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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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Dmitriy789 [7]

Answer:

$- \frac{3}{13} + \frac{15i}{13}$

Step-by-step explanation:

$\frac{ \sqrt{ - 36} }{(2 - 3i) + (3 + 2i)}$

Set up equation

Step 1: Simplify

$\frac{6i}{5 - i}$

Step 2:Multiply by conjugate

$\frac{6i}{5 - i} \times \frac{5 + i}{5 + i}$

Step 3:Simplify

$\frac{30i + 6 {i}^{2} }{ {i}^{2} - 5 {}^{2} }$

We can reduce this and we must make the imaginary number and real number serpate equations.

$- \frac{6}{26} + \frac{30i}{26}$

Reduce each by 2

$- \frac{3}{13} + \frac{15i}{13}$

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2 years ago

A rhombus, which is a quadrilateral with 44 equal sides, is plotted on the coordinate plane. The coordinates of the vertices are

Arturiano [62]

The rhombus is shown in the diagram below

The length of one side of the rhombus is 5 units, hence all the other sides are also 5 units each.

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3 years ago

M(-3,2) is the midpoint of AP. If A has coordinates (-1,5), what are the<br> coordinates of P?

Inessa05 [86]

Answer:

Step-by-step explanation:

If M is midpoint of AP then:

$x_P-x_M=x_M-x_A\qquad\quad\ \wedge\qquad y_P-y_M=y_M-y_A\\\\x_P-(-3)=-3-(-1)\qquad\wedge\qquad y_P-2=2-5\\\\x_P+3=-3+1\qquad\quad\ \wedge\qquad\quad y_P-2=-3\\\\x_P=-3+1-3\qquad\quad\ \wedge\qquad\quad y_P=-3+2\\\\x_P=-5\qquad\qquad\ \wedge\qquad\qquad y_P=-1$

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3 years ago

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kodGreya [7K]

Answer:

Option (a)

Step-by-step explanation:

This question is incomplete without statements; find the statements as followed,

a). Ricky's claim is incorrect since not all rotations that carry a square onto itself are multiples of 30 degrees.

b). Ricky's claim is incorrect since not all rotations that are multiples of 30 degrees carry a square onto itself.

c). Ricky's claim is correct since any rotation that carries a square onto itself is a multiple of 30 degrees.

d). Ricky's claim is correct since any rotation that is a multiple of 30 degrees carries a square onto itself.

Square ABCD will map onto itself when point A comes to B, C or D by a rotation about the center E with a multiple of measure of angle AEB.

m∠AEB = 90° [Diagonals of a square intersect each other at 90°]

In simpler words, if square ABCD is rotated 90° or it's multiple about the center E, square will overlap itself.

Therefore, Option (a) is correct.

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Answer:

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2 years ago