So these are basically isolating the variables.
The first equation is 3g + 5 =17.
In order to isolate the variable, we would have to get g by itself, that means 5 would have to go. In order to do this, we would do the opposite. Since it is positive 5 we would add negative 5, in order for it to disappear. This works because a positive 5 and negative 5 cancel each other out. Whatever you do to one side of the equation you have to do to the other, since we subtract 5 on one side we have to subtract 5 on the other. Therefore we would do 17-5.
Now we have 3g=12
We know that 3g is basically 3 multiplied by g. The opposite of multiplication is division.Therefore we would divide by 3 on both sides.
The answer to the first question would be g= 4.
And if you want to check if your answer is correct you plug the value in.
So
3(4) + 5 =17
Answer:
15 (rounded) 14.7 (not rounded)
Step-by-step explanation:
Answer:
shorter leg = 21 ft
longer leg = 28 ft
hypotenuse = 35 ft
Step-by-step explanation:
Let's call the longer leg of the triangle "b", the shorter leg "a", and the hypotenuse "h"
Then we have the following two equations:
a = b - 7
h = b + 7
And we can use the Pythagorean theorem to relate all three sides of the triangle:
Therefore there are two possible solutions to this equation: b = 0 or b = 28 ft.
So we take the one that is different from zero (since we are looking for the side of a triangle) That is: b = 28 ft
Then hypotenuse = 28 + 7 = 35 ft
and the shorter leg = 28 - 7 = 21 ft
Answer:
B
Step-by-step explanation:
If C is the correct answer and if the final result is multiplied out, where does the minus sign in a^4 - b^4 come from? All pluses don't make a minus. A is incorrect.
If D is correct, then a^2 - b^2 should be further factored producing a different kind of answer, like (a + b)^2(c-d)^2 which is not the same as a^4 - b^4. So D is not correct.
The first step in factoring a^4 - b^4 is (a^2 + b^2)(a^2 - b^2) A doesn't lead you anywhere. A is incorrect. The answer must be B.
a^4 - b^4 = (a^2 - b^2)(a^2 + b^2) The first term factors.
a4 - b^4 = (a + b)(a - b) (a^2 +b^2)