If the equation y = x + 4 is changed to y = x - 2, how will the graph of the equation change? a) the original graph will shift 2 units down. b) the original graph will shift 6 units down. c) the original graph will shift 6 units to the left. d) the original graph will shift 2 units to the left.

The original graph will shift 6 units down.

Step-by-step explanation:

Given : If the equation y = x + 4 is changed to y = x - 2.

To find : How will the graph of the equation change.

Solution : We have given

Original graph equation : y =  x + 4.

Transformed equation : y = x -2.

y =  x + 4 →→ y = x - 2.

If we subtract the 6 from 4 it become - 2

We can see x + 4 -6 = x -2 .

So , y = x +4 -6  →→ y = x - 2.

By the transformation rule : f(x) →→  f(x) - k it mean graph shifted down by k units.

Then the original graph will shift 6 units down.

Therefore, The original graph will shift 6 units down.

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°

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560