The value of x = 4.71, 0.41, or 5.89 radian value
Specification:
sinxtanx + tanx -2sinx + cosx = 0
tanx = sinx / cosx
sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0
cosx to remove the fraction
sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0
sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1
sinx -2sinxcosx + 1 = 0
sinx (1-2cosx) = -1
1-2cosx = -1 / sinx
-2cosx = -1 / sinx -1
2cosx = 1 / sinx + 1
cosx = 1 / 2sinx + 1/2
sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2
Squared on both sides
1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4
4sin ^ 2 (x) Multiply
4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)
4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0
y = sinx
4y ^ 4 -3y ^ 2 + 2y + 1 = 0
sinx = y = -1 or -0.3478
x = 270, 180-22.61 or -22.61 degrees
x = 270, 157.39 or 337 .39 degrees
or
x = 3pi / 2, 0.13pi or 1.87pi radians
or
x = 4.71, 0.41 Or 5.89 radians
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you have piano lessons every 7 days and tuba lessons every 3 days. Today you have both lessons . in how many days will you have both lessons on the same day again
Both lessons will be on the same day again after 21 days.
We will determine the least common multiple when two events occur simultaneously.
If I take tuba lessons every third day and piano lessons every seventh day,
Least common multiple of 3 and 7 will be,
Multiples of 3 = 1 × 3
Multiples of 7 = 1 × 7
Least common multiple (LCM) of 3 and 7 = 1 × 3 × 7
=21
Therefore, I will have both the lessons after 21 days.
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3x-6less than or equal to -3
Answer:
3x-6 is more than -3
Step-by-step explanation:
3x-6=0
+6 +6
3x=6
3/ 3/
x=3
Identify the error(s) and explain the correct answer. 6.5x+3.05x = 38.2 10x = 38.2 10 /10 x = 3.82
Subtract the sum that appears on the same side of the equation as the "x" to isolate the "x" on one side of the algebraic equation. For instance, rewrite the equation "x + 5 = 12" as "x = 12 - 5" and then find "x" in the new equation. The answer is "x = 7"
A linear equation example is what?Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
How should a linear equation be written?A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the numbers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
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Holly needs to buy some cloth to make masks. The following deals are available at various stores. Choose the best deal.
the best deal for holly to do shopping from the first store.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, Holly needs to buy some cloth to make masks. The following deals are available at various stores.
$16.52 per 6 yd$13.85 per 5 ydFor the first store:
Price per yard = 16.52/6$
Price per yard = 2.7533$
For the second store:
Price per yard = 13.85/5$
Price per yard = 2.77$
therefore, it is best for her to buy from the first store.
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Complete question:
The following deals are available at various stores. Choose the best deal.
$16.52 per 6 yd$13.85 per 5 yda
$16.52 for 6 yd
b
$13.85 for 5 yd
c
Neither
Use the drop-down menus to complete the statements to match the information shown by the graph.
Pool A is filling up slower than Pool B because slope of the graph of Pool A is less than that of the graph for Pool B.
The slope of the graph tells you the unit-rate in gallons per minute.
What is graph?Graphs are an essential type of computing tool in mathematics. The nodes and edges that make up a graph are referred to as its elements. Whether "directed" or "undirected," nodes can only move through a graph in a single direction (either direction may be traversed from node to node).
In contrast to a chart, a graph is a representation of linked values in a multidimensional space. Graphs are helpful for examining the various relationships among specific data points.
A graph's search algorithm seeks out the shortest route between any two nodes. The best path is determined by an algorithm that considers the weight of each path on a graph.
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1. Determine whether this quadrilateral is a parallelogram..
A. Yes; opposite sides are parallel
B. Yes; opposite sides are congruent
C. Yes; opposite angles are congruent
D. Yes; diagonals bisect each other
E. Yes; consecutive angles are supplementary
F. Yes; one pair of sides are both congruent and parallel
G. No; not a parallelogram
A parallelogram is a quadrilateral with congruent and parallel opposite sides. Thus, to justify that the given quadrilateral is a parallelogram, option E is correct.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
Quadrilaterals are shaped with four straight sides. Examples are; square, rectangle, parallelogram, trapezium, etc.
