The solution of the trigonometric equation is x = 26.57° or 153.43°
What is a trigonometric equation?A trigonometric equation is an equation that contains the trigonometric ratios.
How to solve for x in the trigonometric equation?Given the trigonometric equation 2cos x - sin x = 3/(2cos x + sin x)
We solve for x in the equation. We proceed as follows.
Since 2cos x - sin x = 3/(2cos x + sin x)
Multiplying both sides by (2cos x + sin x), we have that
(2cos x - sin x)(2cos x + sin x) = 3
Now, we know that (a² - b² = (a + b)(a - b)
Applying this where a = 2cosx and b = sinx, we have that
(2cos x - sin x)(2cos x + sin x) = 3
(2cos x)² - (sin x)² = 3
4cos² x - sin² x = 3
Since sin²x = 1 - cos²x, substituting this into the equation, we have that
4cos² x - sin² x = 3
4cos² x - (1 - cos²x) = 3
4cos² x - 1 + cos²x = 3
4cos² x + cos²x = 3 + 1
5cos²x = 4
cos²x = 4/5
Taking square root of both sides, we have that
cosx = ±√(4/5)
cosx = ±2/√5)
cosx = ±2/√5 × √5/√5
cosx = ±2√5/5
Taking inverse cosine of both sides, we have
x = cos⁻¹(±2√5/5)
x = cos⁻¹(±0.8944)
x = cos⁻¹(0.8944) or x = cos⁻¹(-0.8944)
x = 26.57° or (180 - 26.57)°
x = 26.57° or 153.43°
So, the solution is x = 26.57° or 153.43°
Learn more about trigonometric equation here:
https://brainly.com/question/28025415
#SPJ1
2x + 2 = 5y
This is needed now!!!
Answer:
x = 2.5y - 1
Step-by-step explanation:
Subtract 2 from both sides
then you get 2x = 5y - 2
then divide everything by 2 for the answer
x = 2.5y -1
The enrollment for a school in 2010 was 1510 students. In 2020, the enrollment was 860 students. Find and interpret the rate of change in enrollment from 2010 to 2020.
Answer:
Step-by-step explanation:
The rate of change is the slope of the line formed by connecting the two data points:
1. (2010,1510). and [enrollment for a school in 2010 was 1510 students]
2. (2020, 860) [In 2020, the enrollment was 860 students]
Slope is the Rise/Run of the line. Lets go from the first point to the second.
The Rise: (1510 - 860) = 650
The Run: (2020-2010) = 10
The slope, or rate of change, is = 65
The interpretation is that "The enrollment at the school increase by an average of 65 students every year since 2010 until 2020."
thirteen black and six white hexagonal tiles were used to create the figure below. if a new figure is created by attaching a border of white tiles with the same size and shape as the others, what will be the difference between the total number of white tiles and the total number of black tiles in the new figure?
The difference between the total number of white tiles and the total number of black tiles in the new figure is 11.
Thirteen black and six white hexagonal tiles. If a new figure is created by attaching a border of white tiles with the same size and shape as the others
To find the difference between the total number of white tiles and the total number of black tiles in the new figure.
Now, According to the question:
The solution will be:
The first ring around the middle tile has 6 tiles, and the second has 12. From this pattern, the third ring has 18 tiles. Of these, 6+18=24 are white and 1+12=13 are black, with a difference of 24-13 = 11.
Hence, the difference between the total number of white tiles and the total number of black tiles in the new figure is 11.
Learn more about Hexagonal at:
https://brainly.com/question/29762907
#SPJ4
Is this proportional or not proportional?
HELP ASAP!!!! 20 PTS
What is the solution to this system of equations? 2x+y=40 x-2y=-20
Answer: the solution to the system of equations is x = 12 and y = 16.
Step-by-step explanation: To solve this system of equations, you can use the method of substitution.
