Considering the critical points of the function, we have that:
The function is increasing for |x| > 1.63.The function is decreasing for |x| < 1.63.What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
In this problem, the function is:
[tex]f(x) = 3x^3 - 16x + 2[/tex]
The derivative is:
[tex]f^{\prime}{x} = 6x^2 - 16[/tex]
The critical points are given as follows:
[tex]6x^2 - 16 = 0[/tex]
[tex]x^2 = \frac{16}{6}[/tex]
[tex]x = \pm \sqrt{\frac{16}{6}}[/tex]
[tex]x = \pm 1.63[/tex]
For x < -1.63, one example of the derivative is:
[tex]f^{\prime}{-2} = 6(-2)^2 - 16 = 8[/tex]
Positive, hence increasing.
For -1.63 < x < 1.63, one example of the derivative is:
[tex]f^{\prime}{0} = 6(0)^2 - 16 = -16[/tex]
Negative, hence decreasing.
For x > 1.63, one example of the derivative is:
[tex]f^{\prime}{2} = 6(2)^2 - 16 = 8[/tex]
Positive, hence increasing.
Hence:
The function is increasing for |x| > 1.63.The function is decreasing for |x| < 1.63.More can be learned about critical points at https://brainly.com/question/2256078
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what is the volume of the truck bed which is
10 feet long, 4 feet wide, and has a height of 3
feet?
Answer:
120 ft cubed
Step-by-step explanation:
V=lwh
V=10(4)(3)
V=120 ft cubed
Simplify this expression 3y + 6y + 8y
Answer:
the answer is 17y 3y+6y is 9y plus 8y is 17y
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{3y + 6y + 8y}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{3y + 6y + 8y}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathsf{(3y + 6y + 8y)}[/tex]
[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]
[tex]\mathsf{\rightarrow 9y + 8y}[/tex]
[tex]\mathsf{\rightarrow 17y}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{17}\mathsf{y}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Can someone help me with these problems and show work please !
The domain of g(x)= 3x^2 is Real number and it's range is {y∈R / y≥0}
The domain of h(x)= -3x^2 is Real number and it's range is {y∈R / y ≤0}
The domain of a function f(x) is the set of all values for which the function is defined, and the domain of a function is the set of all values that f takes on. The domain and range are defined for a relation and are the sets of all x-coordinates and all y-coordinates of ordered pairs.
The graph of f(x)= x^2 is given
We need to find the domain and range of g(x)=3x^2 and h(x)= -3x^2
The Graph of 3x^2 is different from x^2 in terms of plotting
When ,
x= -2 g(x)=12
x=-1 g(x)=3
x=0 g(x)=0
x=1 g(x)=3
x=2 g(x)=12
The Graph of -3x^2 is different from x^2 in terms of plotting
When ,
x= -2 g(x)=-12
x=-1 g(x)= -3
x=0 g(x)=0
x=1 g(x)= -3
x=2 g(x)=-12
Domain of g(x) is R and it's range is {y∈R / y≥0}
Domain of h(x) is R and it's range is {y∈R / y ≤0}
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On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3
The linear inequality of the given graph is: D. y < -2x + 3.
How to Determine the Linear Inequality of a Graph?First, using two points on the line, (0, 3) and (1.5, 0), find the slope (m).
Slope (m) = change in y / change in x = (3 - 0) / (0 - 1.5)
Slope (m) = 3/-1.5 = -2.
Next, substitute (x, y) = (0, 3) and m = -2 into y = mx + b to find the value of b.
3 = -2(0) + b
3 = 0 + b
b = 3
Substitute m = -2 and b = 3 into y < mx + b (the shaded part is at the left, so we use the "<" sign)
y < -2x + 3
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help!
Find the missing side lengths. Leave the answers as radicals in simplest form.
Answer:
b = 3.5
a = 7
Step-by-step explanation:
Hello!
This triangle is a 30°-60°-90° triangle, as the missing angle is 30° and the other two angles are 60° and 90°.
There are some important Rules:
The leg that is opposite to the 30° angle is half of the hypotenuse. The leg that is opposite to the 60° angle is the length of the leg opposite to the 30° multiplied by [tex]\sqrt3[/tex].We can first solve for the leg that is opposite to the 30° angle.
Since [tex]\frac{7\sqrt3}{2}[/tex] is [tex]b\sqrt3[/tex]:
[tex]\frac{7\sqrt3}{2} = b\sqrt3[/tex][tex]\frac72 = b[/tex]The length of b is 3.5.
We can multiply 3.5 by 2 to find the length of a.
[tex]\frac a2 = b[/tex][tex]\frac a2 = \frac72[/tex][tex]a = 7[/tex]The length of a is 7.
0 divided by 0 is? 45 points for who answer its correct not for a homework
Answer:
Undefined
Step-by-step explanation:
No multiplicative inverse exists for 0
Answer:
undefined
Step-by-step explanation:
a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.
To find proportion of the area under the normal curve between two Z scores that are both above the mean, it is necessary to examine the ______. Group of answer choices
It is necessary to imagine the sum of the areas between each z-score and the average.
Given as the ratio of the area under the normal curve between two z-scores, both above average.
The Z score accurately measures the number of standard deviations above or below the mean of the data points.
The formula for calculating the z-score is
z = (data points – mean) / (standard deviation).
It is also expressed as z = (x-μ) / σ.
A positive z-score indicates that the data points are above average.A negative z-score indicates that the data points are below average.A z-score close to 0 means that the data points are close to average. The normal curve is symmetric with respect to the mean and needs to be investigated.Therefore, to find the percentage of the area under the normal curve between two z-scores, both above the mean, you need to look at the sum of the areas between the z-score and the mean.
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mann
On a map, 2.5 inches represents 52 miles. What is the actual distance represented by 5 inches on the map?
2.5 5
52 x
Answer:
104 miles.
Step-by-step explanation:
5 inches is 2 * 2.5 inches so the distance required is 2*52 = 104 miles.
A population of a certain city increases exponentially at a rate of 6.5%. Initially, it is 1.50 million. After how many years will the population reach 2.31 million?
6.546
6.643
6.123
6.142
Answer:
Below in bold.
Step-by-step explanation:
P = 1.50(1.065)^t where P = population in millions and t = no. of years.
So we have
2.31 = 1.50(1.065)^t
(1.065)^t = 2.31/1.50
Taking logs:
t log 1.065 = log (2.31/1/50)
t = log (2.31/1/50) / log 1.065
= 6.856 years.
Fill in the blank.
_______ are sample values that lie very far away from the majority of the other sample values.
Outliers are sample values that lie very far away from the majority of the other sample values.
We know that, an outlier is an observation that lies an abnormal distance from other values in a random sample from a population.
It differs significantly from other observations in a sample values.
Outlier is a value that is distant from the majority of the values in a data set.
For a scatter plot, an outlier is the point or points that are farthest from the regression line.
For example in the record of marks 25, 29, 7, 32, 85, 33, 27, 28 both 7 and 85 are outliers.
Therefore, outliers are sample values that lie very far away from the majority of the other sample values.
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The equation 4x2 8x 15 = 0 is being rewritten in vertex form. fill in the missing step. given 4x2 8x 15 = 0 step 1 4(x2 2x ___) 15 ___ = 0 step 2 ✔ step 3 4(x 1)2 11 = 0 4(x2 2x 1) 15 − 4 = 0 4(x2 2x 1) 15 − 1 = 0 4(x2 2x 2) 15 − 2 = 0 4(x2 2x 4) 15 − 4 = 0
Answer:
a) is the correct answer
Help help pls, ASAP!!! (Geometry)
“Complete the proof”
1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)
2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)
3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)
4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)
Use the image below to describe at least three different ratios, written in simplest form. Include at least one part-to-part ratio and one part-to-whole ratio.
8 out of 36 squares unfilled*
HELP ASAP!!!!!!!!!!!!
The different ratios are 2 : 7, 2 : 9 and 7 : 9
How to determine the ratio?The statement is given as:
8 out of 36 squares unfilled
This means that:
There are 36 squares8 are unfilled28 are filledThe part-to-part ratio is represented as:
Ratio = Unfilled : Filled
This gives
Unfilled : Filled = 8 : 28
Simplify
Unfilled : Filled = 2 : 7
The part-to-whole ratios are represented as:
Ratio = Unfilled : Total
Ratio = Filled : Total
So, we have:
Unfilled : Total = 8 : 36
Filled : Total = 28 : 36
Simplify
Unfilled : Total = 2 : 9
Filled : Total = 7 : 9
Hence, the different ratios are 2 : 7, 2 : 9 and 7 : 9
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Rewrite the expression in the form x^n
Answer:
x ^ (1/3)
Step-by-step explanation:
solution:
the answer is in the picture I have sent.
