Answers
The missing angle measures are 50 degrees, 100 degrees, and 80 degrees.
x = 50, we can substitute this value into the expressions for the other two angles:
2x = 2(50) = 100
x + 30 = 50 + 30 = 80
What are angles?When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol stands for the angle. Angle is a derivative of the Latin word "Angulus."
The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the shape of the angle can alternatively be used to symbolize the angle, with the middle letter indicating the location of the angle (i.e.its vertex).
From the question:
The total of the measures of the angles in any triangle is always 180 degrees, as shown by the characteristics of triangle angles.
This knowledge allows us to construct an equation to account for the missing angle measurements:
x + 2x + 30 = 180
Combining like terms, we get:
3x + 30 = 180
Subtracting 30 from both sides, we get:
3x = 150
Dividing both sides by 3, we get:
x = 50
Knowing that x = 50, we can change the formulas for the remaining two angles to reflect this value:
2x = 2(50) = 100
x + 30 = 50 + 30 = 80
As a result, the missing angle measurements are 50, 100, and 80 degrees.
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Related Questions
Find the image of (3, -6) reflected across the y-axis.
Answers
The image of the point after the reflection is (-3, -6).
How to determine the image of the pointTo reflect a point across the y-axis, we simply negate its x-coordinate while keeping the y-coordinate the same.
Thus, the image of point (3, -6) reflected across the y-axis would be (-3, -6).
We can visualize this by drawing a line passing through the point (3, -6) and the y-axis.
The reflection of the point will be at the same distance from the y-axis but on the opposite side.
So, the reflection of the point (3, -6) across the y-axis is (-3, -6).
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Which expression is equivalent to (6−2 • 35)−2? HELP NOW
Answers
In response to the stated question, we can state that here Hence, the linear equation (6 2 • 35) 2 equals 1/4096
What is a linear equation?A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
We must do the following operations in the correct order to simplify the formula (62 • 35)2:
To start, we must multiply 2 by 35, which results in the number 70.
The result is -64 when we remove 70 from 6.
The final step is to raise the unfavorable integer -64 to the power of -2.
Hence, we can write:
[tex](6-2 * 35)-2 = (-64)^{-2}[/tex]
To make this statement easier to understand, keep in mind that taking the reciprocal of a number raised to a positive power is the same as raising it to a negative power. With those words:
[tex]a^-n = 1/a^n\\(-64)^-2 = 1/(-64)^2\\1/(-64)^2 = 1/4096[/tex]
Hence, the expression (6 2 • 35) 2 equals 1/4096.
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express the sum of the angles of this triangle in two different ways
Answers
Answer:
X=60
Step-by-step explanation:
Firstly you must know that a triangle has 180° angle in it's all side.. so in this case you can say x+½x+(1,5)x= 180°
here x equal to 60°
this is a simple way to expres how can find the x angle
And to second way about how to find the x we have to know the lineer algebra. so lineer algebra is a strong way and useful to not only geometric shapes and for all mathematic calculate..
HELPPP! Cari knows that it is a 45 mile drive from her house to the airport. She also knows that it is a 45 mile drive from her house to her grandparents house in the woods. How many miles is it directly from the airport to her grandparents house in the woods? Show your work.
Answers
Answer:
We can use the Pythagorean theorem to solve this problem. Let's assume that Cari's house is at point A, the airport is at point B, and her grandparents' house is at point C. We know that the distance from A to B is 45 miles and the distance from A to C is 45 miles. We want to find the distance from B to C, which we can call x.
We can form a right triangle with sides AB, AC, and BC. The distance we want to find, x, is the length of the hypotenuse of this triangle (side BC).
Using the Pythagorean theorem, we know that:
AB^2 + AC^2 = BC^2
Substituting in the values we know:
45^2 + 45^2 = x^2
Simplifying:
2025 + 2025 = x^2
4050 = x^2
Taking the square root of both sides:
x = sqrt(4050)
x is approximately equal to 63.64 miles (rounded to two decimal places).
Therefore, the direct distance from the airport to Cari's grandparents' house is approximately 63.64 miles.