First, solve one of the equations for one of the variables. For example, you can solve the first equation for x:
2x + y = 40
2x = 40 - y
x = (40 - y)/2
Then, substitute this expression for x in the second equation:
x - 2y = -20
(40 - y)/2 - 2y = -20
Multiplying both sides by 2, we get:
40 - y - 4y = -40
-5y = -80
y = 16
Substituting this value for y in the first equation, we can solve for x:
2x + 16 = 40
2x = 24
x = 12
Therefore, the solution to the system of equations is x = 12 and y = 16.
Follow the steps to solve this equation. 3(2x 6) â€"" 4x = 2(5x â€"" 2) 6 1. use the distributive property: 6x 18 â€"" 4x = 10x â€"" 4 6 2. combine like terms: 2x 18 = 10x 2 3. use the subtraction property of equality: 18 = 8x 2 4. use the subtraction property of equality: 16 = 8x 5. use the division property of equality: = x
The solution of given equation by using the property of equality is x = 2.
Explain the distributive property?The distributive property states that multiplying the total of two or even more operand by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.An equation has been presented to us.
3(2x + 6) -4x = 2(5x -2) + 6
Our given equation has to be solved step-by-step.
Step 1: Utilize the distributive property;
3×2x + 3×6 - 4x = 2×5x -2×2 + 6
6x + 18 -4x = 10x - 4 + 6
Step 2: combine similar phrases.
6x + 18 -4x = 10x - 4 + 6
2x + 18 = 10x + 2
Step 3: Apply the equality's subtraction property
2x - 2x + 18 - 2 = 10x + 2 - 2x - 2
16 = 8x
Step 4: Apply the equality's divisional property:
16/8 = 8x/8
x = 2
As a result, is our given equation's answer is x = 2.
To know more about the distributive property, here
https://brainly.com/question/2807928
#SPJ4
The correct question is-
Follow the steps to solve this equation. 3(2x + 6) – 4x = 2(5x – 2) + 6 1. Use the distributive property: 6x + 18 – 4x = 10x – 4 + 6 2. Combine like terms: 2x + 18 = 10x + 2 3. Use the subtraction property of equality: 18 = 8x + 2 4. Use the subtraction property of equality: 16 = 8x 5. Use the division property of equality:
f’’(x)=cos(x), f’(pi)=2, f(pi)=-1
f(x)=?
PLS URGENT
The required function f(x) is represented by -1 + F(x + sin(x)).
To find the function f(x), you can use the formula for integration by substitution:
f(x) = F(g(x)) + C
where F is an antiderivative of f, g is a function such that g'(x) = f(x), and C is a constant.
In this case, we can take g(x) = x + sin(x). Then g'(x) = cos(x), so f(x) = F(g(x)) + C = F(x + sin(x)) + C.
We are given that f'(π) = 2 and f(π) = -1, so we can use these values to find the constants C and F.
First, we can find F by taking the derivative of F(x + sin(x)). This gives us:
F'(x + sin(x)) = f(x) = cos(x)
Substituting x = π and using the fact that F'(x + sin(x)) = f'(π) = 2, we get:
F'(π + sin(π)) = 2
Since sin(π) = 0, this simplifies to:
F'(π) = 2
Then, using the fact that F(x + sin(x)) = f(π) = -1 when x = π, we can find the value of F(π):
F(π) = -1
Now that we have found the values of F and F', we can use these to find the value of C.
Since F(x + sin(x)) = F(x) + F'(x) sin(x), we can substitute x = π to get:
F(π + sin(π)) = F(π) + F'(π) * sin(π)
Substituting the values we found above, this becomes:
F(π + 0) = -1 + 2 x 0
Which simplifies to:
F(π) = -1
Since F(π) = -1, we can conclude that C = -1.
Therefore, the function f(x) is given by:
f(x) = F(x + sin(x)) + C = F(x + sin(x)) - 1
= -1 + F(x + sin(x))
Learn more about the function here:
brainly.com/question/12431044
#SPJ1
Plant A i 5 centimeter tall and growing at a rate of 2. 5 centimeter per month. Plant B i 4 centimeter and growing at a rate of 4. 5 centimeter per month. When will Plant B exceed the height of Plant A. Write an inequality that repreent the ituation
In linear equation, plant b height will exceed the height of plant a after 16 days.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Plant a: 5 cm tall and rate of change = 2.5 cm per month
Plant b: 4 cm tall and rate of change = 4.5 cm per month.
