Answers
Answer:
See explanation.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FunctionsFunction NotationCalculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Left-Side Limit: [tex]\displaystyle \lim_{x \to c^-} f(x)[/tex]Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left \{ {{\sqrt{x + 1}, \ x < 3} \atop {5 - x, \ x \geq 3}} \right.[/tex]
Step 2: Find Right Limit
Substitute in variables [Right-Side Limit]: [tex]\displaystyle \lim_{x \to 3^+} 5 - x[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 3^+} 5 - x = 5 - 3[/tex]Subtract: [tex]\displaystyle \lim_{x \to 3^+} 5 - x = 2[/tex]∴ the right-side limit equals 2.
Step 3: Find Left Limit
Substitute in variables [Left-Side Limit]: [tex]\displaystyle \lim_{x \to 3^-} \sqrt{x + 1}[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{3 + 1}[/tex][√Radical] Add: [tex]\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{4}[/tex][√Radical] Evaluate: [tex]\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = 2[/tex]∴ the left-side limit equals 2.
Step 4: Find Limit
The right and left-side limits are equal.
∴ [tex]\displaystyle \lim_{x \to 3} f(x) = 2[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Related Questions
Approximately how long will it take $200 to double to $400 when the annual interest rate is 8 1/2?
Answers
Answer:
200/17 years
Step-by-step explanation:
Simple interest = (principle * time * rate) / 100i
Stuck on this one. I can’t remember the process to get the answer
Answers
what is the equation, in point-slope form, of the ljne that is perpendicular to the given line and passes through the point (-4,-3)?
Answers
Answer:y+3=1/4(x+4)
Step-by-step explanation:
First find the slope of the line with the points -1,1 and 0,-3
1-(-3)/-1-0 = -4
perpendicular is negative reciprocal which is 1/4
now we have the slope, and a point so we can put it in point slope form
y+3=1/4(x+4)
point slope form is y-y1 = m(x-x1)
with x1,y1 being the point and m being the slope
find (a) the perimeter and (b) the area of the figure. use 3.13 or 22/7 for n. round your answer to the nearest hundredth, if necessary
Answers
Answer:
;)))
Step-by-step explanation:
A pencil case with a cylinder shape with diameter= 10 cm
and height = 12 cm .
What is the length of the longest pencil that can fit in the pencil case?
Answers
Answer:
length of the longest pencil that can fit must be less than 13cm
Step-by-step explanation:
To get the longest pencil that fit the case, we will use the pythagoras theorem;
diameter = 10cm
radius = 10/2
radius = 5cm
Height = 12cm
Get the length of the longest side
l² = r²+h²
l² = 5²+12²
l² = 25 + 144
l² = 169
l = √169
l = 13cm
Hence the length of the longest pencil that can fit must be less than 13cm
Find the value of x in each triangle. Please help me <33
Answers
Answer:
x = 11
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
5x + 4 + 6x - 3 + 4x + 14 = 180 ← collect like terms on left side
15x + 15 = 180 ( subtract 15 from both sides )
15x = 165 ( divide both sides by 15 )
x = 11
given h (x)=5x-3 find the value of h(-4)
Answers
Answer:
h(- 4) = - 23
Step-by-step explanation:
To evaluate h(- 4) substitute x = - 4 into h(x) , that is
h(- 4) = 5(- 4) - 3 = - 20 - 3 = - 23
h (-3) = 57
why does it keep saying to explain dis.... dont answer that
Find the volume of a regular square pyramid with base edge 10 ft. and height 12 ft.
120 ft
75ft?
400 ft
D 300 ft?
Answers
Answer:
V = 400 ft^3
Step-by-step explanation:
The area of the base of this regular square pyramid is (10 ft)^2, or 100 ft^2.
Recalling that the area of a pyramid is V = (1/3)(base area)(height), in this case we get V = (1/3)(100 ft^2)(12 ft) = 400 ft^3
Mixing 4 ml of red paint and 15 ml of yellow paint makes orange paint. How much red would be needed if you use 1500 ml of yellow paint?
Answers
Answer:
Amount of red paint needed for 1500 ml yellow paint = 400 ml
Step-by-step explanation:
Given:
ration of red paint to yellow paint = 4 ml to 15 ml
Find:
Amount of red paint needed for 1500 ml yellow paint
Computation:
Amount of red paint needed for 1500 ml yellow paint = [ration of red paint to yellow paint]1500
Amount of red paint needed for 1500 ml yellow paint = [4/15]1500
Amount of red paint needed for 1500 ml yellow paint = [4]100
Amount of red paint needed for 1500 ml yellow paint = 400 ml
Enter the value of x so that the expression (1.8a−5.7)+(xa+3.2) is equivalent to −1.6a+2.5.
Answers
Answer:
Step-by-step explanation:
ax+1.8a−2.5
Gary buys a skateboard for
$145. What's the total cost
including 6% sales tax?