An angle measures 8° less than the measure of its complementary angle. What is the
measure of each angle?
and
Answers
According to the problem, x measures 8 degrees less than its complementary angle, so we can set up the equation:
x = (90 - x) - 8
Simplifying and solving for x, we get:
2x = 82
x = 41
Therefore, one of the angles measures 41 degrees, and the other angle (its complementary angle) measures:
90 - x = 90 - 41 = 49 degrees
If you have another question, please let me know!
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use
the binomial probability formula to find the probability of x successes given the
probability p of success on a single trial. Round to three decimal places.
n = 64, x = 3, p = 0. 04
0. 091
0. 139
0. 221
0. 375
Answers
The probability of 3 successes in 64 trials with a probability of 0.04 of success on a single trial is 0.375.
The probability of x successes in n trials with a probability p of success on a single trial can be calculated using the binomial probability formula. This formula is P(x successes) =[tex]nCx * (p^x) * (1-p)^(n-x)[/tex]. In this case, n = 64, x = 3, p = 0.04. Therefore, P(x successes) =[tex]64C3 * (0.04^3) * (1-0.04)^(64-3)[/tex]. Calculating this gives us P(x successes) = 0.375. Therefore, the probability of x successes in n trials with a probability p of success on a single trial is 0.375.
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what is the exact value of tangent of 11 times pi over 12 question mark negative quantity of 2 minus radical 3 end quantity negative quantity of 2 plus radical 3 end quantity 2 minus radical 3
Answers
The exact value of tangent of 11 times pi over 12 is [tex]-2+\sqrt{3}[/tex].
We have to find the exact value of [tex]tan\frac{11\pi}{12}[/tex]
[tex]tan\frac{11\pi}{12}=tan\frac{6\pi+5\pi}{12}[/tex]
[tex]tan\frac{11\pi}{12}=tan(\frac{6\pi}{12}+\frac{5\pi}{12})[/tex]
[tex]=tan(\frac{\pi}{2}+\frac{5\pi}{12})[/tex]
We have [tex]tan(\frac{\pi}{2}+x)=-cotx[/tex]
[tex]tan\frac{11\pi}{12}=-cot(\frac{5\pi}{12})[/tex]
[tex]tan\frac{11\pi}{12}=-cot(\frac{2\pi+3\pi}{12})[/tex]
[tex]tan\frac{11\pi}{12}=-cot(\frac{\pi}{6}+\frac{\pi}{4})[/tex]
We have identity [tex]cot(x+y)=\frac{cotxcoty-1}{coty+cotx}[/tex]
[tex]tan(\frac{\pi}{2}+x)= -\frac{cot\frac{\pi}{6}cot\frac{\pi}{4}-1}{cot\frac{\pi}{4}+ cot\frac{\pi}{6}}[/tex]
[tex]=\frac{-\sqrt{3}(1) - 1}{1+\sqrt{3}}[/tex]
Rationalize the denominator and simplify, we get:
[tex]=-2+\sqrt{3}[/tex]
Therefore, the exact value of [tex]tan\frac{11\pi}{12}[/tex] is [tex]-2+\sqrt{3}[/tex].
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Complete question is:
Find the exact value of [tex]tan\frac{11\pi}{12}[/tex] ?
From a point 48 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 40° and
49° 40',
respectively. find height of steeple
Answers
Answer: Let's call the height of the steeple "h". We can use the tangent function to set up an equation involving the angles of elevation:
tan(40°) = h / x
tan(49° 40') = (h + y) / x
where "x" is the distance from the point to the base of the steeple, and "y" is the height of the point above the ground.
We are given that the distance from the point to the church is 48 feet, so we can use the Pythagorean theorem to find the value of "y":
y^2 = x^2 - 48^2
We can substitute this expression for "y" into the second equation above:
tan(49° 40') = (h + √(x^2 - 48^2)) / x
We can now solve this equation for "h":
h = x tan(49° 40') - x √(1 + tan^2(49° 40')) + 48 tan(40°)
Plugging in the values for the angles and solving for "h", we get:
h ≈ 83.9 feet
Therefore, the height of the steeple is approximately 83.9 feet.
Step-by-step explanation:
simplify the monomial. the final answer should contain positive exponents only
(-8x^4y^3)(2x^5y^2)+7x^9y^5
Answers
The simplified mοnοmial is [tex]-9x^9y^5[/tex].
