Please answer these with lots of detail. I want to be able to understand the topic and material well.
Answers
Step-by-step explanation:
Q3
(a) If 0 < |x − 1| < δ, then |f(x) − 2| < 2
What this means is, how far can x stray from the x=1 line such that f(x) stays within 2 units of the y=2 line (0 < f(x) < 4).
If we move 2 units left of x=1, we get f(x) = 4.
If we move about 3.5 units right of x=1, we get f(x) = 4.
Therefore, δ can't be more than 2.
(b) If 0 < |x| < δ, then |f(x) − 3| < 1
What this means is, how far can x stray from the x=0 line such that f(x) stays within 1 unit of the y=3 line (2 < f(x) < 4).
If we move 1 unit left of x=0, we get f(x) = 4.
If we move 1 unts right of x=0, we get f(x) = 2.
Therefore, δ can't be more than 1.
Since f(x) isn't continuous within this domain, we can't conclude that the limit exists.
Q4
(a) Yes. If δ = 0.25, then 0.75 < x < 1.25, and f(x) > 200.
(b) No. f(1) = 300, so even if δ = 0, f(x) will be less than 400.
(c) Yes. If δ ≈ 0.1, then 0.9 < x < 1, and f(x) > 450.
Related Questions
need help on question 4??
Answers
HK consists of two part, HJ and JK
HK = HJ + JK
We know that:
HK = 12.2ft
JK = 3.1ft
HJ = ?
Let's plug our values into the equation above.
12.2ft = HJ + 3.1ft
Subtract 3.1ft from both sides.
9.1ft = HJ
Which equation is equivalent to x + x - (-3) = 12?
A. x2 + 3 = 12
B. x2 – 3 = 12
C. 2x + 3 = 12
D. 2x – 3 = 12
Answers
Answer:
C.) 2x+3 = 12
Step-by-step explanation:
x+x=2x
2x-(-3) is 2x+3
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can you help me estimate 102.3+4.7
Answers
Answer: 107
Step-by-step explanation:
102.3 can be rounded down to 102 (because the 3 at the end of the number is less than 5)
4.7 can be rounded up to 5 (because the 7 at the end of the number is greater than 5).
102.3 → estimate = 102
4.7 → estimate = 5
estimated sum = 107
Note that estimating the sum is NOT the same as simply adding the numbers and then rounding the sum.
You work side jobs for family and friends
which you charge $15 per job. You have
already made $75. How many more jobs do
you have to work if you try to save for a
concert ticket that costs $300?
Answers
Because
300-75= 225
225/15=15
Therefore 15 is the answer
Answer:
15 more jobs
Step-by-step explanation:
So you do 15 x 15 and that equals 225. Then you take 225 + 75 and that equals 300 so in total you just need 15 more jobs to get 300 dollars.
5 Kari makes a kite in the form of a parallelogram, EDGF, as shown in the diagram. Its diagonals [DF] and [EG] intersect at point H. She plots the vertices on a coordinate system with the following coordinates:
D(3,6), G(1,3), H(4, y) and E(x, 6). Find the values of x and y.
Answers
Answer:
The values of x and y are;
x = 7 and y = 4.5
Step-by-step explanation:
The question is a word problem, given that the shape of the kite Karl makes is a parallelogram
The coordinates of the vertices are;
D(3, 6), G(1, 3), H(4, y), and E(x, 6)
From the properties of a parallelogram we have;
The diagonals bisect each other
Therefore;
GH = EH = 1/2·GE
Therefore, we have;
The coordinates of the point H = The coordinate of the midpoint of the line EG
The coordinates of the midpoint of a line with end points, (x₁, y₁) and (x₂, y₂) is given as follows;
The coordinates of the midpoint of a line = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Therefore;
The coordinates of the midpoint of the line EG are ((1 + x)/2, (3 + 6)/2)
Given that the midpoint of EG is the point H and the coordinate of the point H is (4, y), we have;
(1 + x)/2 = 4, therefore;
2 × 4 = 1 + x
8 = 1 + x
x = 8 - 1 = 7
Similarly, we have from the coordinate of point H which is given as follows;
((1 + x)/2, (3 + 6)/2) = (4, y)
y = (3 + 6)/2 = 9/2 = 4.5
Therefore, x = 7, y = 4.5.
Parallel sides of a parallelogram have the same slope
The values of x and y are 6 and 3, respectively.
The coordinate points are given as:
[tex]\mathbf{D =(3,6)}[/tex]
[tex]\mathbf{G =(1,3)}[/tex]
[tex]\mathbf{H =(4,y)}[/tex]
[tex]\mathbf{E =(x,6)}[/tex]
Lines DG and HE are parallel.
This means that they have the same slope (m)
The slope is calculated as:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m_{DG} = \frac{3 - 6}{1 - 3}}[/tex]
[tex]\mathbf{m_{DG} = \frac{- 3}{- 2}}[/tex]
[tex]\mathbf{m_{DG} = \frac{3}{2}}[/tex]
Similarly
[tex]\mathbf{m_{HE} = \frac{6 - y}{x - 4}}[/tex]
The slopes are equal.
So, we have:
[tex]\mathbf{\frac{6 - y}{x - 4} = \frac 32}[/tex]
By comparison:
[tex]\mathbf{6 - y = 3}[/tex] and [tex]\mathbf{x - 4 = 2}[/tex]
Solve for y in [tex]\mathbf{6 - y = 3}[/tex]
[tex]\mathbf{y = 3}[/tex]
Solve for x in [tex]\mathbf{x - 4 = 2}[/tex]
[tex]\mathbf{x = 6}[/tex]
Hence, the values of x and y are 6 and 3, respectively.
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Put the following numbers in order from least to greatest (put the lowest number on the left)
-63,-34,-68,-44,-47
Answers
Answer:
-68 < -63 < -47 < -44 < -34
QUICK NEED HELP LAST QUESTION ILL GIVE BRAINLY TO WHO EVER ANSWERS FIRST
Answers
Answer:
no
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
15 divided by 6 equals 2.5
An oak tree casts a shadow 18 feet long. If a 4 foot child casts a 3 foot shadow at the same time of day, how tall is the oak tree?
Answers
Answer:
23.99999 rounded 30
Step-by-step explanation:
4/3 x 18
PLEASE HELP
Which graph represents the system of inequalities?
y+3/4x<2
y-1 ≥ 2x
Answers
Inequalities are used to represent unequal expressions.
See attachment for the graph of [tex]y + \frac 34 x < 2[/tex] and [tex]y - 1 \le 2x[/tex]
The inequalities are given as:
[tex]y + \frac 34 x < 2[/tex]
[tex]y - 1 \le 2x[/tex]
Make y the subject in both inequalities
[tex]y < - \frac 34 x + 2[/tex]
[tex]y \le 2x +1[/tex]
[tex]y < - \frac 34 x + 2[/tex]
The above inequality has a negative slope< indicates that the inequality will make use of dotted lines[tex]y \le 2x +1[/tex]
The above inequality have a positive slope< indicates that the inequality will make use of closed linesNone of the given graphs represent the system of the inequalities
See attachment for the graphs of [tex]y + \frac 34 x < 2[/tex] and [tex]y - 1 \le 2x[/tex]
Read more about inequalities at:
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Evaluate a+b+c when a=4.035, b= -17, and c=12.3
Answers
Ariana has atoy car collection. She keeps 14 of the toy cars on her wall, which is 35% of her entire collection. What is the total number of toy cars in Ariana's collection?
Answers
Answer:
40 cars
Step-by-step explanation:
The total percentage of Ariana's car collection should be = 100%
35% of the collection = 14
1 percent = 14/35
1 percent is therefore 0.4
To get the total number of cars in Ariana's collection, we multiply 100 by 0.4
= 100 x 0.4 = 40
Therefore the total number of cars in her collection is equal to 40 and this is the answer to the question.
Another way to solve this is by cross multiplication
35% = 14
100% = ?
When we cross multiply we have:
(100x14)/35
= 1400/35
= 40
Thank you!
How do you find 2-4-n=
Answers
Answer:
[tex]a^{3}[/tex]=-5
Step-by-step explanation:
2) translation: 1 unit left and 2 units up
Answers
Answer:
[tex](x,y)\rightarrow(x-1,y+2)[/tex]
Step-by-step explanation:
One unit left would be subtracting 1 from the pre-image's x-value.
Two units up would be adding 2 to the pre-image's y-value.
The translation rule would be:
[tex](x-1,y+2)[/tex]
Hope this helps.
