Using a system of equations, it is found that there are 5 dimes and 9 quarters in his pocket.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
- Variable x: number of dimes in his pocket.
- Variable y: number of quarters in his pocket.
He has a total of 14 coins, hence:
x + y = 14 -> y = 14 - x.
They are worth $2.75, hence, considering the value of each coin(dimes $0.1 and quarters $0.25), we have that:
0.1x + 0.25y = 2.75
Since y = 14 - x:
0.1x + 0.25(14 - x) = 2.75
x = (0.25*14 - 2.75)/0.15.
x = 5.
y = 14 - x = 14 - 5 = 9.
There are 5 dimes and 9 quarters in his pocket.
More can be learned about a system of equations at brainly.com/question/24342899
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Here is one way to solve for x.
Step 1) 2x^2-7=9
Step 2) 2x^2-7+7=9+7
Step 3) 2x^2=16
Step 4) (2x^2)/2=16/2
Step 5) x^2=8
Step 6) sqrt(x^2)=sqrt(8)
Step 7) |x|=sqrt(8)
Step 8) x=sqrt(8) or x=-sqrt(8)
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Below are explanations/reasons to each of the steps above.
Step 1) Original equation
Step 2) Add 7 to both sides
Step 3) Combine like terms
Step 4) Divide both sides by 2
Step 5) Simplify
Step 6) Apply the square root to both sides. The notation "sqrt" is shorthand for "square root"
Step 7) Use the rule that sqrt(x^2) = |x| for all real numbers x
Step 8) Use the rule that if |x| = k then x = k or x = -k for some fixed number k.
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The two solutions are
x = sqrt(8) or x = -sqrt(8)
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, so let's use the ones provided in that
let's notice, is negative since the population decreased.
Answer:
Perpendicular
Step-by-step explanation:
Put all the points on a graph.
Parallel means that the lines that have the same slope and different y-intercepts. Lines that are parallel to each other will never intersect.
On the graph we made we can see that the lines will have to intersect because the points are in positions that no matter which points we chose to connect together, they would intersect with the other line.
Answer:
b = 5
Step-by-step explanation:
if parallelogram is a rectangle, then the two diagonals has the same length
10/12 x(24/5 x b - 36/5) = 2/3 x (3b + 6)
4b - 6 = 2b + 4
2b = 10
b = 5
