!!!!!!! HELPPPPPP !!!!!! ASAP !!!!!!!!! HELPPPPPP!!!!!!!!!!!!

Step-by-step explanation:

cos 20° cos 40° cos 60° cos 80°

Simplify cos 60° to ½.

½ cos 20° cos 40° cos 80°

We can use double angle formula, sin(2θ) = 2 sin θ cos θ.  Multiply and divide by 2 sin 20°.

½ (2 sin 20° cos 20° cos 40° cos 80°) / (2 sin 20°)

½ (sin 40° cos 40° cos 80°) / (2 sin 20°)

Multiply and divide by 2 and use double angle formula again.

½ (2 sin 40° cos 40° cos 80°) / (4 sin 20°)

½ (sin 80° cos 80°) / (4 sin 20°)

Multiply and divide by 2 and use double angle formula again.

½ (2 sin 80° cos 80°) / (8 sin 20°)

½ (sin 160°) / (8 sin 20°)

Use phase shift identity sin θ = sin(180−θ).

½ (sin 20°) / (8 sin 20°)

1/16

In this case we have the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = 1 / 16, and are asked to prove that this equation is true. Let's start by using the property 'cos(s)cos(t) = cos(s + t) + cos(s - t) / 2.' Taking the bit 'cos(20°)(cos(40°)' we know that s should = 20°, and t should = 40°.

[tex]\mathrm{Using\:the\:following\:identity}:\quad \cos \left(s\right)\cos \left(t\right)=\frac{\cos \left(s+t\right)+\cos \left(s-t\right)}{2},[/tex]

[tex]\cos \left(20^{\circ \:}\right)\cos \left(40^{\circ \:}\right)=\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\\[/tex]

[tex]\mathrm{Substituting\:the\:value\:back}:\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]

This expression is indeed not simplified, but remember that we can use the identities 'cos(- 20°) = cos(20°)' and 'cos(60°) = 1 / 2.' Let's substitute one step and a time.

[tex]\cos \left(-20^{\circ \:}\right)=\cos \left(20^{\circ \:}\right): \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]

[tex]\cos \left(60^{\circ \:}\right)=\frac{1}{2}:\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]

[tex]\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\cos \left(80^{\circ \:}\right)\left(1+2\cos \left(20^{\circ \:}\right)\right)}{8}[/tex]

Now that we have this 'simplified expression,' if we take the numerator as a whole in decimal form, it will = 0.5. Respectively 0.5 / 8 = 1 / 2 / 8 = 1 / 16. Hence our equation is true.

[tex]\cos \left(80^{\circ \:\:}\right)\left(1+2\cos \left(20^{\circ \:\:}\right)\right) = 0.5,\\0.5 / 8 = (1 / 2) / 8 = 1 / 16[/tex]

2x - 1 > 0 ( x = 1)

x + (x − 1) > 5 ( x = 3)

5x − 3x > 9 ( x = 5)

Answer:

2x - 1 > 0 ( x = 1)

x + (x − 1) > 5 ( x = 3)

5x − 3x > 9 ( x = 5)Step-by-step explanation:

Answer: cos(0) = 1

hope this helped

Answer:

[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]

Step-by-step explanation:

Given the rational expression: [tex] \frac{2x + 3}{x^2 - 5x + 4} [/tex], to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

[tex] x^2 - 5x + 4 [/tex]

[tex] x^2 - 4x - x + 4 [/tex]

[tex] (x^2 - 4x) - (x + 4) [/tex]

[tex] x(x - 4) - 1(x - 4) [/tex]

[tex] (x- 1)(x - 4) [/tex]

Thus, we now have: [tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex]

Step 2: Apply the concept of Partial Fraction

Let,

[tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex] = [tex] \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]

Multiply both sides by (x - 1)(x - 4)

[tex] \frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) [/tex] = [tex] (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4) [/tex]

[tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]

Step 3:

Substituting x = 4 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]

[tex] 2(4) + 3 = A(4 - 4) + B(4 - 1) [/tex]

[tex] 8 + 3 = A(0) + B(3) [/tex]

[tex] 11 = 3B [/tex]

[tex] \frac{11}{3} = B [/tex]

[tex] B = \frac{11}{3} [/tex]

Substituting x = 1 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]

[tex] 2(1) + 3 = A(1 - 4) + B(1 - 1) [/tex]

[tex] 2 + 3 = A(-3) + B(0) [/tex]

[tex] 5 = -3A [/tex]

[tex] \frac{5}{-3} = \frac{-3A}{-3} [/tex]

[tex] A = -\frac{5}{3} [/tex]

Step 4: Plug in the values of A and B into the original equation in step 2

[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]

[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]

Answer:

Step-by-step explanation:

Given the rational expression: , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

Thus, we now have:

Step 2: Apply the concept of Partial Fraction

Let,

=

Multiply both sides by (x - 1)(x - 4)

=

Step 3:

Substituting x = 4 in

Substituting x = 1 in

Step 4: Plug in the values of A and B into the original equation in step 2

Step-by-step explanation:

1. The domain of [tex]V (h(r))[/tex] is restricted to values of r greater than 0.

2. [tex]V(h(r)) = 3.5\pi r^3[/tex]

3. The volume depends on the radius of the cylinder

Answer:

Supplementary angles add up to 180 degrees. The key phrase "less than" signifies you are going to subtract angle X from angle Y. Angle Y is 2 times the measure of angle X so you are going to multiply Y by 2. So right now you should have the equation 2y - 19 = 180. Then, plug it in. Add 19 to 180 to move it to the other side and then divide by 2.

