Let f be the function given by f(x)=∣∣x2−2∣∣(x+0.4)(x2−2)(x+0.4). On which of the following open intervals is f continuous?
Answers
Using the continuity concept, it is found that the function is continuous on the following interval:
C. (0, 1).
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In the context of this problem, the numeric values are especially relevant, as the function not continuous at the zeros of the denominator.
The denominator of the function is given as follows:
(x² - 2)(x + 0.4).
Hence the discontinuity points are:
x² - 2 = 0 -> x = -1.41 and x = 1.41.x + 0.4 = 0 -> x = -0.4.Hence the only interval in which the function is continuous over the entire interval is given by option C.
What is the missing information?The function and the possible options are given by the image at the end of the answer.
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Related Questions
Answer Please
F(x)=5x-1
Answers
Answer:
-1
Step-by-step explanation:
Correct option is A)
Given,
f(x)=5x−1
To find: f(0)
Put x=0 in the given eqation.
Therefore, we get
f(0)=5(0)−1
=0−1
=−1
I need to know which is the best estimate for rabbit population after 5 years
Answers
Answer:
[tex]\text{ B: 800 rabbits}[/tex]Explanation:
Here, we want to estimate the rabbit population after 5 years
From the question, there was an approximate increase in the rabbit population by 150 (from 150 to 300) in a space of 2 years
Let us have an exponential relationship for this:
[tex]P=I.a^t[/tex]Let us get the value of t
P is the current population at 300
I is the initial
a is ?
t is the number of years which is 2
Mathematically, we have it that:
[tex]\begin{gathered} 300\text{ =150 }\times a^2 \\ a^2\text{ = 2} \\ a\text{ = }\sqrt[]{2} \end{gathered}[/tex]Now, for the 5 years tenor, we substitute 5 for t
We have that as:
[tex]\begin{gathered} P\text{ = 150}\times\text{ (}\sqrt[]{2})^5 \\ P\text{ = 849} \end{gathered}[/tex]From the option, we have an approximate value of 800 rabbits
Write the equation of the line in slope-intercept form.
The line is parallel to y + x = 3 and passes through the point (-12, 0).
Please help i will give big points
Answers
Answer:
The line is parallel to y + x =3
=> y = -x+3
the slope = -1
passes (-12, 0)
the equation would be :
y-0 = -1(x+12)
y = -x -12 Y=-x+12
Turn into mx+b form.
Y=-x+3
Plug in (-12,0)
0=-12+b
b=12
y=-x+12
It is negative X, because the slope has to be the same since it is paralle
Step-by-step explanation:
Write the equation of the line that passes through the points (0,3) and (2,-1). Put your answer in point-slope form, using fractional form for m and b.
Answers
The equation of the line that passes through the points (0, 3) and (2, - 1) in point-slope form is y - 3 = - 2 · x, that is equivalent to y = - 2 · x + 3 (m = - 2, b = 3).
How to determine the equation of a lineAccording to Euclidean geometry, a line can be constructed by knowing the location of two distinct points on a plane. Then, we can determin the slope of the line from the two points. First, determine the slope of the line by using the secant line formula:
m = (- 1 - 3) / (2 - 0)
m = - 4 / 2
m = - 2
Second, substitute all the variables in the equation of the line in point-slope form:
y - 3 = - 2 · x (Point-slope form)
y = - 2 · x + 3 (Slope-intercept form)
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what's the value of k
Answers
The sum of complementary angles = 90°
The angle shown is a right angle
Therefore:
k + 54.3 = 90
k = 90 - 54.3
k = 35.7°
Help! Please!!!!!!!!!?
