The function is decreasing on the interval (-0, 0)and increasing on the interval (0, 0).The function is increasing on the interval (-0,0)and decreasing on the interval (0, ).The function is increasing on the interval (-00, 0).The function is decreasing on the interval(-0, 0).
Answers
D; The function is decreasing in the interval;
[tex](-\infty,\infty)[/tex]Here, we want to interpret the given rate of change of the function
From what we have, coming from negative infinity, we can see that there is a decrease in the rate of change of the function. As we move closer to zero, we can see a decrease in the range value of the function
Now, moving away from zero, we can see that there is a continuous decrease as we move towards positive infinity. We can therefore conclude that there is a continuous decrease from the point x = 0 towards the point x = positive infinity
So, the correct choice here is that the function is decreasing in the interval negative infinity to positive infinity
Related Questions
Can I have help with this pleasehow would I make a graph
Answers
The Solution:
We are required to make a graph of the situation.
The above graph is the required graph.
Find the area of a trapezoid with bases 24 and 36 with 45 base angles
Answers
A trapezoid with congruent base angles have the other two sides (that are not the bases) congruent to each other:
And the area A of a trapezoid with bases a and b, and height h is given by:
[tex]A=\frac{a+b}{2}\cdot h[/tex]Thus, we need to find the height h of this trapezoid and then use it to calculate its area.
Step 1
We can find h by using the tangent of 45º. We obtain:
[tex]\begin{gathered} \frac{h}{6}=\tan 45^{\circ} \\ \\ \frac{h}{6}=1 \\ \\ h=1\cdot6 \\ \\ h=6 \end{gathered}[/tex]Step 2
Now, we have:
a = 24
b = 36
h = 6
Thus, the area A of the trapezoid is:
[tex]\begin{gathered} A=\frac{24+36}{2}\cdot6 \\ \\ A=\frac{60}{2}\cdot6 \\ \\ A=30\cdot6 \\ \\ A=180 \end{gathered}[/tex]Which function of x would have zeros of 1/3 and -5?
Answers
The functions of x with zeros of 1/3 and -5
[tex]\begin{gathered} x\text{ = }\frac{1}{3}\text{ and x = -5} \\ (x\text{ - }\frac{1}{3})\text{ and (x + 5)} \\ \end{gathered}[/tex][tex]\begin{gathered} (x\text{ -}\frac{1}{3})(x\text{ + 5)} \\ x^2\text{ + 5x - }\frac{x}{3}\text{ - }\frac{5}{3} \\ \text{ multiply through by 3} \\ 3x^2\text{ + 15x - x - 5} \\ 3x^2\text{ + 14x - 5} \\ F(x)\text{ = }3x^2\text{ + 14x - 5} \end{gathered}[/tex]Hence the functions of x with zeros of 1/3 and -5 = 3x² + 14x - 5
Is the triangles similar? If the triangles are similar then this is the statements that we have to use
Answers
When two triangles are similar, their corresponding angles are equal.
So, the first step to solve the exercise is to find the measure of the missing angle in each triangle.
We know that the sum of the interior angles of a triangle is 180. Then, we have:
• Measure of angle R
[tex]\begin{gathered} 54\degree+68\degree+R=180\degree \\ 122\degree+R=180\degree \\ \text{ Subtract 122\degree from both sides} \\ 122\degree+R-122\degree=180\degree-122\degree \\ R=58\degree \end{gathered}[/tex]• Measure of angle U
[tex]\begin{gathered} 54\degree+67\degree+U=180\degree \\ 121\degree+U=180\degree \\ \text{ Subtract 121\degree from both sides} \\ 121\degree+U-121\degree=180\degree-121\degree \\ U=59\degree \end{gathered}[/tex]As we can see, the corresponding angles of the triangles RST and UVW are not equal.
Therefore, the triangles are not similar.
Find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places.