I hope this will help you
sort the sequence according to whether they are arithmetic gemoentic or neither
98.3, 94.1, 89.9, 85.7 (Arithmetic)
1, 0, -1, 0 (Neither)
1.75, 3.5, 7, 14 (Geometric)
-1, 1, -1, 1..... (Geometric)
Determining the type of a sequenceAn arithmetic sequence has a common difference
A geometric sequence has a common ratio
Considering the given sequences one after the other:
For 98.3, 94.1, 89.9, 85.7,..........
The common difference, d = 94.1 - 98.3 = -4.2
Therefore, 98.3, 94.1, 89.9, 85.7 is an arithmetic sequence
For 1, 0, -1, 0......
The sequence does not have a common difference or a common ratio. Therefore, it is neither an arithmetic nor geometric sequence
For 1.75, 3.5, 7, 14,.....
The common ratio = 3/1.75 = 2
Therefore, it is a geometric sequnec
For -1, 1, -1, 1.....
The common ratio = 1/-1 = -1
It is a geometric sequence
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Please give the answer
Answer: See the attached image below for the filled in table.
=========================================================
Explanation:
The domain is the set of all allowed x inputs of a function.
The term "radicand" refers to the stuff under the square root.
We cannot have a negative number under the square root. Therefore, the radicand must be 0 or larger.
The first function must have [tex]4x+6 \ge 0[/tex] which becomes [tex]4x \ge -6[/tex] and leads to [tex]x \ge -\frac{6}{4}[/tex] aka [tex]x \ge -\frac{3}{2}[/tex]
So x = -3/2 is the smallest input allowed. Which is where the interval notation of [tex]\left[-\frac{3}{2}, \infty)[/tex] comes from. It's the interval spanning from -3/2 (inclusive) to infinity. This represents the set of all possible x inputs of the first function.
--------
Follow this same idea for problem 2. The steps would be something like this:
[tex]-20x - 6 \ge 0\\\\-20x \ge 6\\\\x \le \frac{6}{-20}\\\\x \le -\frac{3}{10}\\\\[/tex]
The inequality sign flips because we divided both sides by a negative number. That then leads to the interval notation of [tex](-\infty, -\frac{3}{10}\big][/tex]
The interval spans from negative infinity (exclusive) to -3/10 (inclusive).
--------
Problem 3 would have these steps
[tex]5x-16 \ge 0\\\\5x\ge 16\\\\x\ge \frac{16}{5}\\\\\big[\frac{16}{5}, \infty)\\\\[/tex]
No sign flip happens since we divided both sides by a positive number.
--------
Lastly, here are the steps for problem 4
[tex]20+6x \ge 0\\\\6x \ge -20\\\\x \ge -\frac{20}{6}\\\\x \ge -\frac{10}{3}\\\\\big[-\frac{10}{3}, \infty)[/tex]
Don't forget to use the square bracket to include the endpoints mentioned. We always use curved parenthesis for either infinity because we can't ever reach infinity. In a sense, we "approach" infinity.
Once again, all of this is summarized in the filled out table shown below (attached image). Feel free to ask any questions if they come to mind.
As an oak tree grows taller, it also grows wider. In other
words, the diameter of its trunk increases. Imagine that a
tree's height is about 8 times its diameter. Assume this
relationship will not change, and that the tree trunk is a
rather cylindrical shape. Write a function for the volume of
wood in the tree's trunk as it grows
The volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex]
The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.
Thus, the volume (V) of a right circular cylinder, using the above formula, is, [tex]V = \pi r^2h[/tex] , where
'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
Given:
Height(h) = 8 x diameter = 16 x radius (r) (diameter = 2 x radius )
∴ h = 16r.
V= [tex]\pi r^2h[/tex]
Substituting h = 16r in the volume formula we get
V = [tex]\pi r^2(16r)[/tex] = [tex]16\pi r^3[/tex]
Thus the volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex].
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What is the value of -3/2÷-7/2?
The value of the given division operation is 3/7
Division operationFrom the question, we are to determine the quotient of the given division operation
The given division operation is
-3/2÷-7/2
[tex]\frac{-3}{2} \div \frac{-7}{2}[/tex]
[tex]=\frac{-3}{2} \times \frac{2}{-7}[/tex]
[tex]=\frac{-3}{-7}[/tex]
[tex]=\frac{3}{7}[/tex]
Hence, the value of the given division operation is 3/7
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If you have a savings account, contact your bank and find out the interest rate on that account. (If you don’t have your own account, contact a local bank to ask what the interest rate would be if you set up a savings account today.)
a. State the interest rate the bank quoted.
b. Write an exponential growth equation that models the yearly growth if you put $625 in the account and left it there for years.
c. What will be the value of the account in 25 years?
d. Which of the following would result in more money: $625 deposited in your bank at the current interest rate for 6 years, or deposit $625 into a money market account with a 5% rate for 1 year? Show how you determined your answer.
