9. AM ≅ AT
10. x=3, y=5
AH being the perpendicular bisector of MT means MH ≅ TH. Then ΔAHM ≅ ΔAHT by SAS, and by CPCTC.
... SAS — side-angle-side: if two adjacent sides and the included angle of a triangle are congruent to their corresponding sides and angles in another triangle, the two triangles are congruent.
... CPCTC — Corresponding Parts of Congruent Triangles are Congruent
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Using the result of problem 9 as a guide, you can say that ...
... 2x = x+3 ⇒ . . . . (subtract x from both sides)
... y +4 = 2y -1 ⇒ . . . . (add 1-y to both sides)
Answer:
W
Step-by-step explanation:
On the venn diagram, you can see that everything in the W section is a multiple of 7. Everything in the Z section is an even number and everything in Y(the middle section) is both an even number and a multiple of 7. Since 49 is a multiple of 7 but not an even number, it would go in the W section.
Answer:
<u>C. 16 7/18</u>
Step-by-step explanation:
First find the least common denominator for the fractions: 36
Change the fractions: 15 20/36 + 30/36
Add the fractions: 20/36+30/36=50/36
Turn into proper fraction: 16 14/36
Simplify: <u>16 7/18</u>
The number of possible ways to organize these books based on their number is 240.
<h3>What is the combination?</h3>
In math, this is the concept that describes the organization of a set of elements such as books, people, etc. This concept differs from permutation because in combination, the order does not matter.
<h3>What is the combination formula?</h3>
The genral formula is:
- nCr = n! / ((n – r)! r!) n
- n= total of elements
- r= elements to be used
But in this case, whe can use the n!.
Based on this, let's find out the total ways the books can be arranged:
- Math books: 5! = 5 x 4 x 3 x 2 x 1= 120
- Social studies books = 1! = 1
- Science books= 2! = 2 x 1 = 2
- 120 x 1 x 2 = 240 ways
Note: This question is incomplete; here is the complete question:
Tthere are 5 different math books, 1 social studies book, and 2 different science books on the shelf. how many different ways can the books be arranged if the books of each type must be together?
Learn more about combination in: brainly.com/question/20211959
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Answer:
2.96 = 2 96/100 = 2 24/25