What is mοnοmial ?In algebra, a mοnοmial is an expressiοn that has a single term, with variables and a cοefficient. Fοr example, 2xy is a mοnοmial since it is a single term, has twο variables, and οne cοefficient. Mοnοmials are the building blοcks οf pοlynοmials and are called 'terms' when they are a part οf larger pοlynοmials. In οther wοrds, each term in a pοlynοmial is a mοnοmial.
Mοnοmial is defined as an expressiοn that has a single nοn-zerο term. It cοnsists οf different parts like the variable, the cοefficient, and its degree. The variables in a mοnοmial are the letters present in it. The cοefficients are the numbers that are multiplied by the variables οf the mοnοmial. The degree οf a mοnοmial is the sum οf the expοnents οf all the variables.
When we multiply mοnοmials with the same base, we add their expοnents. Using this prοperty, we can simplify the expressiοn as fοllοws:
[tex](-8x^4y^3)(2x^5y^2)+7x^9y^5[/tex]
[tex]= (-8 * 2)(x^4 * x^5)(y^3 * y^2) + 7x^9y^5[/tex]
[tex]= -16x^9y^5 + 7x^9y^5[/tex]
[tex]= (7 - 16)x^9y^5[/tex]
[tex]= -9x^9y^5[/tex]
Therefοre, the simplified mοnοmial is [tex]-9x^9y^5[/tex].
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X = 5y - W
make W the subject
Pls help
Answers
Answer:
W = -X + 5y
Step-by-step explanation:
Now we have to,
→ Find the required value of W.
The equation is,
→ X = 5y - W
Then the value of W will be,
→ X = 5y - W
→ 5y - W = X
→ -W = X - 5y
→ [ W = -X + 5y ]
Hence, value of W is -X + 5y.
How do you rewrite an equation into slope intercept form
Answers
Answer: y=mx+b
Step-by-step explanation:
To change the equation into slope-intercept form, we write it in the form y=mx+b .
A piece of a plastic poll is shaped like a cylinder. The poll has a length of 15 feet. Which of the following is closest to the volume of the pole? 71 ft² 106 ft² 424 ft² 141 ft² A B C D
Answers
Answer:
Since the pole is in the shape of a cylinder, its volume can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length in this case). We are not given the radius, so we cannot calculate the exact volume. However, we can use an approximation assuming a reasonable radius.
Let's assume a radius of 1 foot. Then, the volume would be V ≈ π(1)²(15) = 15π ≈ 47.1 cubic feet.
The closest answer choice to this approximation is D) 141 ft². However, note that volume is measured in cubic units (feet cubed or ft³), not square units (feet squared or ft²). Therefore, none of the answer choices are in the correct units for the volume of a cylinder.
Can someone please please help! Thank you so much! The picture is attached and I've written out the question! thank you!
The cuboid below is made of nickel and has a mass of 534 g.
Calculate its density, in g/cm³.
If your answer is a decimal, give it to 1 d.p.
Answers
Answer:
8.9 g/cm^3
Step-by-step explanation:
Volume = 5 x 2 x 6 = 60 cm^2
density = m/V = 534/60 = 8.9 g/cm^3
Find the geometric mean of 8 and 32. The geometric mean is _
Answers
Answer:
20
Step-by-step explanation:
you add them and divide by how ever many you added
Find the x- and y-intercepts of the parabola y=−10x2−16x−5
Answers
The x-intercepts are approximately (-1.08, 0) and (-0.42, 0), and the y-intercept is (0, -5).
To find the x-intercepts of a parabola, we set y = 0 and solve for x. Similarly, to find the y-intercept, we set x = 0 and solve for y.
Setting y = 0 in the given equation, we get,
0 = −10x^2 − 16x − 5
We can solve for x by using the quadratic formula:
x = [-(-16) ± sqrt((-16)^2 - 4(-10)(-5))] / (2(-10))
Simplifying, we get,
x = [-(-16) ± sqrt(256 - 200)] / (-20)
x = [-(-16) ± sqrt(56)] / (-20)
x = [8 ± 2sqrt(14)] / (-10)
So the x-intercepts are:
x = [8 + 2sqrt(14)] / (-10) ≈ -1.08
x = [8 - 2sqrt(14)] / (-10) ≈ -0.42
To find the y-intercept, we set x = 0 in the given equation:
y = −10(0)^2 − 16(0) − 5
y = -5
So the y-intercept is -5.
