Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 - ∅), and cos = AB/AC = sin(90 - ∅).
Describe the trigonometric function.The right triangle's angle serves as the domain input value for the six basic trigonometric operations, which produce a range of numbers as their results.Understanding the trigonometric functions of the four quadrants' graphs, domains, differentiation, and integration will be achievable.
Here,
Sinx = perp./hypo.
Cosx equals base/hypo.
So,
Sin = B/C
A= cos(90 -∅ ) = BC/AC
So,
Cos(90 -∅ ) = Sin(BC/AC)
And,
cos = AC/AB
AB/AC = sin(90 -∅ )
So,
cos AB/AC = sin (90 -∅ )
Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 -∅ ), and cos = AB/AC = sin(90 - ∅).
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Solve for the missing side length in this triangle
Answer: C= 30
Step-by-step explanation:
A^2+B^2=C^2
C= √(B²+A²)
C= √(18²+24²)
C=30
Factor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
20q ^10 - 10q⁹+ 30q^8 + 20q^7
The greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.
What is the greatest common factor?The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD).
The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers. The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization.
the factor of 20q¹⁰ is 2*2*5*q*q*q*q*q*q*q*q*q*q
the factor of 10q⁹ is 2*5*q*q*q*q*q*q*q*q*q
the factor of 30q⁸ is 2*3*5*q*q*q*q*q*q*q*q
the factor of 20q⁷ is 2*2*5*q*q*q*q*q*q*q
So that the common factor of all the above terms is 2*5*q*q*q*q*q*q*q
the common factor of all the above terms= 10q⁷
So that the greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.
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What is the domain and range of √ X 2?
The domain of √ X 2 is X ≥ 4. The range is all real numbers.
Here is the proof, In order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. In this case, the radicand is X - 2, so we must have X - 2 ≥ 0, which is equivalent to X ≥ 4. Therefore, the domain of √ X - 2 is all values of X that are greater than or equal to 4. The range of √ X - 2 is all real numbers because the square root of any non-negative value is a real number.
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A cup of tea costs $3.25 at a local cafe. Alan and his wife, Patty, have a coupon for $1 off their order. Alan says the expression 3.25t - 1 represents the cost for t cups of tea. Patty says the expression 3t + (-1) represents the cost. Are their expressions equivalent? Explain.
Answer:
Step-by-step explanation:
The expressions are not equivalent. A cup of tea costs $3.25. $3.25t reprensents the total cost for the number of cups of tea (t) in one order. Subtracting the $1 coupon or adding the coupon as a negative results in the same discount. But Patty is using the wrong cost for a cup of tea, $3 instead of $3.25. Resulting in expressions that are NOT equivalent.
Work out the area of this shape. Give your answer
in cm².
4 cm
4 cm
10 cm
Answer:
48cm^2
Step-by-step explanation:
Rectangle=LxW
Triangle=bh/2
Rectangle: 10x4=40cm^2
Triangle: 4x4=16/2=8cm^2
40+8=48cm^2
Hope this helps :)
Are 5x and 5 like terms?
The statement given here is true as 5x and 5 are like terms.
This is because like terms have the variables of same degree . Therefore, 5x and x are like terms as both of them have x to the power 1 , which means both are of degree 1.
Like terms differs from the unlike terms only in case of numerical component. By summing the coefficients of like terms , similar phrases can be regrouped. Like terms in a polynomial equation are those terms that have the same variables and these variables have the same powers, but with different coefficients.
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please help: solve for x
Answer:
x=3
Step-by-step explanation:
Since the altitude of this triangle is at the midpoint of the base,
It is a isosceles triangle making MJ=MK
9x-18=3x
6x-18=0
6x=18
x=3
Which expression is equivalent to (x^2-2x-37)\(x^2-3x-40)
Therefore , the solution of the given problem of equation comes out to be [tex]x^{2}[/tex]-2x-37/(x-8) (x+5).
Describe equation.An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Here,
Given :([tex]x^{2}[/tex]-2x-37)/([tex]x^{2}[/tex]-3x-40)
[tex]x^{2}[/tex]-3x-40
Factor[tex]x^{2}[/tex]-2x-37
[tex]x^{2}[/tex]-2x-37/(x-8) (x+5)
Thus ,
the factors comes out to be [tex]x^{2}[/tex]-2x-37/(x-8) (x+5)
Therefore , the solution of the given problem of equation comes out to be [tex]x^{2}[/tex]-2x-37/(x-8) (x+5).
