Answers
Answer:
(f o g)(x) = 4x^4 - 24x^2 + 37
(g o f)(x) = 16x^4 + 8x^2 - 2
Step-by-step explanation:
f(x) = 4x^2 + 1
g(x) = x^2 - 3
(f o g)(x) = f(g(x)) = f(x^2 - 3) = 4(x^2 - 3)^2 + 1 =
= 4(x^4 - 6x^2 + 9) + 1
= 4x^4 - 24x^2 + 37
(g o f)(x) = g(f(x)) = g(4x^2 + 1) = (4x^2 + 1)^2 - 3 =
= 16x^4 + 8x^2 - 2
Related Questions
Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)
Answers
Answer: Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational.
Step-by-step explanation:
Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth
A shoreline observation post is located on a cliff such that the observer is 280 feet above sea level. The observer spots a ship approaching the shore and the ship is traveling at a constant speed.
Requried:
a. When the observer initially spots the ship, the angle of depression for the observer's vision is 6 degrees. At this point in time, how far is the ship from the shore?
b. After watching the ship for 43 seconds, the angle of depression for the observer's vision is 16 degrees. At this point in time, how far is the ship from the shore?
Answers
Using the slope concept, it is found that the distances from the shore at each moment are given by:
a) 2664 feet.
b) 976 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
Item a:
The vertical distance is of 280 feet, with an angle of 6º. The distance from the shore is the horizontal distance of x. Hence:
[tex]\tan{6^\circ} = \frac{280}{x}[/tex]
[tex]x = \frac{280}{\tan{6^\circ}}[/tex]
x = 2664.
Item b:
The vertical distance is of 280 feet, with an angle of 16º. The distance from the shore is the horizontal distance of x. Hence:
[tex]\tan{16^\circ} = \frac{280}{x}[/tex]
[tex]x = \frac{280}{\tan{16^\circ}}[/tex]
x = 976.
More can be learned about the slope concept at https://brainly.com/question/18090623
Identify the restrictions on the domain.
x+1x+9÷xx−4
x≠−1,4
x≠−9,4
x≠−1,0
x≠−9,0
[tex]Identify the restrictions on the domain. x+1x+9÷xx−4x≠−1,4x≠−9,4x≠−1,0x≠−9,0[/tex]
Answers
PLEASE HELP WILL MARK BRAINLIEST.Write the log equation as an exponential equation. You do not need to solve for x.
In (5) = 2x
Answers
Answer:
10x ÷ 5x=2x
10x ÷ 5x = 2x
10x÷ 5x = 2x
Answer:
[tex]e^{2x}=5[/tex]
Step-by-step explanation:
Recall that [tex]\log_b a=c\implies b^c=a[/tex].
In this case, we need to find the base of the logarithm. The logarithm [tex]\ln[/tex] denotes natural [tex]\log[/tex] with a base of [tex]e[/tex], a mathematical constant.
Therefore, we can re-write the equation as:
[tex]\log_e5=2x[/tex]
To write the equation as an exponential equation, recall the definition of log (first sentence of explanation):
[tex]\boxed{e^{2x}=5}[/tex]
y'+y=y^2; y(0)=-1/3
Giải phương trình trên
Answers
Step-by-step explanation:
[tex]y' + y = y^2[/tex]
We can rewrite the differential equation above as
[tex]\dfrac{dy}{dx} + y = y^2[/tex]
[tex]dy = (y^2 - y)dx[/tex]
or
[tex]\dfrac{dy}{y^2 -y} = dx[/tex]
We can rewrite the left side of the equation above as
[tex]\dfrac{dy}{y^2-y}=\dfrac{dy}{y(y-1)}= \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy[/tex]
We can the easily integrate this as
[tex]\displaystyle \int \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy = \int dx[/tex]
or
[tex]\displaystyle \int \dfrac{dy}{y-1} - \int \dfrac{dy}{y} = \int dx[/tex]
This will then give us
[tex]\ln |y-1| - \ln |y| + \ln |k| = x[/tex]
where k is the constant of integration. Combining the terms on the left hand side, we get
[tex]\ln \left|\dfrac{k(y-1)}{y} \right| = x[/tex]
or
[tex]\dfrac{y-1}{y} = \frac{1}{k}e^x[/tex]
Solving for y, we get
[tex]y= \dfrac{1}{1- \frac{1}{k} e^x}=\dfrac{k}{k-e^x}[/tex]
We know that [tex]y(0)= \frac{1}{3}[/tex], so when we substitute [tex]x=0[/tex], we find that [tex]k = -\frac{1}{2}[/tex].