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The value of my coins if I have p pennies, n nickels and twice as many quarters as pennies HELPPPPPPPPPP ASAPPWILL AWARD BRAINLIES~T
Answers
p=number of pennies
n=number of nickels
q=number of quarters
You know pennies are worth $0.01, nickels are worth $0.05, and quarters are worth $0.25.
You have twice as many quarters are pennies, so you have 2p quarters.
The value of your coins are: 0.01p+0.05n+0.25(2p)= 0.01p+0.05n+0.5p = 0.06p+0.05n where p is the number of pennies and n is the number of nickels.
Hope this helps!
A company makes flags for a holiday. For every 9 yards of red fabric, it uses 17 yards of blue fabric. This ratio is represented in the diagram. Explain how you would use the diagram to find the number of yards of blue fabric used when 63 yards of red fabric are used.
Answers
The company would use 19.5 yards of blue fabric when 63 yards of red fabric are used, according to the given ratio and diagram.
What are word problems?Word problems are mathematical problems expressed in words, often used to apply mathematical concepts to real-life situations.
To find the number of yards of blue fabric used when 63 yards of red fabric are used, we can use the given ratio of 9 yards of red fabric to 17 yards of blue fabric.
To determine the number of units of red fabric needed for 63 yards divide the number of yards of red fabric by the scale factor for red fabric, which is 3. So, 63 yards ÷ 3 units per yard = 21 units of red fabric.
Use the ratio to determine the number of units of blue fabric needed. Since the ratio of red to blue fabric is 9:17.So, to find the number of units of blue fabric needed for 21 units of red fabric, we can multiply 21 by 17/9, which gives us 39 units of blue fabric.
So, 39 units of blue fabric ÷ 2 units per yard = 19.5 yards of blue fabric.
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In the diagram, E is the midpoint of DF. What is the value of x?
Answers
Answer:
[tex]\large\boxed{\mathtt{x = 10}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the value of x.}[/tex]
[tex]\textsf{Because E is a Midpoint,} \ \overline{DE} \cong \ \overline{EF}.[/tex]
[tex]\textsf{Let's set them equal to each other.}[/tex]
[tex]\mathtt{45=3(x+5)}[/tex]
[tex]\large\underline{\textsf{Begin Solving:}}[/tex]
[tex]\mathtt{45= ( 3 \times x ) +(3 \times 5)}[/tex]
[tex]\mathtt{45= 3x+15}[/tex]
[tex]\large\underline{\textsf{Subtract 15 from Both Sides:}}[/tex]
[tex]\mathtt{3x=30}[/tex]
[tex]\large\underline{\textsf{Divide by 3:}}[/tex]
[tex]\large\boxed{\mathtt{x = 10}}[/tex]
Answer:
x = 10
Step-by-step explanation:
To find:-
The value of x.Answer:-
We are here given that, E is the midpoint of DF. The value of DE is 45 and that of EF is 3(x+5) . We are interested in finding out the value of "x" .
According to Euclid's first axiom , Things which are half of the same thing are equal to one another. So here;
[tex]\sf:\implies DF = DF \\[/tex]
[tex]\sf:\implies \dfrac{DF}{2}=\dfrac{DF}{2} \\[/tex]
[tex]\sf:\implies DE = EF \\[/tex]
On substituting the respective values, we have;
[tex]\sf:\implies 45 = 3(x+5) \\[/tex]
[tex]\sf:\implies 45 = 3x + 15 \\[/tex]
[tex]\sf:\implies 3x = 45-15\\[/tex]
[tex]\sf:\implies 3x = 30 \\[/tex]
[tex]\sf:\implies x =\dfrac{30}{3}\\[/tex]
[tex]\sf:\implies \red{x = 10}\\[/tex]
Hence the value of x is 10 .
I NEED AN ANSWER NOW!!! WILL MARK BRAINLEST!!!
Answers
Answer:
7
Step-by-step explanation:
Question
Divide.
1582
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
Answers
Answer:
1582÷
Step-by-step explanation:
because u haven't told to divide wth any number
Answer:
Your question isn't complete. Kindly correct it.
There were 5 choirs at the choir concert on Friday night. Each choir sang 5 songs.
Which shows how many songs the choirs sang in all?
A.
5 - 5
B.
5 × 5
C.
5 + 5
D.
5 × 6
Answers
A cylinder has a radius of 5 yards. Its volume is 1,177. 5 cubic yards. What is the height of the cylinder?
Answers
The height of the cylinder is 27 yards.
To find the height of a cylinder, we need to use the formula V = πr^2h, where V is the volume, π is the constant pi (3.14), r is the radius, and h is the height.
In this problem, we know the radius is 5 yards, and the volume is 1,177.5 cubic yards. We can rearrange the formula to calculate the height as h = V / (πr^2). Substituting the given values into the equation, we get: h = 1177.5 / (3.14 * 25) = 27 yards. Therefore, the height of the cylinder is 27 yards.
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An arc of length 21 meters subtends a central angle of 287° in a
circle.
a) Find the circumference of the circle & area.
Answers
The circumference and area of the circle with the arc of length 21 meters and a central angle of 287° are 4.35 meters and 1.16 square meters.
An arc of length 21 meters subtends a central angle of 287° in a circle. The circumference of the circle and area are required to be determined.
Here is the solution:
Let us suppose that the radius of the circle is r. Thus, we can write:
r = (L/θ) r = (21/287)
Let us substitute the values of r in the formulae of the circumference of the circle and area of the circle.
Circumference of the circle:
C = 2πr
C = 2π (21/287)
C ≈ 4.35 meters
Area of the circle:
A = πr²
A = π (21/287)²
A ≈ 1.16 square meters
Therefore, the circumference of the circle is 4.35 meters and the area of the circle is 1.16 square meters.
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4 Desiree, Marina, and Raúl each survey random samples of 60 students in their
school about whether they prefer to listen to music while completing homework.
They use the results to infer about what percent of students in the school prefer to
listen to music while completing homework. Based on the results of the three
surveys, what range of inferences is reasonable? Write your answers in the blanks.
Student Who
Gave Survey
Students Who Prefer to Listen to
Music While Completing Homework
48
39
42
Desiree
Marina
Raúl
39
48
From
% to
listen to music while completing homework.
% of the school population prefers to
Answers
Answer:
To calculate the range of inferences, we need to find the minimum and maximum percentages based on the results of the three surveys.
Desiree's survey found that 48 out of 60 students prefer to listen to music while completing homework, which is 80%.
Marina's survey found that 39 out of 60 students prefer to listen to music while completing homework, which is 65%.
Raúl's survey found that 42 out of 60 students prefer to listen to music while completing homework, which is 70%.
To find the minimum percentage, we can take the lowest value of the three surveys, which is 65%. To find the maximum percentage, we can take the highest value of the three surveys, which is 80%. Therefore, a reasonable range of inferences is:
From 65% to 80% of the school population prefers to listen to music while completing homework.
One state has a 6% sales tax on clothing items priced at $75 or higher, and no sales tax on clothing items priced under $75. What is the total tax on the items in the table above?
Answers
The total tax on the items is $6.12.
What is tax?Tax is a financial charge or other levy imposed upon a taxpayer (an individual or other legal entity) by a state or the functional equivalent of a state such that failure to pay is punishable by law.
The total amount of the items purchased is $102+$60+$35 = $197.
Raincoat is priced at $102 which is higher than $75 and is subject to 6% sales tax.
Therefore, the tax on raincoat is $102 x 6% = $6.12.
Slacks and shirt is priced below $75 and are not subject to sales tax. Therefore, the tax on slacks and shirt is $0.
The total tax on the items purchased is $6.12 + $0 = $6.12.
Hence, the correct answer is $6.12.
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I need help with this for math
Answers
The answer of the given question based on finding the new coordinate of c is (1, 5). and to determine if the image of Triangle ABC is similar or congruent to the original triangle is AB / A'B' = BC / B'C' = CA / C'A' = √(2).
What is Congruent triangles?Congruent triangles are triangles that have the same shape and size. More specifically, if two triangles have exactly the same size and shape, then they are congruent triangles. This means that all the corresponding sides and angles of two triangles are equal. Congruent triangles can be thought of as being identical to each other, but they may be positioned and oriented differently in space.
