4 + t + 5 = 3 − √ t + 5 4 + t + 5 = 3 - t + 5
1 answer:
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Answer:
Step-by-step explanation:
Let
c-------> the number of cookies in each batch
we know that
To find the total number of cookies, multiply the number of batches by the number of cookies in each batch
so
------> equation that represent the total number of cookies
If Anna ate cookies
then
The expression to know how many cookies Anna has left is equal to
This is a lowest common multiple question.
to find the lowest common multiple, you need to find the prime factors of the two numbers:
Take out duplicates:
and multiply them together:
and that is your answer.
Easy peasy.
to find the lowest common multiple, you need to find the prime factors of the two numbers:
Take out duplicates:
and multiply them together:
and that is your answer.
Easy peasy.
The shape of the graph of quadratic functions is the shape of a parabola.
The steps for drawing a graph of the function f(x) = 2·(x + 4)² - 3 arranged in the correct order are;
- (a) Plot the vertex (-4, -3)
- (b) Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)
- (c) Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)
- (d) Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)
- (e) Draw the axis of symmetry x = -4
- (f) Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)
- (g) Draw a U shaped parabola.
Reasons:
The given function is; f(x) = 2·(x + 4)² - 3
The function is given in the vertex form; f(x) = a·(x - h)² + k
Therefore, the vertex, (h, k) = (-4, -3)
Step (a);
The vertex can be plotted on the graph
- Plot the vertex (-4, -3)
Step (b);
Given that the quadratic term is 2·x², the pattern that can be used for the points from the vertex is therefore, 2·x²
From the vertex (-4, -3) apply the 2·x² pattern by going to the right 1 unit and up 2 × 1² = 2 units to get the point (-4 + 1, -3 + 2) = (-3. -1)
- Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)
Step (c);
To get the next point, the 2·x² pattern is applied with x = 2, to the vertex to get; (-4 + 2, -3 + (2×2²)) = (-2, 5)
- Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)
Step (d);
A third point on the graph relative to the vertex is obtained again by applying the 2·x² pattern again to the vertex with x = 3, to get;
(-4 + 3, -3 + (2 × 3²)) = (-1, 15)
- Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)
Step (e);
The axis of symmetry can be drawn with a vertical line passing through the vertex, which is the line, x = -4
The line x = -4 can be drawn on the graph next
- Draw the axis of symmetry x = -4
Step (f);
The points obtained relative to the vertex (-3, -1), (-2, 5), (-1, 15) can reflected about the axis of symmetry x = -4, to get;
(-3, -1) (-5, -1)
(-2, 5) (-7, 5)
(-1, 15) (-7, 15)
- Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)
Step (g);
The parabola that is U shaped can be drawn from the points plotted in the steps above.
- Draw a U shaped parabola
Learn more about drawing the graph of a quadratic function here: