What is the exact value of cos (7pi/8)

The expression equivalent to -2log₂x + 4log₂y + 4log₂z is log₂(yz)⁴/x².

To answer the question, we need to know the laws of logarithm

Since we want to find the expression equivalent to -2log₂x + 4log₂y + 4log₂z, we simplify using these laws, we have

-2log₂x + 4log₂y + 4log₂z = log₂x⁻² + log₂y⁴ + log₂z⁴ (appying the power law)

= log₂x⁻²y⁴z⁴ (applying the multiplication law)

= log₂y⁴z⁴/x²

= log₂(yz)⁴/x²

So, the expression equivalent to -2log₂x + 4log₂y + 4log₂z is log₂(yz)⁴/x².

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Answer:

C.log_2(yz^4/x^2)

Step-by-step explanation:

I took the Algebra exam

The value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively

Given the following functions a(x) = 7x + 10 and b(x) = 12x - 18

Take the sum

(a+b)(x) = a(x) + b(x)

(a+b)(x) = 7x + 10 + 12x - 18

(a+b)(x) = 19x- 8

Take the difference

(a-b)(x) = a(x) - b(x)

(a-b)(x) = 7x + 10 - 12x + 18

(a-b)(x) = -5x + 28

For the composite function a[b(x)].

a(12x- 18) = 7(12x-18) - 10

a[b(x)] = 84x - 126 - 10

a[b(x)] = 84x - 136

Hence the value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively

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The given polygon isa pentagon and the sum of its exterior angle is  360°. The value of x from the given polygon is 8

The given polygon isa pentagon and the sum of its exterior angle is  360°.

Take the sum of the angles and equate to  360° as shown;

77 + 66 + 62+ 59 + 12x =  360°

264 + 12x = 360

12x = 96

x = 8

Hence the value of x from the given polygon is 8

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Answer:

5%

Step-by-step explanation:

The first 20 single digit first numbers are 2,3,5 and 7. Thus they are four.

So next we calculate the percentage:

⇒ 4  ×  100% = 1  × 100%  =  5%

   20                20

Answer:

See below ~

Step-by-step explanation:

Question 6(e) :

⇒ x² ≤ 16

Take square root on each side :

⇒ √x² ≤ √16

⇒ x ≤ 4 and x ≥ -4

⇒ -4 ≤ x ≤ 4

⇒ x² ≤ 16

Apply the absolute rule if x² < a then -√a < x < √a

⇒ -√16 ≤ x ≤ +√16

⇒ -4 ≤ x ≤ 4

First of all, The student should have subtracted both sides by 4

What he should have done:

[tex]\rightarrow \sf \dfrac{3}{x-2} > 4[/tex]

[tex]\rightarrow \sf \dfrac{3}{x-2} -4 > 4 -4[/tex]

[tex]\rightarrow \sf \dfrac{3}{x-2} -\dfrac{4(x-2)}{x-2} > 0[/tex]

[tex]\rightarrow \sf \dfrac{3-4(x-2)}{x-2}} > 0[/tex]

[tex]\rightarrow \sf \dfrac{3-4x+8}{x-2}} > 0[/tex]

[tex]\rightarrow \sf \dfrac{-4x+11}{x-2}} > 0[/tex]

[tex]\sf \large \boxed{\sf {\left \{ {{-4x+11 = 0} \atop {x-2 = 0}} \right. }}[/tex]

⇒ -4x + 11 = 0, x - 2 = 0

⇒ -4x = -11, x = 2

⇒ x = 11/4 , x = 2

Solution satisfying the inequality:

⇒ 2 < x < 11/4

Using proportions, it is found that both spaces have the same brightness, as both have 3 candles per m².

The correct question is as given below:-

Nayeli lights a 4 square meter space with 12 candles. Citlali lights a 10 square meter space with 30 of the same type of candles. Whose space is lit brighter? Choose 1 answer: help me im graded at this

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For Nayeli and Citlali, the rate of candles per m² is given by:

N = 12/4 = 3 candles per m².

C = 30/10 = 3 candles per m².

Hence both spaces have the same brightness, as both have 3 candles per m².

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Answer:

the probability is %25 percent :P

Step-by-step explanation:

The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )

A triangle can be defined as a plain shape that has three sides and three angles.

Congruent triangles are triangles that satisfy one or more congruence postulates or laws. The triangles could either be similar based on their angles or sides or angles and side being similar.

In conclusion, The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )

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statement best describes the difference of the mean of the two data sets 2.8 is about 1.5 times the mean absolute deviation of either set.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The mean of William's set.

To find the mean, add all of the data points together and divide by the number of data points:

=89+90+97+74+78/5

=85.6

Now, mean absolute deviation,

=|89-85.6|+|90-85.6|+|97-85.6|+|74-85.6|+|78-85.6|/5

= 3.4+4.4+11.4+11.6+7.6/5

=7.68.

The mean of Andre's set.

To find the mean, add all of the data points together and divide by the number of data points:

=73+81+87+91+82/5

=82.8

Now, mean absolute deviation,

=|73-82.8|+|81-82.8|+|87-82.8|+|91-82.8|+|82-82.8|/5

=9.8+1.8+4.2+8.2+0.8/5

= 4.96.

Hence, the difference between the means of the two sets is

85.6-82.8=2.8.

2.8 is about 1.5 times the mean absolute deviation of either set.

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Answer:

Step-by-step explanation:

nothing im just as lost as everyone else

Answer:

6

Step-by-step explanation:

Answer:

2 or A

Step-by-step explanation:

Correct on edge22

The area of the decagon is 1573.39 square meters

The given parameters are:

The area of a decagon is calculated using:

[tex]A = \frac 52s^2\sqrt{5 + 2\sqrt 5[/tex]

Substitute 14.3 for s

[tex]A = \frac 52 * 14.3^2\sqrt{5 + 2\sqrt 5[/tex]

Evaluate the exponent

[tex]A = \frac 52 * 204.49\sqrt{5 + 2\sqrt 5[/tex]

Evaluate the product and the roots

A = 1573.39

Hence, the area of the decagon is 1573.39 square meters

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Answer:

if I am awake then it is 9 am.

