Answer:
y = 0
Step-by-step explanation:
It is always a good idea to look at the question and make some observations about it. Here, you might observe ...
- all of the bases are powers of 3: 243 = 3^5; 9 = 3^2
- y is a factor of every exponent
The latter observation is important, because it means that when y=0, every exponential expression has a value of 1. Hence y = 0 is a solution.
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To solve the equation, you can write it in terms of powers of 3.
(3^5)^(-y) = (3^-5)^(3y)·(3^2)^(-2y)
3^(-5y) = 3^(-15y)·3^(-4y)
3^(-5y) = 3^(-19y)
-5y = -19y . . . . . . . . equating exponents; equivalent to taking log base 3
14y = 0 . . . . . . . . . . add 19y
y = 0 . . . . . . . . . . . one solution
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The rules of exponents we used are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
1/a^b = a^-b
Answer:
260
Step-by-step explanation:
7 shelves containing 37 cans of pineapples each would give you 259 cans of pineapple. Then, round to the nearest ten would give you 260.
Answer:
B
Step-by-step explanation:
No these triangles are not congruent.
<u>Left triangle</u>
Shortest side = 6 cm
Longest side = 13 cm
3rd side = unknown but < 13
<u>Right triangle</u>
Shortest side = 6 cm
Longest side = unknown but > 13
3rd side = 13 cm
Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.
We do not know if any of the angles are congruent. If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.
B because absolute value means the distance of a point on a number line from 0. So the absolute value of -6 is 6 and you add that to 4
Answer:
The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4
Step-by-step explanation:
let l be the length and w be the width of the rectangle respectively;
Diagonal(D) of a rectangle is given by:
......[1]
As per the given statement we have;
Diagonal(D) = width + 2
and
= 2w
Now, substitute these in [1] we have;
Squaring both the sides we get;
or
or
Simplify:
......[2]
The quadratic equation is in the form of 
the solution is given by: 
On comparing with [1] we get
a= 1 , b = -1 and c = -1
Then the solution is:
Simplify:
and 
Then, the diagonal D = w+2
For
For
therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4
