Which trigonometric ratios are correct for triangle ABC? Check all that apply.

-sin(C) =
-cos(B) =
-tan(C) =
-sin(B) =
-tan(B) =

see the attached figure to better understand the problem

we know that the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Let

[tex]A(-3,3)\ B(3,4))\ C(3,-3)[/tex]  

Step 1

Find the distance AB

[tex]A(-3,3)\ B(3,4)[/tex]  

substitute in the formula

[tex]d=\sqrt{(4-3)^{2}+(3+3)^{2}}[/tex]

[tex]d=\sqrt{(1)^{2}+(6)^{2}}[/tex]

[tex]dAB=\sqrt{37}\ units[/tex]

Step 2

Find the distance BC

[tex]B(3,4))\ C(3,-3)[/tex]  

substitute in the formula

[tex]d=\sqrt{(-3-4)^{2}+(3-3)^{2}}[/tex]

[tex]d=\sqrt{(-7)^{2}+(0)^{2}}[/tex]

[tex]dBC=7\ units[/tex]

Step 3

Find the distance AC

[tex]A(-3,3)\ C(3,-3)[/tex]  

substitute in the formula

[tex]d=\sqrt{(-3-3)^{2}+(3+3)^{2}}[/tex]

[tex]d=\sqrt{(-6)^{2}+(6)^{2}}[/tex]

[tex]dAC=\sqrt{72}\ units[/tex]

Step 4

Find the perimeter of the triangle

we know that

the perimeter of the triangle is the sum of the length sides of the triangle

[tex]P=AB+BC+AC[/tex]

substitute the values

[tex]P=\sqrt{37}\ units+7\ units+\sqrt{72}\ units=21.6\ units[/tex]

therefore

the answer is

the perimeter of the triangle is [tex]21.6\ units[/tex]

The argument is valid by the law of detachment.

The statements that are true about the arguments in the question are;

1) Option C; Law of detachment

2) Option B; Law of detachment

1) We are given the premise that;

If two lines are parallel, then the lines do not intersect.

This premise is true because we know from parallel and perpendicular lines property that parallel lines never intersect each other.

With that premise, we are now given a conclusion that; Lines m and n do not intersect.

This kind of condition is known as law of detachment which states that;

If x is true, then y is also true.

Thus, Option C is correct

2) We are given the premise that;

If a quadrilateral is a square, then the quadrilateral has four right angles.

The given premise is true because from the definition of a square, all sides must be equal and all angles must be right angles.

We are now given the conclusion that;

Quadrilateral JKLM has four right angles.

This conclusion is valid because it follows the given premise.

Again like in 1 above, this follows the law of detachment.

Option B is correct

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The velocity function of an object moving along the {x} - axis would be -

v{t} = sin(t) + t³ + 2.

The acceleration at any instant of time is called instantaneous acceleration. Mathematically -

a = dv/dt

dv = a dt

∫dv = ∫a dt

Given is the acceleration function as -

a(t) = 3t² + cos(t)

We know that -

a = dv/dt

dv = a dt

∫dv = ∫a dt

v{t} = ∫{3t² + cos(t)} dt

v(t) = sin(t) + t³ + C

Now -

v(0) = 2

sin(0) + 0 + C = 2

C = 2

So, we can write the velocity function as -

v{t} = sin(t) + t³ + 2

Therefore, the velocity function of an object moving along the {x} - axis would be -

v{t} = sin(t) + t³ + 2.