Deposit $625 into a money market account with a 5% rate for 1 year would result in more money.
The interest rate of the bankTo do this, we make use of 1.50% interest rate
The exponential growth equationHere, we have:
Initial, a= 625
Rate, r = 1.5%
The exponential growth equation is
A(t) = a * (1 + r)^t
So, we have:
A(t) = 625 * (1 + 1.5%)^t
Evaluate
A(t) = 625 * 1.015^t
Hence, the exponential growth equation is A(t) = 625 * 1.015^t
The value in 25 yearsHere, t = 25.
So, we have:
A(25) = 625 * 1.015^25
Evaluate
A(25) = 906.84
Hence, the value in 25 years is $906.84
The investment with more money#Investment A
a = 625
r = 1.5%
t = 5
So, we have:
A(5) = 625 * 1.015^5
Evaluate
A(5) = 673.3
#Investment B
a = 625
r = 5%
t = 1
So, we have:
A(1) = 625 * 1.5^1
Evaluate
A(1) = 937.5
By comparison, 937.5 is greater than 673.3
Hence, deposit $625 into a money market account with a 5% rate for 1 year would result in more money.
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What is the x-intercept of p(x) = -x + 8?
Answer:
x-intercept = 8
Step-by-step explanation:
Hello!
An x-intercept is when the y-value is 0, or when the graph intersects the x-axis.
We can replace p(x) with 0 and solve for x.
Solve for x[tex]p(x) = -x + 8[/tex][tex]0 = -x + 8[/tex][tex]-8 = -x[/tex][tex]8 = x[/tex]The x-intercept is 8.
write an equation of a line perpendicular to y = 7 and passes through the point (3, -1).
Answer: x = 3
Step-by-step explanation:
The equation of the line perpendicular to a horizontal line is a vertical line, which has an equation of the form x=c.
Which equation can be used to solve for xxx in the following diagram?
Answer: A. 2x + 30 = 90
Step-by-step explanation:
You want to choose answer A because you know that together the section of 2x and the section of 30 equal 90 degrees (we know this because the other side shows the right angle which equals 90 degrees).
The equation 2x + 30 = 90 will be used to determine x so option (A) will be correct.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Given an angle with two participants, one is 2x and another one is 30°.
Now if we look right-hand side angle it is a right-angle i.e. 90°.
Since the complete angle above a straight line is 180°
So,
2x + 30 + 90° = 180°
2x + 30 = 90
Hence "The equation 2x + 30 = 90 will be used to determine x".
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Why is it important to be able to express a clear and coherent argument visually or in writing? Think: where would you use this in the “real-world?”
It is important to be able to express a clear and coherent argument visually or in writing because without establishing coherence, your reader will not be able to know or understand the key points that you are trying to express or show.
Why is it important to have coherence in one's writing?Coherence is known to be a key quality for kind of good academic write up.
Note that in the area of academic writing, the ways that ideas flows is very important and as such, it need to be smooth and logical.
Therefore without coherent argument , the reader cannot understand the key points that a person is trying to show and thus hinders the readability of your work.
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Help me please 10 pts for you mark you brainliest
Answer 1: A and C
Step-by-step explanation:
Use distribution law to see which answer match the equation at the top.
Answer 2: 16q + 4
10q and 6q are like terms
10q + 6q = 16q
+
5 - 1
Answer:
Hello,
Step-by-step explanation:
page 1:
60-36j=12(5-3j) answer C
=6(10-6j) answer A
page 2:
10q+5+6q-1=16q+4=4(4q+1)
page 3:
24j-16=8(3j-2)
page 4:
10h+30+50j=10*(h+3+5j) answer B
=2*(5h+15+25j) answer C
=5(2h+6+10j) not A nor D
A rectangular corral is to be built using 70m of fencing. If the fencing has to enclose
all four sides of the corral, what would be the dimensions to produce the maximum
possible area and what would the area of the corral be? Include a complete solution
Answer:
306 square meters
Step-by-step explanation:
The maximum area is when the length and width are the closest together.
