The area of the circle

[tex] {2x}^{3} + 4 {x}^{2} + 8x \\ \\ 2x( {x}^{2} + 2x + 4)[/tex]

The tan θ and cos θ values of 17π/12 are illustrations of trigonometry ratios

The values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively

We have:

θ = 17π/12

Express as sum

θ = 9π/12 + 8π/12

Simplify

θ = 3π/4 + 2π/3

The above becomes

tan(17π/12) = tan(3π/4 + 2π/3)

Using the sum formula, we have:

tan(A + B) = [tan(A) + tan(B)]/[1 - tan(A)tan(B)]

Substitute known values

tan(3π/4 + 2π/3) = [tan(3π/4) + tan(2π/3)]/[1 - tan(3π/4)tan(2π/3)]

Evaluate the expression

tan(3π/4 + 2π/3) = [-1 - √3]/[1 - (-1)(-√3)]

Evaluate the product

tan(3π/4 + 2π/3) = [-1 - √3]/[1 - √3]

Rationalize

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-1 - \sqrt3}{1 - \sqrt3} * \frac{1 + \sqrt3}{1 + \sqrt3}[/tex]

Evaluate the product

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + \sqrt3)^2}{1 - 3}[/tex]

This gives

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + 3 + 2\sqrt 3)}{-2}[/tex]

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(4 + 2\sqrt 3)}{-2}[/tex]

Divide

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = 2 + \sqrt 3[/tex]

So, we have:

tan(17π/12) = 2 + √3

We have:

θ = 17π/12

Express as difference

θ = 9π/4 - 5π/6

The above becomes

cos(17π/12) = cos(9π/4 - 5π/6)

Using the difference formula, we have:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

So, we have

cos(17π/12) = cos(9π/4)cos(5π/6) + sin(9π/4)sin(5π/6)

Evaluate

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} * - \frac{\sqrt 3}{2} + \frac{\sqrt 2}{2} * \frac 12[/tex]

Evaluate

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (- \frac{\sqrt 3}{2} + \frac 12)[/tex]

Evaluate the difference

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (\frac{1 - \sqrt 3}{2})[/tex]

Expand

cos(17π/12) = (√2 - √6)/4

Hence, the values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively

Read more about trigonometry ratios at:

https://brainly.com/question/11967894

Hope you enjoy  :)))))))

Step-by-step explanation:

pizza = circle

the area of a circle is

pi×r²

r = radius (half of diameter), in our case 15/2 = 7.5 in.

the total area of the whole pizza (circle) is

pi×7.5² = 56.25×pi = 176.7145868... in²

it is cut into 12 slices. Carson eats 5 of these 12 slices.

that means he eats 5/12 of the whole area :

176.7145868... × 5/12 = 73.63107782... in²

Answer:

[tex]y-7=\frac{4}{3} (x+3)[/tex]

Step-by-step explanation:

Hi there!

We are given the point (-3, 7)

We want to write the equation of the line containing that point, in point slope-form, and that is also parallel to 4x-3y=7

Parallel lines contain the same slope

So first, let's find the slope of 4x-3y=7

To do that, we can convert the line from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope, and b is the y intercept)

To do that, we need to isolate y on one side

So start by subtracting 4x from both sides

4x-3y=7

-4x      -4x

________________

-3y=-4x+7

Divide both sides by -3

y=[tex]\frac{4}{3}x[/tex]- [tex]\frac{7}{3}[/tex]

Since 4/3 is in the place of where m should be, the slope of the line is 4/3

It is also the slope of our new line, which we are trying to find

As stated earlier, we want to write this line in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point

This is where the point we were given earlier comes in. We simply need to substitute our values (of the point and the slope) into the formula to find the equation.

First, with the slope; substitute 4/3 as m in the equation

[tex]y-y_1=\frac{4}{3} (x-x_1)[/tex]

Now substitute -3 as [tex]x_1[/tex] in the equation

[tex]y-y_1=\frac{4}{3} (x--3)[/tex]

We can simplify this to:

[tex]y-y_1=\frac{4}{3} (x+3)[/tex]
Now substitute 7 as [tex]y_1[/tex] into the equation

[tex]y-7=\frac{4}{3} (x+3)[/tex]

Hope this helps!

Answer:

-18

Step-by-step explanation:

Simplify: |3 – 10| – (12 / 4 + 2)^2

[tex]|3 - 10| - (\frac{12}{4} + 2)^2\\\\|-7|-(\frac{12}{4} + 2)^2 < == absolute\ numbers\ are\ always\ positive\\\\7-(3+2)^2 < ==add\ numbers\ in\ parenthesis\\\\7-5^2 < ==square\ the\ number\ (5)\\\\7-25 < ==add\ numbers\\\\-18 < ==final\ answer[/tex]

Hope this helps!