The coordinates after the translation of 1 unit left and 2 units up will be (x-1,y+2).
What is geometric transformation?It is described as the alteration of the geometric body's form and coordinates. It is also known as a two-dimensional transformation. Rotation, translation, reflection, and gliding translation are just a few of the geometric transformations that may affect geometry.
It is given that the coordinates of the points are (x,y)
We have to find the coordinates after the translation of 1 unit left and 2 units up.
A sort of transformation called a translation involves moving each point in a figure the same distance in the same direction.
The final unit would be to deduct 1 from the x-value of the pre-image. The pre-y-value images would be increased by 2 by moving two units higher.
Thus, the obtained coordinates will be (x-1,y+2).
The question is incomplete.
The complete question is" if the coordinates of the points are (x,y). What will be the coordinates after the translation of 1 unit left and 2 units up?
Learn more about the geometric transformation here:
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Please help me with this is so important
Answers
Step-by-step explanation:
78 + 119 + 105 + (180 - x) = 360
482 - x = 360
482 - 360 = x
122 = x
x = 122°
Answer:
it is trapezium and all angles value is 360 degree and three angles values are given then let unknown angle be y and add three angles then subtract value from 360 degree then add the value with x and subtract that value from 180 degree
No time is thinking of a six digit number in which all the digits are the same the value of the digit in the thousands place is 8000 what is new Times number
Answers
Answer:
The number is 888888
Step-by-step explanation:
Here, we are interested in knowing the six digit number thought of by No time.
The clue we have here is that the six digit number has same value of digit for all its constituent.
Thus, if the digit in the thousands place is 8,000, then it actually means that it carries a value of 8 and thus, all the digits in the number is 8 alone.
So the 6 digit number is 888888
What are the coordinates of point S?
Answers
Answer:
The coordinates of S is (-2,2)
What is the midpoint of M(6,-1) and S(9,5)
Answers
Answer:
MP= (7.5,2) or another way of it [tex]MP= (\frac{15}{2},2 )[/tex]
Step-by-step explanation:
Midpoint formula: [tex]MP= (\frac{x_1+x_2}{2}),(\frac{y_1+y_2}{2} )[/tex]
[tex]MP= (\frac{6+9}{2}),(\frac{-1+5}{2} )[/tex] 6+9=15 -1+5=4
[tex]MP= (\frac{15}{2}),(\frac{4}{2} )[/tex] 15/2=7.5 4/2=2
[tex]MP= (7.5,2)[/tex]
Solve the equation. 5+4x-7=4x-2-x
Answers
4x-4x+x=-2+7-5
x=0
use the pattern to extend the table.
If the pattern continues. the height of 15 boxes will be how many feet
Answers
Answer:
33.75
Step-by-step explanation:
Every box has a height of 2.25 feet so if you multiply 2.25 times 15, you get 33.75.
I hope this helped!
I need help on question 4 pls explain the answer thanks
Answers
Answer:
1. a
2. b
3. c
Step-by-step explanation:
1. a
For this first graph, we know that it matches a because of the domain. A tells us that the x≠-1. We know this because of the denominator.
(x+1)(x+1)=0 subtract both sides by 1]
x=-1
Therefore, a matches graph 1.
------------------------------------------------------------------------------------------------------
2. b
For graph 2, we can see that the graph is under the x-axis, meaning it is all negative. The only option that gives us a negative point is b. You can tell by the negative sign in front of the square root.
Therefore, b matches graph 2.
------------------------------------------------------------------------------------------------------
3. c
For graph 3, we see that everything is above the x-axis, meaning the graph is always positive. The option that fits this is c. In c, there are absolute values. Absolute values tell us that the answer is always going to be positive.
Therefore, c matches graph 3.
Cual es el perímetro de un rectángulo, si se sabe que el largo mide 6 cm y su ancho, 4 cm?
Answers
Answer:
20
Step-by-step explanation:the trabslation is 'whats the perimiter of a rectanglr if its lenght is 6cm and its width is 4cm'
a group of 4 students needs to share 20 paper clips equally. how many paper clip does each students get
Answers
Answer:
5 paper clips each
Step-by-step explanation:
20/4 = 5
Answer:
They each get 5
Step-by-step explanation:
J is the midpoint of CT
T
If:
CJ = 4x - 9 and
JT = 9x – 34
Find CT.
