Answer:
To add fractions, find the LCD (Least Common Denominator) or any common denominator of the fractions. For example, if you wanted to add 1/3+2/7, you find the LCD, which is 21, because 3x7=21, and 3 and 7 are both prime numbers. Now each fraction will have denominators of 21, so we will get 7/21+6/21. To add them together, add the numerators to get 13/21. Find the least common denominator of two fractions and then add the numerators. Hope it helps!
Step-by-step explanation:
A system of equations that could be used to determine the number of dimes and the number of quarters are:
<h3>What is an equation?</h3>
An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
<h3>What is a system of equations?</h3>
A system of equations can be defined an algebraic equation that only has two (2) variables and can be solved simultaneously.
In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
- Let d represent the number of dimes.
- Let q represent number of quarters.
<u>Note:</u> 1 quarter is equal to 0.25 dollar and 1 dime is equal to 0.1 dollar.
q = 2d ......equation 1.
0.25q + 0.1d = 4.20 .......equation 2.
Multiplying eqn. 2 by 100, we have:
25q + 10d = 420 .......equation 3.
Substituting eqn. 1 into eqn. 3, we have:
25(2d) + 10d = 420
50d + 10d = 420
60d = 420
d = 420/60
d = 7 dime.
For the number of quarters, we have:
q = 2d
q = 2(7)
q = 14 quarter.
Read more on equations here: brainly.com/question/1511173
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Complete Question:
Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters as dimes. Write a system of equations that could be used to determine the number of dimes and the number of quarters that Sophie has. Define the variables that you use to write the system.
<h3>
Answer: C) 3</h3>
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Explanation:
f(x) is the outer function, so the final output -8 corresponds to f(x)
We see that f(-4) = -8 in the first column of the table. I'm starting with the output and working my way backward to get the input. So we started with -8 and worked back to -4.
Then we move to the g(x) function to follow the same pattern: start with the output and move to the input. We start at -4 in the g(x) bubble and move to 3 in the x bubble.
In short, g(3) = -4
So,
f(g(x)) = f(g(3)) = f(-4) = -8
We see that x = 3 leads to f(g(x)) = -8
Answer:
t ≤ 4.24
Step-by-step explanation:
P(t) ≥ 40000 implies
500t/(2t²+9) ≥ 40000
Multiplying through by t², we have
500t ≥ 40000(2t²+9)
500t/40000 ≥ 2t²+9
Collecting like terms
0.0125t ≥ 2t²+9
0 ≥ 2t²+ 9 - 0.0125t
2t²+ 9 - 0.0125t ≤ 0
2t²- 0.0125t + 9 ≤ 0
Using the quadratic formula,
The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)
So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0
(t - 0.00313)² - 4.24² ≤ 0
(t - 0.00313)² ≤ 4.24²
taking square-root of both sides,
√(t - 0.00313)² ≤ √4.24²
t - 0.00313 ≤ 4.24
t ≤ 4.24 + 0.00313
t ≤ 4.24313 ≅ 4.24
t ≤ 4.24
Answer:
k=8/3
Step-by-step explanation:
Let's solve your equation step-by-step.
4k+7=7k−1
Step 1: Subtract 7k from both sides.
4k+7−7k=7k−1−7k
−3k+7=−1
Step 2: Subtract 7 from both sides.
−3k+7−7=−1−7
−3k=−8
Step 3: Divide both sides by -3.
−3k
−3
=
−8
−3
k=
8
3