Now we have to form the linear equations.
Plant a:
y = 2.5x + 5, where y is the total height and "x" be the number of months.
Plant b:
y = 4.5x + 4 , where y is the total height and "x" be the number of months.
Now we have to when the height of the plant a and plant b are the same.
To do that, we have to equivate both the equations and find x.
2.5x + 5 =4. 5x + 4
Isolate the variables terms and constants.
4.5x - 2.5x = 5 - 4
2x = 1
Dividing both sides by 2, we get
x = 1 ÷ 2
x = 0.5 months.
So after 15 days, the height of the plant a and plant b are the same.
Therefore, plant b height will exceed the height of plant a after 16 days.
Learn more about linear equation
brainly.com/question/11897796
#SPJ4
someone help me pls i would appreciate
Answer:
Addition, Distributive, Addition, Multiplication, Division
Step-by-step explanation:
x intercept of y = x-7
The x-intercept of the linear equation is (7, 0).
How to find the x-intercept of the linear function?Here we have the following linear equation:
y = x - 7
We want to find the x-intercept, this is the point where the line intercepts the x-axis, it will happen when we take the value of y = 0, then we need to solve.
0 = x - 7
Solving that, we get:
7 = x
Then we conclude that the x-intercept of the linear equation is (7, 0).
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Cara wants to build an 80 foot long rectangular sheep pen in back of her barn. If she bought 180 feet of fencing and used her barn wall as one side of the pen equaling the width, what would be the area of the sheep pen?.
Area of the sheep pen = 1600feet square
What is area?The amount of space occupied by a flat (2-D) surface or form of an object is known as its area.
180 feet of fence were purchased.
The perimeter of a rectangular sheep pen is equal to two times the length plus the width, or two times the length plus 180. One side of the rectangular sheep pen is covered with a barn, which equals the width.
The rectangular sheep pen's covered side:
180 =2 length + width
180 = 2 x80 +width
180 - 160 = width
20= width
Area = l*b = 80*20
Area of sheep pen = 1600 feet square
To know more about area click the link:
brainly.com/question/28820377
#SPJ4
Despite what he may have told you, Mr. Robeson is actually quite bad at
making free throws in basketball. On average he makes 35% of the free
throws he takes and he doesn't learn from previous shots. What is the
probability that the first time he makes a free throw is on the 5th shot he
attempts?
Answer:
0.009754
Step-by-step explanation:
(.65)^4 x (0.35)
By saying that he makes a free throw on the fifth show, he did not make the first four, therefore 4 of the times he shot, he did not get it in.
If he makes the shot 35% of the time, he doesn't make it 65% of the time: (1-0.35=.65)
On the last shot he made it, which he makes 35% of the time therefore:
You want to multiply : 0.35 (which is = 35%) by itself four times and then multiply that by 0.65 (since the last shot was made)
0.35 x 0.35 x 0.35 x 0.35 x 0.65 = 0.009754 or 0.9754%
There is a 0.9754% chance he makes it BUT a 0.009754 probability
Use the equation y=x2−3x+2 to answer the following questions. Part A: What numeric expression should be added in order to complete the square for the given equation? Part B: What equation is equivalent to the given equation after completing the square? Select two answers: one for Part A and one for Part B.
Part A
[tex](b/2)^2 =(-3/2)^2 =\boxed{9/4}[/tex]
Part B
[tex]-x^2 -3x+2\\\\=-(x^2 +3x)+2\\\\=-(x^2 +3x+2.25-2.25)+2\\ \\=-((x+1.5)^2 -2.25)+2\\\\=-(x+1.5)^2 +2.25+2\\\\\boxed{y=-(x+1.5)^2 +4.25}[/tex]
I NEED ANSWERS QUICK
Equivalent expressions are expressions that have the same result.
The expression in this problem is defined as follows:
13 + 4g.
