Using a trigonometric identity, it is found that the statement is False.
What is the trigonometric identity used in this question?It is for the sine squared, given by:
[tex]\sin^2{x} = \frac{1 - \cos{(2x)}}{2}[/tex]
In this problem, the equality given is:
[tex]\sin{\left(\frac{x}{7}\right)} = \frac{1 - \cos{\left(\frac{2x}{7}\right)}}{2}[/tex]
Since the left side does not have the sine squared, the identity is not valid and the statement is False.
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Answer:
True
Step-by-step explanation:
Just took the quiz
-w=-10+4w
Step by step to please
w=2
Step-by-step explanation:
-w=-10+4w
10=4w+w
10=5w
10/5=w
2=w
whats 2 1/2 X 1 1/2 someone pls help
Answer:
15/4
Step-by-step explanation:
2 1/2 x 1 1/2
First, make them both improper fractions to make them easier to multiply
5/2 x 3/2
Multiply their numerators together to get the numerator and multiply their denominators together to get the denominator.
5 x 3 = 15
2 x 2 = 4
5/2 x 3/2 = 15/4
solve by substitution 3x +y=13 and 5x-2y=7
Answer:
x=3
y=4
Step-by-step explanation:
I'm using 3x+y=13 to find y, then plug y into the second equation.
y= -3x+13
5x-2(-3x+13)=7
find x.
5x+6x-26=7
11x=33
x=3
now plug x into 3x+y=13(you could do it with the other equation too)
3(3)+y=13
y=13-9
y=4
The value of x and y is 3, and 4 respectively by the substitution method.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a system of equations;
3x +y=13 ...(1)
5x-2y=7 ...(2)
By using the substitution method.
[tex]\rm 5\cdot \dfrac{13-y}{3}-2y=7[/tex]
y = 4
Plug y = 4 in equation (1)
3x + 4 = 13
x = 3
Thus, the value of x and y is 3, and 4 respectively by the substitution method.
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If a = 3 what is the value of 2asquared
Answer:
18
Step-by-step explanation:
[tex]2 {a}^{2} = 2 {(3)}^{2} = 2 \times 9 = 18 \\ [/tex]
Answer:
36
Step-by-step explanation:
2 times 3=6 6^2 is 6 times 6
ILL GIVE U A BRAINLIEST! NEED HELP ON TIMER
Which point is located on the x-axis?
On a coordinate plane, point A is at (0, 3), point B is at (3, 3), point C is at (3, 0), and point D is at (negative 3, 3).
Answer:
0,3 hddjbdhfjdndjdkdbdjdnd
Quartile represent what percent of data.
A. 35%
B. 50%
C.25%
D.30%
Other than squares, the polygons that can be the faces of a Platonic solid are
__and ___Check all that apply.
O A. regular pentagons
B. trapezoids
C. circles
D. regular hexagons
O E. equilateral triangles
OF. rectangles
The platonic solids in the given options are A. Regular pentagons and E. Equilateral triangles.
What are platonic solids?The solids that are polyhedrons, all of whose faces are congruent regular polygons and at every vertex, the same number of faces meets are called "Platonic solids"
There are only five types of platonic solids. They are:
CubeTetrahedronOctahedronIcosahedronDodecahedronWhat are the types of faces found on platonic solids?The major types of faces that are found on platonic solids are:
Equilateral triangles: They form Tetrahedron, Octahedron, and IcosahedronSquares: They form Hexahedron and cubePentagons: They form DodecahedronRegular polygons with more than 6 sides are not the faces of the platonic solid.
Thus, from the given shapes,
A. regular pentagons, E. equilateral triangles are used as faces of a Platonic solid.
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Solve 5(2x – 3) = x – 15 + 9x for x.
Answer:
Given
5(2x – 3) = x – 15 + 9xSolving for x
5(2x – 3) = x – 15 + 9x10x - 15 = 10x - 15Both sides are equal, any value of x is a solution, so infinitely many solutions
Step-by-step explanation:
[tex]5(2x - 3) = x - 15 + 9x \\ 10x - 15 = 10 x - 15[/tex]
Both the sides are equal
Hence no specific value of x
Therefore, x has infinite value.
pls help asap no trolls!
Answer:
HI
Step-by-step explanation:
In a triangle, the length size of each side corresponds to the size of the degree of the angle opposite it.
This means, the biggest angle would be opposite the side with the longest length, while the angle with the least degree will be opposite the side that is the smallest.
In ∆HIJ, the least angle measure is <J (54°).
Side length opposite to <J is HI.
Therefore the smallest side of ∆HIJ is HI
Cassandra paid $32 for a shirt that originally cost $50. What percent of the original price did the shirt cost?
Answer:
22%
Step-by-step explanation:
You just subtract the numbers
Answer:
64%
Step-by-step explanation:
To find a percent, you have to divide the new cost by the original cost, then multiply the answer by 100.
(32/50)*100
= 0.64 * 100
= 64%
If adora watched a video that's 21:58 minutes long what time will she have to start watching to finish exactly at 11:59pm
Answer:
11:37.02 pm
Step-by-step explanation:
11:59 pm - 21:58 minutes = 11:37.02 pm
Which list correctly orders A, B, and C from least to greatest when A= |7|, B = _6, and C = |-5|?
O A, B, C
O B, C, A
0 C, B, A
O A, C, B
Answer:
B, C, A
Step-by-step explanation:
A = |7| = 7
B = -6
C = |-5| = 5
Order: B, C, A
Which
graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then
decreases its speed, as time increases?
Answer:
I believe the answer would be
Step-by-step explanation:
a graph that goes up and then is a straight line then it goes down.
In other words the graph would be A.
PLS be quick and answer as best as you can
The following equation was written on the chalkboard: Δ + Δ + ◊ + Ꙫ ─ Δ = Ω. If Δ = 4, Ꙫ = 3 and Ω = 12, what is the value of ◊?
Answer:
4+4+x+3-4=12
8+x-1=12
7+x=12
x=12-7
=5
answer is 5
4(2x - 5)+ 5(3x - 7)
Answer:
=23x−55
Step-by-step explanation:
Let's simplify step-by-step.
4(2x−5)+5(3x−7)
Distribute:
=(4)(2x)+(4)(−5)+(5)(3x)+(5)(−7)
=8x+−20+15x+−35
Combine Like Terms:
=8x+−20+15x+−35
=(8x+15x)+(−20+−35)
=23x+−55
Answer:
22x-55
pemdas works too i guess
Point P is located at (4,8) on a coordinate plane. Point P will be reflected over the x - axis. What will be the coordinates of the image point of point P?
A. (8, 4)
B. (-4, -8)
C. (4, -8
D (-8, 4)
Answer:
C. (4, -8)
Step-by-step explanation:
To reflect a point over a straight horizontal line, start from the original point and count how many units it takes to reach that line (going vertically). Keep that number in mind. Then, at that same point on the line, go vertically again and count that many units going away from the line. The point where you stop would be the reflected point.
In this case, starting from (4, 8) and then going down towards the x-axis would take 8 units. Taking that number and counting another 8 units down would land you at (4, -8). Therefore, (4, -8) is the answer.
Please look at the attached image for a clear visual explanation.
Which of the following values represents the value of the second derivative of y with respect to x for the function defined by ln(xy) = x - y at point (1, 1)?
A. d2y/dx^2 = -1/2
B. d2y/dx^2 = -1/4
C. d2y/dx^2 = 0
D. d2y/dx^2 = 1/4
E. d2y/dx^2 = 1/2
Answer:
E
Step-by-step explanation:
We are given:
[tex]\ln(xy)=x-y[/tex]
And we want to find the second derivative at the point (1, 1).
So, we will take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\big[\ln(xy)\big]=\frac{d}{dx}\big[x-y\big][/tex]
Implicitly differentiate. The left will require the chain rule. Hence:
[tex]\displaystyle \frac{1}{xy}\cdot \frac{d}{dx}\big[xy\big]=1-\frac{dy}{dx}[/tex]
Differentiate:
[tex]\displaystyle \frac{1}{xy}\cdot \big( y+x \frac{dy}{dx} \big) =1-\frac{dy}{dx}[/tex]
Distribute:
[tex]\displaystyle \frac{1}{x}+\frac{1}{y}\frac{dy}{dx}=1-\frac{dy}{dx}[/tex]
Isolate the derivative term:
[tex]\displaystyle \frac{dy}{dx}\big(\frac{1}{y}+1\big)=1-\frac{1}{x}[/tex]
Divide:
[tex]\displaystyle \frac{dy}{dx}=\frac{1-\frac{1}{x}}{\frac{1}{y}+1}}[/tex]
Simplify. We can multiply both layers by xy. Hence:
[tex]\displaystyle\begin{aligned} \frac{dy}{dx}&=\frac{1-\frac{1}{x}}{\frac{1}{y}+1}}\cdot\frac{xy}{xy} \\ &=\frac{xy-y}{x+xy} \end{aligned}[/tex]
We can factor. Hence, our derivative is:
[tex]\displaystyle \frac{dy}{dx}=\frac{y(x-1)}{x(y+1)}[/tex]
Differentiate once more to find the second derivative:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{d}{dx}\Big[\frac{y(x-1)}{x(y+1)}\Big][/tex]
Quotient rule:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{\frac{d}{dx}[y(x-1)](x(y+1))-y(x-1)\frac{d}{dx}[x(y+1)]}{(x(y+1))^2}[/tex]
Differentiate using the product rule:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{ \big[\frac{dy}{dx}(x-1)+y\big](x(y+1))-y(x-1)\big[(y+1)+x\frac{dy}{dx}\big] }{(x(y+1))^2 }[/tex]
You may choose to simplify, but this is not necessary, as we are only interested in the second derivative at (1, 1).
First, since first derivatives exist in our second derivative, we will find them first. Recall that the first derivative is given by:
[tex]\displaystyle \frac{dy}{dx}=\frac{y(x-1)}{x(y+1)}[/tex]
Therefore, at (1, 1), the first derivative is:
[tex]\displaystyle \frac{dy}{dx}_{(1, 1)}=\frac{1(1-1)}{1(1+1)}=\frac{1(0)}{1(2)}=0[/tex]
So, we will substitute 0 for every dy/dx for our second derivative. Thus:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{ \big[(0)(x-1)+y\big](x(y+1))-y(x-1)\big[(y+1)+x(0)\big] }{(x(y+1))^2 }[/tex]
Simplify:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{ y(x(y+1))-y(x-1)\big[(y+1)\big] }{(x(y+1))^2 }[/tex]
So, at the point (1, 1), our second derivative is:
[tex]\displaystyle \frac{d^2y}{dx^2}_{(1, 1)}=\frac{1(1(1+1))-1(1-1)(1+1)}{(1(1+1))^2}=\frac{2-0}{4}=\frac{1}{2}[/tex]
Hence, our final answer is E.
The scatter plot shows a number of CD's (in millions) that were sold from 1999 to 2005. If the trend continued,about how many CDs were sold in 2006?
A. 900
B.850
C.750
D.650
There 650 million CDs were sold in 2006 if there were 800 million CDs sold in 2002, and there were 700 million CDs in 2005 option (D) is correct.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
From the graph:
(2002, 800) and (2005, 700)
We can draw a line for the best fit as follows:
[tex]\rm (y-800) = \frac{700-800}{2005-2002}(x-2002)[/tex]
[tex]\rm (y-800) = 33.33(x-2002)[/tex]
When x = 2006
[tex]\rm (y-800) = -33.33(2006-2002)\\[/tex]
y = 666.68
Which is near 650 million
Thus, there 650 million CDs were sold in 2006 if there were 800 million CDs sold in 2002, and there were 700 million CDs in 2005 option (D) is correct.
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I need help plz! ;((
Answer:
I think option B is correct
n is an integer.
Write the values of n such that -15 < 3 ≤ 6
Help please ❤️❤️
Answer:
-4,-3,-2,-1,0,1
Step-by-step explanation:
First, doublepound and simplify it.
-15<3n
3n<6
Solve:
-5<n
n<2
Compound:
-5<n<2.
So the values are -4,-3,-2,-1,0,1
Hope this helps plz hit the crown :D
Answer:
The values of 'n' such that -15 < 3n ≤ 6 will be:
[tex]-5<n\le \:2[/tex]
[tex]-5<n\le \:2[/tex] can also be represented as: -4, -3, -2, -1, 0, 1, 2
Hence, the values of integer n will be:
-4, -3, -2, -1, 0, 1, 2Thus,
[tex]-15<3n\le \:6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-5<n\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:(-5,\:2]\end{bmatrix}[/tex]
The line graph is also attached below.
