Part 1 - Application
If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of the central
angle associated with the arc? Use 3.14 for It. Give your answer in degrees and radians (approximate to two
decimals and exact).

Answer:

Step-by-step explanation:

We'll look for an equation with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0.

A line parallel to y=3x+6 will have the same slope, 3.

We can write y=3x+b.  Any value of b can be used to generate a parallel line.  

If we want that line to go through a specific point, such as (0,-2), we need to find a value of b that shifts the line so that it includes (0,-2).  This can be done by using that point in the equation y=3x+b:

y=3x+b

-2=3*(0)+b  for point (0,-2)

b = -2

The equation becomes y=3x-2

See the attached plot.

===========================

Do that same thing for the remaining two points.  

For B:  (2,5) The equation is y=3x-1

For C:   (4,1) The equation is y=3x-11

The correct answer is option D which is No because one x-value corresponds to two different y-values.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

We can see from the table that the value of x at 5 is giving two different values of y that is 2 and 3. For a function, it is not possible to have two different outputs for the same input.

Therefore the correct answer is option D which is No because one x-value corresponds to two different y-values.

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x = 6(√2)

Step 1:

Say, 6 is perpendicular and x is the hypotenuse.

Step 2:

As we know sine is the ratio of perpendicular and hypotenuse.

∴ [tex]sin 45 = \frac{perpendicular}{hypotenuse}=\frac{6}{x}[/tex] ......................................(1)

Step 3:

As we know, sin45 = 1/√2

∴ put the value in equation 1

⇒ [tex]\frac{1}{\sqrt{2}} = \frac{6}{x}[/tex]

By solving the above equation, we get,

x = 6(√2)

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Answer: B

[tex]f(x) = 7x-2[/tex] and        [tex]g(x) = \frac{x+2}{7}[/tex]

How to solve:

check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)

f[g(x)] = x

g[f(x)] = x

Step-by-step explanation:

Checking A.

[tex]f(x) = \frac{5}{x} -2[/tex]

[tex]g(x) = \frac{x+2}{5}[/tex]

[tex]f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2[/tex]

This does not equal x, so we know these are not inverses

Checking B.

[tex]f(x) = 7x-2[/tex]

[tex]g(x) = \frac{x+2}{7}[/tex]

[tex]f(g(x)) = f(\frac{x+2}{7} ) = 7(\frac{x+2}{7}) - 2 = x+2-2 = x[/tex]

[tex]g(f(x)) = g(7x-2) = \frac{7x-2 + 2}{7} = \frac{7x}{7} = x[/tex]

since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.

Answer:

term to term rule. • a rule that defines the value of each term in a sequence. if the previous terms are known, e.g. the Fibonacci sequence. xn = xn-1 + xn-1.

Step-by-step explanation:

To work out the term to term rule, give the first term and then the pattern. The first term is 17, and the pattern is to subtract 3 each time, so the term to term rule is 'start at 17 and subtract 3'. The next two terms of the sequence are 5 and 2, giving the sequence as: Question.

Answer: 3/20

Step-by-step explanation:

Probability of drawing a blueball from Urn I is

PI=66+4=610

Probability of drawing a blue ball from Urn II is

PII=22+6=28

Probability that both balls are blue

P=PI⋅PII=610⋅28=320

Answer:

8+3+7=18

probability of brown m&m is

[tex] \frac{3 }{18 } [/tex]

[tex]\dfrac{2x^3+4x^2 -x+8}{x^2 +3x+2}\\\\\\=\dfrac{2x^3+6x^2+4x-2x^2-6x-4+x+12}{}\\\\=\dfrac{2x(x^2 +3x+2)-2(x^2 +3x+2)+x+12}{x^2 +3x+2}\\\\\\=\dfrac{2x(x^2+3x+2)}{x^2 +3x +2 }- \dfrac{2(x^2 +3x +2)}{x^2 +3x +2 } + \dfrac{x+12}{x^2 +3x+2}\\\\\\=2x-2 + \dfrac{x+2}{x^2 +3x +2}\\\\\\=2x-2 + \dfrac{x+12}{x^2 +2x +x +2}\\\\\\=2x-2 + \dfrac{x+12}{x(x+2) + x+2}\\\\\\=2x-2 + \dfrac{x+12}{(x+1)(x+2)}\\[/tex]