The commutative property is applied in this problem, meaning that the order of the terms is exchanged, hence the equivalent expression is given as follows:
4g + 13.
The numeric values of the expression are given as follows:
g = 2: 13 + 4(2) = 21, 4(2) + 13 = 21.g = 10: 13 + 4(10) = 53, 4(10) + 13 = 53.More can be learned about equivalent expressions at https://brainly.com/question/15775046
#SPJ1
Please help
Evaluate numerical expression !
After evaluation of the given expression, the value obtained in mixed fraction form is equal to -4 3/10.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the given expression in the question,
(-5 - (-4 1/2)) × 3 + (-2 4/5)
The expression in simplified form will be,
(-5 + 9/2) × 3 - 14/5
(-10 + 9) × 3 -14/5
-3/2 - 14/5
= (-15 - 28)/10
= -43/10
It can also be written in mixed fraction form,
= -4 3/10
To know more about Expression:
https://brainly.com/question/14083225
#SPJ1
The midpoint of \overline{\text{AB}} AB is M(4, 0)M(4,0). If the coordinates of AA are (3, -1)(3,−1), what are the coordinates of BB?
Answer:
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. If the coordinates of one endpoint are (x1, y1) and the coordinates of the other endpoint are (x2, y2), then the coordinates of the midpoint are given by:
M = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the coordinates of the midpoint are (4, 0), and the coordinates of AA are (3, -1). Therefore, the coordinates of BB must be (5, 1).
You can confirm this by calculating the midpoint using the coordinates of AA and BB:
M = ((3 + 5)/2, (-1 + 1)/2)
= (4, 0)
This shows that the point (5, 1) is indeed the other endpoint of the line segment, and the coordinates of BB are (5, 1).
Step-by-step explanation:
2 1/2 divided by 4 Anwser quick please
Answer:
5/8
Step-by-step explanation:
We can solve this by turning 2 1/2 into a decimal.
2 1/2 = 2.5
2.5 ÷ 4 = 0.625
0.625 = 5/8
2 1/2 divided by 4 is 5/8
In problems 7-11, use the diagram to find the measure of each angle.
From the given triangle diagram figure, angles are -
m∠1 = 72°
m∠2 = 114°
m∠3 = 66°
m∠4 = 66°
m∠5 = 56°
m∠6 = 32°
What is triangle?Depending on how many sides a polygon has, it is given a unique name. Because "tri" is a word that indicates "three," the polygon with three sides is known as a triangle. This polygon has three angles, as indicated by its name. Poly means numerous in the prefix.
Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed at a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.
In the given problem,
m∠6 = 180° - (90° + 58°)
so, m∠6 = 32°
Next, m∠1 +m∠6 = 180° - (42° +34°)
= 104°
so, m∠1 = 104° - 32°
= 72°
Next, m∠5 = 90° - 34°
m∠5 = 56°
Again, m∠4 = 180° - (56° + 58°)
m∠4 = 66°
Now from the figure, m∠3 and m∠4 are vertically opposite angle.
So, m∠3 = 66°
Again, m∠2 = 180° - 66° = 114°
To know more about triangle refer to:
https://brainly.com/question/1058720
#SPJ1
If y varies directly as x and y = 15 when
x = -3. What is y when x = 6?
The value of y is -30.
Direct variation is y = kx
15 = k(-3)
Divide by -3 on both sides
-15/3 = k
-5 = k -------> 1
Substituting 1 and x = 6, in Direct Variation
y = -5*6
y = -30
Therefore, the value of y is -30.
To know more about Direct Variation, please refer to the link below:
brainly.com/question/17430281
If you want to increase an amount by 15%, what is the multiplying factor?
with a clear explanation
Answer:
multiplying factor = 1.15
Step-by-step explanation:
the original amount is 100%
the increase is 15%
then increasing the original amount by 15% is
100% + 15% = 115% = [tex]\frac{115}{100}[/tex] = 1.15
multiplying factor is 1.15
PLEASE HURRY
What is the product of x=8 and 2x^2-5x-3
a 2x^3+16x^2-4x+5
b 2x^3-11x2+43x+24
c 3x^3 2x^2-5x+8
d 2x^3+11x^2-43x-24
Quadratic equation is a type of equation which has the highest power of 2. The product of the given terms is option B. [tex]2x^{3}[/tex] - [tex]11x^{2}[/tex] + 43x + 24
An equation is said to be quadratic if and only if the highest power of the variable in its terms is 2. Thus they can be solved either by completing the square method, graphical method, the use of the quadratic formula etc.
The product of an algebraic term and a quadratic equation involves a stepwise procedure, such that all terms and exponential are considered.
The given question state thus:
what is the product of x - 8 and [tex]2x^{2} -5x-3[/tex]?
Thus using the expansion method, we have:
(x + 8)( [tex]2x^{2} -5x-3[/tex]) = [tex]2x^{3}[/tex] - [tex]5x^{2}[/tex] - 3x + [tex]16x^{2}[/tex] - 40x - 24
= [tex]2x^{3}[/tex] - [tex]11x^{2}[/tex] + 43x + 24
Thus the product of the given question is option B. [tex]2x^{3}[/tex] - [tex]11x^{2}[/tex] + 43x + 24
Learn more about expansion of quadratic equations at https://brainly.com/question/24334139
#SPJ1
Help with this ixl please
Answer:
25°
Step-by-step explanation:
We know the opposite angles must be equal when two lines intersect, so 67 = 42+t. Subtracting 42 from both sides gives t=25, which is our answer
answer:
25 degrees
step-by-step explanation:
67=42+t so using that equation the answer can be determined. hope that helps!
function rule to find f(9).
Answer: 12
Step-by-step explanation:
[tex]f(9)=3+9=12[/tex]
Slope Item 21025
slope =-
slope=
517
Which is the slope of the line that passes through the points (3, 5) and (8, 7)?
slope =
slope =
vijes
37
CLEAR
C
Answer:
Step-by-step explanation:
Well, the x increases by 5
And the Y increases by 2
So the slope is 5/2
And the equation would be 5/2x + b
Which of the following statements is INCORRECT?
A. A triangle with three congruent sides is equiangular.
B. The Isosceles Triangle Theorem can be applied to equilateral triangles.
C. The measure of each angle of an equilateral triangle is 120°.
D. A triangle with three congruent angles is equilateral.
Answer:
C
Step-by-step explanation:
The measure of each angle in an equilateral triangle is [tex]60^{\circ}[/tex], not [tex]120^{\circ}[/tex].
please help: in the figure, ∆LMN ≅ ∆RST. find the values of x and y
Answer:
X=8, y=19
Step-by-step explanation:
These two triangles are congruent. This means that angle STR = angle MNL, so angle STR = 63°. We know the angles in a triangle must sum to 180°, so we can figure out 3x from this, given that we know the other two angles. 63 + 93 = 156, so 3x = 180-156=24. This gives us that x = 8. Now we can solve for x, because we know that SR = ML, so 3x + y = 43. We know x = 8, so we get that 24 + y = 43, or y = 19.
I hope this helps!
simultaneous equations x+5y=6
x+3y=2
Answer:
(- 4, 2 )
Step-by-step explanation:
x + 5y = 6 → (1)
x + 3y = 2 → (2)
subtract (2) from (1) term by term to eliminate x
(x - x) + (5y - 3y) = 6 - 2
0 + 2y = 4
2y = 4 ( divide both sides by 2 )
y = 2
substitute y = 2 into either of the 2 equations and solve for x
substituting into (1)
x + 5(2) = 6
x + 10 = 6 ( subtract 10 from both sides )
x = - 4
solution is (- 4, 2 )
Angel corre en un maratón de 500m y lo hizo en 1,5 horas. ¿Cuál fue la velocidad de
Angel?
In which way should the graph of f(x) = x2 be shifted to produce the graph of g(x) = (x - 3)2?
A.
3 units to the left
B.
3 units to the right
C.
3 units down
D.
3 units up
Answer:
g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x)
Step-by-step explanation:
Answer:
uh nose
Step-by-step explanation: