Can anyone that’s good in math do this problem for me
Use the number line below, where RS=8y+4, ST=2y+4, and RT=58.
a. What is the value of y?
b. Find RS and ST.
Answers
The value of y is 58 and RS is 55.25 and ST is 17.5.
What is Equation?Equation is an expression that consists of variables, constants, and operators, and expresses a relationship between them. It is a mathematical statement that two expressions are equal. Equations can be used to solve a wide variety of problems in mathematics, science, engineering, and other fields. Examples of equations include the Pythagorean Theorem, the equation of a circle, and the equation of a line. Equations can be written in a variety of forms, such as symbolic, graphical, and numerical.
The value of y can be found by solving the equation 8y+4=58. By subtracting 4 from both sides, we get 8y=54.
Dividing both sides by 8, we get y=6.75.
Therefore, RS=8y+4=8(6.75)+4=55.25 and
ST=2y+4=2(6.75)+4=17.5.
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someone please help me on this
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There are many ways to prove this, this is just how I do it. Hope it helps.
n(U) = 147, n(A) = 48, n(B) = 68, n(A ∩ B) = 19, n(A ∩ C) = 22, n(A ∩ B ∩ C) = 10, n(A' ∩ B ∩ C') = 39, and n(A' ∩ B' ∩ C') = 36.
Find n(C).
A) 26
B) 14
C) 30
D) 46
Answers
Answer: D) 46
===========================================================
Explanation:
We have these 8 given facts
N(U) = 147n(A) = 48n(B) = 68n(A ∩ B) = 19n(A ∩ C) = 22n(A ∩ B ∩ C) = 10n(A' ∩ B ∩ C') = 39n(A' ∩ B' ∩ C') = 36Draw out a rectangle to represent the universal set U. Inside this rectangle, draw three overlapping circles. Refer to the diagram below (imagine that none of the values have been written down just yet). These circles are A, B, and C.
Now we'll focus on the 8 facts above. To start off, we'll look at fact 6 which says n(A ∩ B ∩ C) = 10. This means there are 10 items inside all three sets. This is the middle most region where all three circles overlap with one another.
Then move to fact 4 and we see that 19 items are in sets A and B at the same time. Subtract off those 10 items in all three sets and we have 19-10 = 9 items in set A and B, but not set C. We can write this as n(A ∩ B ∩ C') = 9 if you wanted to stay consistent with this math notation. Write "9" in the overlapped region between A and B, but not inside circle C.
Now go to fact 5. We have n(A ∩ C) = 22 telling us there are 22 items in both sets A and C at the same time. Subtract off the 10 in all three sets and we're left with 22-10 = 12 items in set A and set C, but not set B. We can write this as n(A ∩ B' ∩ C) = 12. Write "12" in the region between A and C, but outside of circle B.
If you're stuck anywhere, refer to the diagram below. Imagine that not all of the values have been filled in just yet.
---------------------------
So far you should have the numbers 10, 9 and 12 written in those positions I mentioned. Circle A is mostly filled out. We're missing the region that's inside A but outside both B and C; however, we can find that to be 17. Why is this? Well because n(A) = 48 and the other values (10, 9 and 12) add to 10+9+12 = 31. Then note how 31+17 = 48. So we must have 17 items in circle A but outside the other circles. We can write this as n(A ∩ B' ∩ C') = 17
In short, all of the values in circle A must add to 48. We have 17+10+9+12 = 48.
From fact 7, we can see that n(A' ∩ B ∩ C') = 39 meaning there are 39 items in circle B and not in any other circle. So we'll fill this value in as well.
The last value to fill in is the 36 from fact 8. This goes outside all of the circles.
The venn diagram below shows all of these values filled in that I mentioned so far. The missing two blank regions in circle C can be thought of as one region for the sake of simplicity.
---------------------------
Using that diagram of filled in values, add up every number written down:
17+9+39+12+10+36 = 123
We have 123 items so far in the universal set
We're told that n(U) = 147, meaning there are 147 items total in the universal set.
This must mean that 147-123 = 24 items are in the two blank regions of circle C. We don't need to break down how the 24 splits up.
That 24 adds to the other numbers inside circle C to get to the final answer
12+10+24 = 46
Choice D is the answer.
Side note: you could use n(B) = 68 to help break down those two blank regions of circle C, but that's just unnecessary extra work.
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Hello! :) have a good day!
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Given data ,
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