Answer:

5 units

Step-by-step explanation:

Use Pythagorean Theorem

x = 4 units     y = 3 units

4^2 + 3^2 = L^2

16 + 9 = L^2

L = 5

Answer:

5 units

Step-by-step explanation:

By the Pythagorean theorem:

c² = a² + b²

c = length of the line

a = 4

b = 3

Then:

c² = 4² + 3²

c² = 16 + 9

c² = 25

√c² = √25

c = 5

Answer:

QR = 3

Step-by-step explanation:

given that Q is on the segment PR , then

PQ + QR = PR ( substitute values )

16 + QR = 19 ( subtract 16 from both sides )

QR = 3

The calculated length of the segment QR is 3 units

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

Point Q is on line segment PR

PQ = 16 and PR = 19

using the above as a guide, we have the following:

PQ + QR = PR

substitute the known values in the above equation, so, we have the following representation

16 + QR = 19

So, we have

QR = 19 - 16

Evaluate

QR = 3

Hence. the length of the segment QR is 3

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Answer:

make it more clear its not clear enough to understand the question

Answer:

Step-by-step explanation:

equation of The line L : y = -(1/2)x + 6

A(8 , b) ∈ L  then b = -(1/2)(8) +6 then b = -4 + 6 = 2

Therefore ,

A(8 , 2)

AB = 2

CD = 6

BC = 8

…………………………………………

Area of the trapezoid ABCD

= (CB÷2)×(AB + CD)

= (8÷2)×(6+2)

= 32

The number of months when the gyms cost the same is 5 months.

Total cost of joining the gym = registration fee + (cost per month x number of months)

When the gyms costs are the same, the two above equations would be equal to each other:

50 + 20m = 70 + 10m

20m - 10m = 70 - 20

10m = 50

m = 50 / 10

m = 5

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Answer:

547.40

Step-by-step explanation:

476*15%

15 percent *476

= (15/100)*476

= (15*476)/100

= 7140/100 = 71.40

71.40 + 476 = 547.40 as original price

Answer: 95 cm³

Step-by-step explanation: To find the volume of any prism, you have to multiply the base × width × height.

In this case, this 3D shape is split into 2 parts.

The first part's dimensions are 8×5×2. So the volume is 80 cm³.

The second part's dimensions are 1×3×5. So the volume is 15 cm³.

Finally, you add both volumes together, and the final answer is 95 cm³.

Answer:

s=0.20p

Step-by-step explanation:

20% off an product means to subtract 20% of the original price from the original price.

Based on the amount being deposited into the account each month, and the interest, the account will triple in value on 25 months..

First find the value of the account when tripled:

= 1,000 x 3

= $3,000

We can then use a spreadsheet to find the number of periods it will take to triple.

Convert the interest to a monthly figure as:

= 3.15% / 12

= 0.2625%

When you put the figures into the spreadsheet as shown, the number of months would be 25 months.

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The correct answer is option E which is Cos ( 70 ) = [tex]\dfrac{LN}{8}[/tex].

The complete question is attached with the answer below:-

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

As we can see from the figure that ∠L = 70 and ∠M = 20 We can see that the length LN will be calculated as:-

Cos 70 = Base / Hypotenuse

So for an angle of 70, the base is LN and the hypotenuse is equal to 8 units.

Cos 70 = LN = 8

Therefore the correct answer is option E which is Cos ( 70 ) = [tex]\dfrac{LN}{8}[/tex].

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Answer:

A & E

Step-by-step explanation:

Jus took it on edge

The relationship between the number of tickets is that Hannah sold three times as many tickets as Andrea.

From the question, we have:

Andrea = h

Hannah = 3h

This means that:

Hannah = 3 * Andrea

So, the relationship is that Hannah sold three times as many tickets as Andrea.

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The value of a is 1/4 and the value of h and k is (2,-7/4)

A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.

(x-h)² = 4a(y-k)

It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).

