PLZ HELP, DUE TONIGHT!! Find the values of a and b such that f(x) is continuous at x=1

Mathematics

1 answer:

Sedaia [141]3 years ago

6 0

Answer:

a = 2, b = -4

Step-by-step explanation:

To make the given piecewise function continuous we need:

ax² - b = 6 and 5ax + b = 6 at x = 1

It gives us the system:

a(1²) - b = 6 ⇒ a - b = 6
5a(1) + b = 6 ⇒ 5a + b = 6

Sum of the two:

a - b + 5a + b = 6 + 6
6a = 12
a = 2

Then b is:

2 - b = 6
b = -4

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What is the value of x in the diagram? у X X-20

dem82 [27]

Answer:

y= 35⁰

x = 55⁰

Step-by-step explanation:

total angle of triangle is 180⁰

therefore we can equate:

x + (x-20) + 90 = 180

2x + 70 = 180

x = 55⁰

total of x and y is equal to 90⁰ since it is a right angle;

x + y = 90

x = 55⁰

55⁰ + y = 90

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8 0

3 years ago

Need help here plss

goldenfox [79]

Answer:

see below

Step-by-step explanation:

Thankfully, these inequalities are already simplified, so all we have to do here is graph the inequalities as they are.

To graph y > 2x - 3, first draw the line y = 2x - 3. Make sure to make the line dashed because the sign is ">", which means that the points on the line do not belong to the solution set. Now, we need to figure out which side of the line to shade on. Since the sign is ">", that means that we will shade "above" the line, or on the left side of it. (This is the blue area in the image.)

Repeat a similar process to graph y < x + 1. As usual, first draw the line y = x + 1, and again, make it a dashed line since the sign is "<". And since the sign is "<", that means that we will shade "below" the line, or on the right side of it. (This is the red area in the image.)

The solution set to this system is the area where the two shaded areas overlap, which is the purple area in the image below. Hope this helps!