Answers
Recall that the magnitude and direction of a vector:
[tex]\vec{v}=ai+bj[/tex]are given by the following formulas:
[tex]\begin{gathered} \vec{|v}|=\sqrt{a^2+b^2}, \\ \theta=tan^{-1}(\frac{b}{a}). \end{gathered}[/tex]Substituting
[tex]\begin{gathered} a=2, \\ b=8, \end{gathered}[/tex]in the above formulas, we get:
[tex]\begin{gathered} \vec{|v}|=\sqrt{2^2+8^2}=\sqrt{4+64}=\sqrt{68}. \\ \theta=\tan^{-1}(\frac{8}{2})=\tan^{-1}(4). \end{gathered}[/tex]Finally, we get:
[tex]\begin{gathered} \vec{|v}|=2\sqrt{17}, \\ \theta=75.9638^{\circ}. \end{gathered}[/tex]Answer: (|v|=2√17, θ=75.9638°)
[tex]\begin{gathered} \vec{\lvert\rvert v}\lvert\rvert=2\sqrt{17}, \\ \theta=75.9638^{\operatorname{\circ}}. \end{gathered}[/tex]StorageBoxCrate Size DimensionsWidth8 feet4 inchesHow many boxesfit along thelength of thiscrate?Height 8 feetLength 40 feet6 inches8 inchesA. 16 boxesB. 2 boxesC. 60 boxesD. 5 boxes
Answers
5 boxes fit along the length of the crate (option D)
Explanation:Given:
Length of box = 8 in, width = 4 in, height = 6 in
Length of crate 40 ft, width = 8 ft, height = 8 ft
To find:
The number of boxes that can ft into the length of the crate
To determine the number of boxes that will fit into the length of the crate, we will divide the length of the crate by the length of the box
[tex]\begin{gathered} Number\text{ of boxes on the crate length = }\frac{40\text{ ft}}{8\text{ in}} \\ Number\text{ of boxes on the crate length = 5} \end{gathered}[/tex]5 boxes fit along the length of the crate (option D)
EsparThe shorter leg of a right triangle is 7 m shorter than the longer leg. The hypotenuse is 7 m longer than the longer leg. Findthe side lengths of the triangle.entsLength of the shorter leg:Length of the longer leg:ImLength of the hypotenuse:Х$?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
length of the shorter leg = ?
length of the longer leg = ?
length of the hypotenuse = ?
Step 02:
We must analyze the problem to find the solution.
x = length of the shorter leg
y = length of the longer leg
z = length of the hypotenuse
System of equations:
x = y - 7 (eq.1)
z = y + 7 (eq.2)
z² = x² + y² (eq.3)
eq.2 in eq.3
[tex]\begin{gathered} (y+7)^2=x^2+y^2\text{ } \\ y^2+14y+49=x^2+y^2 \\ 14y+49=x^2 \\ \\ \\ \end{gathered}[/tex]14y + 49 = x²
y - 7 = x * (-14) (eq.1)
14y + 49 = x²
-14y + 98 = -14x (eq.1)
__________________
147 = x² - 14x
x² - 14x - 147 = 0
Step 03:
Quadratic equation:
x² - 14x - 147 = 0
[tex]x=\frac{-(-14)\pm\sqrt[]{(-14)^2-4\cdot1\cdot(-147)}}{2.1}[/tex][tex]\begin{gathered} x1\text{ = }\frac{-(-14)+28_{}}{2}\text{ = 21} \\ x2=\frac{-(-14)-28}{2}\text{ }=\text{ -7} \end{gathered}[/tex]x = 21 (positive solution)
x = y - 7
21 + 7 = y
28 = y
z = y + 7 = 28 + 7 = 35
The answer is:
length of the shorter leg = 21
length of the longer leg = 28
length of the hypotenuse = 35
Need help solving step by step and graphing Problem number 2
Answers
f(x) = |x|
Since the variable x is given with absolute value signs, the function f(x) will always take on positive values for all values (negative or positive) of x.
To solution of a function is the value of the function such that f(x) = 0. The function f(x) = 0 when x = 0 because at every value of x on the graph, y = the same value.
e.g. when x =1, y=1. When x =2, y=2 etc...
This is the graph of f(x) = x (without the absolute value sign):
This is the graph of f(x) = |x| :
which of the following properties are used when rewriting the expression
Answers
We note first that outside the parenthesis there is a negative power, besides, the x is in the denominator of a quotien and it is elevated to a power, then we will use the third opcion
negative power and quotient to a power.
There are 53 members on the board of directors for a certain non-profit institution. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? There are _ different slates of candidates possible.please answer the question above.