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Answer:

A is the mofluffin answer

Step-by-step explanation:

(1) the area of a rectangle with vertices at ​ (−6, 3) ​, ​ (−3, 6) ​ , (1, 2) , and (−2, −1)

To find area of rectangle we need to find the length and width

Length = distance between (−6, 3)  and (−2, −1)

Distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

=  [tex]\sqrt{(-2-(-6))^2 + (-1-3)^2}[/tex]

=  [tex]\sqrt{(4)^2 + (-4)^2}[/tex]=[tex]\sqrt{(16) + 16}[/tex] =[tex]\sqrt{32}[/tex]

width = Distance between (−6, 3) ​, ​ (−3, 6)

Distance = [tex]\sqrt{(-3-(-6))^2 + (6-3)^2}[/tex]

=[tex]\sqrt{3^2+3^2}= \sqrt{18}[/tex]

Area = Length * width = [tex]\sqrt{32} *\sqrt{18} = \sqrt{576}= 24[/tex]

(2)  the area of a triangle with vertices at (0, −2) , ​ (8, −2) ​ , and ​ (9, 1) ​

Area of triangle = [tex]\frac{1}{2} * base * height[/tex]

base  is the distance between (0,-2) and (8,-2)

Distance =  [tex]\sqrt{(8-0)^2 + (-2-(-2))^2}[/tex] = 8

To find out height we take two vertices (8,-2) and (9,1)

Height is the change in y values = 1- (-2) = 3

base = 8  and height = 3

So area of triangle = [tex]\frac{1}{2} * 8 * 3 = 12[/tex]

(3) the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 4) ​, (2, 7) , ​ (6, 4) ​, and (6, 1) ​

To find perimeter we add  the length of all the sides

Distance between (−2, 1)  and (−2, 4) = [tex]\sqrt{(-2+2)^2 + (4-1)^2}[/tex]= 3

Distance between(−2, 4) ​and (2, 7) = [tex]\sqrt{(2+2)^2 + (7-4)^2}[/tex]= 5

Distance between (2, 7)  and (6, 4) = [tex]\sqrt{(6 - 2)^2 + (4-7)^2}[/tex]= 5

Distance between (6, 4) ​ and (6, 1) ​= [tex]\sqrt{(6 - 6)^2 + (1-4)^2}[/tex]= 3

Distance between  (6, 1) and (−2, 1) ​= [tex]\sqrt{(-2-6)^2 + (1-1)^2}[/tex]= 8

Perimeter = 3 + 5 + 5 + 3 + 8 = 24

(4) four coordinates are (-7,-1) (-6,4) (3,-3) and (4,2)

Length = Distance between  (3,-3) and (4,2) ​= [tex]\sqrt{(4-3)^2 + (2+3)^2}[/tex]= [tex]\sqrt{26}[/tex]

Width = Distance between (-6,4) and (4,2) ​= [tex]\sqrt{(4+6)^2 + (2-4)^2}[/tex]= [tex]\sqrt{104}[/tex]

Perimeter = 2(lenght + width) = 2*( [tex]\sqrt{26}[/tex]+[tex]\sqrt{104}[/tex] )

= 30.6 units

The area of the rectangle is [tex]24\;square\;units[/tex].

1. According to the question, the vertices of the rectagle are at ​ [tex](-6, 3) ;(-3, 6) ;(1, 2)[/tex] , and [tex](-2, -1)[/tex].

The distance between two vertices on the coordinate plane is

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

So,

[tex]Length=D_1\\D_1=\sqrt{(6-3)^2+(-3+6)^2}\\D_1=\sqrt{9+9}\\D_1=3\sqrt 2 units[/tex]

Similarly,

[tex]Width=D_2\\D_2=\sqrt{(-2+6)^2+(-1-3)^2}\\D_2=\sqrt{16+16}\\D_2=16\sqrt 2\;units[/tex]

The area of the rectangle is equals to product of length and width of the rectabgle.

So,

[tex]Area=length\times width\\Area=3\sqrt{2}\times 4\sqrt{2}\\Area=24\;square\;units[/tex]

Hence, the area of the rectangle is [tex]24\;square\;units[/tex].

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Answer: y = 3x - 2

Step-by-step explanation:

Equation of a straight line is

y=mx + c

m is the slope and c is the intercept

comparing it with the equation

y=3x - 2

m = slope =3

and c= intercept= -2

Answer:

B

Step-by-step explanation:

edge

To make m the subject of the equation x-2m=p, add 2m to both sides, subtract p, and divide by 2. The result is m as the subject of the equation, represented as the fraction (x - p)/2.

