Use a double angle, half angle, or power reducing formula to rewrite cos^4(x)sin^2(x) without exponents.

The measurements are shown in the solution

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Given are right triangles, we need to find the value of x in each,

We will use Trigonometric ratios to find the same,

The sine is the ratio between the length of the opposite leg and the length of the hypotenuse.

The cosine is the ratio between the length of the adjacent leg and the length of the hypotenuse.

The tangent is the ratio between the length of the opposite leg divided by the length of the adjacent leg.

1) sin 21° = 11/x

x = 30.7

2) cos 34° = x/28

x = 23.21

3) tan 49° = 33/x

x = 28.68

4) T =  cos⁻¹ (11/23)

=  61.42°

5) T = sin⁻¹(21/44)

= 28.50°

6) T = tan⁻¹(8/12)

= 33.7°

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B

-6

...................

The answer using positive exponents only is 16x^(24)y^(16).

To simplify the expression (2x^(6)y^(4))^(4), we need to use the properties of exponents. Specifically, we need to use the property that states (a^(m))^n = a^(m*n). This means that when we raise a power to another power, we multiply the exponents.

Using this property, we can simplify the expression as follows:

(2x^(6)y^(4))^(4) = 2^(4) * x^(6*4) * y^(4*4) = 16 * x^(24) * y^(16)

So, the simplified expression is 16x^(24)y^(16).

Therefore, the answer using positive exponents only is 16x^(24)y^(16).

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The functions that are odd or even can be determined by replacing x with -x and seeing if the function remains the same or changes sign.

(a) f(x) = -tan(x) is an odd function because f(-x) = -tan(-x) = tan(x) = -f(x)

(b) f(x) = tan(x+T/2) is an odd function because f(-x) = tan(-x+T/2) = -tan(x+T/2) = -f(x)

(c) f(x) = tan(x)+cot(x) is neither an odd nor an even function because f(-x) = tan(-x)+cot(-x) = -tan(x)-cot(x) ≠ f(x) or -f(x)

(d) f(x) = 5cot(x) is an even function because f(-x) = 5cot(-x) = 5cot(x) = f(x)

(e) f(x) = (tan(x))2 is an even function because f(-x) = (tan(-x))2 = (tan(x))2 = f(x)

(f) f(x) = tan(4x) is an odd function because f(-x) = tan(4(-x)) = -tan(4x) = -f(x)

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\pi (3)^2(4)\implies \stackrel{ \pi =3.14 }{V=113.04}[/tex]

What is Trapezium ?

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper. In Euclidean Geometry, a quadrilateral is defined as a polygon with four sides and four vertices. Hence, a trapezium also has four sides, four angles and four vertices.

ABCD is a trapezium, AB || DC

The area of ABCD = 180 cm²

AB = 17 cm

CD = 13 cm

Formula Used:

Area of trapezium = 1/2 x height x (Sum of parallel sides)

Calculation:

Area of trapezium = 1/2 x height x (Sum of parallel sides)

⇒ 180 = 1/2 x height x (AB + CD)

⇒ 180 x 2 = Height x (17 +13)

Height=360/30

Height = 12

.:. The height of the trapezium is 12 cm.

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Answer:

Step-by-step explanation:

OK so im not that smart im only in 8th grade but i think the answers either A or B. hope i kind of helped you and good luck and have a nice day.

Answer:

answer is D

Step-by-step explanation:

if you replace X with 4 the equation should give you a 0.

after the long division method, you will obtain a quadratic equation.

to solve the quadratic equation you can use either of the known methods like factorisation or graphical methods or the quadratic formula.

t

Answer: A: 20,40,120

Step-by-step explanation:

Angle A is smaller than Angle B as it is less than 1 time as big as it.

The list of angles from smallest to largest is C, A, and B.

120 x (1/3) = 40

20 < 40

Hope this helps!

Answer:

2 and -2

Step-by-step explanation:

For the expression to be equal to 0, it means it has to be undefined, so all we need do, is equate the denominator to 0, since any number divided by 0 = 0

Therefore,

5x² - 20 = 0

5x² = 0 + 20

5x² = 20

Divide both sides by 5,

x² = 20/5

x² = 4

Square root both sides,

x² = √4

x = ±2

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Thanks.

The formula for the polynomial P(x) with degree 3, real coefficients, zeros at x=3-3i and x=1, and y-intercept at (0,-36) is P(x) = -4(x-1)(x-(3-3i))(x-(3+3i)).

To find the formula for the polynomial, we first need to find the conjugate of the complex zero, which is 3+3i. This is because a polynomial with real coefficients must have complex zeros in conjugate pairs.

