Answer:
1) (-3,-2)
2) x=-3
Step-by-step explanation:
1) The vertex of a parabola is the turning point that is the minimum or maximum of the graph, based on the shape of the parabola. In this case, the vertex is the minimum. By looking at the coordinate points, we can tell that the minimum value where the graph changes the direction is at (-3,-2).
2) The line of symmetry is the line on the graph that cuts the shape exactly in half. This means that if you were to fold the graph along this line, the two sides would be identical. All parabolas have a line of symmetry and it always matches the vertex. The equation for the line of symmetry will be x= whatever the x-value of the vertex is. So, for this graph, the line of symmetry is x=-3.
Answer:
1=27
2=34
Step-by-step explanation:
1)9y power 2÷3
or, y=9 power 2÷3
or, y=9×9÷3
or, y=81÷3
or, y=27
2) (8x power 2+4x)÷2
=(8x×8+4x)÷2
=(64x+4x)÷2
=68x÷2
or, x=68÷2
or, x=34
From your equation, you can see that you have a difference of two cubes (aka two cubes being subtracted): 64, which is
, and
.
There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.
That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are
and
. The difference of those two cubes is:
In our problem, a = 4 (since
= 64) and b = y (since
. Plug these values into the rule to find the factor of
:
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Answer: 
Answer:
The best way of writing this answer in an inequality pattern is 50 ≤ x ≥ 70
Step-by-step explanation:
The variable "x" is said to be greater than or equal to 50, that means that x could be 50, 51, 52, 53, 54......to infinity, all these values are true for x.
The second solution said x is greater or equal to 70. This also means that x could be 70, 71, 72, 73, ......... to infinity.
The inference that can be drawn from here is that x actually started from 50, so anything lesser than 50 is lesser than x, so 50 ≤ x. We can join the two answers together to get a range in a form like: 50 ≤ x ≥ 70
Answer:
5 hamburger packages and 6 bun packages
Step-by-step explanation:
It is asking for the highest common multiple of 12 and 10. the first time a multiple of 12 is divisible by 10 is at 12x5, which is 60. now divide 60 by 12 and 10, 5 and 6.