Therefore, the final form of the solution to the differential equation above is
[tex]y = \dfrac{1}{1+2e^x}[/tex]
What is the answer to this equation
Answers
Answer:
[tex]x = - \frac{494}{3}[/tex] [tex]= - 164\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]75 + \frac{3}{8} x = 13\frac{1}{4}\\\\75 + \frac{3}{8} x = \frac{53}{4}\\\\\frac{3}{8}x = \frac{53}{ 4} - 75\\\\\frac{3}{8}x = \frac{53-300}{4}\\\\\frac{3}{8}x = - \frac{247}{4}\\\\x = -\frac{247 \times 8}{4 \times 3} \\\\x = -\frac{494}{3}[/tex]
Executives from Six Flags, a well-known amusement park chain, had interest in constructing a Six Flags theme park in a location near Ames city limits. Experts believed that approximately 15% of the surrounding population would be interested in becoming season ticket holders. A random sample of 500 residents of Story County was collected (of the approximately 80,000 residents of Story County). Of the 500 people sampled, 124 said that they would be interested in purchasing season tickets to a Six Flags in Ames. The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to ___________.
Answers
Answer:
The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to 0.248.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Of the 500 people sampled, 124 said that they would be interested in purchasing season tickets to a Six Flags in Ames.
This means that [tex]p = \frac{124}{500} = 0.248[/tex]
The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to
By the Central Limit Theorem, it is equal to the sample proportion of 0.248.
write a recursive formula for the following sequence 25,43,61,79,97
F(1)= 25
F(n)= F (n-1) +18
Answers
Given:
The sequence is:
25,43,61,79,97
To find:
The recursive formula for the given sequence.
Solution:
We have,
25,43,61,79,97
Here, the first term is 25. Now, the differences between the two consecutive terms are:
[tex]43-25=18[/tex]
[tex]61-43=18[/tex]
[tex]79-61=18[/tex]
[tex]97-79=18[/tex]
The differences between the two consecutive terms is common, i.e., 18. So, the given sequence is an arithmetic sequence.
The recursive formula of an arithmetic sequence is:
[tex]F(n)=F(n-1)+d[/tex]
Where, d is the common difference and F(1) is the first term.
Putting [tex]d=18[/tex], we get
[tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex].
Therefore, the required recursive formula is [tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex].
Write the point-slope form of the equation for a line that passes through (-1, 4) with a slope of 2.
The value of xt is
The value of yn is
The point-slope form of the equation is
Answers
Answer:
67 f
Step-by-step explanation:
If ⃗ = + + is perpendicular to both ⃗ = 5 + − 2 and = 3 − 3 + 6 , find and .
Answers
Answer:
The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.
Step-by-step explanation:
If [tex]\vec {c} = m\,\hat{i} + n\,\hat{j} + \hat{k}[/tex] is perpendicular to [tex]\vec {a} = 5\,\hat{i} + \hat{j} -2\,\hat{k}[/tex] and [tex]\vec {b} = 3\,\hat{i} - 3\,\hat{j} + 6\,\hat{k}[/tex], then the following relationships must be observed:
[tex]\vec {c}\,\bullet\,\vec {a} = 0[/tex] (1)
[tex]\vec{c}\,\bullet \,\vec{a} = 0[/tex] (2)
Then, we expand the previous expressions:
[tex](m, n, 1)\,\bullet\,(5, 1, -2) = 0[/tex]
[tex]5\cdot m + n = 2[/tex] (1b)
[tex](m, n, 1)\,\bullet\,(3, -3, 6) = 0[/tex]
[tex]3\cdot m - 3\cdot n = -6[/tex] (2b)
Then, we solve for [tex]m[/tex] and [tex]n[/tex]:
[tex]m = 0, n = 2[/tex]
The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.
I need this math problem to be solved ASAP!!! Solve for X.
-8x + 3 ≥ 27 AND −13x + 5 ≥ 57
Choose ONE and ONLY the CORRECT answer.
A: x ≤ −4
B: x ≤ −3
C: −4 ≤ x ≤ −3
D: There are NO solutions.
E: All values of X are solutions.
Answers
Answer:
A: x ≤ −4
Step-by-step explanation:
Hi there!
We're given the two inequalities -8x + 3 ≥ 27 and −13x + 5 ≥ 57
we need to find the set of solutions that make the two inequalities true (the intersection)
First, let's solve the two inequalities, starting with -8x + 3 ≥ 27
-8x + 3 ≥ 27
subtract 3 from both sides
-8x≥24
divide both sides by -8 and remember to FLIP the inequality sign, as we're dividing with a negative
x ≤ -3
now for the other inequality:
−13x + 5 ≥ 57
subtract 5 from both sides
-13x ≥ 52
divide both sides by -13 and remember to FLIP the sign
x ≤ -4
please see below for the graph to find the intersection, as well as the final answer
Hope this helps! :)
What is the slope of the linear relationship shown in this table of values?