Answers
The estimates for [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{10}{21}[/tex]
The actual answer of [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{30}{63}[/tex]
How to estimate fractions?The estimated answer of the fraction can be done as follows:
[tex]6\frac{1}{9}. 1\frac{5}{7}[/tex]
Hence,
[tex]6\frac{1}{9} = \frac{55}{9}[/tex]
[tex]1\frac{5}{7} = \frac{12}{7}[/tex]
Therefore, the actual answer of the fractions is as follows:
[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = 10\frac{30}{63}[/tex]
Hence, the estimated answer of the fractions can be calculated as follows
[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = \frac{220}{21} = 10\frac{10}{21}[/tex]
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The telephone company offers two billing plans for local calls. Plan 1 charges $29 per month for unlimited calls and plan 2 charges $17 per month plus $0.03 per call. Use and inequality to find the number of monthly calls for which plan is more economically than plan 2
Answers
Calls greater than 400 would be more economical in plan 1 than plan 2 and the inequality is 29 < 17 + 0.03x
How to determine the more economical plan?The given parameters are:
Plan 1
Charges per month = $29Plan 2
Charges per month = $17Monthly rate = $0.03Let the number of months be x.
So, we have the following equation
Plan 1: 29
Plan 2: 17 + 0.03x
For plan 1 to be more economical plan than plan 2, then we have the following inequality
Plan 1 < Plan 2
This is represented as
29 < 17 + 0.03x
Subtract 0.03x from both sides of the inequality
So, we have
0.03x > 12
Divide both sides by 0.03
x > 400
How to interpret the result in (a)?
In (a), we have
x > 400
This means that the number of calls for the plan 1 to be more economical than plan 2, then the number of calls must be greater than 400
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A and B shares a certain amount of money in the ratio x:y. B then
shares his money with C & D in the ratio of p:q respectively. What
fraction out of the total money does C receive?
Answers
So C receives py/(x+y)(p+q) share of money out of the total money
The ratio of money shared between A and B = x:y
Sum of the ratios is x+y
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.
B' share of money = y/(x+y)
The ratio of money between C & D = p:q
Sum of the ratio = p+q
B's share of the money is further divided among C & D in the ratio of p:q therefore:
C's share of money = y/(x+y)*p/(p+q)
= py/(x+y)(p+q)
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8=3+2i and z9 = 4+3i.
Answers
Answer:
8 - 3 = 5
5 divided by 2 = 2.5
i = 2.5
3 x 2.5 = 7.5
4 + 7.5 = 11.5
11.5 divided by 9 = 1.277
z = 1.277
Hope this helps!
AlphaFay
Solve the equation.
−3=z−8
z=
Answers
The answer is 5
Step-by-step explanation:
-3=z-8
put +8 underneath -8. Then cross it out.
Put +8 underneath -3. -3+8=5
The answer is 5.
I hope this helped you!
Consider the following expression 2(x+3). Which of the following represents the correct use of the distributive property? A. 2x+3 B. 2x+6 C. X + 6 D. X^2 + 6x + 9
Answers
denmark uses kroner as its currency. Before a trip to denmark. Mia wants to exchange
$1700 for kroner.
bank a
dollars kroner
80 408
100 510
120 612
Answers
Denmark uses kroner as its currency. Before a trip to Denmark. Mia will get 8670 Kroner in exchange for $ 1700.
bank A
Dollars ($) Kroner
80 408
100 510
120 612
Since $ 80 = 408 Kroner
=> $ 1 = 408 / 80 = 5.1 Kroner . . . . . . conversion rate of $ to Kroner)
=> $ 1700 = 1700 x 5.1 = 8670 Kroner
Hence Mia will get 8670 Kroner in exchange for $ 1700
The exchange rate of conversion from $ to Kroner is arrived at by applying Unitary System of calculation in arithmetic (mathematics).
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A linear function is transformed from y = 3/4x + 1/2 to y = 3/4x + 5/2. What is the corresponding vertical change?A)The graph is shifted up 2 units,B)The graph is shifted down 2 units. C)The graph is shifted up 4 unitsD)The graph is shifted up 5/2 units
Answers
A. The graph is shifted up 2 units
Protein bars come in a 4 pack box or a 12 pack box the 4 pack costs 7.68 and the 12 pack costs 22.32 which box is the better
Answers
Buying 12 pack is better as it is cheaper than 4 pack.
What is unitary method?A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. The unitary method involves determining the value of a single unit before determining the value of the necessary quantity of units.