A parallelogram is a type of quadrilateral that has opposite sides to be equal and parallel. It has some distinguishing properties which can be used to differentiate it from other quadrilaterals. Some of the are:
opposite sides are equalopposite sides are parallelconsecutive angles are supplementaryopposite angles are congruentThus, in the given question the required option is C. consecutive angles are supplementary.
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Integration by parts can only be used to integrate functions that include either polynomials or exponential functions. True False
Integration by parts can only be used to integrate functions that include either polynomials or exponential functions is False.
What is integration ?
Integration is a process of finding an antiderivative of a function, it is the reverse process of differentiation. It can be thought of as the area under the curve of the function or the accumulation of the function over a certain interval.
Integration by parts is a technique that can be used to integrate a wide variety of functions, not only functions that include polynomials or exponential functions. In fact, integration by parts can be used to integrate any function that can be expressed as the product of two functions, where one of the functions is the derivative of the other function. In other words, integration by parts allows us to evaluate an integral of the form ∫u(x)dv(x)dx by expressing it in terms of an integral of the form ∫v(x)du(x)dx.
It's just that those types of functions are more commonly used when applying this technique.
Hence , Integration by parts can only be used to integrate functions that include either polynomials or exponential functions is False.
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Tom works in chilled food department in a supermarket all fresh juices should be kept at a certain temperature as shown on thermometer
The temperature change that is required is; A reduction in temperature by 8°C.
How to find the change in temperature?We are told that;
The freezer should be working at -18°C.
The temperature on the freezer marks -10°C.
Now, what we see here is basic arithmetic because we simply want to find the additional temperature that will make the current reading to be equal to the ideal temperature required for it to wor. Thus, what we will do is to simply subtract the current temperature from the ideal one to find out the temperature required to make it work well.
Thus;
Temperature change = -18 - (-10)
Temperature change = -18 + 10
Temperature change = -8°C.
We see that the freezer still needs its' temperature to be reduced by 8°C.
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Complete question is;
Tom works in the cold food department in a supermarket. The thermometer shows the temperature of one of the freezers. The freezer should be working at -18°C. The temperature on the freezer marks -10 The temperature should increase or decrease by how many °C?
Recall swinging on a swingset as a kid. Assuming the chains or ropes for the swing were kept taut, the seat of the swing traced a circular arc. Now suppose you're on a swing hanging from ropes which are 6 ft long such that the seat is positioned 2 ft above the ground at rest. You swing forth to a terminal position /4 radians from your initial position at rest on the swing. At the height of your swing forth how high are you off the ground?
At the height of the swing forth, the swing seat would be at a maximum height of 2 + (6 * (1 - cos(pi/4))) = 4 feet above the ground.
What is cosine?
Cosine is a trigonometric function that relates the length of the adjacent side of a right triangle to the length of the opposite side to the hypotenuse. It is represented by "cos" and its formula is cos(x) = adjacent / hypotenuse. It is commonly used in mathematics, physics, and engineering to solve problems related to angles and vectors.
Cosine is a fundamental trigonometric function that is used in many areas of mathematics, physics, and engineering. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. It can also be defined as the dot product of the unit vector pointing in the direction of the angle and the unit vector pointing in the direction of the adjacent side. Cosine is periodic with a period of 2π and is always between -1 and 1, inclusive. It has many important properties and relationships with other trigonometric functions such as sine, tangent, and cotangent.
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-6.2353535353535 as a fraction
6.2353535353535 as a fraction is 623535353535/1000000.
This fraction is written as a mixed number by dividing the numerator by the denominator to get 623,535,353,535/1,000,000. This can be further simplified to 623,535/1,000, which is the same as 623 5/8.
NEED HELP ASAP PLEASE
The equation that represent y, the total number of letters Natasha put in an envelope in x hours is y = 42x.
How to represent equation?Natasha has a job putting letters to the envelope to be mailed. In one hour she put 42 letters in the envelope.
