Perfomance task pre-cal
Part 1: Determine the limits of a function given a graph
Answers
The value of limits and function values for a, b, c, d, e, f, g, h, i, and j are 3, -1, does not exist, 3, 1, 2, does not exist, 2 +∞, and -∞ and doesn't follow continuity conditions and its jump continuity.
What is the limit?A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.
We have a graph of a function:
For [tex]\lim_{x \to -1^{-1}} f(x)[/tex]
As we can see x approaches -1 and it is a left-hand limit.
[tex]\lim_{x \to -1^{-1}} f(x) = 3[/tex]
For [tex]\lim_{x \to -1^{+1}} f(x)[/tex]
The x approaches the +1 and it is the right-hand limit.
[tex]\lim_{x \to -1^{+1}} f(x) = -1[/tex]
For [tex]\lim_{x \to -1} f(x)[/tex]
Since the left hand and right-hand limits are not the same,
[tex]\lim_{x \to -1^{+1}} f(x)[/tex] = does not exist
From the graph:
f(-1) = 3
Similarly, we can find further values of the limits and functions value:
[tex]\lim_{x \to 2^{-1}} f(x) = 1[/tex]
[tex]\lim_{x \to 2^{+1}} f(x) = 2[/tex]
For [tex]\lim_{x \to 2^{}} f(x)[/tex]
Since the left hand and right-hand limits are not the same,
[tex]\lim_{x \to 2^{}} f(x)[/tex] = does not exist
f(2) = 2
[tex]\lim_{x \to -\infty} f(x) = +\infty[/tex]
[tex]\lim_{x \to +\infty} f(x) = -\infty[/tex]
There are three conditions a graph must follow:
1) function value defined at any given point.
2) left-hand limit and right-hand limit must be equal
3) function value at the point and limit value at the same point must be the same.
In the given function the graph doesn't follow these conditions and its jump continuity.
Thus, the value of limits and function values for a, b, c, d, e, f, g, h, i, and j are 3, -1, does not exist, 3, 1, 2, does not exist, 2 +∞, and -∞ and doesn't follow continuity conditions and its jump continuity.
Learn more about the limit here:
https://brainly.com/question/8533149
#SPJ1
Related Questions
Help
…… asap no links
Answers
Answer:
Answer Linked below
Step-by-step explanation:
solve for x ~
[tex]16x - 4 = 0[/tex]
thankyou ~
Answers
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
Here we go ~
[tex]\qquad \tt \dashrightarrow \:16x - 4 = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:16x - 4 + 4 = 0 + 4[/tex]
[tex]\qquad \tt \dashrightarrow \:16x = 4[/tex]
[tex]\qquad \tt \dashrightarrow \:x = 4 \div 16[/tex]
[tex]\qquad \tt \dashrightarrow \:x = \frac{1}{4} [/tex]
The Value of x is :-
16x - 4 = 0
16x = 4
x = 4/16
x = 1/4
PLEASE ANSWER AS SOON AS POSSIBLE WILL GIVE "Brainliest" TO THE FIRST CORRECT PERSON!!!
Find the values of x and y. Write your answers in the simplest form.
Answers
Answer: [tex]x=18[/tex] ; [tex]y=6\sqrt{3}[/tex]
Step-by-step explanation:
You can write two expressions that are in terms of 'x' and 'y'. This is a right triangle, so Pythagorean's theorem can be used. We can also use the angle to find the sine of 30 degrees.
Pythagorean's Theorem:
The values 'a' and 'b' are the two shorter sides of the triangle, while the value 'c' is the longest side of the triangle; the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
[tex]x^2+y^2=(12\sqrt{3} )^2[/tex]
[tex]x^2+y^2=12^2*\sqrt{3} ^2=432[/tex]
Sine of the Angle:
Sine is defined to be the opposite side divided by the hypotenuse. Let's take the sine of 30 degrees:
[tex]sin(\alpha )=opposite/hypotenuse[/tex]
[tex]sin(30)=y/12\sqrt{3}[/tex]
[tex]\frac{1}{2} =y/12\sqrt{3}[/tex]
[tex]y=6\sqrt{3}[/tex]
Plug this value of 'y' into the first expression derived from Pythagorean's theorem:
[tex]x^2+y^2=432[/tex]
[tex]x^2+(6\sqrt{3} )^2=432[/tex]
[tex]x^2+108=432[/tex]
[tex]x^2=432-108=324[/tex]
[tex]x=\sqrt{324}[/tex]
[tex]x=18[/tex]
Use this value of 'x' to solve for 'y' in the expression from Pythagorean's theorem:
[tex](\sqrt{324})^2+y^2=432[/tex]
[tex]324+y^2=432[/tex]
[tex]y^2=432-324=108[/tex]
[tex]y=\sqrt{108}[/tex]
[tex]y=\sqrt{36*3}[/tex]
[tex]y=6\sqrt{3}[/tex]
Tristan is comparing two number patterns based on the information below.