Answers
Answer:
$8.6
Step-by-step explanation:
The total tax is 8 dollars and 60 cents
Answer:
$153.70
Step-by-step explanation:
Sales tax is applied to things that are sold by a retailer. So if it says 6% tax is levied on the item, that means the total cost will be the initial cost of skateboard ($145) + sales tax (6% of 145) = 145 + 8.7 = $153.70
Someone help please, I’ll mark brainliest (look at the image) (50 points)
Answers
Answer:
S=54fr^2 T=81ft^2 U= 54 ft^2 V= 54 ft^2 W= 54 ft^2 X= 81 ft^2
Step-by-step explanation:
You got it correct, dont stress!
Answer :
Area of S = 6*9 = 54
Areas of T = 9*9 = 81
Area of V = 6*9= 54
Area of X= 9*9= 81
Area of U = 9*6 = 54
Area of W = 9*6 = 54
Surface area is 378 ft^3
Explanation
Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces.
A cuboid when opened gives the following view:
Please help fast!! What is the range of the scores shown in the stem and leaf plot
95
40
58
37
Answers
Answer:
37
Step-by-step explanation:
Highest take the lowest
95-58=37
Y’all know the answer?
Answers
9514 1404 393
Answer:
(b) 36 in²
Step-by-step explanation:
The right triangle at lower right has a vertical leg of 3 and a hypotenuse of 5. Then the horizontal leg is ...
√(5² -3²) = √16 = 4
Then the horizontal diagonal is 4+4 = 8. The vertical diagonal is 6+3 = 9. The area is half the product of the diagonals, so is ...
A = 1/2(d1)(d2) = 1/2(8 in)(9 in) = 36 in²
__
You could figure the areas of the triangles separately, but you would come to the same result. This formula is good for a rhombus or a kite (or a square, which is also a rhombus), because the diagonals are perpendicular to each other.
if a/4=2/3, then (a-4)/4 would equal
a. -2/3
b. -1/3
c. 0
d. 1/3
Answers
Answer:
b. -1/3
Step-by-step explanation:
a/4=2/3
a=8/3
(a-4)/4
(8-12)/12
=-4/12
=-1/3
Answer:
-1/3
Step-by-step explanation:
a/4=2/3
Multiply each side by 4
a/4 *4=2/3 *4
a = 8/3
(a-4)/4
(8/3 - 4) /4
Getting a common denominator
(8/4 - 12/3) /4
(-4/3)/4
-1/3
The coordinates of the turning point of the parabola whose equation is y = x2 — 6x + 8 are A. (3, 35) C. (-3, 35) B. (-3, —1) D. (3. —1)
Answers
Answer:
D. (3. —1)
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Turning point of a quadratic function:
The turning point of a quadratic function is the vertex.
y = x2 — 6x + 8
This means that [tex]a = 1, b = -6, c = 8[/tex]
Now, we find the vertex.
[tex]x_{v} = -\frac{b}{2a} = -\frac{-6}{2(1)} = 3[/tex]
[tex]\Delta = b^2-4ac = (-6)^2-4(1)(8) = 36 - 32 = 4[/tex]
[tex]y_{v} = -\frac{4}{4(-1)} = -1[/tex]
(x,y) = (3,-1), and the correct answer is given by option D.
A line has a slope of -1/4 and passes through point
(-5/4, 1)
What is the equation of the line?
Answers
Answer:
y = -1/4 x+11/16
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -1/4x+b
Substitute the point in for x and y
1 = -1/4(-5/4) +b
1 = 5/16 +b
16/16 = 5/16 +b
Subtract 5/16 from each side
11/16 = b
y = -1/4 x+11/16
Answer:
y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{11}{16}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
To find c substitute ( - [tex]\frac{5}{4}[/tex], 1 ) into the partial equation
1 = [tex]\frac{5}{16}[/tex] + c ⇒ c = 1 - [tex]\frac{5}{16}[/tex] = [tex]\frac{11}{16}[/tex]
y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{11}{16}[/tex]
A teacher is buying supplies for two art classes. For class 1, the teacher buys 24 tubes of paint, 12 brushes, and 17 canvasses. For class 2, the teacher buys 20 tubes of paint, 14 brushes, and 15 canvasses. Each tube of paint costs $3.35, each brush costs $1.75, and each canvas costs $4.50. Compute the following matrix multiplication to determine how much the teacher spent on each class.
Answers
Class 2 =$159
Class 1
24 tube of paint / $3.35 each
12 brushes/ $1.75 each
17 canvases/$4.50 each
Total cost of paint= $80.40
Total cost of brushes=$21
Total cost of canvases= $76.50
Total spent on class 1 = $177.90
Class 2
20 tubes of paint/$3.35 each
14 brushes/$1.75 each
15 canvases/ $4.50 each
Total cost of paint=$67
Total cost of brushes =$24.50
Total cost of canvases=$67.50
Total spent on class 2 = $159
Which polynomial below could produce this graph?
