We have 5 different robots and we want to arrange them all in a line. How many different ways are thereto arrange them?

120 ways

Step-by-step explanation:

The question here says that there are 5 different robots and we want to arrange them all in a line. How many different ways are thereto arrange them?

---Total number of robots is 5 and since we are dealing with the arrangements without order,then we are talking about combinations

And since the arrangements requires them to be lined up in a single line, we are going to work this out without much stress.

5! ÷ 1! = 5 × 4 × 3 × 2 × 1 ÷ 1

= 120 ways

120

Step-by-step explanation:

Khan Academy

93.8

step-by-step explanation:

lets say, first number = x

second number = 3x+7

total = 49

(x)+(3x+7)= 49

4x+7 = 49

4x = 42

x = 42/4

x= 10.5

x= 10.5

3x+7 = 3(10.5)+7 = 93.8

hope this

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°