Both patterns start with the number 1.
Pattern A follows the rule “add 3”.
Pattern B follows the rule “add 4”.
How does each of the first 5 terms in Pattern A compare to the first 5 terms in Pattern B?
As part of your answer, list the first 5 terms of each pattern.
Explain your answer.
Answers
Pattern A = 1, 4, 7, 10, 13
Pattern B = 1, 5, 9, 13, 17
Each term is increases at a faster rate in pattern B; the difference between terms increases by one per step. In pattern A, 1 jumps to 4, while in pattern B, 1 jumps to 5. There is a difference of one. But when in pattern A, 4 jumps to 7, in pattern B, 5 jumps to 9. The is a difference of two between these two terms even though they are on the same "jump." This difference increases by one per "jump." (Jump is not the official word for this but I'm assuming this isn't a sequence problem.)
Help will give thanks to the first to answer
Answers
Answer:
x-4
Step-by-step explanation:
because a number could be x and all you have to do is subtract 4 from a number making it x-4
Answer:
4-x
Step-by-step explanation:
Because it says that x is subtracted from 4 which would make it understood that 4 is the first term and then x.
If 1/4in on a map represents 1 meter, how many meters does 4/5in represent?
Answers
Answer:
3 1/5 meters
Step-by-step explanation:
1/4 in. on map ⇒ 1 meter in real life
1/4 can also be written as 5/20⇒ 1/20 = 1/5 meter⇒ 4/5 in. = 16/20 inches
⇒ 16/20 inches = 1/5 x 16 = 3 1/5 meters
If 9% of a number is 75, find 3% of that number.
Delta math again.
Answers
Answer:
25
Step-by-step explanation:
[tex]0.09a=75\\a=\frac{75}{0.09} \\0.03*a=0.03*\frac{75}{0.09} =25[/tex]
factor completely 36x-60
Answers
Explanation:
1) Highest common factor is 6, as 36 and 60 are both divisible by 6.
2) Take the highest common factor (6) outside of brackets and throw everything else inside the brackets.
3) 6 times ?= 36x
?= 6x so we get: 6(6x___)
4) 6 times?= -60
?= -10 so we get: 6(__-10)
5) Combine your knowledge of both and get the answer: 6(6x-10)
Hope that helps and is simple enough!
help!
factor as the product of biomionals
64-16x+x^2
Answers
Answer:
(x-8)(x-8) are the factors of the following biominals
Answer:
Step-by-step explanation:
How many significant figures are represented in 0.00509?
Answers
Answer:
there are three significant numbers
Answer:
three
Step-by-step explanation: 0.00509; the first three zeros are not significant since they come before a non-zero number, the final three digits are significant
I need help please. I have no idea how to do this
Answers
Answer:
Letter A is 100 degrees.
Letter B is 80 degrees.
Step-by-step explanation:
50+60= 110
180-110= 80 <- the leftover degrees for the triangle
a line is 180 degrees, so 100 degrees is left over for letter A.
WILL GIVE BRAINLEST! Pls answer fast :)
An oil company uses cylindrical storage tanks. Each tank has a radius of 14 ft and is 27 ft tall.
What is the volume of a tank?