Therefore
(x -2)² = 4a(y +2)

The parabola passes through the point (3,-1)

(3-2)² = 4*a(-1+2)

1 = 4 a

a = 1/4

Now to determine the value of focus point , (h,k)

(h = 2)

k = - 2 +1/4 = -7/4

Therefore The value of a is 1/4 and the value of h and k is (2,-7/4)

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Answer:

= x + 5

Step-by-step explanation:

(4x+1) - (3x-4)

= (4x+1) -3x + 4

= 4x - 3x + 1 + 4

= x + 5

A. Distance between A and B is: 5 units.

B. Triangle ABC is not an equilateral triangle because only two of its sides are equal.

An equilateral triangle has three sides that have the same length.

Given the vertices with their coordinate points as:

A (-3, 2)

B (-6, -2)

C (0, -2)

Use the distance formula, [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB, BC, and AC:

AB = √[(−6−(−3))² + (−2−2)²]

AB = √25

AB = 5 units

BC = √[(−6−0)² + (−2−(−2))²]

BC = √36

BC = 6 units

AC = √[(−3−0)² + (2−(−2))²]

AC = 25

AC = 5 units

Only two of the sides of the triangle, AB and AC, are equal. Therefore, it is not an equilateral triangle.

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The slope of the line is 745, the y-intercept of the line is 500 and the equation of the line is y = 745x + 500

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]

We have points on the graph:

(2, 1990) (5, 4225) (9, 7205)

The slope can be found using two points:

[tex]\rm m =\dfrac{4225-1990}{5-2}\\[/tex]

m = 745

The line can be written as:

y = mx + c

y = 745x + c

Plug point (2, 1990)

1990 = 745x + c

1990 = 745(2) + c

c = 500

y = 745x + 500

The pace of increase in money per month is represented by the slope.

Every month, the sum increases by $745.

The initial quantity of money when the business opened is represented by the y-intercept.

The company began with a $500 investment.

Thus, the slope of the line is 745, the y-intercept of the line is 500 and the equation of the line is y = 745x + 500

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Answer:

  D.  20 m

Step-by-step explanation:

The potential energy at Point B will be the sum of the potential and kinetic energies at point A.

__

For mass M, the potential energy at h meters above a rest height is ...

  PE = Mgh

The kinetic energy of mass M with velocity v is ...

  KE = 1/2Mv²

A pendulum with mass M launched downward at v = 14 m/s will have a total energy of ...

  PE +KE = M(9.8 m/s²)(10 m) +1/2(M)(14 m/s)² = M(98 +98) = 196M J/kg

When the pendulum comes to rest at point B, its energy will all have been converted to potential energy. Then the height at point B is given by ...

  PE = Mgh

  196M J/kg = M(9.8 m/s²)h

  h = (196M)/(9.8M) m = 20 m

The height of the mass at point B will be 20 meters.

Answer:

b=204

Step-by-step explanation:

The law of sine states that: [tex]\frac{SinA}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]

We know that a triangle has 180° total, so we can subtract the two angle measures we know to find the third angle: [tex]180-90-41=49[/tex]°.

Using these two things, we can come up with the equality [tex]\frac{Sin90^{o} }{270} =\frac{Sin49^o}{b}[/tex], which we can use to solve for side b.

[tex]\frac{Sin90^o}{270} =\frac{1}{270}[/tex], so we know that [tex]\frac{1}{270} =\frac{Sin49^o}{b}[/tex].

Next, we would multiply both sides by b to get [tex]\frac{1}{270}b=Sin49^o[/tex].

Sin49°≈0.75471, so to find b we would multiply 0.75471×270=203.77

Since the problem asks us to round to the nearest whole number, b=204

Hope this helps! :)

Answer:

Step-by-step explanation

2 * [3 * (16 + 1)] - 8 =

2 * [3 * 17] - 8 =

2 * 51 - 8

102 - 8 =

94

..:

[tex]12 {x}^{3} y - 18x {y}^{2} \\ [/tex]

Factor out 6xy:

[tex]\boxed{(6xy)(2 {x}^{2} - 3y)} [/tex]

(which is the maximum you could get(atleast in this problem))

Answer:

a, b, d, e

maybe c

Step-by-step explanation: