[tex]if \: x = 1 - \sin( \alpha ) \: and \: y = 1 + \cos( \alpha ) \\ [/tex]
Express y in terms of x and alpha only
​

Answer:

x = 4.9

Step-by-step explanation:

We can use the intersecting chords formula:

(segment piece) x (segment piece) =    (segment piece) x (segment piece)

7*7 = 10x

49 = 10x

Divide each side by 10

49/10=10x/10

4.9 = x

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The area of a shape is the amount of space, the shape can occupy. The equation to calculate the value of x is: [tex](e)\ x^2 + 11x -42= 0[/tex]

The space on the border is given as:

[tex]Top = 2[/tex]

[tex]Others = 3[/tex]

So, the dimension of the sheet of paper is:

[tex]Length = x + 2 + 3[/tex]

[tex]Length = x + 5[/tex]

[tex]Width = x + 3 + 3[/tex]

[tex]Width = x + 6[/tex]

The area of the sheet is then calculated as follows:

[tex]Area= Length \times Width[/tex]

[tex]Area= (x + 5) \times (x + 6)[/tex]

Open brackets

[tex]Area= x^2 + 5x + 6x + 30[/tex]

[tex]Area= x^2 + 11x + 30[/tex]

From the question, we understand that the area of the sheet is [tex]72cm^2[/tex]

So, the equation becomes

[tex]x^2 + 11x + 30 = 72[/tex]

Subtract 72 from both sides

[tex]x^2 + 11x + 30 -72= 0[/tex]

[tex]x^2 + 11x -42= 0[/tex]

Hence,

[tex](e)\ x^2 + 11x -42= 0[/tex] can be used to calculate the value of x

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Answer:

D. P(10|blue)

Step-by-step explanation:

Answer:

P(blue|10)

Step-by-step explanation:

Let A = "number is 10" and let B = "blue paper."

Given:

The function is:

[tex]y=x+2[/tex]

To find:

The inverse of the given function.

[tex]y=x+2[/tex]

Solution:

We have,

[tex]y=x+2[/tex]

Step 1: Interchange x and y.

[tex]x=y+2[/tex]

Step 2: Solve to y.

[tex]x-2=y[/tex]

[tex]y=x-2[/tex]

Therefore, the inverse of the given function is [tex]y=x-2[/tex].

Answer:

Step-by-step explanation:

The amounts of goo after each hour are given as follows:

The time that it takes for the goo to return to original size is given as follows:

n hours, for which:

[tex](2)^n(0.25)^n = 1[/tex]

An increasing exponential function is defined as follows:

y = a(1 + r)^x.

For which the parameters are given as follows:

Her sample is of 10 grams, and the amopunt of goo increases by 100%, hence the parameter values' are given as follows:

a = 10, r = 1.

Thus the exponential function is defined as follows:

y = 10(2)^n.

Then the amounts are given as follows:

A decreasing exponential function is given as follows:

y = a(1 - r)^x.

The goo shrinks by 75% every hour, hence:

r = 0.75.

The amount after n hours is of 10(2)^n, hence the shrinking function is given as follows:

[tex]y = 10(2)^n(0.25)^n[/tex]

It returns to the original amount when:

y = 10.

Hence:

[tex]10 = 10(2)^n(0.25)^n[/tex]

[tex](2)^n(0.25)^n = 1[/tex]

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Answer:

-3

Step-by-step explanation:

i hope this helps

draw a small table with x and y

whenever x is 1 y becomes 14

using y=mx + c

y= 12(1) + 2

12×1=12

12+2=14

therefore x is 1

Answer:

x=0

Step-by-step explanation:

[tex]16^{x^2}=8^0\\\\16^{x^2}=1\\\\x^2\ln(16)=0\\\\x^2=0\\\\x=0[/tex]

Answer:

Step-by-step explanation:

Formula

t = 1.06 * p

Givens

p = 8.5

Solution

t = 1.06 * 8.5

t = 9.01

Answer:

The 4th one

Step-by-step explanation:

Right on edge!

The  answer is distance from P to l. is equal to square root of 2

Line I contains points (0, -3) and (7,4). Point P has coordinates (4,3)

Find the slope of line l we have the points (0, -3) and (7,4)

m=(4+3)/(7-0) m=7/7 m=1

Find the equation of the line perpendicular to the line l that passes through the point P

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1, the slope of the perpendicular line is

m=-1 .Find the equation in point slope form

y-y1=m(x-x1)

(x1,y1)=P(4,3)

substitute

y-3=-1(x-4)

y-3=-x+4

y=-x+7

m=1 (see the step 1)

and we have the point (0,-3) -----> y-intercept

so the equation of the line l is

y=x-3

Find the intersection point line l and its perpendicular line

y=x-3 ------> equation A

y=-x+7 -----> equation B

solve the system of equations

Adds equation A and equation B

2y=-3+7

2y=4

y=2

substitute in equation A

2=x-3 x=2+3 x=5

the intersection point is (5,2)

Find the distance between point (5,2) and point P(4,3)

Remember that, this distance is the distance from P to l.

the formula to calculate the distance between two points is equal to

we have

(x1,y1)=(5,2)

(x2,y2)=(4,3)

substitute in the formula

therefore

The  answer is distance from P to l. is equal to square root of 2

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Answer:

Step-by-step explanation:

We know that:

So the value of the expression is:

Answer:

75°

Step-by-step explanation:

Recall the common trigonometric angles:

  [tex]\sin 30^{\circ}=\dfrac{1}{2}[/tex]

  [tex]\tan 45^{\circ}=1[/tex]

Arcsin is the inverse of sin.