Step-by-step explanation:
Given the expression
-15 < 3n ≤ 6
Lets us solve the inequality for n
[tex]-15<\:3n\le \:6[/tex]
Divide all parts by n
[tex]\:-\frac{15}{3}<\frac{3n}{3}\le \frac{6}{3}[/tex]
simplify
[tex]-5<n\le \:2[/tex]
Therefore, the values of 'n' such that -15 < 3n ≤ 6 will be:
[tex]-5<n\le \:2[/tex]
[tex]-5<n\le \:2[/tex] can also be represented as: -4, -3, -2, -1, 0, 1, 2
Hence, the values of integer n will be:
-4, -3, -2, -1, 0, 1, 2Thus,
[tex]-15<3n\le \:6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-5<n\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:(-5,\:2]\end{bmatrix}[/tex]
The line graph is also attached below.
lest common multiple of 60 and 90
Answer:
180
Step-by-step explanation:
Evaluate the expression for the given value of x.
6.5x - 3.5 for x = 9
The solution is...
Answer:
55
Step-by-step explanation:
6.5x - 3.5 [x = 9]
6.5(9) - 3.5
58.5 - 3.5 = 55
Allison sent and received 240 text messages last month. 20% of those messages were sent to her best friend. How many text messages did Allison send to her best friend last month?
Answer:
48
Step-by-step explanation:
because 20% of 240 is 48.
Please help, worth 20+ points! Please, help give answers!
Answer:
1. 0.34
2. 0.46
3. 0.75
4. 0.3 with a bar over 3
5. 0.63 with a bar over 63
6. 0.259 with a bar over 259
7. 0.1875
8. 0.35
Find the equation of the line that passes through(-2,-5) and (1,7).
Answer:
Where is the pic?
Step-by-step explanation:
please answer asap no trolls!
Answer:
pqe?
Step-by-step explanation:15446556
what unit would you use to measure the area of a checkerboard
Answer:
I'd assume inches, hope this helps!
A bag contains 28 counters all of different colours. Colin chooses one counter and gives it to
Obi, and another counter and gives it to Zeema. In how many ways can Colin do this?
Answer:
756 ways
Step-by-step explanation:
Given
[tex]Counters = 28[/tex]
[tex]Selection = 2[/tex]
Required
Determine the number of ways
The first counter can be selected in 28 ways
The second can be selected in (28 - 1) ways
The number of selection is:
[tex]Selection = 28 * (28 -1)[/tex]
[tex]Selection = 28 * 27[/tex]
[tex]Selection = 756[/tex]
Hence, number of possible selection is 756
if i bike travels 15m in 2 sec, what is its speen in km/h?
Answer:
x=27 km
Step-by-step explanation:
Make an equation 2/.015=3600/x
Multiply 3600 by .015 to get 54
Divide 54 by 2 to get 27.
9514 1404 393
Answer:
27 km/h
Step-by-step explanation:
(15 m)/(2 s) = (15 m)/(2 s)×(1 km)/(1000 m)×(3600 s)/(1 h)
= (15×1×3600)/(2×1000×1) km/h = 15×1.8 km/h = 27 km/h
Solve the following system of equations. 4y+3z=-7
12x-3y+z=-7
-6x+2y-2z=12
Step-by-step explanation:
12x-3y+z＝-7 ‖-12x+3y
z＝-7-12x+3y
so you can replace z with (-7-12x+3y)
4y+3*(-7-12x+3y)＝-7
4y+(-21-36x+9y)＝-7
13y-21-36x＝-7 ‖+21
13y-36x＝14 ‖-13y
-36x＝14-13y ‖*(-1)
36x＝-14+13y ‖/3
12x＝-14/3+13/3y
so-6x＝+14/6-13/6y
(+14/6-13/6y)+2y-2*(-7-(-14/3+13/3y)+3y)＝12
(+14/6-13/6y)+2y+14-28/3+26/3y-6y＝12
(+14/6-13/6y)+2y+14-56/6+52/6y-6y＝12
7+2.5y＝12 ‖-7
2.5y＝5 ‖/2.5
y＝2
so
4y+3z＝-7
4*2+3z＝-7
8+3z＝-7 ‖-8
3z＝-15 ‖/3
z＝-5
12x-3*2+(-5)＝-7
12x-6-5＝-7
12x-11＝-7 ‖+11
12x＝4 ‖/12
x＝1/3