Answer:
Step-by-step explanation:
eq. of a circle is (x-h)²+(y-k)²=r²
where center=(h,k)
and radius=r
so (x+2)²+(y+5)²=4²
Answer:
never true
Step-by-step explanation:
on the left, you subtract 13 from x
on the right, you add 1 to x
because each side adjusts x differently, there will never be a solution.
Answer: The common number is 26.
Step-by-step explanation:
We know that the n-th term of a sequence is:
aₙ = 3*n^2 - 1
And the n-th term of another sequence is:
bₙ = 30 - n^2
Remember that in a sequence n is always an integer number.
We want to find a number that belongs to both sequences, then we want to find a pair of integers x and n, such that:
aₙ = bₓ
This is:
3*n^2 - 1 = 30 - x^2
Let's isolate one of the variables, i will isolate n.
3*n^2 = 30 - x^2 + 1 = 31 - x^2
n^2 = (31 - x^2)/3
n = √( (31 - x^2)/3)
Now we can try with different integer values of x, and see if n is also an integer.
if x = 1
n = √( (31 - 1^2)/3) = √10
We know that √10 is not an integer, so we need to try with another value of x.
if x = 2:
n = √( (31 - x^2)/3) = √(27/3) = √9 = 3
Then if we have x= 2, n is also an integer, n = 3.
Then we have:
a₃ = b₂
The common number between both sequences is:
a₃ = 3*(3)^2 - 1 = 26
b₂ = 30 - 2^2 = 26
Answer:
The mass of the exotic fruit is 20 grams.
Step-by-step explanation:
For the system to be in equilibrium,
i. the resultant of all masses must be zero
ii. the total mass on the left of the hanger must be equal to that on the right
Thus,
84 g = 42 g + 42 g
mass of each carrot = 12 g
mass of each mushroom = 10 g
mass of each cherry = 2.5 g
mass of each strawberry = 5 g
So that;
On the left of the hanger,
(2 x 5) + (2 x 10) + 12 = 42
10 + 20 + 12 = 42
42 = 42
On the right of the hanger, let the mass of exotic fruit be represented by x.
x + 12 + 5 + (2 x 2.5) = 42
x + 12 + 5 + 5 = 42
x + 22 = 42
x = 20 g
The mass of the exotic fruit is 20 grams.
Answer:
14x+6z
Step-by-step explanation:
distribute 2 into (4x-3z) and 3 into (2x+4z)
8x-6z+6x+12z
combine like terms
8x+6x=14x
12z-6z=6z
14x+6z
hope this helps