Answers
Answer: -2 (b)
Step-by-step explanation:
So the slope of the line is the amount that the line changes as it goes along the x or y axis. Think of it like a ramp- goes up or down, steep or flat.
Take a pair of points like (-4, 11) and (2, -1)
{But you can use other points in the chart too. }
-4 to 2 is a distance of 6 --> that is the x
11 to -1 is a distance of -12 --> that is the y
We want the change in y over (or divided by) change in x.
-12 / 6 = -2
Answer:
B
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 11) and (x₂, y₂ ) = (2, - 1) ← 2 ordered pairs from the table
m = [tex]\frac{-1-11}{2-(-4)}[/tex] = [tex]\frac{-12}{2+4}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2 → B
y=6x/5 +27 find y-intercept and slope
Answers
Answer:
General equation of a line is given by y = mx +c, where m is the gradient /slope, c is the intercept. To find for the intercept on y- axis, put x = 0.[tex]y = \frac{6(0)}{5 } + 27 \\ y = \frac{0}{5} + 27 \\ y = 27 \\ therefore \: the \: intercept \: on \: y \: is \: 27 \\ [/tex]By comparison, [tex]y = mx + \: c \\ y = \frac{6}{5} x \: +27 \\ m = \frac{6}{5 \: } \: \\ hence \: slope \: is \: \frac{6}{5} [/tex]
Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
Answers
Answer:
The relationship between the above two triangles is SAS and they are congruent
Find the value of x
Answers
Answer:
x = 40
Step-by-step explanation:
Two triangles are similar so we can use similarity ratio to find x
x/16 = 35/14 cross multiply expressions
14x = 560 divide both sides by 14
x = 40
The diameter of the stem of a wheat plant is an important trait because of its relationship to breakage of the stem. An agronomist measured stem diameter in eight plants of a particular type of wheat. The mean of these data is 2.275 and the standard deviation is 0.238. Construct a 80% confidence interval for the population mean.
Answers
Answer:
7.79771≤x≤8.20229
Step-by-step explanation:
Given the following
sample size n = 8
standard deviation s = 0.238
Sample mean = 2.275
z-score at 980% = 1.282
Confidence Interval = x ± z×s/√n
Confidence Interval = 8 ± 1.282×0.238/1.5083)
Confidence Interval = 8 ± (1.282×0.15779)
Confidence Interval = 8 ±0.20229
CI = {8-0.20229, 8+0.20229}
CI = {7.79771, 8.20229}
Hence the required confidence interval is 7.79771≤x≤8.20229
Which of the following describes the end behavior of the function ƒ(x) = –5x3 + 3x2 + x – 9?
A)
As x → –∞, y → +∞ and as x → +∞, y → –∞
B)
As x → –∞, y → –∞ and as x → +∞, y → +∞
C)
As x → –∞, y → –∞ and as x → +∞, y → –∞
D)
As x → –∞, y → +∞ and as x → +∞, y → +∞
Answers
Answer:
A
Step-by-step explanation:
f(x)=-5x³+3x²+x-9
leading coefficient is negative and it is of odd degree.
so it starts from above onthe left and ends at the bottom ont he right.
A rectangular area is to be enclosed using an existing
wall as one side 100m of fencing are available for the
three side. It is desire to make the areas as large as
possible. Find the necessary dimension of the
enclosure and the maximum area.
Answers
Answer:
[tex]\text{Dimensions: 25 x 50},\\\text{Area: }1,250\:\mathrm{m^2}[/tex]
Step-by-step explanation:
Let the one of the side lengths of the rectangle be [tex]x[/tex] and the other be [tex]y[/tex].
We can write the following equations, where [tex]x[/tex] will be the side opposite to the wall:
[tex]x+2y=100,\\xy=\text{Area}[/tex]
From the first equation, we can isolate [tex]x=100-2y[/tex] and substitute into the second equation:
[tex](100-2y)y=\text{Area},\\-2y^2+100=\text{Area}[/tex]
Therefore, the parabola [tex]-2y^2+100y[/tex] denotes the area of this rectangular enclosure. The maximum area possible will occur at the vertex of this parabola.
The x-coordinate of the vertex of a parabola in standard form [tex]ax^2+bx+c[/tex] is given by [tex]\frac{-b}{2a}[/tex].
