Suppose 0: G-→ G be a homomorphism of groups. Show that: (i) Kere is normal in G (ii) The mappping o: G/ Ker0 →0(G) defined by þ(gKer0) = 0(g) is an isomorphism of groups.

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You fill a box with 6 more apples than pears. Create an equation that represents the number of fruit inside the box. First label the unknowns: Let a be the number of apples in the box. Let p be the number of pears.

ww 5. Laura cuts 64 inches of ribbon into two parts and gives her mom one part. Laura's part is 28 inches long. Her mom cuts her ribbon into 6 equal pieces. How long is one of her mom's pieces of ribbon?

Determine whether x=3, x=4, or x=5 is the solution. 8x=328x=32

2. Jake swims for 12 minutes before school. He swims for x more minutes after school. Write an algebraic equation that represents the total number of minutes, y, that Jake read. Enter your answer: 12 + x =y

Joel brought a sum of money for his trip. On the first day, he spent 1/4 of his money and misplaced $4. On the second day, he spent 1/4 of his money on 2 identical boxes of tea leaves. On the third day, he decided to buy another 5 boxes of tea leaves. He had $6.40 left in the end. How much money did he have at first? Djemekekekek