Lucas writes a numerical expression that has a value of 37. Which of the following expressions did Lucas write?

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:

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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.

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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.

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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.

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:

169×5=845

Step-by-step explanation:

ok now mark me brainlist

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:

Se debe fabricar y vender 553 escritorios para lograr una utilidad de S/ 25000.

Step-by-step explanation:

La utilidad por cada escritorio se obtiene al sustraer los costes fijos y variables del precio, es decir:

[tex]u = S/ \,125 -S/\,4,75 - S/\,75[/tex]

[tex]u = S/\,45.25[/tex]

El número de escritorios a vender para obtener [tex]S/\,25000[/tex] se calcula mediante la siguiente regla de tres simple:

[tex]x = \frac{S/\,25000}{S/\,45,25} \times 1\,esc[/tex]

[tex]x = 552.486[/tex]

Puesto que la cantidad a vender es una variable entera, se debe redondear al entero más cercano. En consecuencia, se debe fabricar y vender 553 escritorios para lograr una utilidad de S/ 25000.

Answer:BC=68

DE=36

CE=34

Step-by-step explanation:

Since  D, E and F are the midpoints, they follow the midpoint theorm which states that "The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side." As for others, it's just the calculation.

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.  

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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:

surface area of the cuboid

(2×2×5)+(2×12×5)+(2×12×2)

20+120+48

188 cm²

Answer:

t = (t₁ · vr)/ (vj - vr) = 45 seconds

Step-by-step explanation:

Given:

Initial time from Ricardo  t₁ = 15 seconds, Ricardo's velocity (speed) vr = 3 ft/s,

John's velocity (speed) vj = 4 ft/s

Requested time when John catch Ricardo t = ?

During 15 seconds, Ricardo moved away

S = vr · t₁ = 3 ft/s · 15 s = 45 feet.

From that moment, the same time runs for both of them

Ricardo's path is S₁ = vr · t  and John's path is S₂ = vj · t

S + S₁ = S₂ =>  S = S₂ - S₁  => 45 = vj · t - vr · t  

When we draw t we get:

t ( vj - vr) = 45   t = 45 / (vj - vr) = 45 / (4 - 3) = 45 / 1 = 45 seconds

t = 45 seconds

S₁ = vr · t = 3 · 45 = 135 ft

S₂ = vj · t = 4 · 45 = 180 ft

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

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

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:

SAS

Step-by-step explanation:

One of the postulates is called SAS and it states that if two triangles have 2 sides with the same length and the angles between the two sides are the same then the two triangles are congruent. This is exactly what we see on the diagram shown in the question, therefore the correct postulate is SAS

Answer:

D

Step-by-step explanation:

there are 9 digits.

and round it off to the nearest hundred million which is 3.

There are 8 digits before the 3... so 10 gets to the power of 8.___ 10⁸

3,0×10⁸ m.s^-1

Answer:

120 Books

Step-by-step explanation:

60% of 120 is 72

Answer:

The answer would be 96

Step-by-step explanation:

Because 20/2=10x2=20

                         19x4=76

20+76=96

Answer:

I cant see the different side measurements

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!!!

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:

11 hours

Step-by-step explanation:

Using an inequality, find how many additional hours must she work in order to reach this goal?

From the above question, the term at least means less than or equal to and it is represented by the inequality = ≤

Hence,

Let the number of additional hours = h

Last summer Myrtle, worked 45 hours and earned $443.70.

The amount she earned per hour = $443.70/45

= $9.86

Our inequality equation is written as;

She wanted to make at least $550 this summer.

$9.86 × h ≤ $550

= 9.86h ≤ 550

h = 550/9.86

h = 55.780933063 hours

Approximately the additional hours she has to work =

55.780933063 - 45 hours

= 10 .780933063 hours

Approximately = 11 hours

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:

Let's walk through the steps together!

Step-by-step explanation:

1

a) we know that the Pythagorean theorem is a^2+b^2=c^2

a^2+b^2=c^2 means that if we add the squared values for each of the two sides of the triangle (these sides need to have an angle of 90 degrees together. Basically they are the ones that aren't the hypotenuse) we get the value of the hypotenuse (the longest side that doesn't help to make the right angle).

We see that we have the values of a and b in this formula (these sides need to have an angle of 90 degrees together.) Plugging the values in problem 1a into this formula, we see that 16^2+12^2=x^2 (x is the value we need to find)

16^2=236

12^2=144

so the formula now says that 236+144=x^2

236+144=400, so x= [tex]\sqrt{400}[/tex] , which is 20.

so x=20

b) we can use the same knowledge we used in the first problem in this problem as well. In this problem, we are given the values of c (the hypotenuse) and one of the sides (which for our purposes can be a).

a^2+b^2=c^2     ->      100+b^2=289

This means that b=[tex]\sqrt{289-100}[/tex]

so b=[tex]\sqrt{189}[/tex]

so b=[tex]3\sqrt{21}[/tex]

2

These ones are pretty basic, having any common knowledge of ratios should lead you right to the answer. I will help you with a and d

a) we are given the values 6 and 9 as a ratio, which is the same as a 2:3 ratio. 12 corresponds to 6, so 12 would be the 2 in 2:3, meaning the answer (for the value of x) is 18

d) we are given the values 6 and 8, and the corresponding value to 8 is 12. 6 and 8 make a ratio of 3:4, and if we plug 12 in as the 3, the 4->4*4=16

3

I can't see the full problem so unfortunately, I cannot help you

I hope this helped in your understanding!

-Suvi

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