the coefficients.
a = 1
2a + b = 0
2b + d = c
2d + 4 = 4
Solving, a = 1, b = -2, and d = 0. So c = -4.
We can also solve this using long division (see picture).
