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2 years ago

Determine the sum of the Natural numbers up to 1000 which are not divisible by 5

Mathematics

1 answer:

Andrews [41]2 years ago

5 0

Sum the first 1000 natural numbers:

$\displaystyle 1 + 2 + 3 + \cdots + 100 = \sum_{i=1}^{1000} i = \frac{1000 \cdot 1001}2 = 500,500$

Since 1000/5 = 200, there are 200 multiples of 5 in the range 1-1000. Sum them up:

$\displaystyle 5 + 10 + 15 + \cdots + 1000 = 5 (1 + 2 + 3 + \cdots + 200) = 5\sum_{i=1}^{200}i = 5\cdot\frac{200\cdot201}2 = 100,500$

Then the sum we want is

$\displaystyle 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 11 + \cdots + 999 = 500,500-100,500 = \boxed{400,000}$

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WILL GIVE BRAINIEST! WHAT IS THE INVERSE OF Y=4X?

tigry1 [53]

Answer:

Divide each term in yln(4)=ln(x) y ln ( 4 ) = ln ( x ) by ln(4) ln ( 4 ) . Cancel the common factor of ln(4) ln ( 4 ) . Divide y y by 1 1 . Solve for y and replace with f−1(x) f - 1 ( x

Step-by-step explanation:

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3 years ago

seropon [69]

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)

(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) $\underrightarrow {R_{(x = -4)}}$ (-5, -1)