Given Data
Protein bars come in a 4 pack box or a 12 pack box
4 pack costs 7.68 and the 12 pack costs 22.32
In 4 pack
4 pack = 7.68
1 pack = 1.92
In 12 pack,
12 pack = 22.32
1 pack = 1.86
4 pack > 12 pack
Buying 12 pack is better as it is cheaper than 4 pack.
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The data valo showed a mouse driven on a single day by random sample of 13 student calculate the 38th and the 60th percent all of the data
Answers
To get the percentile
Step 1: Write the formula
[tex]\begin{gathered} P_i=(\frac{i(n+1)}{100})^{th} \\ \\ \text{where n = 13} \end{gathered}[/tex]For the 38th percentile
[tex]P_{38}=(\frac{38(13+1)}{100})^{th}[/tex][tex]P_{38}=5.32^{th}\text{ number}[/tex]This means that the 38th percentile is between the 5th and 6th number
[tex]\begin{gathered} P_{38}=5^{th}\text{ observation}+0.32\lbrack6^{th}-5^{th}\rbrack \\ P_{38}=41+0.32(43-41)=41.64 \\ P_{38}=41.64 \end{gathered}[/tex]P38 = 41.64This means that approximately 38% of the data lie below 43, when the data are ranked
For the 60th percentile,
[tex]P_{60}=(\frac{60(13+1)}{100})^{th}[/tex][tex]P_{60}=8.4^{th\text{ }}n\nu mber[/tex]6089
[tex]P_{}=8^{th}\text{ observation}+0.4\lbrack9^{th}-8^{th}\rbrack[/tex][tex]\begin{gathered} P_{60}=56+0.4(58-56) \\ P_{60}=56.8 \end{gathered}[/tex]60
Mrs. Parkow gives her class clues
about a 5-digit mystery number,
• The 3 is in a place that is 100 times
greater than the place of the 4,
The 2 is in a place that is 10 times
less than the place of the 3.
The 8 is in a place that is 10 times
less than the place of the 4.
The 7 is in a place that is 100 times
greater than the 2
•
•
What is Mrs. Parkow's
5-digit mystery number?
Answers
Mrs. Parkow's 5-digit mystery number is 73248.
What are Numbers up to 5-Digits?Ten thousand is the starting point for five-digit numbers, which go up to ninety-nine million, nine hundred and ninety-nine. Integers are present in the places of ones, tens, hundreds, thousands, and ten thousands in these numbers. Any positive number may be placed at these places, with the exception of 0 at the ten thousands place.
A general 5-digit number can be written as:
a×10000 + b×1000 + c×100 + d×10 + e where a, b, c, and d are single-digit numbers.
a is the ten thousands digit
b is the thousands digit
c is the hundreds digit
d is the tens digit
e is the units digit.
Let 8 be at one's place that is e
Now, it is given that 8 is in a place that is 10 times less than the place of the 4.
This implies 4 is at the ten's place that is d.
Next, it is given that 3 is in a place that is 100 times greater than the place of the 4.
That is 100×10 = 1000 place
So, 3 is at the place of b.
The 2 is in a place that is 10 times less than the place of the 3. So, 2 is at the place of c.
The 7 is in a place that is 100 times greater than the 2. That is 100×100 = 10,000 place.
Thus, 7 is at the place of a.
Thus, we obtain
a= 7
b= 3
c= 2
d= 4
e= 8
Therefore, the 5-digit mystery number is 73248.
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LESSON 1 SESSION
Solve.
Numbers with more than three digits have a comma to separate groups
of three digits. Digits in groups of three places are called periods.
Thousands Period
Hundred
Thousands
2
Ten
Thousands
8
Thousands Hundreds
4
Ones Period
3
Tens
7
Ones
1
Write the number shown above in standard form (the way you usually see it).
Answers
A method of notation in which digits are divided into groups of three by commas is known as the standard form of a number.
When a number has three digits, these groups are termed periods?
The periods are separated by commas.
Large numbers have three spots between each group of digits. Periods are the names of the groups.