70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle
35/2=17.5, find the 2 closest integers, they are 17 and 18
17*18=306
Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows
the results found when copying a design x times. Use the graph to write the equation modeling this relationship.
-10
2 3 4
6 7 8
Enter the correct answer in the box by feplacing the values of a and b.
The correct values for a and b which models this relationship through an exponential function are 8 and 2 respectively.
What is an exponential function?An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = eˣ
How to write an equation modeling this relationship?Based on the information provided, we can logically deduce that the other copy machine can reduce image dimensions by a different percentage and this is defined by the following exponential function:
f(x) = abˣ
From the graph (see attachment), we have;
When x = 0, y = f(x) = 8. Thus, f(0) = 8
f(x) = abˣ
8 = ab⁰
8 = a × 1
a = 8.
Also, from the graph (see attachment), we have;
When x = 1, y = f(x) = 4
f(x) = abˣ
4 = 8b¹
4 = 8 × b
4 = 8b.
b = 8/4
b = 2.
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Explain all of the steps needed to simplify the equation 8(x+2) = 4(2x+9) using the order of operations.
Answer:
First, use the distributive property and distribute 8 to the [tex](x,2)[/tex] in the first part of the equation to get [tex]8x + 16[/tex].
Next, also use the distributive property to distribute the 4 to the [tex](2x+9)[/tex] in the second part of the equation to get [tex]8x+36[/tex].
The simplified equation looks like this: [tex]8x+16=8x+36[/tex].
Laura is walking quickly and finds that she travels 54 feet in a span of 12 seconds witch of the following is the speed of Laura’s walking
Laura's walking speed is 4.50 feet per second.
What is Laura's walking speed?Speed is the total distance travelled per time. Speed can be determined by dividing the distance walked by Laura by the time.
Average speed = total distance / total time
54 / 12 = 4.50 feet per second
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PLEASE HELP ME AS SOON AS POSSIBLE
Answer: [tex]f^{-1}(\text{x}) = (\text{x}-9)^2+4[/tex] when [tex]\text{x} \ge 9[/tex]
=================================================
Work Shown:
[tex]f(\text{x}) = 9 + \sqrt{\text{x} - 4}\\\\\text{y} = 9 + \sqrt{\text{x} - 4}\\\\\text{x} = 9 + \sqrt{\text{y} - 4}\\\\\text{x}-9 = \sqrt{\text{y} - 4}\\\\(\text{x}-9)^2 = (\sqrt{\text{y} - 4})^2\\\\(\text{x}-9)^2 = \text{y}-4\\\\(\text{x}-9)^2+4 = \text{y}\\\\f^{-1}(x) = (\text{x} - 9)^2+4[/tex]
Explanation:
I replaced f(x) with y. After that I swapped x and y, then solved for y to get the inverse.
The smallest that [tex]\sqrt{\text{x}-4}[/tex] can get is 0, which means the smallest f(x) can get is 9+0 = 9. The range for f(x) is [tex]\text{y} \ge 9[/tex]
Since x and y swap to determine the inverse, the domain and range swap roles. Therefore, the domain of the inverse [tex]f^{-1}(\text{x})[/tex] is [tex]\text{x} \ge 9[/tex]
So we will only consider the right half portion of the parabola.
The graph is below. The red curve mirrors over the black dashed line to get the blue curve, and vice versa.
Answer:
[tex]f^-^1(x)=(x-9)^2+4[/tex] OR [tex]x^2-18x+85[/tex] if you simplify it
Step-by-step explanation:
to find the inverse function you have to switch x and y with each other and solve for y.
[tex]y=9+\sqrt{x-4}\\x=9+\sqrt{y-4}[/tex] step 1: switch x and y with each other
[tex]x-9=\sqrt{y-4}[/tex] step 2: subtract 9 from both sides
[tex](x-9)^2=\sqrt{y-4}^2[/tex] step 3: square both sides to get rid of the square root
[tex](x-9)^2=y-4\\(x-9)^2+4=y\\[/tex] step 4: add 4 to both sides
you could leave the answer like this or you can simplify to get [tex]x^2-18x+85[/tex]
a set of data has the values 11,14,23 and 16 what value would have to be added to set for the mean of the 5 numbers to be 18
Answer:
26.
Step-by-step explanation:
(11+14+23+16+x) / 5 = 18 where x is the value to be added.
(64 + x) / 5 = 18
64 + x = 90
x = 90 - 64
= 26.