Answers
Answer:
C. 5,292[tex]\pi[/tex]ft²
Step-by-step explanation:
V=[tex]\pi r^2h[/tex]
V=[tex]\pi *14^2 *27[/tex]
[tex]14^2*27= 5,292[/tex]
Answer is C. 5,292[tex]\pi[/tex]ft²
Hope this helps! Have a good day! :)
Answer:
c
Step-by-step explanation:
hope this helps have a nice day:)
how much longer is 18.25 centimeters than 75.4 milimeters
Answers
Answer:
10.71
Step-by-step explanation:
You first convert 75.4 millimeters to centimeters, and you will get 7.54. Now you subtract 18.25 and 7.54 to get the answer 10.71
Which point is not on the graph of the function y = x - 1?
(9, 8)
(8, 7)
(5, 6)
(4, 3)
Answers
Answer:
C. (5,6)
Step-by-step explanation:
Hope this helps. please give brainliest
Help will give thanks to the first to answer
Answers
Answer:
[tex]56[/tex]
Step-by-step explanation:
[tex]10 \times 5 + 6[/tex]
[tex]50 + 6 = 56[/tex]
10 (5) + 6
50 + 6 = 56
The area of the triangle below is 29.25 square centimeters. What is the length of the base?
Answers
Answer:
b = 9
Step-by-step explanation:
0.5 bh= 29.25
thus
(0.5)(b)(6.5)=29.25
thus
b= 58.5/6.5 = 9
Answer:
9?
Step-by-step explanation:
Graded Assignment
Unit Test, Part 2: Two-Dimensional Geometry
Answer the questions below. When you have finished, submit this assignment to your teacher by the due date for
full credit.
Total score:
of 15 points
(Score for Question 1:,
of 5 points)
1.
The iS diagram shown is two intersecting lines. The measure of 25 is 47°.
(a) What is the measure of 27 ? How do you know. Explain you answer in complete sentences.
(b) Suppose the measure of 26 can be represented by (2x-5)). What equation can be written to solve
for the value of x?
(c) What is the value of x?
Answer:
Answers
By using what we know about intersecting lines, we will see that:
a) ∡7 = 47°b) 47° + (2x - 5)° = 180°c) x = 69How to get the measures of the angles for two intersecting lines?When two lines intersect, 4 angles are formed. There are two properties that these angles have.
If the angles are adjacent, then their measures add up to 180°If the angles are not adjacent, these angles have the same measure.a) We know that ∡5 = 47°
And 7 is not adjacent to 5, then 7 has the same measure:
∡7 = 47°
b) 6 and 5 are adjacent, then we must have that:
∡5 + ∡6 = 180°
47° + (2x - 5)° = 180°
That is the equation we need to solve to get the value of x.
c) To solve the linear equation we need to isolate x, let's do that:
47° + (2x - 5)° = 180°
(2x - 5)° = 180° - 47° = 133°
2x - 5 = 133
2x = 133 + 5 = 138
x = 138/2 = 69.
If you want to learn more about linear equations, you can read:
https://brainly.com/question/1884491
Answer:
a) <5 and <7 have congruent angles. That means that both angles are equal, they have the same measure. This means that the measure of <7 is 47°.
<7 = 47°
b) 5 and 6 are adjacent, so this is the equation that we have to do to solve for the value of x.
<5 + <6 = 180°
47° + (2x - 5)° = 180°
c) To solve the linear equation we need to isolate x.
47° + (2x - 5)° = 180°
(2x - 5)° = 180° - 47° = 133°
2x - 5 = 133
2x = 133 + 5 = 138
x = 138/2 = 69
The dot plot below shows the number of books 26 students read in a month:
Dot plot labeled Number of Books Read shows 10 dots over 0, 7 dots over 1, 3 dots over 2, 2 dots over 3, 1 dot over 4, and 3 dots over 10.
Is the median or the mean a better center for this data and why?
Mean; because the data is skewed and there are outliers
Mean; because the data is symmetric and there are outliers
Median; because the data is skewed and there are outliers
Median; because the data is symmetric and there are outliers
Answers
Answer:
The answer is A. Mean; because the data is skewed and there are outliers
Answer:
The answer is A
Jake is enclosing a rectangular field that is 47 yards by 158 yards with wood fencing. The cost per foot of wood fencing is $3.28.
How much will the wood fencing cost?
Answer options with 4 options
A.
$672.40
B.
$1,344.80
C.
$2,017.20
D.