The periods are typically separated by commas.
number follows 100000 and 100001
nonetheless, does not include decimals, negative integers, or fractions. Let's first express the quantity in numerical form, so 100,000 represents 100,000. The next whole number after 100,000 is the one obtained by adding 1 to the previous amount. As a result, 100000 + 1 Equals 100001, the following whole number.
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||x+4|-7|<5 how to solve this?
Answers
Answer: [tex](-16, -6) \cup (-2, 8)[/tex]
Step-by-step explanation:
[tex]||x+4|-7| < 5\\\\-5 < |x+4|-7 < 5\\\\2 < |x+4| < 12\\\\1. -2 < x+4 < 2 \implies -6 < x < -2\\\\2. -12 < x+4 < 12 \implies -16 < x < 8\\\\\therefore (-16, -6) \cup (-2, 8)[/tex]
Calculate the circumference of a circle with a radius of 15 inches .Use 3.14 for pi.Round answer to the nearest tenth ,if necessary
Answers
The circumference of a circle whose radius is 15 inches measures 94.2 inches.
How to find the circumference of the circle?For a circle of radius R, the circumference is given by the formula:
C = 2*pi*R
Where pi is 3.14
In this case, we know that the radius is 15 inches, then we can write:
R = 15 in
Replacing that in the circumference formula we get:
C = 2*3.14*15 in = 94.2 inches.
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Find the area of a pantry shelf that measures 3 yards by yard. 6.4yd? 6.4 yd 1żyd 1 fyd
Answers
Option (c)
Given:
The measure of pantry shelf is 3 yard by 3/7 yrds.
The objective is to find the area of the pantry shelf.
The area of shelf can be calculated as,
[tex]\begin{gathered} A=3\times\frac{3}{7} \\ =\frac{9}{7} \\ =1\frac{2}{7}yd^2 \end{gathered}[/tex]Hence, option (c) is the correct answer.
Algebra 2, 50 points, include steps please
(6-4i)(1+5i)-(3-i)
Answers
The simplified representation of the complex number expression is
23 + 37i
a + bi, where a and b are real numbers, can be used to represent any complex number.
A complex number is a component of a number system that includes an element with the symbol I, sometimes known as the imaginary unit, and that extends the real numbers by satisfying the equation i² = -1. i was described as an imaginary number by René Descartes since no real number can fulfil the aforementioned equation. The complex number a + bi is known as having real and imaginary parts, respectively, A and b. The group of complex numbers is denoted by the letter C.The complex number expression is (6-4i)(1+5i)-(3-i)
now let us simplify,
or, (6-4i)(1+5i)-(3-i)
or, 6 + 30i - 4i -20i² -3 + i
or, 6 + 36i + 20 - 3 + i (we know that i² = -1)
or, 23 + 37i
Therefore the simplified complex expression is 23 + 37i
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(05.03 MC)
Two families visited an amusement park. The first family bought 3 hot dogs and 5 bottles of waters, which totaled $20. The second family bought 6 hot dogs and 3 bottles of
waters, which totaled $33. How much did one hot dog cost?
$3
$4
$5
$6
Answers
The cost of one hotdog based on the given situation is $5
The correct answer option is Option C
How to find the cost of one hotdog?let
Cost of hotdogs = hCost of bottle water = wFamily A:
3h + 5w = 20
Family B:
6h + 3w = 33
Solve the two equations simultaneously:
3h + 5w = 20
6h + 3w = 33
Multiply (1) by 2
6h + 10w = 40
6h + 3w = 33
Substract the equations to eliminate h
10w - 3w = 40 - 33
7w = 7
divide both sides by 7
w = 7/7
w = 1
Substitute w = 1 into
3h + 5w = 20
3h + 5(1) = 20
3h + 5 = 20
3h = 20 - 5
3h = 15
divide both sides by 3
h = 15/3
h = 5
So therefore, the cost of one hotdog and one bottle water is $5 and $1 respectively.
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Answer: the answer is 5 dollars
Step-by-step explanation:
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90% confidence interval for the mean score, μ, of all students taking the test?