Therefore, the equation that best represent y, the total number of letters Natasha put in an envelope in x hours if she continue at the same rate can be calculated as follows;
1 hours = 42 envelopes
x hours = ?
cross multiply
Therefore,
y = 42x
where
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The size of an animal population in a year t is given by P(t)=210t+400/(t+2). Here t=0 represents the year 2004 and P(t) is the size of population in thousands of individuals. find the size of population in year 2004
The size of the animal population in year 2004 (t=0) is 200 thousands individuals.
What is population?Population is a term used to describe the total number of people that live in a specific geographic area. This can be a country, a state, a city, or any other area of the world. Population size and density are important factors in understanding the landscape of an area and its resources.
The size of the animal population in year 2004 (t=0) can be calculated by substituting t=0 into the given equation:
P(t)=210t+400/(t+2)
P(0)=210 × 0 + 400/(0+2)
P(0)=400/2
P(0)=200
Therefore, the size of the animal population in year 2004 (t=0) is 200 thousands individuals.
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What is the domain of the following function represented by ordered pairs?
{(4, 9), (–6, 1), (–2, 5), (3, 1)}
{5, 9}
{1, 5, 9}
{–6, –2, 3, 4}
{–6, –2, 1, 3, 4, 5, 9}
The domain of the ordered pairs {(4, 9), (–6, 1), (–2, 5), (3, 1)} is (c) {–6, –2, 3, 4}
How to determine the domain of the ordered pairs?From the question, we have the following parameters that can be used in our computation:
{(4, 9), (–6, 1), (–2, 5), (3, 1)}
Rewrite as
(x, y) = {(4, 9), (–6, 1), (–2, 5), (3, 1)}
The domain is the set of the x values
So, we have the following representation
x = {4,–6, –2, 3}
Remove repeated entries and reorder
x = {–6, –2, 3, 4}
So, the domain is x = {–6, –2, 3, 4}
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A and B are vertical angles if mA=(x+27) and mB = (2x+20) then find value of x
The value of x is 7.
What are vertically opposite angles?Two or more angles are said to be vertical angles if only they are formed by same two lines intersecting at a point. Thus the two angles have equal measure of value.
Given that A and B are vertical angles, then this implies that there is a relationship between them i.e they are opposite and equal.
Such that;
m<A = m<B
(x + 27) = (2x + 20)
x + 27 = 2x + 20
collect like terms,
-20 + 27 = 2x - x
7 = x
x = 7
Therefore, the value of x is 7.
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Evelyn has a bag containing red (R), blue (B), and green (G) marbles as shown below.
3 red marbles, 3 green marbles, and 2 blue marbles.
If each marble is replaced after it is drawn, what is the probability of randomly drawing three consecutive red (R) marbles?
StartFraction 3 over 256 EndFraction
StartFraction 1 over 56 EndFraction
StartFraction 1 over 27 EndFraction
StartFraction 27 over 512 EndFraction
The probability of randomly drawing three consecutive red marbles is [tex]\frac{27}{512}[/tex]
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Here Total number of marbles = 3+3+2 = 8.
Now probability of randomly drawing three consecutive red (R) marbles is
=> P(3 consecutive red) = P(red)×P(red)×P(red)
=> P(3 consecutive red) = [tex]\frac{3}{8}\times \frac{3}{8}\times \frac{3}{8}[/tex] = [tex]\frac{27}{512}[/tex]
Hence the probability of randomly drawing three consecutive red marbles is [tex]\frac{27}{512}[/tex] .
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Glen drew the model shown below for 1.95÷5
Answer:
0.39 is the answer to this question
Given A = 5i +7j , B= 2i +3j Find the magnitude of A-B Select one: a.6 0 b. 5 c. 2 d. 4
In order to find the magnitude of a vector, we use the Pythagorean theorem. The magnitude, also known as the length or the norm, of a vector, is the square root of the sum of the squares of its components.
In this case, we are given two vectors A and B, which are defined as
A = 5i + 7j
B = 2i + 3j.
The i and j components represent the x and y values of the vector respectively.