$4,034.40
Answers
Answer:D
Step-by-step explanation: Perimeter of field is 2(length +breadth)
=2(47+158)
=410 yards.
Convert to feet= 1230ft
1ft =$3.28
1230ft will be 1230×3.28
Ans $4034.4
1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Answers
weekly raise= $145
solution:let's assume the first paycheck as x.
she got a weekly raise of $145.
So, after concluding the first week she'll get $ (x+145).
likewise, after completing the second week she'll get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
therefore, this is how her salary will get increased by $145 at the end of every week.
Please help me with this. (Geometry)
Answers
Step-by-step explanation:
Pythagoras's rule: [tex]a^2 + b^2 = c^2[/tex] becomes [tex]x^2 + 10^2 = y^2[/tex]
If we say b = 10: [tex]b = 10 = \sqrt{c^2 - a^2} = \sqrt{y^2 - x^2}[/tex]
You only need to look at the left triangle
Which of the options follows Pythagoras's rule?
Let's try the options until we get the right one (in no particular order)
If we try: 3) x = 4 y = [tex]29\sqrt{2}[/tex]...
[tex]\sqrt{(29\sqrt{2})^2 - 4^4} = 7\sqrt{34} \neq 10[/tex]
If we try: 4) x = 16 y = 116...
[tex]\sqrt{116^2 - 16^2} = 20\sqrt{3} \neq 10[/tex]
If we try: 2) x = 16 y = 29...
[tex]\sqrt{29^2 - 16^2} = 3\sqrt{65} \neq 10[/tex]
If we try: 1) x = 4 y = [tex]2\sqrt{29}[/tex]...
[tex]\sqrt{(2\sqrt{29})^2 - 4^2} = 10[/tex]
Solve by factoring.
4m2−3m−27=0
Answers
Answer:
[tex]m = 3 m = - \frac{9}{4} [/tex]
Step-by-step explanation:
correct me if I'm wrong
the sum of the digits of a two - digit number is 14 . if the digits are reversed, the number increases by 36 . find the number .
Answers
Let the tens digit of the number be x .
ones digit = ( 14 - x ) ( since the sum of the 2 digits is 14 )
Two - Digit number = 10 ( tens digit ) + ones digit
Required number ,
10x + ( 14 - x ) 10x - x + 14 9x + 14Reversed number ,
10 ( 14 - x ) + x 140 - 10x + x 140 - 9xGiven ,
Reversed number - Required number = 36
✯ 140 - 9x - ( 9x + 14 ) = 36
✯ 140 - 9x - 9x - 14 = 36
✯ 126 - 18x = 36
✯ 126 - 36 = 18x
✯ 18x = 90
✯ x = 5
Ten digits , x = 5 Ones digits = ( 14 - x ) = 14 - 5 = 9♧ Thus , Required number is 10 × 5 + 9 = 59
Given -
the sum of the digits of a two - digit number is 14.i.e, if two numbers are x and y then, x + y = 14
if the digits are reversed, the number increases by 36i.e, if 10y + x then 10y + x = 10x + y + 36.
To find -
the numberConcept -
If a, b and c are real number (and if a and b both are not equal to 0) then ax+by=c is called a linear equation in two variables (The two variables are x and y)
The numbers a and b are called the coefficient of the equation ax+by=c. The number r is called the constant of the equation ax+by = c
PS - first we will construct two linear equations and then we'll find the number.
Solution -
Let, x + y = 14
➜ y = 14 - x ----(i)
and we'll solve 10y + x = 10x + y + 36 further,
➜ 10y + x = 10x + y + 36
➜ 10y - y = 10x - x + 36
➜ 9y = 9x + 36
➜ 9x - 9y = -36
➜ 9(x - y) = -36
➜ x - y = -4 ----(ii)
Substituting the value of y (in equation (i)) in equation (ii),
➜ x - (14 - x) = -4
➜ x - 14 + x = -4
➜ 2x = -4 + 14
➜ 2x = 10
➜ x = 10/2
➜ x = 5
Now to find the value of y we will substitute the value of x in equation (i),
➜ y = 14 - 5
➜ y = 9
Therefore, the number is {10(5)+9,i.e,} 59.
