Find the value of x that makes m ∥ n

Mathematics

2 answers:

AURORKA [14]3 years ago

5 0

Those two angles are alternate interior angles, so they must be congruent.

3x = 2x + 20

x = 20

Alex73 [517]3 years ago

4 0

Answer:

The value of x that makes m || n is x = 20

Step-by-step explanation:

Given a line that is intersected by another two lines (for example line ''m'' and line ''n'' like in the exercise) one of the conditions that makes m || n is that the alternate interior angles must be congruent. Understanding that congruent means the same.

In the exercise, one pair of alternate interior angles are (2x+20)° and 3x°.

We need this two angles to be congruent ⇒ $3x=2x+20$

Solving this for ''x'' :

$3x=2x+20\\3x-2x=20\\x=20$

The value of x that makes 3x° congruent to 2x+20° (that makes the alternate interior angles congruents) is x = 20

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If a person takes a prescribed dose of 10 milligrams of Valium, the amount of Valium in that person's bloodstream at any time ca

aleksandr82 [10.1K]

Answer:

(a)8.0mg

(b)36.87 hours

(c)-0.168

Step-by-step explanation:

The amount of Valium in that person's bloodstream at any time can be modeled with the exponential decay function $A ( t ) = 10 e^{ -0.0188 t$ (t in hours)

(a)After 12 Hours

$A ( 12) = 10 e^{ -0.0188*12}\\=7.98\\\approx 8.0 mg $(to the nearest tenth of a milligram)$

(b)If A(t)=5mg

Then:

$5= 10 e^{ -0.0188 t}\\$Divide both sides by 10\\0.5=e^{ -0.0188 t}\\$Take the natural logarithm of both sides\\ln (0.5)=-0.0188 t\\t=ln (0.5) \div (-0.0188)\\$t=36.87 hours (to two decimal places.)$

(c)

$A ( t ) = 10 e^{ -0.0188 t}\\A'(t)=10(-0.0188)e^{ -0.0188 t}\\A'(t)=-0.188e^{ -0.0188 t}\\$At 6 hours, the rate at which the amount of Valium is decaying therefore is:\\A'(6)=-0.188e^{ -0.0188*6}\\$=-0.168 ( to three decimal places)$