Answer:

i). x³ + 9x² + yz - 15

ii). -21m³np - 8p⁵q + mnp + 4mn + 100

Step-by-step explanation:

Question (38)

i). Two expressions are -5x² - 4yz + 15 and x³+ 4x²- 3yz

  By subtracting expression (1) from expression (2) we can the expression by addition which we can get expression (1).

 (x³+ 4x²- 3yz) - (-5x² - 4yz + 15) = x³ + 4x² - 3yz + 5x² + 4yz - 15

                                                    = x³ + 9x² + yz - 15

ii). -15m³np + 2p⁵q - 6m³pn + mnp + 4mn - 10qp⁵+ 100

  = (-15m³np - 6m³np) + (2p⁵q - 10qp⁵) + mnp + 4mn + 100

  = -21m³np - 8p⁵q + mnp + 4mn + 100

Answer:

Let N be the unknown number

The we have 6 x reciprocal of N/7  which is 6 x 7/N which is 42/N

HOPE THIS HELPS YOU

Multiply six and the reciprocal of the quotient of a number and seven can be written as 42/M.

Where M is the number.

Given,

Multiply six and the reciprocal of the quotient of a number and seven.

We need to find this expression.

It means to divide.

The quotient of a and b:

=  a ÷ b.

= a / b

Find the expression.

Let the number be M.

Now,

The quotient of a number and 7 can be written as:

= M ÷ 7

= M / 7

Reciprocal of the quotient of a number and seven.

= 1 / (M/7)

= 7 / M

Now,

Multiply six and the reciprocal of the quotient of a number and seven.

It can be written as:

= 6 x 7 / M

= 42 / M

Thus multiply six and the reciprocal of the quotient of a number and seven can be written as 42/M.

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Four more than twice a number is –10 is the same as 2n + 4 = 10

Steps to solve:

2n + 4 = 10

~Subtract 4 to both sides

2n = 6

~Divide 2 to both sides

n = 3

Best of Luck!

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 15 °}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{x + 30 ° + 100 ° + 3x - 10 ° = 180 °}[/tex]

( Sum of angle in straight line )

Collect like terms

⇒[tex] \sf{4x + 30 ° + 100 ° - 10 ° = 180 °}[/tex]

Calculate the sum or difference

⇒[tex] \sf{4x + 120 ° = 180 °} [/tex]

Move 120 to right hand side hand change it's sign

⇒[tex] \sf{4x = 180 ° - 120 °}[/tex]

Subtract 120 from 180

⇒[tex] \sf{4x = 60 ° }[/tex]

Divide both sides of the equation by 4

⇒[tex] \sf{ \frac{4x}{4} = \frac{60}{4} }[/tex]

Calculate

⇒[tex] \sf{x = 15  °}[/tex]

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

The function  has a domain x ≥ 5.

This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.

Hence, (x - 5) ≥ 0

⇒ x ≥ 5

Now, for all x values that are greater than equal to 5 the value of  will be negative.

So,  

⇒  

⇒ y ≤ 3

Therefore, the range of the function is y ≤ 3. (Answer)

Note: Thanks rani

Answer:

Line CD

Step-by-step explanation:

The another name for line P is line [tex]\over (CD)[/tex].

It is required to find the  another name for line P.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

To answer this type of problem we have to know the axiom.

At least two points define a line.

Then I can call line p as (see below attached picture)

The line p cuts the 2 different points , point C and point D, so we can.t indicate a line in a single letter of the Western Alphabet.

Therefore, the another name for line P is line [tex]\over (CD)[/tex].

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Answer:

5y=9x-2

y=mx-b

m=slope

y=9/5x-2/5

m=9/5=1.8 slope of pArallel

slope of pARALLEL=-1/M SLOPE OF A LINE PERPENDICULAR

m=-5/9 slope of a line perpendiculr

Answer:

7, 14, 14,21, and 28

Step-by-step explanation:

Only 1, 7 is pair of numbers that has 7 as its least common multiple.

Given that,
Pairs ( 1, 7 ), ( 3, 4 ), ( 7, 21), ( 14, 28).
A pair or pairs to be determined that have 7 as its least common multiple.

In mathematics, it deals with numbers of operations according to the statements.

In arithmetic, LCM is defined as the lowest common multiple of two integers X and Y, usually represented as by LCM X, Y, and is the smallest favorable integer that is dividable by both X and Y.

Since the Least common multiple of pair of numbers has 7, this is only possible for 1 * 7, because the LCM of 1 and7 is 7. So from given option 1, 7 is the required pair.

Thus, only 1, 7 is pair of numbers that has 7 as its least common multiple.

