The common minimum multiple between A) 2,3 and 6 B) 8,9 and 12 C) -4,2 and 8

Dmitry [639]

Answer:

JK ≅ MN

Step-by-step explanation:

SAS states that any two sides of the angle and the angle itself, if , of two triangles are equal the two triangles are equal.

It is given that ∠J ≅ ∠M and JL ≅ MR i.e an angle and a side are equal. We need one more side to prove that the two triangles are equal.

If we look at the diagram closely we see that the angles J and M are formed by the sides JK & JL and MN& MR.

It is given that JL ≅ MR so we are left with JK ≅ MN

6 0

2 years ago

Read 2 more answers

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

3 years ago

Find the distance CD rounded to the nearest tenth C=(10,-1) and D=(-6,3)

Fynjy0 [20]

Answer:

CD = 16.5

Step-by-step explanation:

To find the distance between two points, use this formula: $L = \sqrt{(x_{2} -x_{1})^{2}+(y_{2} -y_{1})^{2} }$

point C can be info set 1: (10, -1) x₁ = 10 y₁ = -1

point D can be info set 2: (-6, 3) x₂ = -6 y₂ = 3

Substitute the information into the formula

$L = \sqrt{(x_{2} -x_{1})^{2}+(y_{2} -y_{1})^{2} }$

$CD = \sqrt{(-6 -10)^{2}+(3 -(-1))^{2} }$ Simplify inside each bracket

$CD = \sqrt{(-16)^{2}+(4)^{2} }$ Square the numbers

$CD = \sqrt{256+16 }$ Add inside the root

$CD = \sqrt{272}$ Enter into calculator

$CD = 16.5$ Rounded to the nearest tenth, the first decimal

The distance CD is 16.5.

4 0

3 years ago

DVD Video Rentals (Refer to Example 3.) The func-

Neporo4naja [7]

Answer:

$(a)\ V = \{(N,30),(R,37),(S,17)\}$

$(b)$

$Domain = \{N,R,S\}$

$Range = \{37,30,17\}$

Step-by-step explanation:

Given

$V(R) = 37,\ V(N) = 30,\ V(S) = 17$

Solving (a): Set of ordered pair

A function y = f(x) is represented as (x,y)

So, the ordered pair of V is:

$V = \{(R,37),(N,30),(S,17)\}$

Order the alphabets in increasing order

$V = \{(N,30),(R,37),(S,17)\}$

Solving (b): The domain and the range

In a function $\{(x_1,y_1),...,(x_n,y_n)\}$

The domain and the range are represented as:

$Domain = \{x_1,x_2....x_n\}$

$Range = \{y_1,y_2....y_n\}$

So, we have:

$Domain = \{N,R,S\}$

$Range = \{37,30,17\}$

5 0

3 years ago

What is a, b, and c in this quadratic equation?

Vilka [71]

A = 7
b = -18
c = -52
Do you know what the Quadratic formula is to solve?

4 0

3 years ago