The vertex is when x=-b/2a, which is also the line of symmetry.
in this case, b=6, a=3, so x=-6/6=-1
when x=-1. y=3-6-1=-4
another way to do it is to write the equation into vertex form by making a square:
3x²+6x-1
3(x²+2x-1/3)
3(x²+2x+1-1-1/3))
3(x²+2x+1-4/3))
notice the bold part makes a square:
3(x+1)²-4
Either way,
the vertex is (-1, -4)
the axis of symmetry is x=-1
the coefficient of x² is 3, a positive number, so this parabola opens upward. the function has a minimum value of y=-4
the range is all real number larger than -4
What you do is divide the sum by 2. You will come out with and answer of 1891. Now, to figure out the years they were invented you take the difference of 192 and divide that in half also. It will come out to 96. Now, you subtract 1891 by 96 and that is the year the pencil was invented (1795=pencil) now with the other half (1891) you add on 96 and you’ll come out with the answer of 1987.
Pencil=1795
Laptop computer=1987.
Hope this helped!
Answer:
The new pyramid has a volume that is half the volume of the original pyramid.
Step-by-step explanation:
The volume of a pyramid is given by the following equation:
In which h is the height, l is the length and w is the width.
Modified volume:
height doubled, length and width cut in half. So
= 0.5V[/tex]
That is
The new pyramid has a volume that is half the volume of the original pyramid.
Let's go through this problem step by step while bearing in mind the concept of
PEMDAS.
Step 1:
Declaration of the expression. Nothing wrong here yet.
Step 2:
Clarise evaluated what's inside the parenthesis first - which was the right thing to do! There are no mistakes in this step.
Step 3:
In this step she subtracted first. This should not be the case! PEMDAS tells us that the exponents and division gets higher priority than subtraction. This is therefore the first mistake Clarise makes.
Step 4:
In this step Clarise evaluates the exponent. This does not violate any rules (relative to the previous expression) since PEMDAS tells us that exponents take higher priority than division.
Step 5:
(Clarise's final answer)
In Clarise's final step, she manages to get the wrong answer! Dividing 51.68 by 0.16 would give us 323. This is another mistake of Clarise.
Looking at the choices, we can now identify what mistakes Clarise made:
-She subtracted before evaluating the exponents
-She subtracted before she divided
-She divided incorrectly
Answer:
X < -0.84
Step-by-step explanation: