Please someone help me ?!?!?

As the name implies, there are 3 parts or conditions that must be held true in order for the function to be continuous at x = a.

Those three conditions are:

---------------------------

In this case, a = -1 as this is where the junction happens. It's where f(x) swaps identity from the first piece x^2-3 to the second piece 3x+1

To compute f(a), aka f(-1), we'll use the second piece

f(x) = 3x+1

f(-1) = 3(-1)+1

f(-1) = -2

We see that f(a) does indeed exist, so condition (1) is held true.

----------------------------

To compute the limit, we'll need the left hand limit (LHL) and right hand limit (RHL)

The LHL is found by having x approach -1 from the left. So you'll start with something like x = -2, then move to x = -1.5 then to x = -1.1 then to x = -1.01, and so on, getting steadily closer to x = -1. We won't actually arrive at x = -1 itself.

But because x^2-3 is a polynomial, and all polynomials are continuous, we can simply plug x = -1 into this to find that...

y = x^2-3

y = (-1)^2 - 3

y = -2

The input x = -1 leads to the output y = -2 for the first piece. This is the LHL.

We found earlier that x = -1 lead to y = -2 for the second piece. This is the RHL.

Because LHL = RHL, we have proven condition (2) is true. It also means condition (3) is true because f(a) is part of the RHL, more or less.

----------------------------

In layman's terms, we can think of the two curves as roads. For the function to be continuous, the road cannot have any jumps, gaps, or potholes. Condition (1) says that the point must exist, aka there isn't a pothole there. Condition (2) says that the two pieces of the road, on either side of the point in question, must connect together. Hence there are no gaps or jumps. Condition (3) effectively ties everything together.

You might be asking if condition (3) is a bit redundant. Surely if f(a) exists and the limit exists, then that's enough to prove continuity, right? Unfortunately no that's not the case. Consider the situation where the limit exists, but f(a) was some other value. That means we have a removable discontinuity. That point in the road is a pothole but the two roads do connect.

One could argue that conditions (2) and (3) are sufficient, and condition (1) isn't really needed. This is because if condition (3) was the case, then we automatically have shown that f(a) must exist. This is of course assuming we found that the limit exists as well, and it's not plus/minus infinity.

Answer:

The correct answer is - 3 hours.

Step-by-step explanation:

Given:

Price of parts: $200

Price of labor: $75/hour

Total cost: $425

Solution:

Let x = x of hours work done on the car

The inequality can be represented as:

425 = 75x + 200

Solving this inequality, we find that

225 =75x

or

x = 3

Thus, It means that the mechanic will take at least 3 hrs to work on his car.

Answer:

Let his net salary = x.

He spent 1/4th of x on School fees

Remainder = 1-1/4 = 3x/4

He spent 1/4th THE REMAINDER on Electricity and Water Bils

1/4 of remainder (3x/4) = 1/4 x 3x/4 = 3x/16

He spent 3x/16 of this salary on Electricity and Water Bills... We should subtract this to know our current value or cash at hand

New Remainder = 3x/4 - 3x/16

= 9x/16.

He spent 1/9th OF WHAT REMAINED ON TRANSPORT.

1/9 x 9x/16

=x/16

New Remainder

= 9x/16 - x/16

=x/2.

If he finally had 8,400

Then

x/2=8,400

x=2x8,400

x= 16,800.

This answer is Correct. You can check it by using our x as 16,800 and solve from the start... You'll arrive at 8400 as your remainder. Have a great day!!!

============================================================

Explanation:

For now, let's focus on the probability of getting one "5".

There are 4 of these cards (one of each suit) and 52 total. The probability of getting the card we're after is 4/52 = 1/13.

We can think of it like saying "if we focus on one suit only, then there's a 1 in 13 chance of getting a '5' from this pile".

The probability of getting two "5"s in a row is (1/13)*(1/13) = 1/169 assuming we put the first card back. If the first card is not put back, then we would compute it like so: (4/52)*(3/51). I'll leave it unevaluated for you to try out as practice.

Side note: 1/169 = 0.0059 = 0.59% approximately

Answer:

18 cm^3

Step-by-step explanation:

To find the volume, count the number of cubes, since each cube has a side length of 1 cm

The volume of 1 cube is 1*1*1 = 1 cm^3

There are 6 rows of 3 cubes each or 18 cubes

18 cubes of 1 cm^3 = 18 cm^3

Answer: 18 cubic cm

Step-by-step explanation:

Answer 18 :D !!!

Answer:

D

Step-by-step explanation:

y - 4 = 7(x - 6)                    Remove the brackets

y - 4 = 7x - 42                    Add 4 to both sides

y = 7x - 42 + 4

y = 7x - 38                  

Note when you put this in slope, y intercept form, the ordered pair is easier to find.

Let x = 5

y = 7*5 - 38

y = 35 - 38

y = -3          (5,4) isn't right

Let x = 6

y = 7*6 - 38

y = 42 - 38

y = 4                 That does not work either.

The answer is D

Answer:

The answer would be 96

Step-by-step explanation:

Because 20/2=10x2=20

                         19x4=76

20+76=96

Answer:

x=13 y=10 z=3 d) 260

Step-by-step explanation:

vertex angles are congruent so you can set them equal to each other and solve

and then a straight like adds up to 180 so 180-(7(x-3)+5y)= your missing angle and then that angles is congruent to its opposite so 2(5z+15)=60

Answer:

option 4

Step-by-step explanation:

[tex]perpendicular means = slope_1 \times sope_2 = -1\\[/tex]

                                [tex]-2 \times slope_2 = -1\\\\slope_2 = \frac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

The slopes of perpendicular lines are negative reciproclas. That means their product equals -1.

If you know the slope of a line, to find the slope of a perpendicular line, flip the slope and change the sign.

Given line: slope = -2

-2 is the same as -2/1

Flip it: -1/2

Change the sign: 1/2

Answer: 1/2

Answer: 10/25 is the probability of choosing a blue marble.

Step-by-step explanation:

First, find out how many marbles there are in total. 3 + 10 + 8 + 4 = 25

Then, each number of marbles is how many out of 25. So, for example, red would be 3/25. Blue - 10/25. Green - 8/25. Yellow - 4/25

It asks you what the probability is, so, find the blue fraction that is out of 25, and thats the probability.

Answer:

Step-by-step explanation:

1.25 yd x 2 yd x 1.5 yd

= 2.5 yd^2 x 1.5 yd

= 3 3/4 yd^3

answer is D

Answer:

169×5=845

Step-by-step explanation:

ok now mark me brainlist

Answer:

surface area of the cuboid

(2×2×5)+(2×12×5)+(2×12×2)

20+120+48

188 cm²

Answer:

Logan played for 22 minutes during the second half.

Step-by-step explanation:

Since Keith played the first 22 minutes of a soccer game and Logan then replaced him for the rest of the half, and Logan started the second half and was replaced by Wilson with 18 minutes left in the game, if each half is 40 minutes long To determine how long did Logan play during the second half, the following calculation must be performed:

Second Half Total - Time Played by Wilson = Time Played by Logan

40 - 18 = X

22 = X

Therefore, Logan played for 22 minutes during the second half.

Step-by-step explanation:

Hey there!

Here;

Diameter (d) = 13 ft

Radius (r) = 13/2 = 6.5 ft

Now,

Area of a circle= πr²

= (22/7)*(6.5)²

= 132.78 ft²

Therefore, the area is 133 ft².

Hope it helps!

Step-by-step explanation:

Hey there!

Here;

Diameter (d) = 13 ft

Radius (r) = 13/2 = 6.5 ft

Now,

Area of a circle= πr²

= (22/7)*(6.5)²

= 132.78 ft²

Therefore, the area is 133 ft².

Hope it helps!

Answer:

system has 1 solution at (2.5, -1.5)

Step-by-step explanation:

y = x - 4     this equation has a slope of 1 and a y-intercept of -4

3y - x = -7   this equation has a slope of 1/3 and a y-intercept of -7/3

Answer: Initial height before launch

Step-by-step explanation:

Given

The equation [tex]y=-9.8t+109.7t+7.4[/tex]  the height of toy rocket after t sec

when the rocket is launched, time is [tex]t=0[/tex]

Substituting 0 for [tex]t[/tex] in the equation

[tex]\Rightarrow y(0)=-9.8(0)+109.7(0)+7.4\\\Rightarrow y(0)=7.4[/tex]

Here, [tex]7.4[/tex] represents that rocket is already at a height of [tex]7.4[/tex] m before the launch.

Answer:

120 Books

Step-by-step explanation:

60% of 120 is 72

Answer:

1 1/4 mile/hr (Answer B)

Step-by-step explanation:

Distance traveled:  1/4 mile; elapsed time:  1/5 hour.  Then:

 1/4 mile

--------------- = 5/4 mile/hr, or 1 1/4 mile/hr (Answer B)

  1/5 hour

Answer:

4.8 slices each

Step-by-step explanation:

8*3= 24

24/5= 4.8

Answer: A

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]m=\boxed{\frac{2}{5}}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Slope Formula:}}\\\\\frac{y_2-y_1}{x_2-x_1}\\\\\rightarrow (x_1,y_1),(x_2,x_1) - \text{Two Points Given}[/tex]

⸻⸻⸻⸻

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the Slope:}}\\\\\rightarrow m=\frac{7-5}{8-3}\\\\\rightarrow \boxed{m=\frac{2}{5}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

,,,,,,,,,,,,,,,,,,,,,,,,$$$$

,,,,,,,,,,,,,,,,,,,,,,,,$$$$

,,,,,,,,,,,$$$$$$$$$$$$$$$$$

,,,,,,,$$$$$$$$$$$$$$$$$$$$$$

,,,,,$$$$$$$,,,,,$$$$,,,,$$$$$$$$

,,,$$$$$$,,,,,,,,,$$$$,,,,,,,,$$$$$$$

,,$$$$$$,,,,,,,,,,$$$$,,,,,,,,,,$$$$$$

,,$$$$$$,,,,,,,,,,$$$$

,,$$$$$$,,,,,,,,,,$$$$

,,,$$$$$$,,,,,,,,,$$$$

,,,,$$$$$$$$,,,,$$$$

,,,,,,$$$$$$$$$$$$$$$

,,,,,,,,,,$$$$$$$$$$$$$$$$$

,,,,,,,,,,,,,,,,,$$$$$$$$$$$$$$$

,,,,,,,,,,,,,,,,,,,,,,,,$$$$,,$$$$$$$$

,,,,,,,,,,,,,,,,,,,,,,,,$$$$,,,,,,,$$$$$$

,,,,,,,,,,,,,,,,,,,,,,,,$$$$,,,,,,,,,,$$$$$

,,,,,,,,,,,,,,,,,,,,,,,,$$$$,,,,,,,,,,,$$$$$

$$$$$$$,,,,,,,,,,$$$$,,,,,,,,,,,,$$$$$

,$$$$$$,,,,,,,,,,,$$$$,,,,,,,,,,,,$$$$$

,,$$$$$$$,,,,,,,,$$$$,,,,,,,,,,,$$$$$

,,,$$$$$$$$,,,,,$$$$,,,,,,,,,,$$$$$

,,,,,,$$$$$$$$$$$$$$$$$$$$$$

,,,,,,,,,,$$$$$$$$$$$$$$$$$$$

,,,,,,,,,,,,,,,,,,$$$$$$$$$$$$

,,,,,,,,,,,,,,,,,,,,,,,,$$$$

,,,,,,,,,,,,,,,,,,,,,,,,$$$$

Answer:

5x² + 9x + 1

Step-by-step explanation:

Given:

A = 3x² + 5x - 6

B = 2x² + 4x + 7

A + B:

3x² + 5x - 6 + 2x² + 4x + 7

(3x² + 2x²) + (5x + 4x) - 6 + 7

5x² + 9x + 1

Answer:

75%

Step-by-step explanation:

Mallards = 3/4 of the ducks in the pond

What percentage of the ducks are mallards?

percentage of the ducks that are mallards = 3/4 × 100

= (3 * 100) / 4

= 300/4

= 75%

percentage of the ducks that are mallards = 75%

Answer:

288 pages

Step-by-step explanation:

Step 1: Set up a fraction (Since 75% is 216, 100% is x. We don't need the percent (%).)

[tex]\frac{216}{75} = \frac{x}{100}\\\\[/tex]

Step 2: Solve; Divide the given values (All we are doing is finding what is between those values.)

[tex]\frac{216}{75}\\\\216 \div 75\\\\= 2.88[/tex]

Step 3: Multiply the result to the value (Now we multiply the result to 100 because that would make it equal.)

[tex]100\\\\2.88 \times 100\\\\= 288[/tex]

Therefore, the book is 288 pages long.

Answer:

(x + 8)

Step-by-step explanation:

If you factor x2 + 5x – 24 using the AC method, it equals (x - 3) and (x + 8).

Answer:

D on edge :)

Step-by-step explanation: