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Work Shown:
sin(2x) = sin(x)
sin(2x) - sin(x) = 0
2*sin(x)*cos(x) - sin(x) = 0
sin(x)*(2cos(x) - 1) = 0
sin(x) = 0 or 2cos(x)-1 = 0
sin(x) = 0 or cos(x) = 1/2
Using the unit circle, the solutions to sin(x) = 0 are x = 0, x = pi, x = 2pi
Also, the solutions to cos(x) = 1/2 are x = pi/3, x = 5pi/3
So the entire solution set on the interval [0,2pi] is {0, pi/3, pi, 5pi/3, 2pi} when written in increasing order.
All solutions to the equation in the interval [0, 2[tex]\pi[/tex]] is {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}.
What is solution to an equation?A solution is an assignment of values to the unknown variables that makes the equality in the equation true.
As sin2x = 2 sinx cosx,
sin2x = sinx is equivalent to
2 sinx cosx = sinx or 2 sinx cosx − sinx = 0 or
sinx (2cosx − 1) = 0 i.e.
either sinx = 0 and x = 0, π, 2π
or 2cosx − 1 = 0 i.e. cosx = [tex]\frac{1}{2}[/tex] i.e. x = [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]
Hence, solution to an equation is x = {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}
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PLZZZ HELPP.
Given the following matrices, what is the correct product matrix CD?
А. [21 10]
B. The matrix is undefined.
C. [29 53]
D. [53 29]
Answer:
D
Step-by-step explanation:
you will be multiplying Matrix C with Matrix D so, after using the rule for multiplication of matrices
[ 5x2 +9x4 + 7x1 5x(-4) + 9x0 + 7x7]
[ 10 + 36 + 7 -20 + 0 + 49 ]
[ 53 29]
hope this helps.
Brainly is an awesome app, but there is an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from tutors.
The product of matrices C and D is [53 29]. Therefore, option D is the correct answer.
What is the product of two matrix?The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined. If AB and BA are both defined, it is not necessary that AB = BA.
Given that, C=[5 9 7] and D= [tex]\left[\begin{array}{ccc}2&-4\\4&0\\1&7\end{array}\right][/tex]
Here, CD = [5×2+9×4+7×1 5×(-4)+9×0+7×7]
= [10+36+7 -20+49]
= [53 29]
Therefore, option D is the correct answer.
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A total of 937 people attend the play. Admission was $2.00 for adults and $0.75 for students. The totral ticket sales amounted to $1,109. How many students and adults attended the school play? - Applying Linear Systems in the Real World
Answer:
x = students
y = adults
Linear Systems of Equations :
x + y = 937
0.75x + 2y = 1,109
Step-by-step explanation:
Step 1 : eliminate one of the variables
x + y = 937
0.75x + 2y = 1,109
-2(x + y = 937) = -2x - 2y = -1874
-2x - 2y = -1874
0.75x + 2y = 1109
We can eliminate y since -2y + 2y = 0
Step 2: Find x number of students.
-2x = -1874
+0.75x = 1109
____________
-1.25x = -765
____________ = 612 students attended
-1.25
937 - 612 = 325 adults
Check Answer :
612 x 0.75 = $459
325 x 2 = $650
$650 + $459 = $1,109
Therefore, there will be 612 students attending and 325 adults.
A rhombus is cut along the diagonals to make four triangles.
Which three statements are correct for any rhombus.
A: All four triangles are isosceles.
B: All four triangles are congruent.
C: All four triangles are right-angled.
D: Perimeter of rhombus = 4 times the perimeter of one triangle.
E; Area of rhombus = 4 times the area of one triangle.
Answer:
B: All four triangles are congruent.
C: All four triangles are right-angled.
E; Area of rhombus = 4 times the area of one triangle.
Step-by-step explanation:
A rhombus is a quadrilateral with equal length of sides. It stands on one of its edges, and a simple example is the shape of a diamond. It has two diagonals which bisect the angles of the rhombus.
When a rhombus is cut along its diagonals, the following properties of the shape formed can be observed:
B: All four triangles are congruent.
C: All four triangles are right-angled.
E; Area of rhombus = 4 times the area of one triangle.
What is the constant variation, k, of the direct variation, y= kx, through (-3,2)
Answer:
k = -2/3
Step-by-step explanation:
y = kx
plug in the x,y values
2 = k(-3)
divude both sides by-3
-2/3 = k
k = -2/3
ILL MARK BRAINLIEST !!!
29.
Select the three statements that are true.
a. -11 > -6
b. -5 > -7
c. -4 > -6
d. -9 > 7
e. 8 < -1
f. -5 < -4
Answer:
BCF is the correct answer
Answer:
b, c, and f
Step-by-step explanation:
because on the negative scale -5 is closer to 0 than -7, -4 is closer to 0 than -6, and -4 is closer to 0 than -5. So in this case b, c, and f are true because it is greater than. Sorry if I explained it badly, but im pretty sure its b, c, and f.
I need help with number 35 please help
Answer:
B. shelves × 51
Reason:
sum of all books= 357
sum of shelves= 17
no of shelves × 21
or, 17 × 21= 357
which is the number of books.
What is the following sum?
[/xy)+ s(t/x+y)
o 7(1984
o 7(1024x2)
(8/643)
Answer:
Option C
Step-by-step explanation:
[tex] \sqrt[5]{x {}^{2} y} (4 + 3) \\ 7 \sqrt[5]{x {}^{2} y} [/tex]
Hurry hurry hurry please help in 5 mins
Answer:
nkknknknjobbjojobihgghighigugyghugughuugbhibhi
Step-by-step explanation:
hibbihib
gbuhbuhb
buying hi
hnununnhon
jinonoonno
Find any domain restrictions on the given rational equation:
X/2x+14 + x-4/6 = 3/x^2 + 2x -35. Someone please answer I’m doing summer school not tryna redo math AGAIN
Answer:
[tex]\dfrac{x}{2 \cdot x + 14} + \dfrac{x - 4}{6} = \dfrac{3}{x^2} + 2\cdot x - 35; Domain \ restriction \ x \neq 0 \ or \ -7[/tex]
Step-by-step explanation:
The given rational equation is presented here as follows;
[tex]\dfrac{x}{2 \cdot x + 14} + \dfrac{x - 4}{6} = \dfrac{3}{x^2} + 2\cdot x - 35[/tex]
A domain restriction are the limits to the ranges of input values (x-values) of a function
The three main types of domain restrictions are the reciprocal function, the log function, and the root function
The form of restriction in the given rational are reciprocal form, which are;
[tex]\dfrac{x}{2 \cdot x + 14}[/tex], and [tex]\dfrac{3}{x^2}[/tex], from which the function is undefined when;
2·x + 14 = 0, therefore when x = -7, or x² = 0, when x = 0
Therefore, the domain restrictions are that the function is defines for all x, except x = -7 and x = 0
The domain restrictions are x ≠ -7 and x ≠ 0.
Answer:
it's -7 and 5
Step-by-step explanation:
used his and got it wrong
Express each ratio as a fraction in simplest form.
5 miles to 35 miles
Answer:
1 : 7
Step-by-step explanation:
Given
5 miles : 35 miles ( divide both parts by 5 )
= 1 : 7 ← in simplest form
Which terms could have a greatest common factor of 5m2n2? (Two options need to be selected)
m5n5
5m4n3
10m4n
15m2n2
24m3n4
Answer:
There are two terms that could have a greatest common factor of 5m2n2, and those are 5m4n3 and 15m2n2.
The only correct option will be 5m^4n^3 since 5m²n² can go in the expression,
What is the greatest common factor?The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers
From the question, we are to find the equivalent expression that has 5m²n² as a factor
The only correct option will be 5m^4n^3 since 5m²n² can go in the expression,
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whats the factor:81x3-3000
aikskdjjsiwwjjjwjwkkwkwkwkwkwkwkwkwkw
Answer:
3(3x - 10)(9x² + 30x + 100)
Step-by-step explanation:
Given
81x³ - 3000 ← factor out 3 from each term
= 3(27x³ - 1000 )← a difference of cubes which factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
27x³ - 1000
= (3x)³ - 10³
= (3x - 10)((3x)² + (3x)(10) + 10²)
= (3x - 10)(9x² + 30x + 100)
Then
81x³ - 3000 = 3(3x - 10)(9x² + 30x + 100) ← in factored form
1. In a class of students the ratio of the number of students who like to play football and the number of students who like to play volleyball is 5:3. If the number of students who like volleyball only is 15 and the number of students who like football only is 35, then a. Find the number of students who like both games.