Answers
Answer:
Step-by-step explanation:
4x - 9 = 9x - 34
-5x - 9 = -34
-5x = -25
x = 5
4(5) - 9 + 9(5) - 34
20 - 9 + 45 - 34
11 + 11 = 22
The value of CT such that J is the midpoint of CT will be 22.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
As per the given,
J is the midpoint of CT
CJ = JT
4x - 9 = 9x - 34
-9 + 34 = 9x - 4x
25 = 5x
x = 5
So CT = 2(CJ) = 2(4 x 5 - 9) = 22
Hence "The value of CT such that J is the midpoint of CT will be 22".
For more about the number system,
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Amy has $30 to spend she wants to buy 3 pounds of lemons at two dollars per pound a box of rice for four dollars and seven frozen dinners for three dollars each Will Amy have one dollar left over
Answers
Answer: Amy will not have one dollar left over , but she will have to add an extra dollar to buy all that stuff.
Step-by-step explanation:
First find the cost of the items she want to buy in total.
So she wants to buy 3 pound of lemons at two dollars per pound that will cost her $6.
Seven frozen dinners for three dollars each will cost her $21.
The box of rice will cost her $4.
Add the total cost together.
21 + 4 + 6 = 31
This means she will have to spend $31 in total and that is beyond her budget which is $30 dollars. This also means that Amy will not have one dollar left over but she will need to add one dollar.
Answer:
Amy won't have 1 dollar left, she will actually need 1 dollar because all of that would be 31 dollars.
Step-by-step explanation:
3 pounds of lemons= $6
1 box of rice= $4
7 frozen diners= $21
6+4=10
10+21=31
Polynomials: I’ll give brainliest. What is the perimeter of this?
Answers
2(5x - 4)
Step-by-step explanation:Perimeter formula
P = 2l + 2w
P = 2(3x - 5) + 2(2x + 1)
= 6x - 10 + 4x + 2
= 10x - 8
= 2(5x - 4)
Thomas the giant gorilla climbed to the top of the building 650 feet tall. He broke loose a statue and threw it down with an initial velocity of 50 feet per second. How long will it take for the statue to hit the ground. First person to answer gets brainliest
Answers
Answer:
13
Step-by-step explanation:
time=distance÷speed
650÷50=13
The time taken by the gorilla to hit the ground will be 13 seconds.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that Thomas the giant gorilla climbed to the top of the building 650 feet tall. He broke loose a statue and threw it down with an initial velocity of 50 feet per second.
The time taken by the gorilla will be calculated by the formula of speed below,
Speed = Distance / Time
Time = Distance / Speed
Time = 650 / 50
Time = 13 seconds
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Zelly works 10 hours a week at a food market for $6.50 an hour she takes Home $5.20 an hour after deductions what is her rate for deductions use an equation to model the problem and solve it use our to represent the rate for her deductions
Answers
Answer:
$1.40/ hour
Step-by-step explanation:
The rate of the deductions is
Full amount minus new amount. This is the amount taken per hour
$6.50/ hour -$5.2/hour = rate
$1.40/ hour
Solve by elimination
3x-30=Y
7y-6=3x
Answers
HELP PLS WILL GIVE BRAINLISTE
Answers
Answer:
C.
Step-by-step explanation:
all you have to do is replace the x with 14 until the equation is true.
Answer: C and H
Step-by-step explanation:
plugging in for each equation for the first one C is the only one that comes up with a whole number and with H you divide and then add to get the answer :)
This triangle has an exterior angle labeled ZA.
All of the interior angles are labeled correctly.
800
ZA
600
400
Which statement about the exterior angle is
correct?
A. It is 140° because it is supplementary to 40°.
B. It is 50° because it is complementary to 40°.
C. It is 120° because 40° +80° = 120°.
D. It is 60° because 60° + 40° = 100°.
Answers
Answer:
A. It is 140° because It is supplementary to 40°
It is 140° because it is supplementary to 40°. Then the correct option is A.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Angle ∠A and angle 40° are supplementary angles. Then the equation is given as,
∠A + 40° = 180°
∠A = 140°
The proportion of point ∠A will be 140°. It is 140° in light of the fact that it is strengthening to 40°. Then the right choice is A.
More about the angled link is given below.
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