Answers
Answer:
f(x) = (x + 20)(x - 24)(x + 10)(x + 12)
Step-by-step explanation:
This is an equation of degree 4 and as the beginning of the graph descends from negative x the polynomial will have a positive leading coefficient. The graph is roughly W shaped.
It also has zeroes at x = -20,-12 ,-10 and x = 24.
So it is the first option.
Malik wanted to give away \frac{1}{5} 5 1 of his bag of balloons to his 3 friends. What fraction of balloons will he give away?
Answers
Answer:
The answer is 3/5
Step-by-step explanation:
The amount of balloon to be given away= 1/5
The number of friends to
receive the balloon = 3
Therefore the total fraction of balloons that he gave away = 1/5 × 3
=3/5
SOMEONE PLEASE HELP THIS IS DUE TOMROROW EZ WORK
PLEASE ANSWER THEM PROPERY FULL SENTENCES
Answers
Answer:
1.) At times, designing a good structure with a specific function may often be difficult. If the structure is not well-designed or strong enough for the function it will not properly work. So in order for the design to be well-built, both the structure and function must cooperate.
2.) Symmetry is a balanced arrangement on the opposite sides of a structure. In order for for a structure to be stable and properly work without complications, it most commonly needs to be symmetrical. This is a very important part of designing a structure.
3.) If the structure cannot withstand the function nor the possible forces that it may encounter. It is likely that it will break or even be completely destroyed.
4.) Shape, line, color, texture, movement, space. The designer may have taken into consideration whom the desk may be used by for the shape and space. Color, texture, and line may have been based on the environment (ex. A carpenter, student, computer desk) it would be in. Although the designer may not have an exact knowledge of where the desk would be, he still could consider what the desk could "possibly" be used for. Once again, the designer could take into consideration the user, for the movement of the desk. If the desk was to be moved around on wheels, or possibly could even fold. The designer must take into consideration EVERY detail.
6.) When people design something, often times you do not know how well that design is going to work without testing it with a prototype. Yes, prototypes are expensive. Yet, if they were to build something without testing their design, something may be wrong with it. So as a result, you will spend more money manufacturing something with a defect than testing it with a prototype.
For question 5, I think it might be best if you answer that one. It is based on YOUR opinion and what YOU use. If you are asked about it, they will know it's from you and your opinion. Lol! But I hope I helped you out with the other questions! ;)
During the carnival, tickets were sold for a raffle. Carnival workers counted sales every 30 minutes. The number of tickets sold were: 123, 145, 110, 256, 123. What was the median number of tickets sold?
Answers
Answer:
123
Step-by-step explanation:
First arrange in ascending or descending order
110,123,123,145,256
Then pick the number in the middle which is 123
but if you have 2 middle numbers add them together and divide by 2
Please help. I am very confused about this problem.
Answers
jzgsgßiqhwgwgah I don't know
Answers:
number of sides = 15regular polygon name = regular 15-gon=======================================================
Explanation:
If 156 degrees is the interior angle measure, then 180-156 = 24 is the exterior angle measure.
Divide 360 over this to find that 360/24 = 15
This means the regular polygon has 15 sides.
I'm using the idea that if n is the number of sides, then 360/n is the exterior angle measure. So 180 - (360/n) is the interior measure.
Match the solution set given in inequality notation with the solution set given in interval motion x > 7.8
Answers
Answer:
(7.8, ∞)
Step-by-step explanation:
Given the inequality :
x > 7.8 ; the inequality can be explicitly interpreted as x greater than 8 ; this means that the inequality holds for all values of x above 7.8
The interval for which the inequality holds true is :
x > 7. 8 - - - > (7.8, ∞)
can you help me find the code
link/picture in the comments
Answers
Answer:
????? sus
Step-by-step explanation:
sussy baka????
among sus
An arc on a circle of radius 10 has an arc length of 49/9 . What is the degree measure of the corresponding central angle?
Answers
Hope this help!!!
Have a nice day!!!
Answer:
Central angle = 98 degrees
Step-by-step explanation:
Radius (r) = 10 Arc length = 49[tex]\pi[/tex]/9
Let 0 be the central angle
Arc Length = 2[tex]\pi[/tex]r0/360
49[tex]\pi[/tex]/9 = 2[tex]\pi[/tex]r0/360
49[tex]\pi[/tex]/9 = [tex]\pi[/tex]x0/18
49[tex]\pi[/tex]/9 x 18/[tex]\pi[/tex] = 0
0 = 49x2
0 = 98 degrees
Find the area of the equilateral triangle when the base is 2.0 cm and the top angle is 50°
Answers
Answer:
There is an error in the question.
All angles in an equilateral triange are 60º
simpifly this expression, i only need answer b :)
Answers
Answer:
1) x³y²
2) 6x²y³
Step-by-step explanation:
hope it helps...
which pairs of angles in the figure below are vertical angles select all that apply
Answers
Answer:the left one
Step-by-step explanation:
0.202 round to the hundredth
Answers
Answer:
0.20
Step-by-step explanation:
