The <em><u>correct answers</u></em> are:
A-theorem
; B-corollary
; C-Postulate
; and E-Definition.
Explanation:
In a proof, we are tasked with proving one statement using other information that has already been proven.
Theorems are statements that have already been proven, and are used to prove other statements.
A postulate is a statement that is assumed to be true, and is used to prove other statements.
A corollary is a direct consequence of a proven fact, and as such, are used to prove other statements.
A definition is an absolute truth, so it can also be used to prove another statement.
Answer:
18
Step-by-step explanation:
Take a breath :) . I've got your back.
If she caught 6 carp + 8 bass + 7 catfish, she caught 6 +8 +7 fish total = 21.
7 of 21 were catfish.
If she catches 54 fish instead of 21, (and we have to assume the ratio stays the same), how many will be catfish?
Ratios are 7:21 and x:54, but we'll write them as fractions:
7/21 = x/54
Then cross multiply:
21x = (54)(7)
21x = 378
divide both sides by 21
x = 18
If she catches 54 fish total, we predict she will catch 18 catfish.
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If we go back to the original 7/21, we can reduce that to 1/3. Then ask what is 1/3 of 54? 18.
Answer:
The number of penguins on the island is 17 and the number of bears on the island is 4.
Step-by-step explanation:
We are given that an island's only residents are penguins and bears, and if there are 21 heads and 50 feet on the island.
Let the number of penguins on the island be 'x' and the number of bears on the island be 'y'.
Also, we know that bears and penguins both have one head, and the bear has 4 feet and the penguin has 2 feet.
<u>So, according to the question;</u>
- The first condition states that there are 21 heads, that means;
x + y = 21
x = 21 - y ---------------- [equation 1]
- The second condition states that there are 50 feet on the island, that means;
2x + 4y = 50
x + 2y = 25
21 - y + 2y = 25 {from equation 1}
y = 25 - 21
y = 4
Now, putting the value of y in equation 1, we get;
x = 21 - y
x = 21 - 4 = 17
Hence, the number of penguins on the island is 17 and the number of bears on the island is 4.
Answer:

Step-by-step explanation:
Hi there!
Let
represent "the number".
A number added by 7 is the same as that number times four minus eleven.
A number added by 7 ⇒ 
Is the same as ⇒ 
The number times four ⇒ 
Minus eleven ⇒ 
I hope this helps!