Answer:
Both sports = 15
Step-by-step explanation:
Remark
What an interesting question. At first I didn't think it was possible. Then I saw the word only. That made all the difference in the world.
Givens
Football only = 35
Volleyball only = 15
Ratio = 5/3
Equation
Let the number of students who play both = x
Volleyball / Football = (x + 15) /(x + 35) = 3/5
Solution
(x + 15) / (x + 35) = 3/5 Cross multiply
5*(x + 15) = 3(x + 35) Remove the brackets
5x + 75 = 3x + 105 Subtract 3x from both sides
3x 3x
2x + 75 = 105 Subtract 75 from both sides
- 75 -75
2x = 30 Divide by 2
2x/2 = 30/2
x = 15
15 people play both sports.
The graphs below have the same shape. What is the equation of the blue graph ?
Answer:
A G(x) = (x - 5)²
Step-by-step explanation:
Plug in x = 5 into the given choices
only G(x) = (x - 5)² correctly returns G(5) = 0
This afternoon Greta left school, rode the bus 7/12 of a mile, and then walked 1/3 of a mile to get home. How much farther did Greta ride than walk?
A candy store held a contest to guess the total number of jelly beans in a jar. All of the jelly beans in the jar were either green or orange. There were 1,872 jelly beans in the jar in total. There were 12 times as many green jelly beans as orange jelly beans. How many green jelly beans were in the jar?
Answer:
Step-by-step explanation:
Let the number of orange jelly beans be x , as we do not know the exact value of it yet. There are 12 times as many green jelly beans than the orange ones. So , if the number of orange jelly beans is x , the number of green jelly beans will be = 12 times x , which can be written as 12x. Now there are a total of 1872 jelly beans , but they are either orange or green , so we already know that the number of orange jbs is x , and the number of green jelly beans is 12x. So if we the green jelly beans and orange jelly beans , it should be 1872.
Now all we need to do is to find x.
We know that ,
x + 12x = 1872
Now we add x and 12x on the left hand side
13x = 1872
Now we divide both sides by 13 to get x. (That includes 1872 as well)
x = 144
Now we have the value of x which is 144
We know that the number of green jelly beans was 12 times x
So the number of green jelly beans in numeric value is : 12 * 144
As x is equal to 144
Ans . : The number of green jelly beans is 1728.
The number of green jelly beans is 1728.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Let the number of orange jelly beans = x ,
So, the number of green jelly beans will be = 12 times x ,
which can be written as, 12x.
Now, there are a total of 1872 jelly beans , but they are either orange or green , so we already know that the number of orange is x , and the number of green jelly beans is 12x.
So if we the green jelly beans and orange jelly beans , it should be 1872.
Now, We get;
x + 12x = 1872
13x = 1872
Divide both sides by 13,
x = 144
So, the number of green jelly beans in numeric value is :
⇒ 12 × 144
⇒ 1728
Thus, The number of green jelly beans is 1728.
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i need help fast in these questions.
What is the coefficient in the expression 5x2 +3 ?
O
A. 2
O
B. 3
O
C. 5
O
D. x
Answer:
C: 5
Step-by-step explanation:
Here the variable x shows up specifically only once, with coefficient 5:
5x^2 + 3
This actually represents 5x^2 + 0x + 3.
The coefficient of the explicily-given x-term is 5. The other coefficients are 0 and 3.
Which graph shows the solution to the system of linear inequalities below?
y2 2x+1
y<-2x-3
Since there isn't a picture of the graphs, I attached one, of my graph, to this answer.
I'm also assuming (y2 2x+1) is actually (y< 2x+1).
Possible solutions are within the purple section of the attached image.
I hope this is helpful to you.
Graph that represents both the inequality is attached below.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
First, we make the graph,
The border of the inequality y = 2x + 1 has a slope of 2 and a y-intercept of 1. Plotting the y-intercept at (0, 1) and using the slope to determine further points will allow us to draw this line.
For instance, if we move two units up (in the positive y-direction) and one unit to the right (in the positive x-direction), we get the point (1, 3).