Answers
For this problem the order of selection matter (the first person is the chairperson, the second the first vice chairperson and so on); since this is the case we need to use permutations. The permutation is given by:
[tex]_nP_k=\frac{n!}{(n-k)!}[/tex]we have a total of 53 members and the slates contain 4 people, then we have:
[tex]_{53}P_4=\frac{53!}{(53-4)!}=7027800[/tex]Therefore, there are 7,027,800 different slates of candidates.
The current student population of Tucson is 2500. If the population increase at a rate of 15% each year. What will the student population be in 10 years?Write an exponential growth model for the future population (y) in terms of time x: y=What will the population be in 10 years? (Round to nearest student)
Answers
Let's assume that we have a certain quantity y that increases at a rate of p% every x years. If the initial quantity (i.e. the quntity at x=0) is "a" then the value of y after x years is given by:
[tex]y=a\cdot(1+\frac{p}{100})^x[/tex]We are told that the current student population of Tucson is 2500 and that it will increase at a rate of 15% per year. Then the student population after x years is given by:
[tex]\begin{gathered} y=2500\cdot(1+\frac{15}{100})^x \\ y=2500\cdot1.15^x \end{gathered}[/tex]Then the student population after 10 years is given by:
[tex]y=2,500\cdot1.15^{10}=10113.89[/tex]AnswerThen the answers are:
[tex]y=2500\cdot1.15^x[/tex]The population will be 10114.
Given that 2x+7=27 and 3x+1=28, does 2x+7= 3x+1? Explain.
Answers
No, 2x+7 is not equal to 3x+1.
The value of 2x+7 is 27, where as value of 3x+1 is 28, which is one more than tha value of 2x+7. So the correct equation is.
[tex]\begin{gathered} 2x+7=3x+1-1 \\ 2x+7=3x \end{gathered}[/tex]Hence it can be said that,
[tex]2x+7\ne3x+1[/tex]Which is the image of vertex P after the triangle is rotated 180 degreesabout the origin?
Answers
For this case we know that the vertex P has the following coordinates:
[tex]P=(-3,2)[/tex]And we want to find the coordinates after rotate 180 degrees about the origin we assume that the translation is anticlockwise so then we just need to do the following :
[tex]P^{\prime}=(-x,-y)=(3,-2)[/tex]And then the solution ofr this case would be (3,-2)
A spinner with the colors purple, red, green, and yellow is spun. What is the theoretical probability of landing on purple? O P(purple) = 20% • O O P(purple) = 50% O P(purple) = 100% O P(purple) = 33.3% - O P(purple) = 25%
Answers
Answer:
25%
Explanation:
Probability is the likelihood or chance that an event will occur. Mathematically;
Probability = Expected outcome/Total outcome
Since there are 4 colours to spun (purple, red, green, and yellow)
Total outcome = 4
If purple landed, then the expected outcome = 1
Substitute into the formula;
P(Purple) = 1/4
P(Purple) = 0.25
P(Purple) = 25%
Hence the theoretical probability of landing on purple is 25%
the measure of an interior angle of a regular polygon is given find the number of sides in the polygon show all work
Answers
Answer:
The polygon has 5 sides;
[tex]n=5[/tex]Explanation:
The measure of an interior angles of a regular polygon can be given by the formula;
[tex]x=\frac{(n-2)180}{n}[/tex]Where;
n = number of sides of the polygon
x = measure of each interior angle of the polygon
Given;
4.
[tex]x=108[/tex]substituting into the formula and solving for n, we have;
[tex]\begin{gathered} x=\frac{(n-2)180}{n} \\ 108=\frac{(n-2)180}{n} \\ \text{cross multiply and expand;} \\ 108n=180n-360 \\ 180n-108n=360 \\ 72n=360 \\ n=\frac{360}{72} \\ n=5 \end{gathered}[/tex]Therefore, the polygon has 5 sides;
[tex]n=5[/tex]finding radius of cones base when only given the area of the base
Answers
Given
A cone's height is equal to the radius of its base.
And, the base area is 1386 square units.
To find:
The radius and volume of the cone.
Explanation:
It is given that,
A cone's height is equal to the radius of its base.
And, the base area is 1386 square units.