Arctan is the inverse of tan.

[tex]\implies \arcsin \left(\dfrac{1}{2}\right)=30^{\circ}[/tex]

[tex]\implies \arctan (1) = 45^{\circ}[/tex]

Therefore:

[tex]\implies \arcsin \left(\dfrac{1}{2}\right)+\arctan (1) = 30^{\circ}+ 45^{\circ}=75^{\circ}[/tex]

Answer: 125y³

To rise a product to a power, rise each factor to that power:

(5y)³ = 5³y³ = 125y³

According to the question the angle between right angle triangle hence the   M∠1 = [tex]90^{0}[/tex] .

90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°.

Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees (they are complementary).

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A function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

A relation is a function if it has only One y-value for each x-value.

Given a a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45

and that g(0) = -2 and g(-9) = 6,

x=-20 then g(-20)=-5

x=-19 then g(-19)=-4

x=-18 then g(-18)=-3

x=-17 then g(-17)=-2

x=-16 then g(-16)=-1

x=-15 then g(-15)=0

x=0 then g(0)=-2

x=-9 then g(-9)=6

By observing this we can say that as x values are decreasing the function values are increasing and vice versa

So option D is correct

Hence, a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

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Answer:  -7/5

Step-by-step explanation:

Answer:

transmission   absorption

Step-by-step explanation:

This is because the sound of the foot striking the floor is being transmitted through the air. The sun's light is absorbed when it strikes the sidewalk.

What is absorption and transmission?

Absorption is the process or action by which one thing absorbs or is absorbed by another.

The act of sending something, such as a cold or a message, or the component of a machine that transfers power from the engine to the moving parts is known as transmission.

Because of the air pressure, people can hear when their foot strikes the ground. In a similar manner, when sunlight strikes a sidewalk, it warms up as a result of absorbing the heat.

Therefore, the first statement is transmission and second statement is absorption.

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The number of sheets of stickers that Kyle needs will be 7 sheets.

The equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

From the information, Kyle has a notebook for each of his 13 classes. He puts 5 stickers on

each notebook and there are 10 stickers on each sheet.

The number of sheets of stickers that Kyle needs will be:

= (13 × 5) / 10

= 65 / 10.

= 6.5

= 7 approximately

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Answer:

? = -1/2    dark gray box = - 1

y = -1/2 x - 1       or

y = -0.5x - 1

Step-by-step explanation:

The place to start is at 0.

When x = 0 then y = - 1

That means that the second box (the dark gray one) is - 1

So far what you know about the equation is

y = ?x - 1

We need to check two more points.

x =  4

y =  - 3

- 3 = ? 4 - 1             Add 1 to both sides

-3 +1 = ?4 - 1 + 1     Combine   The -1 and + 1 Cancel

-2 = ?4                   Divide by 4

-2/4 = ?

?  = -1/2 or - 0.5

Now we need 1 more point to check the result

Let x = 2. Do we get - 2 for y

y = -1/2 * 2 - 1

y = -1 - 1

y = - 2       just as it should

Answer:108.6

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

V= 5,000(1.035)*

9614 1404 393

Answer:

  31.5 ft

Step-by-step explanation:

The length of the arc is the product of the radius of the circle, 11 ft, and the angle measure in radians. Arc PS has radian measure ...

  (180° -16°)/180°×π = 41π/45

So, the length of arc PS is ...

  s = rθ

  s = (11 ft)(41π/45) = 451π/45 ft

  s ≈ 31.5 ft

Answer:

C

Step-by-step explanation:

The sum of the angles is 90

2x + x = 90

3x = 90

x = 30

the angle ABC is 2x, so it means that is the double of x, so it is 60 degrees

The total cost of the item after the sales tax of 8 % is given by the equation t = 1.08p , where p is the initial price of the item

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost price of the item be represented as t

Let the initial cost price of the item be represented as p

Now , the sales tax percentage = 8 %

So , the equation will be

The total cost price of the item t = sales tax percentage ( initial cost price of the item ) + initial cost price of the item

Substituting the values in the equation , we get

The total cost price of the item t = 8 % ( p ) + p

On simplifying the equation , we get

The total cost price of the item t = ( 8/100 ) p + p

The total cost price of the item t = 0.08p + p

The total cost price of the item t = 1.08p

Hence , the equation is t = 1.08p , where p is the initial price of the item

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