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Answer:

X= 139

Step-by-step explanation:

the square on the E means its a right side so that would be 90 degrees.  All triangles add up to 180.  F would be 41 degrees.  that mean X is  139 i think.

Answer:

36.083

Step-by-step explanation:

SOHCAHTOA

Cosine is adjacent over hypotenuse, so the

cos(49) = the adjacent side (x) || over the hypotenuse (55)

cos(49) = x/55

55cos(49) = x

x = 36.083

Answer:

[tex]54^\circ[/tex]

Step-by-step explanation:

Given :

[tex]m\angle A=(2x+10)^{\circ}[/tex]

[tex]m\angle B=(3x+15)^{\circ}[/tex]

And angles [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.

To find:

The measure of [tex]\angle B[/tex].

Solution:

First of all, let us learn about complementary angles.

Complementary angles are the angles whose sum is equal to [tex]90^\circ[/tex].

And we are given that angles [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.

Therefore [tex]\angle A[/tex] + [tex]\angle B[/tex] = [tex]90^\circ[/tex]

[tex]\Rightarrow 2x+10+3x+15=90\\\Rightarrow 5x+25=90\\\Rightarrow 5x=65\\\Rightarrow x =13[/tex]

Putting the value in [tex]\angle B[/tex].

[tex]m\angle B=(3\times 13+15)^{\circ} = 54^\circ[/tex]

Therefore, the answer is [tex]\bold{\angle B = 54^\circ}[/tex]

Answer:

B

Step-by-step explanation:

First, note that the figure is a parallelogram.

The area of a parallelogram is given by:

[tex]A=bh[/tex]

Where b is the base length and h is the vertical height.

The base length is 5+2 or 7, and the vertical height is 2.

Thus:

[tex]A=7(2)\\A=14\text{ in}^2[/tex]

The answer is B.

D. The distribution for town A is positively skewed, but the

distribution for town B is symmetric.

The distribution for town A is positively skewed, but the distribution for town B is symmetric. The correct option is D.

Box plots, also known as box-and-whisker plots, are a way to visualize the distribution of a set of numerical data.

To compare the shapes of the box plots, we need to look at the position of the median, the length of the box, and the length of the whiskers.

In the box plot for town A, the median is closer to the bottom of the box, indicating that the lower half of the data is more spread out than the upper half.

The whisker on the left side of the box plot is longer than the whisker on the right side, which indicates that there are some extreme values on the lower end of the data. This is consistent with a positively skewed distribution.

In contrast, the box plot for town B has a symmetrical box, with the median located near the center.

The whiskers on both sides of the box plot are roughly the same length, indicating that there are no extreme values on either end of the data. This is consistent with a symmetric distribution.

Thus, the correct option is D.

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In 422.5 years, the two populations will be the same

Let the year when the two populations will be the same be represented by x.

The equation to solve the question will be:

126.5 - 0.2x = 109.6 - 0.16x

Collect like terms

0.2x - 0.16x = 126.5 - 109.6

0.04x = 16.9

x = 16.9/0.04

x = 422.5

In conclusion, in 422.5 years, the two populations will be the same.

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Step-by-step explanation:

BD bisects ∠ABC.  Therefore:

m∠DBC = ½ m∠ABC

y + 5 = ½ (5/2 y)

y + 5 = 5/4 y

4y + 20 = 5y

y = 20

Therefore, m∠ABC = 50°, and m∠ABD = 25°.

Answer:

x=6

Step-by-step explanation:

first we'll use distributive property: we will distribute and multiply 3 by x and - 2

2x + 3x -6 = 24

then we'll add like terms which are 2x and 3x , 24 and 6 the sign of 6 will change from negative to positive:

2x + 3x =24 + 6

5x = 30

after that we will divide both sides by 5 in order to get x

5x/5 = 30/ 5

x = 6

Answer:

68

Step-by-step explanation:

We can see that the nth term would be the sum of the previous two terms. Continuing this would result in 68.

Answer:

24

Step-by-step explanation:

Answer: You would owe $1,263 and 75c! Have a fantastic day!

x = - 5

2x + 2 = - 8

2x = - 8 - 2

2x = - 10

x = - 10 : 2

x = - 5

Answer:

x=-5

Step-by-step explanation:

1.) 2x+2=-8   start to isolate the variable by subtracting 2 to -8

2.) 2x=-10 divide both sides by 2

3.) x=-5

Hope this helped

Answer:

5.6

Step-by-step explanation:

(2+3+5+7+11)/5

=5.6

Answer:

5

Step-by-step explanation:

A factor is a number or an expression that is multiplying something.

5 is multiplying -3n + 8.

Answer: 5 is a factor.

Answer:

2. 14

4. -6

Step-by-step explanation:

#2

(x²-4y)/2, given x=4, y=-3

 [(4)²-4(-3)]/2

=[16+12]/2

=28/2

=14

------------------------

#4

19-x², given x=-5

 19-(-5)²

=19-25

=-6

Answer:

$1,020

Step-by-step explanation:

There is a $200 difference in the every monthly pay.

Because of this we know that the first month was an amount minus $200.

If we subtract 1220 and 200, you get the pay of 1020 for 0 hours.