Answers
The 90% confidence interval for the mean score, μ, of all students taking the test is; CI = (28.36, 30.64)
What is the Confidence Interval?
The formula for confidence interval is;
CI = x' ± z(s/√n)
where;
CI = Confidence Interval
x' is sample mean
z is critical value at confidence level
s is standard deviation
n is sample size
We are given;
n = 59
x' = 29.5
s = 5.2
z at CL 0f 90% = 1.645
Thus;
CI = 29.5 ± 1.645(5.2/√59)
CI = 29.5 ± 1.136
CI = (28.36, 30.64)
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The probability that a new machine will not need any repairs within t years from now is modeled by an exponential function of t. This probability is multiplied by 0.2 whenever the time period t is extended by 3 years as shown by the function belowf(t) = (0.2)^t/3 If the probability that the machine does not need repairs right now is 1, what is the probability that the machine will not need repairs within 12 years from now, according to the model? 0.8 0.05 0.008 0.0016
Answers
viven
t = time
function
[tex]f(t)=0.2^{t/3}[/tex]what is the probability that the machine will not need repairs within 12
rocedure
[tex]\begin{gathered} f(12)=0.2^{12/3} \\ f(12)=0.0016 \end{gathered}[/tex]
The probability would be 0.0016
The table represents a quadratic function. Write an equation of the function in
standard form.
X- -3,-2,-1,0
f(x)-6,0,-2,0
WILL GIVE BRAINLIEST
Answers
Answer:
[tex]y=2x^2+4x[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} x & -3 & -2 & -1 & 0\\\cline{1-5} f(x) & 6 & 0 & -2 & 0\\\cline{1-5}\end{array}[/tex]
The x-intercepts of a quadratic function are when f(x) = 0.
Therefore, the x-intercepts are: x = -2 and x = 0.
Intercept form of a quadratic equation
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-intercepts.a is some constant.Substitute the found x-intercepts and one of the points from the table into the formula and solve for a:
[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies6&=a(-3-(-2))(-3-0)\\6&=a(-1)(-3)\\6&=3a\\a&=\dfrac{6}{3}\\\implies a&=2\end{aligned}[/tex]
Substitute the x-intercepts and the found value of a into the formula:
[tex]\implies y=2(x+2)(x-0)[/tex]
Expand to standard form:
[tex]\implies y=2(x+2)(x-0)[/tex]
[tex]\implies y=2x(x+2)[/tex]
[tex]\implies y=2x^2+4x[/tex]
Hello, I need some assistance with this homework question please for precalculusHW Q10
Answers
SOLUTION
Recall that a quadratic equation is of the form
[tex]ax^2+bx+c=0[/tex]The possible number of zeros of a quadratic function is 2The zeroes of a quadratic function could be real or complex
Therefore a quadratic function can have zero real roots
or 1 real root or 2 real roots.
Which of the following rational fractions is graphed below?
Help please!
Answers
Answer:
[tex]\textsf{A.} \quad f(x)=\dfrac{1}{x-4}[/tex]
Step-by-step explanation:
An asymptote is a line that the curve gets infinitely close to, but never touches.
A vertical asymptote occurs when the denominator of a rational function is zero.
From inspection of the given graph, there is a vertical asymptote at [tex]x=4[/tex] .
Therefore, the denominator of the rational function must equal zero when [tex]x=4[/tex] .
Therefore, the only solution where the denominator is zero when [tex]x=4[/tex] is:
[tex]\boxed{f(x)=\dfrac{1}{x-4}}[/tex]
I need help with the whole question
Answers
Given:
[tex]\begin{gathered} f(x)=2x^2-4x-6 \\ g(x)\text{ = 3x-4} \\ h(x)\text{ = }\frac{2}{x} \\ \end{gathered}[/tex]1.1.1 The equation of the reflection of g(x) in the x-axis is of the form:
The rule for the reflection in the x-axis:
[tex](x,y)\rightarrow\text{ (x,-y)}[/tex]Applying the rule:
[tex]\begin{gathered} g^{\prime}(x)\text{ = -g(x)} \\ =-(3x\text{ -4)} \\ =\text{ 4 -3x} \end{gathered}[/tex]Hence, g'(x) = 4-3x
1.1.2 The equation of the reflection of h(x) in the y-axis.
The rule for reflection in the y-axis:
[tex](x,y)\rightarrow\text{ (-x,y)}[/tex]Applying the rule:
[tex]h^{\prime}(x)\text{ = }\frac{2}{-x}[/tex]Hence, h('x) = 2/-x
1.1.3 The values of k for which :
[tex]k=2x^2-4x-6[/tex]Re-arranging:
[tex]\begin{gathered} 2x^2-4x-6-k\text{ =0} \\ 2x^2-4x\text{ -(6+k) = 0} \end{gathered}[/tex]Using the rule that for an equation to have non-real roots, the discriminant (D) must be less than zero.
[tex]\begin{gathered} D=b^2-4ac \\ (-4)^2\text{ -4(2)-(6+k) }<\text{ 0} \end{gathered}[/tex]Simplifying we have:
[tex]\begin{gathered} 16\text{ +48+8k }<\text{ 0} \\ 64\text{ + 8k }<\text{ 0} \\ 8k\text{ }<\text{ -64} \\ \text{Divide both sides by 8} \\ \frac{8k}{8}\text{ }<\frac{-64}{8} \\ k\text{ }<\text{ -8} \end{gathered}[/tex]Hence, the values of k for which the equation has non-real roots is that k must be less than -8
1.1.4 The average gradient of f(x) between x=-4 and x=0:
First, we need to find the value of f(x) at x=-4.
[tex]\begin{gathered} f(-4)=2(-4)^2\text{ -4(-4) -6} \\ =\text{ 32+16 -6} \\ =\text{ 42} \end{gathered}[/tex]Next, we must find the value of f(x) at x=0:
[tex]\begin{gathered} f(0)=2(0)^2-4(0)\text{ -6} \\ =\text{ -6} \end{gathered}[/tex]Using the average gradient formula:
[tex]\begin{gathered} \text{Average gradient = }\frac{y_B-y_A}{x_B-x_A} \\ =\text{ }\frac{-6-42}{0-(-4)} \\ =\frac{-48}{4} \\ =\text{ -12} \end{gathered}[/tex]Hence, the average gradient is -12
Choose the most convenient method to graph the line y=-1/4x+3
Answers
The graph for the function (y = -(1/4)x + 3) is given in the attached image. See the explanation below.
How do you plot the graph of y = -(1/4)x + 3?
Step 1 Find (x,y) pairs
Step 2: plot the points
Step 3 Draw the line on the graph.
Let's look at Step 1.
Using the graph as an example, our first pair of x,y is (0, 3)
This is obtained by substituting 0 in the equation y = -(1/4)x + 3
⇒ y = -(1/4)0 + 3
y = 0 +3
y = 3, where x = 0
If we repeat this process with x = 1, x = 2, x = 3, we will get the corresponding y for case.
Step 2: Plotting the x,y pairs will give us points on the graph.
Step 3: connecting the dots will give us the same line in the graph that is attached.
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Please help me solve both a and b of this problem.
Answers
A. The relationship between number of towers and number of customers is proportional.
B. 12 customers.
What is a Proportional Relationship?A proportional relationship between two variables, x and y, is a relationship whereby the ratio y/x is the same all through the table of values.
Thus, the value of y/x is constant, and is referred to as the unit rate or constant of proportionality, k.
Part A:
Given the table of values, we have:
Constant of proportionality (k) = y/x = 252/5.25 = 300/6.25 = 348/7.25 = 444/9.25 = 48.
Therefore, it is a proportional relationship because it has a constant of proportionality, k = 48.
Part B:
Substitute k = 48 into y = kx (proportional relationship)
y = 48x.
The equation for the relationship is, y = 48x. Substitute y = 576 into the equation to find the value of x, number of customers:
576 = 48x
Divide both sides by 48
576/48 = 48x/48 [division property of equality]
12 = x
x = 12
The number of customers is 12.
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