I have a bunch more questions im sorry i just haveva F in math and need help!
Answers
Answer:
option I
Step-by-step explanation:
Option I 168 yd²
The surface area =168 yd²
I hope it helped you
There are 57 people touring the mooresville zoo. The wagons at the zoo can only carry 7 people. How many wagons will this group need for their tour?
Answers
Since you can’t have 0.1 of a wagon, you would need to have 9 wagons to fit everyone.
Answer: 9 wagons
Find the value of (110) base two leaving your answer in base two
Answers
[tex](110)_{2} = (1 \times 2^2 + 1 \times 2^1 + 0 \times 2^ 0)_{10}\\\\~~~~~~~~~~=(4+2+0)_{10}\\\\~~~~~~~~~~=(6)_{10}[/tex]
What is the range for y=-3x^2-12x-17?
PLEASE ANSWER I WILL GIVE OUT FREE MORE POINT AND MARK BRAINIST ONLY IF YOU GOT IT RIGHT THO I WILL CHECK ! PLEASE AND THANK YOU :))))
Answers
Answer:
RANGE: y greater than or equal to -5 (b)
Graph the function
Attached
Vertex at (-2,-5)Then
y=-(3x²+12x+17)y=-(9x²+36x+51)y=-[(3x)²+2(3x)(6)+51-25+25]y=-[(3x)²+2(3x)(6)+36+25]y=-[(3x+6)²+25]y=-[(3x+6)²+5²]We know
a²+b²=(a-b)²+2abVertex form of parabola
a(x-h)²+kvertex:-
(h,k)=(-2,-5)Range:-
y≤-5y
The equation y=-x2 - 8x – 18 is shown by graph
B
The equation y=x2 - 4x + 7 is shown by graph
6
A
2
NO
2
r
The equation y=x+5 is shown by graph
-10
2
10
The equation y=-3x - 6 is shown by graph
С
DONE
D
Intro
Answers
Answer:
y=-x2 - 8x – 18 is shown by graph D.
y=x2 - 4x + 7 is shown by graph A.
y=X+5 is shown by graph C.
y=-3x - 6 is shown by graph B.
Step-by-step explanation:
In y=-x2 - 8x – 18, the coefficient of x2 is less than 0.So the graph only has a maximum value.Thefore , the graph is point upward.
In y=x2 - 4x + 7, coefficient of x2 is greater than 0.
So the graph has a minimum point and is pointed downward.
for y =x + 5, the gradient is positive.so it is graph C.There is another way to find out too but this is quicker for now.
for y = -3x - 6, the gradient is negative ,-3.So it is the graph B.
Answer:
D A C B
Step-by-step explanation:
if 5 songs can be downloaded for $6, what
is the cost of seven songs?
Answers
Answer:
7 songs costs $8.4
Step-by-step explanation:
6/5= $1.2 for each song
1.2 times 7= $8.4
7 songs costs $8.4
The scatter plot shows the average monthly temperature, x, and a family's monthly heating cost, y, for 23 different months.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the monthly heating cost for a month with an average temperature of 35 °F.
Note that you can use the graphing tools to help you approximate the line.
Answers
1. The equation of the line of best fit is: y = -1.15x + 102.8
2. Using the equation of the line of best fit, the predicted cost is: $62.55
What is the Equation of a Line of Best Fit?The equation of a line of best fit is represented by the equation, y = mx + b, where m is the slope and b is the initial value.
1. Using two points, (72, 20) and (20, 80):
Slope (m) = change in y / change in x = (80 - 20)/(20 - 72) = 60/-52
Slope (m) = -1.15.
Substitute m = -3 and (a, b) = (72, 20) into y - b = m(x - a)
y - 20 = -1.15(x - 72)
y - 20 = -1.15x + 82.8
y = -1.15x + 82.8 + 20
y = -1.15x + 102.8
The equation of the best line of fit is y = -1.15x + 102.8.
2. Monthly heating cost, y, for a month with an average temperature of 35°F (x) will be calculated by substituting x = 35 into y = -1.15x + 102.8.
y = -1.15(35) + 102.8
y = 62.55
The predicted monthly cost is $62.55.
Learn more about the line of best fit on:
https://brainly.com/question/17261411