Then,
[tex][/tex]Wire the explicit expression that can be used to find the nth term in this sequence 3,7,11,15,19An = What would be the 20th term A20 =
Answers
From the sequence given 3,7,11,15,19
first term (a) = 3
common difference(d) = 4
Hence to find the nth term, the expression is given as shown below
[tex]\begin{gathered} T_n\text{ = a + (n -1)d} \\ T_n\text{ = 3 + (n - 1)4} \\ \text{ = 3 + 4n -4} \\ \text{ = 4n - 4+ 3} \\ \text{ = 4n - 1} \end{gathered}[/tex]To find the 20th term, we have
[tex]\begin{gathered} T_n\text{ = a + (n -1)d} \\ a\text{ = 3, d = 4},\text{ n = 20} \\ T_n\text{ = a + (n -1)d} \\ T_n\text{ = 3 + (20 - 1)4} \\ T_{20}\text{ = 3 + (19)4 } \\ T_{20}\text{ = 3 +76} \\ T_{20}\text{ = 79} \end{gathered}[/tex]
If the angles of a triangle are 45°, 45°, and 90°,show that the length of the hypotenuse is 3 times as long as eachleg.V 1. Substitute the side lengths of the triangle into the Pythagoreantheoremq² + ² = 22. Combine like terms.
Answers
Acording to pythagoras theorem,
[tex]\text{hypotenuse}^2=base^2+height^2[/tex]Here,
[tex]\begin{gathered} \text{hypotenuse}=c \\ \text{height}=a \\ \text{base}=a \end{gathered}[/tex]Therefore we have,
[tex]\begin{gathered} c^2=a^2+a^2 \\ c^2=2a^2 \\ c=\sqrt[]{2}a \end{gathered}[/tex]Hence the proof.
Hudson bought 4 pounds of cantaloupe for $11.25.What is the price, in dollars, of 2 lbs of cantaloupe?
Answers
If 4 pounds of cantaloupe cost $11.25
then, 1 pound of cantaloupe will cost
[tex]\frac{11.25}{4}=\text{ \$2}.8125[/tex]if 1 pound of cantaloupe costs $2.8125
then, 2 pounds of cantaloupe will cost $2.8125 x 2
[tex]=\text{ \$5.625}[/tex]The answer is $5.625
Find y This is geometry (please start off with solution )
Answers
Answer:
Explanation:
Given:
To find:
The value of y
We'll go ahead and use the cosine rule to find the value of y as seen below;
[tex]y^2=e^2+s^2-2es\cos E[/tex][tex]\begin{gathered} y^2=42^2+32^2-2*42*32*\cos78 \\ y^2=1764+1024-558.8666 \\ y^2=2788-558.8666 \\ y=\sqrt{2229.1334} \\ y=47.2\text{ cm} \end{gathered}[/tex]Therefore, the value of y is 47.2 cm
I need help with this problem.I will need to send you the picture of the problem because it couldn’t fit into the screenshot
Answers
EXPLANATION :
From the problem, we have the radical expression :
[tex]\sqrt{36}+\sqrt{49}-\sqrt{16}[/tex]Note that the given radicals are perfect squares :
36 = 6^2
49 = 7^2
16 = 4^2
Then :
[tex]\begin{gathered} \sqrt{6^2}+\sqrt{7^2}-\sqrt{4^2} \\ =6+7-4 \\ =9 \end{gathered}[/tex]ANSWER :
The answer is 1 only
Determine the number of solutions for the following system of linear equations. If there is only onesolution, find the solution.- 5x + 2y + 6z = -2x + 3y + 4z = - 36x + y – 2z = -1AnswerKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected option does not have anyassociated text boxes, then no further input is required.O No SolutionO Only One Solution=こ%3DO Infinitely Many Solutions
Answers
We are given the following system of linear equations
[tex]\begin{gathered} -5x+2y+6z=-2 \\ x+3y+4z=-3 \\ 6x+y-2z=-1 \end{gathered}[/tex]Let us solve the given system of equations.
First, let us find the determinant.
The determinant is given by
[tex]\begin{gathered} D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5\begin{bmatrix}{3} & {4} \\ 1 & {-2}\end{bmatrix}-2\begin{bmatrix}{1} & {4} \\ {6} & {-2}\end{bmatrix}+6\begin{bmatrix}{1} & {3} \\ {6} & {1}\end{bmatrix} \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(3\cdot-2-4\cdot1)-2(1\cdot-2-4\cdot6)+6(1\cdot1-3\cdot6) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(-6-4)-2(-2-24)+6(1-18) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(-10)-2(-26)+6(-17) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=50+52-102 \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=102-102 \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=0 \end{gathered}[/tex]As you can see, the determinant of the matrix is 0
This means that the given system of equations has no solution.