Step-by-step explanation:

if p then q the converse is if q then p.

The volume of the cylinder will be equal to 1017.87 cubic feet.

Volume is defined as the space occupied by any object in the three-Dimensions. For the cylinder, the volume will be calculated by radius and the height of the cylinder.

Given that:-

The volume of the cylinder will be calculated by using the formulas below:-

V = πr²h

V = π ( 9 )² 4

V = 1017.87 cubic feet.

Therefore the volume of the cylinder will be equal to 1017.87 cubic feet.

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Answer: Y = 6  1/2

Step-by-step explanation: Let's begin,

step 1) Isolate the variable by dividing each side by factors that don't contain the variable.

Then, Exact Form:

y = 13/2

Decimal Form:

y = 6.5

Mixed Number Form:

y = 6  1/2

see the attachment..........

The answer to your question would be 43/15 or 2.866 and ongoing.

Answer:

[tex] \boxed{\rm \: Slope(m)= \cfrac{4}{ 3} }[/tex]

OR

[tex] \boxed{\rm \: Slope(m) \approx \: 1.30} \rm \: (nearest \: tenth)[/tex]

Step-by-step explanation:

Given two coordinates:

To Find:

Solution:

In this case,we'll need to use the slope's formula,to get the slope.

Here's the formula:

[tex] \rm \: Slope(m)= \: \cfrac{ y_2 -y_1 }{x_2 - x_1} [/tex]

According to the question:

Substitute them accordingly:

[tex] \rm \: Slope(m)= \cfrac{3 - ( - 1)}{ - 1 - ( - 4)} [/tex]

Simplify then, using a rule called PEMDAS.

[tex] \rm \: Slope(m)= \cfrac{3 + 1}{ - 1 +4 } [/tex]

[tex] \rm \: Slope(m)= \cfrac{4}{ 3} [/tex]

[tex] \rm \: Slope(m) \approx \: 1.30[/tex]

Hence, we can conclude that:

Hi student, let me help you out! :)

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We are asked to find the slope of a line parallel to the line that passes through

[tex]\star~\mathrm{(-4,-1)}\star[/tex]

[tex]\star~\mathrm{(-1,3)}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's the formula:

[tex]\star\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]

y2 and y1 are y-coordinates

x2 and x1 are x-coordinates

Substitute the given values:

[tex]\star\mathrm{\cfrac{3-(-1)}{-1-(-4)}}[/tex]

Simplify!

[tex]\star\mathrm{\cfrac{3+1}{-1+4}}[/tex]

Simplify more!

[tex]\star\mathrm{\cfrac{4}{3}}[/tex]

Now, what is the slope of the line parallel to this one?

Well, parallel lines have the same slope.

[tex]\star \ \mathrm{The \ slope \ of \ the \ line \ parallel \ to \ this \ one \ is \ \cfrac{4}{3}}.[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

Bhāskara was a 7th-century mathematician and astronomer, who was the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work. 

Aryabhatta is the father of Indian mathematics. He was a great mathematician and astronomer of ancient India. His major work is known as Aryabhatiya. It consists of spherical trigonometry, quadratic equations, algebra, plane trigonometry, sums of power series, arithmetic.

Step-by-step explanation:

hope it helps you and give brainliest

Answer:

One of the problems humans have made is a large amount of pollution.

And so some of the ways we can fix this is;

1- Using electric cars.

2- Using reusable packaging.

3- For the final one you could use stuff that easily and quickly to break down naturally materials.

Step-by-step explanation:

Answer:

9/21

= 1/7

Step-by-step explanation:

ratio means the comparison of two things

Answer:

The experimental probability is 4%

Step-by-step explanation:

Answer:

[tex] \text{C.} \: f(x) \: = \: |x| [/tex]

Step-by-step explanation:

To identify the absolute value of a number, it will always be represented between two sticks.

Step-by-step explanation:

3x + y = 8.4

2x + 2y = 10.08

x + y = 5.04

y = 5.04 - x

we use this then in the first equation

3x + 5.04 - x = 8.4

2x = 3.36

x = 3.36/2 = $1.68

y = 5.04 - x = 5.04 - 1.68 = $3.36

blueberries cost $3.36 per pound.

The tangent of an angle is the ratio of perpendicular to the base. The angle will the guy wire makes with the ground will be 80.91°.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

A tower, 50 feet high, is secured with a guy wire anchored 8 feet from the base of the tower.

The angle will the guy wire makes with the ground will be given by the tangent.

The tangent of an angle is the ratio of perpendicular to the base.

Then we have

tan θ = 50/8

tan θ = 6.25

     θ = tan ⁻¹ (6.25)

     θ = 80.9097

     θ ≅ 80.91°

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A function on a graph to figure it out you can do the line test where you draw a line through the graph and if the line touches two points its not a function. With this in mind bottom right is for sure one and the top left looks like one but i cant really tell...

Step-by-step explanation:

Answer:

In two spins, there are 9 possible outcomes:  AA, AB, AC, BA, BB, BC, CA, CB, CCIf we assume each of these is equally likely, then the probability of AB or BA is ...  2/9

Step-by-step explanation:

The probability that a student has a dog given that they do not have a cat is 1/14.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

In a class of 28 students, 21 have a cat and 9 have a dog.

There are 7 students who have a cat and a dog.

The probability that a student has a dog given that they do not have a cat

= 2/ 28

= 1/14

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