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What is the x-coordinate of the solution to the system shown?
3x - y = 6
3x + y = 34
Answer:
6[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
In this equation I will do the elimination method.
3x-y=6
3x+y=34
6x=40
Simplify
x=6[tex]\frac{2}{3}[/tex].
Check:
3(6.666...)-y=6
20-y=6
-20 from 6
-y=-14
y=14
20-14=6
6=6
3x(6.666...)+y=34
20+14=34
34=34
Is polynomial Y^4+4Y^2+5 have zeroes or not?
Yes, polynomial Y^4+4Y^2+5 has zeroes. Its zeroes can be found by factoring or using the quadratic formula: Y = -2 +/- sqrt(4-5) / 2 = -1 +/- sqrt(-1) / 2 = -1 +/- i/2.
[tex]Y^4+4Y^2+5[/tex]
=[tex](Y^2+1)²-3[/tex]
=([tex]\sqrt{Y^2+1-sqrt3}[/tex])([tex]\sqrt{Y^2+1+sqrt3}[/tex])
=(Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1)
=(Y+ sqrt3)(Y-sqrt3)(Y²-1)
=(Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1)
=0
Therefore the zeroes are Y=-√3, Y=1, Y=√3, Y=-1
Polynomial Y^4+4Y^2+5 is a fourth degree polynomial equation and can be solved by factoring or using the quadratic formula. To solve this equation by factoring, we need to use the difference of squares method. First, we rewrite the equation as (Y^2+1)²-3. Then we factor out the square of the binomial (Y^2+1): (Y^2+1-sqrt3)(Y^2+1+sqrt3). Next, we expand the first binomial to get (Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1). Then, we factor out the second binomial from the first two terms to get (Y+ sqrt3)(Y-sqrt3)(Y²-1). Finally, we expand the last binomial to get (Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1). This results in a product of zero, which means the equation has zeroes. The zeroes are Y=-√3, Y=1, Y=√3, and Y=-1.
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A circular mirror is surrounded by a square metal frame. The radius of the mirror is 3x. The side length of the metal frame is 15x. What is the area of the metal frame? (Type your answer in factored form. Type an exact answer in terms of pi.
The area of the frame is __ square units
The area of the frame is 196.73 x²
What is area ?
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth.
(15x)^2 = 225x^2
Area of the frame
= π (3x)²
= 28.27 x²
Metal area surrounding the frame
225 x² - 28.27 x²
= 196.73 x²
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Pill bluethooth Speaker consists two semisphere and cyclinder. The diameter of the cylinder and semisphere is 2 inches. the height of the cylinder is a foot. The According to the Statement please fill in the blanks. please answer the following in inch format and round it to
The volume of Pill Bluetooth Speaker is 39.78 cubic inches.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, Pill Bluetooth Speaker consists two semi sphere and cylinder.
The diameter of the cylinder and semi sphere is 2 inches. the height of the cylinder is a foot.
Radius =2/2 1 inch
We know that, the volume of semi sphere is 2/3 πr³
= 2/3 ×3.14×1³
= 2.1 cubic inches
We know that, 1 foot =12 inches
The volume of cylinder is πr²h
= 3.14×1²×12
= 37.68 cubic inches
Total volume =37.68+2.1
= 39.78 cubic inches
Therefore, the volume of Pill Bluetooth Speaker is 39.78 cubic inches.
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"Your question is incomplete, probably the complete question/missing part is:"
Pill bluethooth Speaker consists two semisphere and cyclinder. The diameter of the cylinder and semisphere is 2 inches. the height of the cylinder is a foot. The According to the Statement please fill in the blanks. please answer the following in inch format and round it to nearest tenth.
a) Volume of the Bluetooth Speaker ______
From the top of a lighthouse, the angles of depression to the top and bottom of a flagpole are 23° and 42°, respectively. If the flagpole is 75 feet from the lighthouse, how tall is the pole? [Round your answer to the nearest tenth of a foot. Type in the number only.]
Back with the braids.
Write −0.39¯¯¯¯¯ as a fraction in simplest form.
Answer:
-0.3999... = -⅖
-0.393939... = -13/33
Step-by-step explanation:
Only ones I could think of.
Answer:
-39/100
Step-by-step explanation:
An approximate solution to an equation is found using this iterative process.
(x, Jº-1
X,+1
and x, = -1
4
The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.
What is iteration ?
iteration can be defined as the repeating itself to perform a particular task.
Given
X2 is when n=1
X2 = X1+1 = X1 ^ 3 - 5/10
because X1 = -1
so X2 = -1-5/10 = -6/10 = -0.6
X3 is when n=2
X3 = X2+1
= X2 ^ 3 -5/10
because X2 = -3/5
so X3 could be
X3 = (-0.6*-0.6*-0.6) - 5 / 10
X3 = -0.041600
Hence, The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.
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What is the quotient (3x2 4x − 15) ÷ (x 3)? 3x 5 3x − 5 3x 1 3x − 1, r = 1
By solving the expression (3x2 +4x − 15) ÷ (x +3) the quotient is 3x-5 and r=0
What do you meant by quotient?When solving a division problem, the quotient is obtained by dividing the dividend by the divisor.
Mathematically, we denote the outcome of this division by separating the quotient and remainder with a capital R. (see below). The entire number that results from simplifying a fraction is known as the quotient.
We can do it by long division method the required quotient is 3x-5 and r=0
not 3x-1 , r=1
multiply the divisor with 3x we will get 3x²+9x to cancel out the first term of dividend.
Now after solving we will get -5x -15
Now, multiply the divisor by -5 we will get -5x-15 which will cancel the entire dividend.
So that the quotient is 3x-5 and r=0
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Can u please help? .
Answer:
x= 43
Step-by-step explanation:
The angles are corresponding angles which mean that they are equal to each other.
3x + 5 = 134 Subtract 5 from both sides
3x + 5 - 5 = 134 - 5
3x = 129 Divide both sides by 3
[tex]\frac{3x}{3}[/tex] = [tex]\frac{129}{3}[/tex]
x = 43
When two rotations are performed on a single figure, does the order of the rotations sometimes, always, or never affect the location of the final image? Explain.
When two rotations are performed on a single figure, the order of the rotations never affect the location of the final image.
What is the rotation?In mathematics, rotation is defined as that of the circular movement of an object around with a center, an axis, or a fixed point. Since rotations are rigid transformations, the size, length, shape, and angle measurements of the figure are maintained.
Precession, nutation, and intrinsic rotation are the names of these rotations. The rotation of the earth on its axis is one of the greatest instances of rotation in nature.
There are broad guidelines for rotations of 90, 180, and 270 degrees around the origin that are both clockwise and anticlockwise. Counterclockwise. X and Y are rotated by 90 degrees that means (x , y) ----> (-y , x); Rotation of 180 degrees: (x, y) —- (-x , -y); Rotation of 270 degrees: (x, y) —- (y , -x).
Here two times rotation means 180 degrees that means no change in the final image.
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what is the value of x?
Answer:119
Step-by-step explanation:
because it's on oppisite sides on the outside
Answer:
C) 119°------------------------------
The two given two angles are alternate exterior angles and therefore congruent according to alternate exterior angles theorem:
x = 119°Definition:
Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.solve for x. each figure is a parallelogram
9) x = 6
10) x = 1
11) x = 0
12) x = 6
This can be solved from the property of parallelogram.
What is parallelogram?A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles.
Properties are:
The opposing sides are equally spaced and parallel.Angles on either side are equal.The angles that are consecutive or contiguous are supplementary.All of the angles will be at right angles if any one of them is a right angle.The two diagonals cut across one another.9) As we know, from the property of parallelogram,
SR = TQ and ST = RQ
Now, 4 + 2x = 3x - 2
or, x = 6
10) As we know, from the property of parallelogram,
EF = DC and ED = FC
17x + 1 = 18x
or, x = 1
11) As we know, from the property of parallelogram,
YZ = XW and YX = ZW
2x + 9 = 9
2x = 0
x = 0
12) As we know, from the property of parallelogram,
TU = SV and TS = UV
6 + 2x = 4x - 6
or, 2x = 12
or, x = 6
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The price of an article is fixed at a certain percent above the cp and sold it at 5% discount . If the cp is rs16000 and sp is rs20900 with 10% vat ,how much percentage is mp more then cp ?
Markup price is 30% more then Cost price.
What is VAT?The selling price includes a VAT (which is a form of tax) and a discount.
A Vat is a form of tax which increases the price of a good and a discount reduces the price.
The marked price is mp = cp(1 + 5%) = 1.50cp
The selling price is sp = mp(1 -10%) = 0.90mp
The gain is profit =sp -cp
= (0.90(1.50cp)) -cp
= cp(0.90·1.50 -1)
= 0.04cp
Mark up = (selling price - cost price) / cost price
(20900 - 16,000) / 16,000 = 0.306 = 30.6 %
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Hannah either walks or cycles to school. The probability that she walks to school is 0.75 If she walks, the probability that she is late is 0.6 If she cycles, the probability that she is late is 0.2 Work out the probability that on any one day Hannah will not be late for school.
If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.
If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.
0.48 + 0.3 = 0.78.
In other words, there is a 78% probability of her not being late.
there are 32 students who studied maths and 28 geography and 26 social science if there are total 40 students in school if they all studies one subject atleast then find maximum number of students who studied all subjects
The maximum number of students who studied all subjects is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total students = 40
Number of students who studied maths = 32
Number of students who studied geography = 28
Number of students who studied social science = 26
The maximum number of students who studied all subjects.
= Highest number of students who studied one subject - Least number of students who studied a subject
= 32 - 26
= 6
Thus,
6 is the maximum number of students who studied all subjects.
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How many times would you expect to roll a 5 if you rolled a fair die 1,300 times? Round your answer, if needed.
A.
0.1667
B.
1,083
C.
217
D.
95
Answer: C, 217
Step-by-step explanation:
An item costs $430 before tax , and the sales tax is $34. 40. Find the sales tax rate. Write your answer as a percentage
The sales tax rate on the item = 8%
We know that the sales tax is nothing but the purchase price times the percentage of tax.
An item costs $430 before tax.
This means, the purchase price is 430 dollars.
The sales tax is $34. 40
To find: the sales tax rate as a percentage
First we find a ratio of the sales tax to the cost of the items before tax.
Sales tax / Pre-tax value of item = (34.40) / 430
Now we write a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.
i.e., (34.40) / 430 = sales tax percent / 100
So, the sales tax percent = 8%
Therefore, the sales tax is of 8%
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Josefina wants to prove that figures d and d are similar.
What seguence of transformation could Josefina perform to prove the figures are similar?
The left shift required to translate from D to D" is 6 units and scale factor for dilation of D" from D' is 2.5.
What is Scale factor?The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.
Compare the corresponding vertex of the given figures.
It is given as,
(-5, 0) → (1, 0)
It can be concluded that the graph of D is shifted (1 - (-5)) = 6 units towards left.
The scale factor is given as,
Length of side of D" ÷ Length of side of D'
⇒ 10 ÷ 4 = 2.5
Hence, the required shift and the scale factor are obtained as 6 units and 2.5 respectively.
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Can a/the variable in a algebraic expression be a base?
Answer:
yes
Step-by-step explanation:
yes
yes
yes
yes
yeyed
yes
I just need help with number 9 in this picture if anyone could pls help!
What is the degree of the polynomial 2x² 3xy 5y² 2?
The degree of the given polynomial is 2 because the highest exponent is 2 present in terms 2x^2 or 5y^2.
First, try to understand what is polynomial.
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x^2+ 3x - 5 is an illustration of a polynomial with a single variable. There are three terms in this example: x^2, 3x, and -5.
The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases."
Now let's talk about the degree of the polynomial.
The highest exponent of a monomial contained within a polynomial is referred to as the polynomial's degree. As a result, a polynomial equation with one variable having the biggest exponent is referred to as a polynomial degree.
The terms of a given polynomial is 2x^2, 3xy, 5y^2, and 2 Highest exponent is 2 in 2x^2 or 5y^2.
So the degree of the polynomial is 2.
The given Question is an incomplete complete question here.
[tex]2x^2 + 3xy + 5y^2 +2[/tex].
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What are 2 examples of composite number?
Composite numbers are whole numbers that contain more than two elements.. Examples of composite numbers include 36 and 42. These numbers are divisible by more than just 1 and themselves. 36 is divisible by 1, 2, 3, 4, 6, 9, 12, and 18. 42 is divisible by 1, 2, 3, 6, 7, 14, and 21.
Example 1: To find the factors of 36
Step 1: Start by dividing 36 by 2, which gives us 18.
Step 2: Divide 18 by 2, which gives us 9.
Step 3: Divide 9 by 3, which gives us 3.
Step 4: Divide 3 by 3 which gives us 1.
Step 5: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, and 18.
Example 2: To find the factors of 42
Step 1: Start by dividing 42 by 2, which gives us 21.
Step 2: Divide 21 by 3, which gives us 7.
Step 3: Divide 7 by 7 which gives us 1.
Step 4: The factors of 42 are 1, 2, 3, 6, 7, 14, and 21.
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