The commutative property of addition says that changing the order of addends does not change the sum.Select one:TrueFalse
Answers
TRUE
Explanations:Given two integers A and B according to commutative law, if these two integers are added no matter the arrangement of the integers, the sum of the integers will not be affected.
According to the commutative law;
[tex]A+B=B+A[/tex]For instance, let us assume the integers are 4 and 5 where A = 4 and B = 5. Applying the commutative law to the sum, we will have;
[tex]\begin{gathered} 4+5=9 \\ 5+4=9 \\ \text{Hence, 4 + 5 = 5 + 4 (Commutative law of addition)} \end{gathered}[/tex]Based on the above postulate, we can conclude that the commutative property of addition says that changing the order of addends does not change the sum
help me with this question
Answers
what we wrer asked to find is BUC
which means B union C
that also means numbers that are found both in set B and set C
so for
set B {4, 7, 11, 12,14}
set C {2, 4, 8, 10, 11, 12, 13}
therefore,
BUC {2, 4, 7, 8, 10, 11, 12, 13, 14}
so the correct option is B
if Teresa used five and a third gallons of gas on Sunday and two and a quarter gallons of gas on Monday how many more gallons of gas did she use on Sunday
Answers
Hence the difference is
[tex]5\frac{1}{3}-2\frac{1}{4}=3\frac{4-3}{12}=3\frac{1}{12}[/tex]Hence she used 3 1/12 more gallons of gas on Sunday
Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer.A. right angle 3 is congruent to right angle 7B. m right angle 7 + m right angle 12 = 180
Answers
Situation A.
Angle 3 is congruent with angle 7.
That means that line a and b are parallel, because: Angle 3 and Angle 5 are vertical angles, and if Angle 3 is congruent with Angle 7, then Angle 5 is also congruent with Angle 7, therefore, the lines a an b are parallel.
Situation B.
Angle 7 is supplementary of Angle 12.
Angle 12 is supplementary to Angle 13.
Then Angle 13 and Angle 7 are congruent.
Then a and b are parallel and l and m are parallel.
Triangle KAB is similar to triangle KML. Find the length of AB.L36B5430K50A
Answers
Given the figure in the attached image;
The triangles KAB and KML are similar
[tex]\Delta KAB\text{ \textasciitilde}\Delta KML[/tex]So, the sides of the triangles are proportional.
[tex]\frac{KB}{KL}=\frac{AB}{ML}[/tex]Given in the figure;
[tex]\begin{gathered} KB=30 \\ KL=36 \\ ML=54 \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} \frac{KB}{KL}=\frac{AB}{ML} \\ \frac{30}{36}=\frac{AB}{54} \\ AB=\frac{30\times54}{36} \\ AB=45 \end{gathered}[/tex]Therefore, the length of side AB is;
[tex]45\text{ units}[/tex]What is 1827 plus 1938?
Answers
1 1
1827
+
1938
____
3765
= 3765
explanation: 7 + 8 = 15, 30 + 20 = 50, 800 + 900 = 1600, 1000 + 1000 = 2000. adding them all together equals 3765
Given the figure below, determine the angle that is a same side exterior angle with respect to1. To answer this question, click on the appropriate angle.
Answers
The angle that is a same side exterior angle with respect to <8 is ;
<2
Same side exterior angles are supplementary angles on the same side of the transversal , t , and outside the parallel lines l and m
The answer is : < 2
Use the formula for finding a z-score to determine the missing value in the following table. Round your answer to two decimal places, if necessary
Answers
Explanation
We are given the following:
[tex]\begin{gathered} z=0.64 \\ x=-34.90 \\ \sigma=9.48 \end{gathered}[/tex]We are required to determine the missing value μ.
This is achieved thus:
We know that the formula for z-score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Therefore, we have:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 0.64=\frac{-34.90-\mu}{9.48} \\ \text{ Cross multiply } \\ -34.90-\mu=0.64\times9.48 \\ -34.90-\mu=6.0672 \\ -\mu=6.0672+34.90 \\ -\mu=40.9672 \\ \mu=-40.9672 \\ \mu\approx-40.97 \end{gathered}[/tex]Hence, the answer is:
[tex]\mu\approx-40.97[/tex]