Next, we can use the factored form of a polynomial, P(x) = a(x-r1)(x-r2)(x-r3), where r1, r2, and r3 are the zeros of the polynomial and a is a constant. In this case, r1 = 1, r2 = 3-3i, and r3 = 3+3i.

Finally, we can use the y-intercept to find the value of a. When x = 0, P(x) = -36, so we can plug in the values and solve for a:
-36 = a(0-1)(0-(3-3i))(0-(3+3i))
-36 = a(-1)(-3+3i)(-3-3i)
-36 = a(9+9i-9i-9)
-36 = a(-36)
a = 4

So the formula for the polynomial is P(x) = 4(x-1)(x-(3-3i))(x-(3+3i)). However, since we want the y-intercept to be negative, we can multiply the entire polynomial by -1 to get P(x) = -4(x-1)(x-(3-3i))(x-(3+3i)).

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The value of x is

x=-5

Generally, An angle is a figure formed by two rays (or line segments) that share a common endpoint. Angles are usually measured in degrees, with a full angle measuring 360 degrees.

Considering that the angle on a point is 630 , we have that the missing angle is

y=360-(148+92)

y=120

Therefore

y=x+125

Hence

x=y-125

x=120-125

x=-5

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The concession stand made 18 fewer cups of coffee than cups of hot chocolate.

To find out how many fewer cups of coffee they made than cups of hot chocolate, we need to add together the number of cups of hot chocolate with marshmallows and the number of cups without marshmallows:

20 cups + 15 cups = 35 cups of hot chocolate

Now, we can subtract the number of cups of coffee from the number of cups of hot chocolate to find out how many fewer cups of coffee they made:

35 cups - 17 cups = 18 cups

So, the concession stand made 18 fewer cups of coffee than cups of hot chocolate.

In conclusion, the concession stand made 18 fewer cups of coffee than cups of hot chocolate.

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Answer:

To express the value 0.0000547 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point.

0.0000547 = 5.47 × 10^(-5)

The exponent -5 indicates that we moved the decimal point 5 places to the right.

(a) For a line, the ratio of the change in y to the change in x is called the slope of the line.
(b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is y - y1 = m(x - x1).

The slope of a line is a measure of its steepness and is calculated by finding the ratio of the change in y (the rise) to the change in x (the run) between two points on the line.

The point-slope form of the equation of a line is a way to write the equation of a line when you know its slope and one point on the line. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.

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Answer:

$4.8

Step-by-step explanation:

5 for $3

So $3 ÷ 5 to get the price of one

Answer is 60c or $0.6

Then you multiply $0.6 with 8 to get the price of 8 oranges

So $0.6 x 8 = $4.8

Answer:

the cost of 8 oranges is 4.8$

step by step explanation

using ratio amd proportion

let x be the unknown amount

[tex]5 = 3 \\ 8 = x \\ cross \: multiply \\ 5x = 24 \\ divide \: \: both \: sides \: by \: 5 \\ \frac{5x}{5} = \frac{24}{5} \\ x = \frac{24}{5} \\ x = 4.8[/tex]

therefore the answer is 4.8 dollars will buy 8 oranges

thank you

Jane can buy 20 melons for the price of 32 apples.

To find out how many melons Jane can buy for the price of 32 apples, we need to use the given ratios to find the equivalent value of melons in terms of apples.

First, we know that 6 apples are equivalent to 3 bananas. So, we can simplify this ratio to 2 apples per 1 banana.

Next, we know that 4 bananas are equivalent to 5 melons. So, we can simplify this ratio to 4/5 of a banana per 1 melon.

Now, we can use these ratios to find the equivalent value of melons in terms of apples. If 2 apples are equivalent to 1 banana, and 4/5 of a banana is equivalent to 1 melon, then we can multiply these ratios together to find the equivalent value of melons in terms of apples:

2 apples/1 banana × 4/5 banana/1 melon = 8/5 apples/1 melon

This means that 1 melon is equivalent to 8/5 apples, or 1.6 apples.

Finally, we can use this ratio to find out how many melons Jane can buy for the price of 32 apples:

32 apples × 1 melon/1.6 apples = 20 melons

Therefore, Jane can buy 20 melons for the price of 32 apples.

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The equation that shows the relationship between the age of Danny and Terry is D = T - 6.

Let's represent Danny's age with the variable D and Terry's age with the variable T. We know that Danny is 22 years old, so we can write the equation D = 22.

We also know that Danny is 6 years younger than Terry, so we can write the equation D = T - 6. Now we can substitute the value of D from the first equation into the second equation to find the value of T.

D = T - 6

22 = T - 6

Add 6 to both sides of the equation:

22 + 6 = T

28 = T

So Terry is 28 years old.

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False, for both statements.