Answer:

simplify the matrix:

36,−32,−18,3,−6

Answer:

  7. inverse relationship; equation: y = 16/x

  8. no relationship; no equation

Step-by-step explanation:

The attachment shows the support for the conclusions. The relationship can be chosen from those offered by looking at differences, ratios, or products of y-values for sequential x-values.

__

In the first problem, we note that the relationship between y-values varies inversely as the relationship between x-values: when x goes up by a factor of (n+1)/n, the value of y goes down by its inverse factor: n/(n+1). That same relationship is observed by noting that the product of x and y is a constant, 16.

 relationship: inverse

  y = 16/x

__

As we looked at the table, we thought this might be an exponential function. Each y-value seemed to be twice the one before—until we got to x=5. As x went from 4 to 5, the y-value increased by a factor of 16, not 2. This means there is no simple relationship between x and y, and no simple equation that will describe the sequence of y-values.

Answer:

Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.

Inverse relationship:  the value of one variable decreases as the value of the other variable increases.

Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)

Question 7

As the x-value increases (by one unit), the y-value decreases.

Therefore, this is an inverse relationship.

The y-values are calculated by dividing 16 by the x-value.

[tex]\sf y=\dfrac{16}{x}[/tex]

Question 8

As the x-value increases, the y-value increases.  

The y-value increases by a factor of 2 for each x-value increase of 1 unit from 1 ≤ x ≤ 4 and 5 ≤ x ≤ 6.

[tex]\sf y=2^x \ for \ 1\leq x\leq 4[/tex]

[tex]\sf y=2^{(x+3)} \ for \ 5\leq x \leq 6[/tex]

These are separate exponential relations for restricted domains.

So there doesn't appear to be one relationship for a non-restricted domain.

Answer:

The aswer is 88

Step-by-step explanation:

Hope this helps

Answer: 208

Step-by-step explanation:

The number 3536 is called the numerator or dividend, and the number 17 is called the denominator or divisor.

The quotient of 3536 and 17, the ratio of 3536 and 17, as well as the fraction of 3536 and 17 all mean (almost) the same:

3536 divided by 17, often written as 3536/17 = 208

Answer:

The answer is the second option

Step-by-step explanation:

Answer:8x3/5=4.8

Step-by-step explanation:

Answer:

in simple form its 4.8

for a improper fraction its 43/5

I will comment for the mixed number but if this is correct can u mark me brainliest

Answer:

For 3 pounds, 3 ÷ 1/8 = 54

For 7 pounds, 7 ÷ 1/8 = 56

Answer:

the answer is x=15.....

Answer:

Step-by-step explanation:

(5x+30)=7x Subtract 7x from both sides. 5x+30−7x=0 Combine 5x and −7x to get −2x. −2x+30=0 Subtract 30 from both sides. Anything subtracted from zero gives its negation. −2x=−30 Divide both sides by −2. x= −2 −30 ​ Divide −30 by −2 to get 15.                 answer should be x=15

Answer:

B.shapes A and D

Step-by-step explanation:

Cuz if u see very carefully u will see they are cubes (except b) and A and D had one of its side's covered so the answer is simply A and D

Answer:

78.6

Step-by-step explanation:

Area of  circle = Pi*r^2

r=5

for pi use calculator or pi=3.142

area =Pi*r2=(3.142)*5^2=(3.142)*25=78.55 = 78.6 (1 decimal place which is same with tenth)

Answer:

30 degrees

Step-by-step explanation:

inscribed angle angle x encompasses   360 - 120 - 180 = 60 degrees of arc

  this is 2 times the measure if the inscribed angle

 angle B = 30 degrees

Answer:

Answer:

minden new yemilew yihegnaw tiyake

Answer:

Step-by-step explanation:

Answer:

1/13

Step-by-step explanation:

There are 2 red 5's in a standard 52-card deck ( a red 5 of hearts and a red 5 of diamonds ) and then there are 2 black 6's in a 52-card deck ( a black 6 of clubs and a black 6 of spades )

So in total there are 4 cards that we want out of 52.

So the probability of getting a red five or a black six is 4/52 or 1/13

Answer:

Step-by-step explanation:

This is an or question. You can choose either one; both are possible and the smaller probability add.

Red 5: 2/52

There are 26 red cards. 2 of them are 5s (diamonds / hearts). You are still drawing from a complete pack of 52

Black 6: 2 / 52

There are 26 black cards. 2 of them are 6s (Clubs / spades). You are still drawing from a complete pack of 52

2/52 + 2/52 = 4/52

Divide top and bottom by 4

4/4 // 52 /4

1 / 13

Answer: 1/13 or 0.077

16m2 – 24mn + 9n2

((16 • (m2)) - 24mn) + 32n2

(24m2 - 24mn) + 32n2

= (4m - 3n)2

Answer:

The answer is:

B. c¹⁰/d¹⁰

Answer:

Already answered in advance in the comments section

Step-by-step explanation:

Feel free to ask more questions if any!

Answer:

sin(3pi/4)

Step-by-step explanation:

I got it right on edg

Answer:

The answer is letter c

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

23+47