Ask question

Ask question

All categories

2 years ago

8

Six identically shaped place mats, marked a, b, c, d, e and f, are piled neatly in a stack. how many arrangements are possible i

f a and b must touch each other?

1 answer:

Sedaia [141]2 years ago

5 0

6
1. A, b, c
2. A, b, d
3. A, b, e
4. C, a, b
5. D, a, b
6. E, a, b

Hope I helped!

You might be interested in

Which transformations are needed to change the parent cosine function to y = 3 cosine (10 (x minus pi))?

Alekssandra [29.7K]

Answer:

See Explanation

Step-by-step explanation:

Given

New function: $y = 3 \cos(10 (x -\pi))$

We can assume the parent function to be:

$y = \cos (x)$

The new function can be represented as:

$y = A*\cos((\frac{2\pi}{B})(x-c))$

Where

A = Vertical stretch factor

B = Period

C = Right shift

By comparison:

$y = A*\cos((\frac{2\pi}{B})(x-c))$ to $y = 3 \cos(10 (x -\pi))$

$A = 3$

$c = \pi$

$\frac{2\pi}{B} = 10$

Solve for B

$B = \frac{2\pi}{10}$

$B = \frac{\pi}{5}$

Using the calculated values of $A,\ B\ and\ c.$ This implies that, the following transformations occur on the parent function:

<em>Vertically stretched by </em> $3$ <em />
<em>Horizontally compressed by </em> $\frac{\pi}{5}$ <em />
<em>Right shifted by </em> $\pi$ <em />

5 0

3 years ago

Read 2 more answers

2. In a relationship between variables, what is the variable called that changes in response to

valkas [14]

Answer:

A dependent variable

Step-by-step explanation:

is a variable whose value will change depending on the value of another variable, called the independent variable. Dependent variables are also known as outcome variables, left-hand-side variables, or response variables.

4 0

2 years ago

What is the measure of an angle whose sine is√3/2 ? 60 45 30

dem82 [27]

ANSWER

The required angle is
$60 \degree$

EXPLANATION

Let the angle whose sine is
$\frac{ \sqrt{3} }{2}$
be
$x \degree$

Then

$\sin(x \degree) = \frac{ \sqrt{3} }{2}$

We take the inverse sign of both sides to obtain,

$x = \sin ^{ - 1} ( \frac{ \sqrt{3} }{2} )$

We use our scientific calculator to evaluate and obtain,

$x = 60 \degree$

8 0

2 years ago

Read 2 more answers

Express 6.83 as a mixed number

Maksim231197 [3]

6.83 as a mixed number is:

6 83/100

4 0

3 years ago

State whether the triangles could be proven congruent, if possible, by SSS or SAS.

Helen [10]

Answer:

1. SSS

2. SAS

3. SAS

4. SSS

5. SAS

6. SAS

Step-by-step explanation:

1) Side FY ≅ Side CW Given

Side FP ≅ Side CM Given

Side YP ≅ Side MW Given

∴ΔMCW ≅ ΔFPY by the Side-Side-Side (SSS) rule of congruency

2) ∠CBD ≅ ∠BCA given that both are alternate interior angles

Side EB ≅ Side EC and Side DB ≅ Side CA Given

ΔBED ≅ ΔAEC by Side-Angle-Side (SAS) rule of congruency

3. ∠SVU ≅ ∠SVT Given

Side SV ≅ Side SV by reflexive property

Side VT ≅ Side VU Given

∴ ΔVSU ≅ ΔVST by Side-Angle-Side (SAS) rule of congruency

4. Side MN ≅ Side QP Given

Side MQ ≅ Side NP Given

Side NQ ≅ Side NQ by reflexive property

∴ΔQNM ≅ ΔQNP by the Side-Side-Side (SSS) rule of congruency

5. Indirect proof

Side GL ≅ Side HL Given

Side GJ ≅ Side HK Given

∠JLG ≅ ∠HLK vertically opposite angles

By sine rule

GJ/sin(∠JLG) = GL/n(∠GJL)

Similarly

HK/sin(∠HLK) = HL/n(∠HKL)

∴ ∠GJL ≅ ∠HKL

∴ ∠LGJ ≅ ∠LHK third angle of two triangles given the other two angles are congruent

∴ΔQNM ≅ ΔQNP by the Side-Angle-Side (SAS) rule of congruency

6. ∠XZY ≅ ∠XZW Supplementary ∠s with ∠XZY = 90°

Side XZ ≅ Side XZ by reflexive property

Side ZW ≅ Side ZY Given

∴ ΔXYZ ≅ ΔXWZ by Side-Angle-Side (SAS) rule of congruency.

3 0

2 years ago