For the first statement, let A be an n x n matrix. If for two vectors y and z of Rⁿ we have Ay = Az, it does not necessarily mean that y=z. It is possible that A is a singular matrix, meaning that it does not have an inverse. In this case, there could be multiple vectors that would give the same result when multiplied by A. Therefore, it is not always true that y=z.

For the second statement, if A is a matrix of size n x n such that A³ = Iⁿ (where Iⁿ is the identity matrix of size n), it does not necessarily mean that A is invertible. It is possible for a matrix to have a power that equals the identity matrix, but not have an inverse. For example, consider the matrix A = [[0,1],[0,0]]. A² = [[0,0],[0,0]], and A³ = [[0,0],[0,0]], which is equal to I². However, A does not have an inverse, as its determinant is 0. Therefore, it is not always true that A is invertible if A³ = Iⁿ.

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The simplified expression is x^(454)y^(584) * 2^(109).

To simplify the given expression, we need to use the laws of exponents. The laws of exponents are:

- (a^m)^n = a^(mn)
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)

Using these laws, we can simplify the given expression as follows:

(x^3y^3)^31 * (32x^13y^18)^31 / (2xy^3)^2 * (2xy^3)^2 * (2x)^2 * (2x^3y^5)^3 * (4xy)^5 * (2x^3y^5)^3 * (4x)^5

= x^(3*31)y^(3*31) * 32^31x^(13*31)y^(18*31) / 2^2x^2y^(3*2) * 2^2x^2y^(3*2) * 2^2x^2 * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5y^(5*5) * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5

= x^(93)y^(93) * 32^31x^(403)y^(558) / 2^6x^6y^6 * 2^6x^6y^6 * 2^2x^2 * 2^6x^9y^15 * 4^5x^5y^25 * 2^6x^9y^15 * 4^5x^5

= x^(93+403)y^(93+558) * 32^31 / 2^6 * 2^6 * 2^2 * 2^6 * 4^5 * 2^6 * 4^5 * x^(6+6+2+9+5+9+5) * y^(6+6+15+25+15)

= x^(496)y^(651) * 32^31 / 2^(6+6+2+6+6) * 4^(5+5) * x^42 * y^67

= x^(496-42)y^(651-67) * 32^31 / 2^26 * 4^10

= x^(454)y^(584) * 32^31 / 2^26 * 4^10

= x^(454)y^(584) * 2^(5*31) / 2^26 * 2^(2*10)

= x^(454)y^(584) * 2^(155) / 2^(26+20)

= x^(454)y^(584) * 2^(155-46)

= x^(454)y^(584) * 2^(109)

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The product of 4/6-2a x 3-a/2 is equal to 2a-1. To calculate this, the fractions must first be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Next, the two terms should be multiplied together, resulting in 2a-1.

The product of 4/6-2a x 3-a/2 can be found by expanding the terms and then solving the equation. First, the fractions must be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Once the fractions are simplified, the two terms should be multiplied together, resulting in 2a-1. Now that the two terms have been multiplied, the equation can be expanded by using the Distributive Property. The equation should be written as (2/3-2a) x (3-a/2). This can be simplified by distributing the 2/3 and 3 across the parentheses. This results in (2-6a+2a^2) x (3-1/2a). Finally, the equation should be simplified by combining like terms. This results in 2-6a+2a^2+3-1/2a, which simplifies to 2a-1. Therefore, the product of 4/6-2a x 3-a/2 is equal to 2a-1.

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Answer:

Sin A = [tex]\frac{12}{13}[/tex] ; Cos A = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

The sine of a given angle is  [tex]\frac{opposite}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length opposite to angle A is 24, and the hypotenuse is 26. This gives  [tex]\frac{24}{26} = 12/13[/tex].

The cosine of a given angle is   [tex]\frac{adjacent}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length adjacent to angle A is 10, and the hypotenuse is 26. This gives  [tex]\frac{10}{26} = 5/13[/tex].

Answer:

8cfct on cypur574 6th 9

Step-by-step explanation:

f5g uh yo h tu g fn l dl uge ser k

Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

4x + 21 + x - 10 + 2x + 8 = 180

7x + 19 = 180 ( subtract 19 from both sides )

7x = 161 ( divide both sides by 7 )

x = 23

Then angles in triangle are

4x + 21 = 4(23) + 21 = 92 + 21 = 113°

x - 10 = 23 - 10 = 13°

7x + 8 = 7(23) + 8 = 161 + 8 = 169°

the only 2 possible angle measures are A and E

The image of the point (-1, -2, 0) under a dilation with center (0, 0, 0) and scale factor 3 is (-3, -6, 0).

From the question, we have the following parameters that can be used in our computation:

Center = (0, 0, 0).

Point = (-1, -2, 0)

Scale factor = 3

A dilation with center (0, 0, 0) and scale factor k multiplies the coordinates of a point by k.

So, to find the image of the point (-1, -2, 0) under a dilation with scale factor 3, we multiply each coordinate by 3:

(-1, -2, 0) --> (3(-1), 3(-2), 3(0))

Image = (-3, -6, 0)

Hence, the image of the point (-1, -2, 0)is (-3, -6, 0).

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There are three possible triangles that can be formed using the given measurements.

Measurement is the process of quantifying or comparing the amount, size, or extent of something. It is an important concept for scientists, engineers, and other professionals in order to compare and understand the world around them. Measurement involves the use of physical tools, such as rulers, scales, and protractors, and mathematical equations, such as formulas and equations.

We can use the Law of Cosines to solve for the missing side:

[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 43^2 + 15^2 - 2(43)(15)\cos(123^\circ)$\\$b^2 \approx 799.5$\\$b \approx 28.3$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.977$\\$A \approx 79.4^\circ$\\$B \approx 23.6^\circ$[/tex]

So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=79.4^\circ$[/tex], [tex]$B=23.6^\circ$[/tex], [tex]$C=77^\circ$[/tex], [tex]$a=43$[/tex], [tex]$b\approx 28.3$[/tex] , and [tex]$c=15$[/tex].

We can use the Law of Cosines to solve for the missing side:

[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 36^2 + 47^2 - 2(36)(47)\cos(47^\circ)$\\$b^2 \approx 1666.5$\\$b \approx 40.8$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.647$\\$A \approx 40.9^\circ$\\$C \approx 92.1^\circ$[/tex]

So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=40.9^\circ$[/tex], [tex]$B=47^\circ$[/tex], [tex]C\approx 92.1^\circ, a\ =36$[/tex], [tex]$b\approx 40.8$[/tex],

We can use the Law of Cosines to solve for the missing side:

[tex]h^2 = k^2 + p^2 - 2kp\cos(K)\\$h^2 = 47^2 + 10^2 - 2(47)(10)\cos(139^\circ)$\\$h^2 \approx 2363.7$\\$h \approx 48.6$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

So the triangle is [tex]$\triangle KHP$[/tex] were [tex]$K=139^\circ$[/tex], [tex]$H\approx 56.5^\circ$[/tex], [tex]$P\approx 124.5^\circ$[/tex], [tex]$k=47$[/tex], [tex]$h\approx 48.6$[/tex], and [tex]$p=10$[/tex].

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The total number of entities depicted by the given requirements is the sum of the number of students, teachers, and classrooms, which is 100 + 10 + 5 = 115. Hence, the answer is (C) 115.

What is the algebraic operation?

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

The question asks us to determine the number of entities depicted by the given requirements, which include School XYZ keeping track of its 100 students, 10 teachers, and 5 classrooms.

An entity can be defined as a distinct object or concept that is represented in a system, such as a database or software application.

In this case, the entities can be identified as follows:

Students: There are 100 students in the school, and each student can be considered as a separate entity.

Teachers: There are 10 teachers in the school, and each teacher can be considered as a separate entity.

Classrooms: There are 5 classrooms in the school, and each classroom can be considered separate.

Therefore, the total number of entities depicted by the given requirements is the sum of the number of students, teachers, and classrooms, which is 100 + 10 + 5 = 115. Hence, the answer is (C) 115.

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Answer:

Step-by-step explanation:

where is the image don't see

cosx = cos4x = cos5x.

19. Using the identity sin2x + cos2x = 1, we can rewrite the equation as:

sin2x/2 - sin2x/2 = cosx/sinx

Simplifying both sides: cosx/sinx = 0

Therefore, cosx = 0 and sinx = 0.


20. Using the identities secx = 1/cosx, tanx = sinx/cosx, and sec2x = 1 + tan2x, we can rewrite the equation as:

secx(secx tanx) - sec4x(secx tanx) = sec5x tanx

Simplifying: secx - sec4x = sec5x

Therefore, secx = sec4x = sec5x.

Simplifying further: 1/cosx = 1/cos4x = 1/cos5x

Therefore, cosx = cos4x = cos5x.

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In interval notation, the the solution set in interval notation. (5)/(y-4)<9 is   (41/9, ∞).

Inequality is a mathematical statement that two values or expressions are not equal. It is represented by symbols, like >, <, or ≠, and is used to compare quantities or values.

To solve the inequality (5)/(y-4)<9, we need to isolate the variable on one side of the inequality. We can do this by multiplying both sides of the inequality by (y-4) and then simplifying.

(5)/(y-4)<9

5 < 9(y-4)

5 < 9y - 36

41 < 9y

y > 41/9

This means that any value of y greater than 41/9 will satisfy the inequality.

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