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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Answer: See explanation
Step-by-step explanation:
By the Triangle Inequality Theorem, the length of the side must be greater than 1 ft because the sum of two side lengths must be greater than the length of the third side. The third side must be less than 7 ft but greater than 1 ft.
Triangle inequality: 1 < x < 7
Hope that helped!
Answer:
The effect of doubling all the dimensions of a triangular pyramid will have on the volume of the pyramid is to increase it by 8 times.
Step-by-step explanation:
i) volume of triangular pyramid = 
Area height
= (Base of triangle perpendicular height of triangle) height
ii) if we double all the dimensions then the three variables((Base of triangle, perpendicular height of triangle, height of pyramid) will be doubled
and the volume of the new pyramid will be 8 times that of the original one.
That would be 400 / 28 = 14.29 gallons to nearest hundredth
Answer:
Step-by-step explanation:
Step 1: Convert into improper fractions
Step 2: Find least common denominator and find equivalent fractions
Step 3 : Do the required operation
Least common denominator of 2 , 4 = 4