To find the magnitude of vector A-B, we need to first find the difference between the two vectors. This can be done by subtracting the components of vector B from the corresponding components of vector A. So,
A-B = (5i + 7j) - (2i + 3j) = 3i + 4j.
Now we can use the Pythagorean theorem to find the magnitude of this vector. The square root of the sum of the squares of the x and y components of the vector is the magnitude of the vector. So, the magnitude of
A-B = √(3^2 + 4^2)
A-B = √(9 + 16)
A-B= √25
A-B = 5. Therefore, the answer is (b) 5.
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What is the surface area of this shape?
Answer:
88 square cm
Step-by-step explanation:
Surface area of combined solids:Surface area of down rectangular prism:
l = 6cm ; w = 3 cm & h = 2 cm
[tex]\sf \boxed{Total \ surface \ area \ of \ rectangular \ prism = 2*(lw + wh+hl)}[/tex]
= 2*(6*3 + 3*2 + 2*6)
= 2* (18 + 6 + 12)
= 2 * 36
= 72 cm²
Lateral surface area of the top rectangular prism:
l = 3 cm
w = 1 cm
h = 4 - 2 = 2 cm
LSA = 2h( l + w)
= 2*2 *( 3 + 1)
= 4 * 4
= 16 cm²
Surface area of the shape = 72 + 16
= 88 cm²
Answer:
a = 88 cm2
Step-by-step explanation:
[tex]a=(4)(3)+2(4)(1)+2(5)(2)+2(3)(2)+(1)(3)+6(3)+5(3)=12+8+20+12+3+18+15[/tex]
[tex]a=88cm^{2}[/tex]
Hope this helps
What is the first step in isolating the variable in this equation? (½)p + 75 = 100 A Subtract 75 from both sides. B Subtract ½ from both sides. C Divide both sides by 75. D Divide both sides by ½.
The first step in isolating the variable in this equation is to subtract 75 from both sides. Option A is correct.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Given expression,
1/2p + 75 = 100
In order to isolate the variable our first step should be to subtract 75 from both sides
1/2P = 25
Then, multiply by 2 on both sides
P = 50
Thus, the first step in isolating the variable in this equation is to subtract 75 from both sides. Option A is correct.
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What are the factors of the cubic function f(x) = 8x³ +64?
Choose each correct answer.
(2x + 4)
(4x² +8x+16)
(4x²-8x+16)
(2x-4)
hello my friend if i am being helpful please please please rate my work and give me a like
The cubic function of the given expression would be = (2x + 4). That is option A.
What is cubic function?Cubic function is defined as the multiplication of variables by itself into three different times.
The factors of the given cubic function f(x) = 8x³ +64 can be calculated using the following steps:
(2x + 4)³ = X
(2x)³ = 8x³
(4)³ = 64
Therefore the cubic function of the given equation is (2x + 4).
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Evaluate the expression when n=2. n^2-5n+8
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{n^2 - 5n + 8}[/tex]
[tex]\mathsf{= 2^2 - 5(2) + 8}[/tex]
[tex]\mathsf{= 2\times 2 - 10 + 8}[/tex]
[tex]\mathsf{= 4 - 10 + 8}[/tex]
[tex]\mathsf{= -6 + 8}[/tex]
[tex]\mathsf{= 2}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The measure of an angle is 89
Find the measure of its supplement.
We can conclude that the supplement angle of 89° will be 91°.
What do we mean by supplement angles?Angles that add up to 180 degrees are referred to as supplementary angles.
For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.
The sum of complementary angles is 90 degrees.
Two angles are complementary if their sum equals 90 degrees, and supplementary if their sum equals 180 degrees.
So, we have an angle of 89°.
We know that the supplement angle is an angle of measure 180°.
Now, the supplement angle of 89° will be as follows:
180 - 89
91°
Therefore, we can conclude that the supplement angle of 89° will be 91°.
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Based on the correct answer from part A ( m/m times a1/1) + (1/1 times F/m) which of the following is the correct symbolic expression for a?
The correct symbolic expression for a is option C) [tex]\frac{ma_{1} +F}{m}[/tex]
A symbolic expression, also known as a mathematical expression, is a combination of numbers, variables, and mathematical operators (such as +, -, *, /) that can be evaluated to produce a numerical result.
Symbolic expressions can also contain functions, constants, and mathematical operations like logarithms, trigonometric functions, etc. They can be used to model physical phenomena or to solve mathematical problems.
A logarithmic function is a mathematical function that expresses the power (or exponent) to which a fixed number (the base) must be raised to produce a given value.
It is typically written in the form "logb(x)" where b is the base and x is the value being evaluated. The most common base used is 10 (common logarithm) or e (natural logarithm)
These expressions can be used to represent mathematical concepts, relationships, or equations.
Therefore, The correct symbolic expression for a is option C) [tex]\frac{ma_{1} +F}{m}[/tex].
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Find the sum of the equation
36,323-17,209 rounding to the nearest thousand
Answer:
36,323-17,000
Step-by-step explanation:
just go to the thousands place and look back one place value
I need help with this please
Answer:
1/7
Step-by-step explanation:
4/4 is 1 and 28/4 is 7 so 1/7
The answer is 1/7.
To simplify : 4/28
To simplify fractions, we should follow these steps:
Step 1: Write the factors of the numbers in the numerator and denominator in step one.Step 2: Determine the shared factors that both the numerator and the denominator share.Step 3: At this point, we must divide the numerator and denominator by each other until there is only one other common component left.
Here, the given fraction is 4/28.
At first, we need to write the factors of the numerator and the denominator
Factors of the numerator, 4 = 1, 2, 4.
Factors of the denominator, 28 = 1, 2, 4, 7, 14, 28.
So, the common factors are 1, 2 and 4.
Dividing the numerator and denominator by the common factor, 2;
(4/2) / (28/2) or,
2/14
And,
(2/2) / (14/2) or,
1 / 7.
Hence, 1/7 is the simplified fraction of 4/28.
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2
4
2
X =
X
[?]
2 answer?
x = 2
All the sides are 2 so if the length on the bottom is 2, then it would be the same for the top :)
Answer:
x=2
Step-by-step explanation:
This shape is a regular polygon so all the sides are the same length
You start with 5 negative tiles, write on addition expression and one subtraction expression where -3 is the final value.
Therefore , the solution of the given problem of expression comes out to be for addition +2 and subtraction -2.
Expression : what is it?Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.
Here,
Given :
So, for addition expression:
=> -5 + 2 = -3
So , for the subtraction expression:
=> -5 -(-2) = -3
Therefore , the solution of the given problem of expression comes out to be for addition +2 and subtraction -2.
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sketch the graph of the function. f(x, y) = 9 − 9x2 − y2
A function is defined as a relation between a set of inputs, each with an output. The sketch of the function f(x,y) = 9 - 9x² - y² is given below.
f(x,y) = 9 - 9x² - y²
Let the given function is equal to 0, Then
9 - 9x² - y² = 0
y² = 9 - 9x²
The function can be written as
y² = 9 - 9x²
A function is a relationship between inputs, each associated with exactly one output. Each function has a domain and a codomain or scope. Functions are commonly denoted by f(x). x is the input. Here's the technical definition of the function:
A relationship from a set of inputs to a set of possible outputs.
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Which choice is the solution set of the inequality below?
|x>5.2
A. X > -5.2
B. -5.2
C. -5.2
D. x < 5.2
E. 0
F. x< -5.2 or x> 5.2
The solution set x<-5.2 or x>5.2 is true for the inequality |x|>5.2.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.
The given inequality is |x|>5.2.
So, the value of x should be greater than 5.2.
For example take x=6, then the given inequality will be -
|6|>5.2 = 6>5.2, so this is true.
Now take x=-6, then the given inequality will be -
|-6|>5.2 = 6>5.2, so this is also true.
Similarly, among the different choices x<-5.2 or x>5.2
The condition x>5.2 is already true.
Also, the condition x<-5.2 is also true for x if the value is lower than -5.2.
Therefore, the inequality x<-5.2 or x>5.2 is true.
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