To rotate a point 180° degrees counterclockwise about the origin, we can simply multiply its coordinates by the matrix:
[ -1 0 ]
[ 0 -1 ]
So, the coordinates of the rotated point C would be:
[ -1 0 ] [ 3 ]
[ 0 -1 ]*[ 8 ] =[ -3 ]
[ 1 ]
we translate this point 4 units to the right and 4 units up by adding 4 to the x-coordinate and 4 to the y-coordinate:
[ -3 + 4 ]
[ 1 + 4 ] = [ 1, 5 ]
Therefore, the new coordinates of point C are (1, 5).
To determine if the image of triangle ABC is similar or congruent to the original triangle, we can check if the ratios of the corresponding sides are the same. Let's calculate the lengths of the sides of the original triangle:
AB = √((8-3)² + (3-3)²) = 5
BC = √((3-8)² + (8-3)²) = 5*√(2)
CA = √((3-3)² + (3-8)²) = 5
Now, let's calculate the lengths of the sides of the image triangle, using the new coordinates:
A'B' = √((8-1)² + (3-5)²) = 5*√(2)
B'C' = √((1-1)² + (5-8)²) = 3
C'A' = √((1-8)² + (5-3)²) = 5*√(2)
We can see that the ratios of the corresponding sides are the same:
AB / A'B' = BC / B'C' = CA / C'A' = √(2)
Therefore, the image of triangle ABC is similar to the original triangle.
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The vertex of a parabola is (0, 0) and the focus is (1/8,0). What is the equation of the parabola?
Answers
if the vertex is at the origin, and the focus point horizontally to the right-side 1/8 units away from the vertex, well, that means is a horizontal parabola with a "p" value of +1/8, so
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=0\\ p=\frac{1}{8} \end{cases}\implies 4(\frac{1}{8})(~~x-0~~) = (~~y-0~~)^2\implies \cfrac{1}{2}x=y^2\implies \boxed{x=2y^2}[/tex]
Solve from [0, 2pi)
cos x/2 = (sqrt(2))/2
Answers
Thus, cos x/2 = (sqrt(2))/2 has the solution for x = 4kx ± π/2 in the intervals [0, 2pi).
Explain about the cosine function?The ratio of the hypotenuse to the side adjacent to the acute angle together in right triangle is the cosine function, which is a trigonometric function.
This cosine function for only a specified range of angles is represented graphically by the cos graph. A trigonometric graph's horizontal axis is the angle, which is typically denoted by the symbol, and the y-axis is really the sine function of just that angle. The maximum and minimum values are 1 and 1.
There are amplitudes for both the sine and cosine functions. This is due to the scope limitations of each function. Both functions typically have an amplitude of 1, though this can vary depending on the way the function is constructed.
Given function:
cos x/2 = (sqrt(2))/2
OR,
cos x/2 = √2/2
cos x/2 = cos (2kx ± π/4) , k ∈ R (real number)
x/2 = 2kx ± π/4
x = 4kx ± π/2
Thus, cos x/2 = (sqrt(2))/2 has the solution for x = 4kx ± π/2 in the intervals [0, 2pi).
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How do you solve for x?
Answers
Answer:
Step-by-step explanation:
Using little bottom triangle:
[tex]y^2=10^2+20^2[/tex] (Pythagoras Theorem)
[tex]y^2=500[/tex]
Using big triangle:
[tex]y^2+z^2=(10+x)^2[/tex] (Pythagoras Theorem)
[tex]500+z^2=(10+x)^2[/tex] (Since we know [tex]y^2=500[/tex])
[tex]500+z^2=x^2+20x+100[/tex]
[tex]z^2=x^2+20x-400[/tex] [tex](a)[/tex]
Using little top triangle:
[tex]z^2=x^2+20^2[/tex] (Pythagoras Theorem)
[tex]z^2=x^2+400[/tex] [tex](b)[/tex]
Substitute [tex](a)[/tex] into [tex](b)[/tex]:
[tex]x^2+20x-400=x^2+400[/tex] (since we know both sides[tex]=z^2[/tex])
[tex]20x=800[/tex]
[tex]x=40[/tex]
X+y=9??? Can u give me a correct meaning of variable/s.
Answers
Answer:
In the equation X + y = 9, X and y are variables. Variables are used to represent unknown quantities or quantities that can vary. In this case, X and y represent two unknown numbers whose sum is equal to 9. We can use algebraic techniques to solve for either X or y, or both, depending on the situation. The values of X and y could represent anything, such as the number of apples and oranges in a basket, the length and width of a rectangle, or the ages of two people.