The given equations are simultaneous equations. We need to find the values of 'a' and 'b'. To do so, we convert the ratio into equation and substitute into the original equation. Then solving will give 'a = 12' and 'b = 18'.
In this question, we are given two simultaneous equations to solve for the unknowns 'a' and 'b'. The given equations are 'a + b = 30' and the ratio 'a:b' is equivalent to '2:3'.
Since the ratio 'a:b' is equal to '2:3', we can consider 'a' to be '2x' and 'b' to be '3x'. Substituting this into the first equation, we get '2x + 3x = 30', which simplifies to '5x = 30'. Solving for 'x', we find that 'x = 6'.
Substituting 'x = 6' into the expressions for 'a' and 'b', we find that 'a = 2*6 = 12' and 'b = 3*6 = 18'. Therefore, the solutions to the equations are 'a = 12' and 'b = 18'.
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2 inches is equal to 5.08 centimeters
Hope this helps you. :-)
b) Explain why these expressions are not equal when $x=-\dfrac12.$
c) Show that these expressions are equal for all $x$ other than $-\dfrac12.$
In parts (a) and (c), begin by explaining what your strategy for solving will be.
Part (a) We shall simplify both of them in order to find the solution to the equation.
Part (b) When x=-1/2, the answers to the second expression, 2x2, change to -1, and we eventually arrive in 1.
Part (c) As we can see, the expressions are identical, thus we can demonstrate that they are equal if x is any number other than -1/2.
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Answer:
Part a) In order to solve the equation, we will simplify both of them. Once we do that, if we notice, they are the same equation, so therefore, if x=10, then we will be able to match the equation.
Part b) The reason the expressions are not equal when x=-1/2 is because if we see, that in the second expression, 2x^2, if x=-1/2, then the answer becomes -1, and we eventually end up with 1.
Part c) As we can see, the expressions are the same, so if x is any number other than -1/2, then we will be able to show that the expressions are equal.
Step-by-step explanation:
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By the way, this question is from the Art of Problem Solving, and you should not just copy answers or copy of them.
b. For a large family, is it possible that member would join for free? If so, which member would it be? Explain your reasoning.
c. Other than $0, what is the lowest amount that a member would pay to join? Which member would it be? Explain your reasoning.
a. If we subtract 75 from 550 twice, we get 400, which is the third member to join. Subtract 75 from 400, we get $325, the fourth member to join.
b. It is not possible that a member would join for free if it was a large family. 75 does not fit into 550 evenly. You can prove this by solving the expression 550÷75.
c. The lowest amount that a member would pay to join is $25.00. It would be the 7th member.
The answer is 1.25 meters.
hope it helps
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