Therefore, the vertex is:
[tex]\frac{-100}{2(-2)}=\frac{100}{4}=25[/tex]
Plug in [tex]x=25[/tex] to the equation to get the y-coordinate:
[tex]-2(25^2)+100(25)=\boxed{1,250}[/tex]
Thus the vertex of the parabola is at [tex](25, 1250)[/tex]. This tells us the following:
The maximum area occurs when one side (y) of the rectangle is equal to 25The maximum area of the enclosure is 1,250 square meters The other dimension, from [tex]x+2y=100[/tex], must be [tex]50[/tex]And therefore, the desired answers are:
[tex]\text{Dimensions: 25 x 50},\\\text{Area: }1,250\:\mathrm{m^2}[/tex]
In triangle ABC, AC = 4, BC = 5, and 1 < AB < 9. Let D, E and F be the
midpoints of BC, CA, and AB, respectively. If AD and BE intersect at G
and point G is on CF, how long is AB?
A. 2
B. 3
C. 4
D. 5
Answers
Which expression has the same value as the one below?
38 + (-18)
O A. 38
O B. 38 - 18
O C. 38 + 18
O D. 56
Answers
Answer:
answer is B 38-18
Step-by-step explanation:
38 + (-18)
38-18
38+ (-18) turns into 38-18 because after removing the parentheses around -18 there is no need for the +
Somebody else has to comment for me to Mark u as BRAINLIEST!! It won't let me
Answers
Answer:
7.5 is the difference
Step-by-step explanation:
basketball mean
(13+22+23+24+36+37+42+43+58+69) ÷10 = 36.7
tennis mean
(14+23+24+38+47+48+57+58+66+67) ÷10 = 44.2
tennis mean - basketball mean
44.2 - 36.7= 7.5
Solve for d.
d + 67 = 87
р
Submit
Answers
Answer:
[tex]d=20[/tex]
Step-by-step explanation:
[tex]d+67=87[/tex]
Subtract 67 from both sides
[tex]d=20[/tex]
Hope this is helpful
Answer:
d = 20
Step-by-step explanation:
Get brainiest if right!!
Answers
Answer:
4 1/8 units
Step-by-step explanation:
I believe this to be so if these points were on a number line. You would add the two points together to get the distance between the two points.
What is the radius of a circular swimming pool with a diameter of 20 feet?
Answers
Answer:
10 feet
Step-by-step explanation:
The half of 20 is 10. So, hence it is 10 feet.
The radius of a circular swimming pool with a diameter of 20 feet will be 10 feet.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Assume 'r' is the radius of the circle and 'd' is the diameter of the circle.
The radius of the circle is half of the diameter of the circle. Then the equation is given as,
r = d / 2
The diameter of the swimming pool is 20 feet. Then the radius of the swimming pool is given as,
r = 20 / 2
r = 10 feet
The radius of a roundabout pool with a measurement of 20 feet will be 10 feet.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
Is the triangle a right angle? Pythagorean Theorem.
Answers
Answer:
yes it is
Step-by-step explanation:
hopefully that helps
195ft i think because 10 x 19.5
because 39 divided by 2 is 19.5
so then 19.5 x 10 = 195ft
Solve for x. See the image below!
Answers
Answer:
x = 17
Step-by-step explanation:
in such a constellation (two beams from the same point of origin cut through the same circle) the relative relation between the segments of these beams to the overall length of the beam have to be the same :
7 × (7+x) = 8 × (8+13)
49 + 7x = 8 × 21 = 168
7x = 119
x = 17
Which of the following relations represents a function? (0, 3), (0.-3). (-3,0). (3.0)) (-2. 4). (-1.0), (2.0), (2.6) -1.-1), (0.0), (2, 2), (5, 5]] None of these
Answers
Answer:
(-1.0) (2.0) is the answer
The function y = sin 2 (x – π∕2) has a period of Question 2 options: A) 4π. B) π. C) 2π. D) π∕2.
Answers
Answer:
B) π
Step-by-step explanation:
y = sin 2 (x – π∕2)
y = sin (2x -π)
=> 2x = 2π
x = π
The period of function sin(2x−π) is π, which is correct option(B).
What is the period of the function?The period of the function is defined as the interval between repetitions of any function. A trigonometric function's period is the length of one one completed cycle.
What is the Trigonometric functions?The trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.
Given the function as :
y = sin 2 (x – π/2)
y = sin (2x − π)
Use the form asin(bx−c) + d to determine the variables used to find the amplitude, period, phase shift, and vertical shift.
a = 1
b = 2
c = π
d = 0
Determine the period of sin(2x−π).
y = sin (2x -π)
So, the period = c = π
Hence, the period of function sin(2x−π) is π.
Learn more about period of the function here:
https://brainly.com/question/26369761
#SPJ2
A country's population in 1993 was 204 million. In 2000 it was 208 million. Estimate the population in 2015 using the exponential growth formula. Round your answer to the nearest million. P- Aekt
Answers
Answer:
217
Step-by-step explanation:
Answer ASAP! Please answer! please answer (NOT HARD)
Answers
Answer:
221
Step-by-step explanation:
5(3)2-4
Answer:
221
Step-by-step explanation: