The given options are 1) y = (cos x) / x is neither and 2) y = (sin x) / x is even.
What are the six trigonometric ratios?
Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right-angled (not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
1) y = (cos x) / x is neither, since cos x is even and x is odd.
2) y = (sin x) / x is even since sin x and x would either both be positive at the same time or negative at the same time.
We know that (-) / (-) is positive, just as (+) / (+) is positive.
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Final answer:
1. The function y=cos(x)/x is neither even nor odd due to its lack of symmetry properties
2. y=sin(x)/x is an odd function as it satisfies the symmetry condition about the origin.
Explanation:
To determine if the functions y=cos(x)/x and y=sin(x)/x are even, odd, or neither, we need to understand the definitions of even and odd functions and apply them accordingly.
Even and Odd Functions:
An even function satisfies the condition f(-x) = f(x), meaning the function's graph is symmetric about the y-axis. An odd function satisfies the condition f(-x) = -f(x), indicating symmetry about the origin.
Analysis of y=cos(x)/x:
To determine if y=cos(x)/x is even, odd, or neither, replace x with -x:
y=cos(-x)/(-x) = cos(x)/(-x) because cos(-x) = cos(x), an even function property.
This contradicts the definitions of both even and odd functions; hence, y=cos(x)/x is neither even nor odd.
Analysis of y=sin(x)/x:
Similarly, for y=sin(x)/x, replace x with -x:
y=sin(-x)/(-x) = -sin(x)/(-x) because sin(-x) = -sin(x), an odd function property.
This simplifies to y=sin(x)/x, which satisfies the condition for an odd function.
Therefore, y=sin(x)/x is an odd function.
Which is an equivalent form of the compound inequality −44 > −2x − 8 ≥ −8?
Answer:
22 and 0
Step-by-step explanation:
−44 > −2x − 8 ≥ −8?
/-2 - 44 > -2x / . -2 -8 ≥ -8
= 22 +8 =0
Answer:
An equivalent form of the compound inequality is the pair of single inequalities:
-2x - 8 < - 44, and −2x − 8 ≥ −8Explanation:
You can split the compound inequality into two equivalent inequalities by taking each side from the variable.
The compound inequality −44 > −2x − 8 ≥ −8 means that two conditions must be satisfied:
1. From the left side: - 44 > - 2x - 8
2. From the right side: −2x − 8 ≥ −8
Then, as a first approach you can tell that an equivalent form of the compound inequality is the pair of single inequalities:
-44 > -2x - 8, and −2x − 8 ≥ −8You should put the variable on the left sides, which will yield the best form of an equivalent pair of inequalitis.
- 2x - 8 < -44, and- 2x - 8 ≥ - 8That is the best choice of an equivalent form, and from there you can solve the inequalities which will permit to obtain the solution. Of course, you can manipulate the variable and find many other equivalent forms.
Notice, that both inequalities must be satisfied simultaneously.
This is how you solve that system
- 2x - 8 < -44nAdd 8 to both sides: - 2x < -36
Divide both sides by - 2 (you have to change the sign): x > 18
- 2x - 8 ≥ - 8-
Add 8 to both sides: - 2x ≥ 0
Divide by - 2 (again, you must change the sign): x ≤ 0
Then, the solution set is:
x > 18 and x ≤ 0 and that is an empty set, since x cannot be at the same time greater than 18 and less or equal to 0.This is, you conclude that the compound inequality is false, because there is not a value of x which is a solution.
How is finding the fourth vertex of a parallelogram that is not a rectangle or a square the same as it is for a rectangle or square? How is it different?
well, the only difference from a parallelogram that is a square or a rectangle and one that isn't, is that the interior angles are 90° in the square and rectangle, however for other ones, like the one in the picture below, they are not 90°.
however, getting to any vertex, is just a matter of moving horizontally and vertically the same distances, as you see those arrows on the picture, since both pair of sides are parallel, one moves the same distance horizontall and vertically to get to the next vertex, so on that, is the same as for a square or rectangle as well.
is only different in that you're not moving alongside the segment, in a rectangle or a square, the lines are only vertical or horizontal, so you simply move straight to get the next vertex, on other parallelograms like the one below, you do move the same but is not alongside the segments.
PLEASE HELP! SEE ATTACHMENT
Answer:
-24 - 4ε
Step-by-step explanation:
100000000000 = 10¹¹ [One hundred billion]
You multiply this by -5 to get -500000000000. Now, "⁻²" means you will be taking the Multiplicative Inverse of whatever this result is, and since it is a long answer, I decided to give it to you in Calculus [Calculator] Notation.
Answer:the answer is ten to the eleventh minus five and then minus itself twice times ten
Step-by-step explanation:
Find the probability of selecting a class that runs between 51.25 and 51.75 minutes
Answer:
0.05
Step-by-step explanation:
This question is on probability
A uniform distribution means there is equal probability density for every number.
This graph will be distributed to form a rectangle with area 1 unit square.
The base/range = 58-48 =10
Height of rectangle should be such that the area is 1 square unit. i.e 1/10 units
The probability will be found by calculating the area under the graph;
P( 51.25≤ x ≤ 51.75) , Area = (51.75-51.25)×1/10
0.5/10 =0.05
Please help me! I don’t need a long explanation
Answer:
- [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex]
Step-by-step explanation:
Note that [tex]\frac{5\pi }{8}[/tex] is in the second quadrant
where cos < 0 , hence overall sign will be negative
Using the half- angle formula
cos [tex]\frac{5\pi }{8}[/tex]
= - [tex]\sqrt{\frac{1+cos\frac{5\pi }{4} }{2} }[/tex]
= - [tex]\sqrt{\frac{1-\frac{\sqrt{2} }{2} }{2} }[/tex]
= - [tex]\sqrt{\frac{2-\sqrt{2} }{4} }[/tex]
= - [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex]
You have a normal distribution of hours per week that music students practice. The mean of the values is 8 and the standard deviation of the values is 4. According to the normal distribution, half of the music students practice between 5.3 to 10.7 hours each week. What percentage of the students study less than 5.3 hours each week? 12.5% 20% 25% 50%
Answer:
25%
Step-by-step explanation:
Since Normal Distribution is symmetrical Distribution and 5.3 and 10.7 are both 2.7 below and 2.7 above the mean respectively.
So, % of students less than 5.3 hours per week is 25%
help pleeesea!!!!!!!!!!!.Trina downloaded 3 music albums and 5 audio books one week at a cost of $49.60. The next week she downloaded 1 music album and 2 audio books at a cost of $20.50. Her mother wants to write a system of equations to determine the price of one music album and one audio book. She uses the variables x and y. She lets x represent the cost of one music album. What will y represent?
Y is the Audio Book.
"determine the price of one music album and one audio book"
"She lets x represent the cost of one music album."
According to this information "One Audio Book" should be the correct answer. Have a great day!
Answer:
y will represent the cost of one audio book.
Step-by-step explanation:
Here, the cost of 3 music albums and 5 audio books is $49.60 and 1 music album and 2 audio books is $20.50,
Since, there are two unknown values,
First one is the cost of one music album,
Second one is the cost of one audio book,
We know that, for finding an unknown value we take a variable,
If we have variables x and y in which x represent the cost of one music album, then y must represent the cost of one audio album.
help answer question 2
What is the distance between (-5,8) and (4,6)
Answer:
[tex]\sqrt{85}[/tex] (about 9.2195) units
Step-by-step explanation:
The formula for the distance between two points is: [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Substitute the values. [tex]\sqrt{(-5 - 4)^2 + (8 - 6)^2}[/tex]
Subtract. [tex]\sqrt{(-9)^2 + 2^2}[/tex]
Solve the exponents. [tex]\sqrt{81 + 4}[/tex]
Add. [tex]\sqrt{85}[/tex]
This is as simple as the solution can get without estimating, but we can use a calculator to estimate that the distance is about 9.2195 units.
Hey there! :)
Find the distance between (-5, 8) (4, 6)
The formula to find the distance is : d = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2[/tex]
Where : -5 = x1 , 4 = x2 , 8 = y1 , 6 = y2
Now, simply plug everything into our equation.
[tex]d = \sqrt{(4 + 5)^2 + (6 - 8)^2}[/tex]
Let's simplify this now.
[tex]d = \sqrt{9^2 - 2^2}[/tex]
Simplify again.
[tex]d = \sqrt{81 + 4} = \sqrt{85}[/tex]
Therefore, our distance is [tex]\sqrt{85}[/tex] OR 9.22
Hope this helped! :)
What is the interquartile range of this day at set?
Answer: 49
Step-by-step explanation
Am god
Who can help me?
please
Thank you
The sum of the interior triangles in a triangle is 180, so if we add all the angle measures together, we should get 180. Therefore, we can make an equation like this,
[tex]110-2x+x+50+5x-40=180[/tex]
Simplify this.
[tex]4x+120=180[/tex]
[tex]4x=60[/tex]
[tex]x=15[/tex]
Now we can find each angle measure.
[tex]110-2x[/tex]
[tex]110-2(15)[/tex]
[tex]110-30[/tex]
[tex]80[/tex]
[tex]x+50[/tex]
[tex]15+50[/tex]
[tex]65[/tex]
[tex]5x-40[/tex]
[tex]5(15)-40[/tex]
[tex]75-40[/tex]
[tex]35[/tex]
So the angle labeled [tex]110-2x[/tex] is the largest angle in the triangle.
Answer:
x=15
biggest angle is 110-2x
Step-by-step explanation:
Which is a reasonable first step that can be used to solve the equation
Answer:
Use distributive property:
2x + 12 = 3x - 12 + 5
Step-by-step explanation:
This can allow for combining like terms later on, and eventually isolating x as a variable.
For this case we have the following equation:
[tex]2 (x + 6) = 3 (x-4) +5[/tex]
The first step we must follow to solve the equation is to apply distributive property to the terms within the parenthesis:
[tex]a (b + c) = ab + ac[/tex]
Then, the equation is:
[tex]2x + 12 = 3x-12 + 5[/tex]
Answer:
The first step is to apply distributive property to the terms within parentheses.
the price of one share of XYZ inc's stock drop by $0.02 on Monday. On Tuesday the price goes back up by $0.05.
Write an expression with three terms to show the change in price of XYZ stock.
_____________________________________________________________
If one share of XYZ stock cost $34.18 at the start of business on Monday morning, what is the price of the one share of XYZ stock at the close of business on Tuesday evening?
Answer:
1. $(x+0.03) - $x
2. $ 34.21
Step-by-step explanation:
Let the price of XYZ inc's share to be = $ x
On Monday, the price drops by $ 0.02 = $ x- $ 0.02 = $ (x-0.02)
New price of shares on Monday is = $ (x- 0.02)
On Tuesday the price goes up by $0.05 = $ (x-0.02) + $ 0.05 = $(x-0.02+0.05)
New price on Tuesday = $( x+ 0.03)..............................................(a)
Change in price of one share of XYZ's stock= Price on Tuesday - price of share
= $(x+0.03) - $x..........................................(b)
2. Give that x= $34.18 solve equation (a) above
Price on Tuesday at close of business= $ (x+0.03)
= $ (34.18+0.03)
= $ 34.21
Bill will rent a car for the weekend. He can choose one of two plans. The first plan has no
initial fee but costs $0.70 per mile driven. The second plan has an initial fee of $50 and
costs an additional $0.50 per mile driven. How many miles would Bill need to drive for the
two plans to cost the same?
Clear
Undo Help
Answer:
250 miles
Step-by-step explanation:
Let number of mile driven be x
plan 1: Cost = 0.7x
plan 2: Cost = 50 + 0.5x
for both plans to cost the same,
Plan 1 Cost = Plan 2 Cost
0.7x = 50 + 0.5x (solve for x)
0.7x - 0.5x = 50
0.2x = 50
x = 250 miles
find the interior angle of a regular polygon which has 6 sides
Answer:
120°.
Step-by-step explanation:
The sum of all interior angles in a polygon with [tex]n[/tex] sides ([tex]n\in \mathbb{Z}[/tex], [tex]n \ge 3[/tex]) is equal to [tex](n - 2) \cdot 180^{\circ}[/tex]. (Credit: Mathsisfun.)
The polygon here has 6 sides. [tex]n = 6[/tex]. Its interior angles shall add up to [tex](6 - 2) \times 180^{\circ} = 720^{\circ}[/tex].
Consider the properties of a regular polygon. (Credit: Mathsisfun.)
All sides in a regular polygon are equal in length. All angles in a regular polygon are also equal.There are six interior angles in a polygon with 6 sides. All six of them are equal. Thus, each of the six interior angle will be
[tex]\displaystyle \frac{1}{6}\times 720^{\circ} = 120^{\circ}[/tex].
If 32x+1 - 3^x+5, what is the value of x?
Answer:
x = 4
Step-by-step explanation:
hope this helps!!!
Select all the correct statements.
The amount in dollars an electrician charges in terms of the number of hours worked is represented by the function y = 22x + 42.
From the function, identify all the phrases that hold true for the situation.
The electrician charges an initial fee of $22
The y-variable represents the number of hours
The electrician charges an initial fee of $42
The electrician charges $22 for every hour worked
The X-variable represents the electricians charges in dollars
The electrician charges $42 for every hour worked
Answer:
"The electrician charges an initial fee of $42", AND "The electrician charges $22 for every hour worked" is true.
Step-by-step explanation:
The equation is y=22x+42.
The formula is y=mx+b.
m is the slope, or is this case, the number of dollars for every "x", which is the number of hours worked. So you have to pay $22 for every hour the electrician works.
b is the y-intercept, or the amount it starts with, in this case, you have to pay a fee of $42 even when the electrician worked 0 hours. This is because $42 is the amount it starts with.
On a graph, the line will start at (0,42) because that is when you start paying. And then it will increase by 22 for each hour, so the next coordinate would be (1,64).
The equation y = 22x + 42 indicates that an electrician charges a base fee of $42, plus an additional $22 for every hour worked. Thus, the correct statements are 'The electrician charges an initial fee of $42' and 'The electrician charges $22 for every hour worked.'
Explanation:The equation y = 22x + 42 is a linear function where the y-variable represents the total dollars the electrician charges and the x-variable represents the number of hours worked. From this equation, we can immediately discern two truths:
The electrician charges an initial fee of $42. This is the y-intercept of the function, indicating the base charge before any work has been done.The electrician charges $22 for every hour worked. This is the slope, or 'm', of the function and indicates the rate at which the total cost changes per hour of work.Learn more about Linear Function Interpretation here:https://brainly.com/question/32914656
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The surface area of a rectangular prism is increased by a factor of 16.
By what factor is the volume of the figure increased?
Answer:
The factor of the volume of the figure increased is 64
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared and the ratio of its volumes is equal to the scale factor elevated to the cube
step 1
Find the scale factor
Let
z ----> the scale factor
z²=16
z=4 -----> scale factor
so
z³=4³=64
The factor of the volume of the figure increased is 64
Answer:
The volume of the rectangular prism will increase by a factor of 64.
Step-by-step explanation:
Surface area = [tex]length\times length[/tex]
or [tex]\sqrt{surface area} =length[/tex]
Therefore, the increase in the length of the sides will be = [tex]\sqrt{16}=4[/tex]
We know the volume is =[tex]length\times width\times height[/tex]
When there is increase in length of sides by 4 times, then volume will increase by [tex]4^{3}[/tex]
And [tex]4^{3}[/tex] = [tex]4\times4\times4=64[/tex]
Hence, the volume of the rectangular prism will increase by a factor of 64.
The figure shown is a composite figure. What is its volume?
2,622
2,109
3,648
1,387
Answer:
2622
Step-by-step explanation:
The answer can be found by adding up the volume of the two parts of the composite figure, which consists of a triangular prism and a rectangular prism
Volume of the rectangular prism=(Width)(Height)(Length)
=12*7*19
=1596
Volume of the triangular prism=(Base area)(Height)
If the triangle consisting of the sides 9, 12, 15 is a right angled triangle, 9²+12²=15²
The statement above is true
The triangle above is a right angled triangle, where 9 is the height and 12 is the base
Triangle area=(height)(base)(0.5)
=9*12*0.5
=54
Volume of triangular prism=54*19
=1026
Adding up both=1596+1026=2622
V = V1 + V2
V1 = 0.5 x 9 x 12 x 19
V1 = 1,026
V2 = 12 x 19 x 7
V2 = 1,596
V = V1 + V2
V = 1,026 + 1,596
V = 2,622
The answer is 2,622.
what is the equation of the linear function represented by the table?
Answer:
y = -3x+17
Step-by-step explanation:
1. Find the change in y corresponding to the change in x. In this case x is changing by +3 and y is changing by -3. That is your m in y=mx=b.
2. y= -3x + b
To find b substitute a set into the equation. I used 4 and 5.
5= -3(4) +b
3. 5= -12 +b ,add 12 to both sides.
17= b
4. y = -3x+17
Answer:
a y= -x+9
Step-by-step explanation:
How to write an equation of the line through the point (-2,1) that is perpendicular to the line 5x+9y=-9
Answer:
[tex]\large\boxed{y=\dfrac{5}{9}x+\dfrac{19}{9}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation i the standard form.}\\\text{ Convert it to the slope-intercept form}\ y=mx+b:\\\\5x+9y=-9\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\9y=-5x-9\qquad\text{divide both sides by 9}\\\\y=-\dfrac{5}{9}x-1\to m_1=-\dfrac{5}{9}\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{-\frac{5}{9}}=\dfrac{9}{5}[/tex]
[tex]\text{We have the equation:}\\\\y=\dfrac{5}{9}x+b\\\\\text{Put the coordinates of the point (-2, 1) to the equation:}\\\\1=\dfrac{5}{9}(-2)+b\\\\1=-\dfrac{10}{9}+b\qquad\text{add}\ \dfrac{10}{5}\ \text{to both sides}\\\\\dfrac{19}{9}=b\to b=\dfrac{19}{9}[/tex]
which function is represented by the graph?
a. f(x)=|x-1|+3
b. f(x)=|x+1|-3
c. f(x)=|x-1|-3
d. f(x)=|x+1|+3
Answer with Step-by-step explanation:
As we can clearly see from the graph the value of f(x)=0 at x=2 and x= -4
a. f(x)=|x-1|+3
at x=2
f(2)=|2-1|+3
= 1+3
=4
Hence, this function is not represented by the graph
c. f(x)=|x-1|-3
at x=2
f(2)= |2-1|-3
= 1-3
= -2
Hence, this function is not represented by the graph
d. f(x)=|x+1|+3
at x=2
f(2)= |2+1|+3
= 3+3
= 6
Hence, this function is not represented by the graph
Hence, Correct option is:
b. f(x)=|x+1|-3
Answer:
The answer is B
Step-by-step explanation:
Which of the following represents a region of a circle?
A. Sector
B. Arc
C. Tangent
D. Circumference
Answer:
A. Sector
Step-by-step explanation:
A Sector represents a region of a circle.
Answer:
The one that represents a region of a circle is A: Sector.
Step-by-step explanation:
It is a slice, a piece-slice part of a circle the area between two radiuses and the connecting arc of a circle. The segment of a circle is the region bounded by a chord and the arc subtended by the chord. It differs from the segment because the segment is the region bounded by a chord and the arc subtended by the chord.
d/dx(1+x^4+x^6/x^2+x+1)
A)2x+1
B)2x-1
C)2
D)0
\frac{d}{dx}\left(\frac{1+x^4+x^6}{x^2+x+1}\right)=\frac{4x^7+5x^6+8x^5+3x^4+4x^3-2x-1}{\left(x^2+x+1\right)^2}
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F(x)=5/6x+3 Which of the following is true
What is the 47th term of the arithmetic sequence with this explicit formula?
an= -11 + (n - 1)(-3)
Answer:
-149
Step-by-step explanation:
Just plug in 47
-11+(47-1)(-3)
-11+46(-3)
-11+-138
- 149
Answer:
= -149
Step-by-step explanation:
an= -11 + (n - 1)(-3)
The 47th term means n = 47
a47 = -11 + (47-1) (-3)
= -11 + 46 (-3)
= -11 -138
= -149
john played his xbox 180 times over a 12 week period. if john played the same number of times each week, how many times did john played in one week?
Answer:
15
Explanation:
180 times / 12 weeks = 15 times in one week
Use the diagram and given information to answer the questions and prove the statement.
Re-draw the diagram of the overlapping triangles so that the two triangles are separated.
What additional information would be necessary to prove that the two triangles, XBY and ZAY, are congruent? What congruency theorem would be applied?
Prove AZ ≅ BX using a flow chart proof.
Answer:
See explanation
Step-by-step explanation:
ASA Postulate (Angle-Side-Angle):
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Consider triangles XYB and ZYA. In these triangles
∠X≅∠Z (given)XY≅ZY (given)∠Y is common angleBy ASA Postulate, triangles XYB and ZYA are congruent. Congruent triangles have congruent corresponding sides, so
BX≅AZ
[tex]\rm \overline{AZ} \cong \overline{BX}[/tex]
Please refer the below solution.
Step-by-step explanation:
Given :
[tex]\rm \angle X \cong \angle Z[/tex][tex]\rm \angle Y \;is\;common[/tex]
[tex]\rm \overline{XY} \cong \overline{ZY}[/tex]
Solution :
According to ASA (Angle Side Angle) postulate:
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then both the triangles are congruent.
Now, consider triangle XBY and ZAY
[tex]\rm \angle X \cong \angle Z[/tex]
[tex]\rm \overline{XY} \cong \overline{ZY}[/tex]
[tex]\rm \angle Y \; is \; common[/tex]
According to ASA postulate triangle XBY and ZAY are congruent. And congruent triangles have congruent corresponding sides, therefore
[tex]\rm \overline{AZ} \cong \overline{BX}[/tex]
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Find y. Round to the nearest tenth.
Please help me!!!
Answer:
y ≈ 358.3 ft
Step-by-step explanation:
The angle in the right side of the triangle = 28° ( alternate angle )
Using the tangent ratio in the right triangle to solve for y
tan28° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{350}{y}[/tex]
Multiply both sides by y
y × tan28° = 350 ( divide both sides by tan28° )
y = [tex]\frac{350}{tan28}[/tex] ≈ 658.3 ft
y = 658.3ft. The value of the side y of the right triangle shown in the image is 658.3ft.
The key to solve this problem we have to use the trigonometric functions tan θ = opposite leg/adjacent leg
To find side y, where opposite leg = 350ft, adjacent leg = y, and θ = 28° by symmetry:
tan θ = opposite leg/adjacent leg
tan 28° = 350ft/y
Clear y:
y = 350ft/tan 28°
y = 658.254ft
Round to the nearest tenths y = 658.3ft
Someone please help
Evaluate the formula
V= Bh/3 for B= 15in ^2
And
H=28in
Answer:
[tex]\large\boxed{V=140\ in^3}[/tex]
Step-by-step explanation:
[tex]V=\dfrac{Bh}{3}\to\text{it's a formula of a volume of a pyramid or a cone}\\\\B-base\ area\\h-height\\\\\text{We have}\ B=15\ in^2\ \text{and}\ h=28\ in.\\\\\text{Put the given values to the formula of a volume:}\\\\V=\dfrac{(15)(28)}{3}=(5)(28)=140\ in^3[/tex]