The answer to y < 2x + 1 may be represented by connecting these points with a dashed line and darkening the area below the line.
A boundary line for the inequality y -2x - 3 has a slope of -2 and a y-intercept of -3. Plotting the y-intercept at (0, -3) and using the slope to determine further points will allow us to draw this line.
For instance, if we move two units down (in the negative y-direction) and one unit to the right (in the positive x-direction), we get the point (1, -5).
The answer to y < -2x - 3 may be represented by connecting these points with a dashed line and coloring the area below the line.
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11. Kurtis is a video salesman. On each sale he earns a commission of 12%. One of
his customers bought a TV for $550 and a VCR for $400. How much did he
earn in commission?
Answer:
114
Step-by-step explanation:
550*12%=66
400*12%=48
48+66=114
use the function below to find f(3)
[tex]f(x) = \frac{1}{3} \times {4}^{x} [/tex]
Answer:
f(3) = [tex]\frac{64}{3}[/tex]
Step-by-step explanation
f(3) = [tex]\frac{1}{3}[/tex] x [tex]4^{3}[/tex]
f(3) = [tex]\frac{1}{3}[/tex] x 64
f(3) = [tex]\frac{64}{3}[/tex]
anyone know how to do this??
Answer:
csc²(x)
Step-by-step explanation:
csc(x) = 1/sin(x)
sin²(x) + cos²(x) = 1
=> cos²(x) = 1 - sin²(x)
cos(2x) = cos²(x) - sin²(x) = (1 - sin²(x)) - sin²(x) =
= 1 - 2×sin²(x)
=> 2×sin²(x) = 1 - cos(2x)
sin²(x) = 1/2×(1-cos(2x))
=> 1 - cos(2x) = 2×(1/2×(1-cos(2x)) = 2×sin²(x)
=> 2 / (1-cos(2x)) = 2 / (2×sin²(x)) = 1/sin²(x) =
= 1/sin(x) × 1/sin(x) = csc(x)×csc(x) = csc²(x)
find the value of 525²-475² using suitable identity
Answer to this question:
I think the answer is 3
OPQR is a tetrahedron. Given that the area of its base is 12 m and its height is 4 m, find the , volume of the tetrahedron.
Answer:
[tex]16m^{3}[/tex]
Step-by-step explanation:
The volume of a tetrahedron shape is calculated by first multiplying the base area by 1/3. Then you multiply the product obtained by the height of the tetrahedron. This will give you the volume of the tetrahedron. For example, using the values provided, the volume would be the following...
(12 * 1/3) * 4 = x
4 * 4 = x
16 = x
Finally, we can see that the volume of the tetrahedron is [tex]16m^{3}[/tex]
Find m
Please and thank you.
Answer:
43
Step-by-step explanation:
We have to find angle CXY
So,
YE/EX=DY/CX
Therefore XY//CD [Theorem]
Angle D =Angle Y [Corresponding Angles]
Angle E + Angle Y +Angle X=180
Angle X=180-(Angle E + Angle Y)
Angle X=180-(89+48)
Angle X=180-137
Angle X=43
Angle CXY=43 Degree
answer the question below please
Answer:
A
Step-by-step explanation:
because linear modelling can include population change
help y’all
What are the diferences between volume & area?
The table shows marks for 40 students obtained in the test. Use the given information to determine the mode,median and mean of the data probability that a student selected at random will would have obtain a mark greater than 5
Marks. Frequency
1. 3
2. 5
3. 6
4. 9
5. 5
6. 2
7. 6
8. 4
Answer:
mode=4 cos it occurred 9times
median=11122222333333444444444455555667777778888
=4 and 4= 4
mean= sum fx/sum f
The tables represent the functions f(x) and g(x).
A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, f(x), has the entries, negative 5, negative 3, negative 1, 1, 3, 5. A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, g(x), has the entries, negative 13, negative 9, negative 5, negative 1, 3, 7.
Which input value produces the same output value for the two functions?
Answer:
rtyujn
Step-by-step explanation:
er456y7ujm
What is the volume of a rectangle prism with a height of 6 and base dimensions 5 in and 7 in
Answer:
210
Step-by-step explanation:
5x7x6