To solve the equation x-2m=p for m as the subject, we want to isolate m on one side of the equation. Here is the step-by-step process:

Now m is the subject of the equation, and it is represented as a fraction as requested.

Answer:

The endpoints of the line segment lie on each other

Explanation

To understand the question, follow the practical steps below

1. Take a sheet of plane paper

2. Label the edges of the top of the paper A and B

3. Fold the paper in such a way that edge A lies on B.

You'll notice the following;

1. The top of the paper lies in itself; hence, we can say that the line segment lies on itself

2. You have a new line at the centre of the paper. The point at the top of this center line is the midpoint of the line segment

3. The edges that lie on each other translates to the endpoints lying on each other.

Number (3) above is the required observation and the right answer.

Answer:

0.34 miles per minute

Step-by-step explanation:

We have to convert 30 feet per second to miles per minute.

1 minute = 60 seconds

Therefore, in one minute = 60 × 30 = 1800 feet

5280 feet = 1 mile

180 feet =  [tex]\frac{1800}{5280}[/tex]

              = 0.3409 ≈ 0.34 mile

Therefore, 0.34 mile per minute.

The measure of the vertex angle is 72 degrees

The sum of the interior angle of a triangle is 180 degrees. Of the base angles are equal hence;

54 + 54 + x = 180

where

x is the vertex angles

Simplify

108 + x = 180

x = 180 - 108

x = 72 degrees

Hence the measure of the vertex angle is 72 degrees

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The reason for each step in the solution of the inequality must be mathematical operations such as;  the distributive property

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.

We have given that -2(x + 3) - 4 > 4x + 30

First, apply the distributive property

-2x - 6 - 4 > 4x + 30

Now combine like terms;

-2x - 10 > 4x + 30

Then subtraction property

-6x - 10 > 30

The addition property

-6x > 40

The division property

x < -20/3

Hence, we get the answer equal to x < -20/3.

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Final answer:

To find the total cost of the game based on Yolanda's savings of $30, which is five-sixths of the cost, multiply $30 by the reciprocal of 5/6, resulting in a total cost of $36.

Explanation:

The question asks how much a game would cost if Yolanda has already saved $30, which is five-sixths of the total cost of the game. To find the total cost of the game, we consider the amount saved ($30) as five-sixths of the total cost (which we'll call x).

So the equation to solve is 5/6 * x = $30. To find x, we divide $30 by 5/6, which is the same as multiplying $30 by the reciprocal of 5/6 (which is 6/5). Therefore, x = $30 * (6/5) = $36. Thus, the total cost of the game is $36.

The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is determined in the following steps given below.

[tex]\rm Probability=\dfrac{10}{3}\times \left (\dfrac{1}{3} \right ) ^3\times \left (\dfrac{5}{6} \right ) ^7\\\\Probability= \dfrac{10}{3}\times \dfrac{1}{27} \times \dfrac{78125}{279936}\\\\Probability=0.034[/tex]

Hence, the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.

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To solve this problem, we use the formula for binomial probability:

P = [n! / (n – r)! r!] p^r * q^(n – r)

where,

n = total number of adults = 4

r = number of adults who believe in reincarnation = 3

p = chance of believing in reincarnation = 50% = 0.50

q = 1 – p = 0.50

P = [4! / (4 – 3)! 3!] 0.50^3 * 0.50^(4 – 3)

P = 0.25 = 25%

Answer:

Answer is 0.096

Step-by-step explanation:

Here 44 adults are randomly selected.

Each adult selected is independent of the other to believe in reincarnation.

Also there are only two outcomes, probability for success in each trial = 0.50

Hence X no of adults who believe in reincarnation is binomial with n =50 and p = 0.50

[tex]a) P(X=23) = 50C23 (0.5)^{50} =0.096[/tex]

Working notes:

50C23 =108043253365600

0.5^50) = 8.8178x10^(-14)

Simplifying we get answer as 0.096

An equation is formed when two equal expressions. The number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that you are choosing between two plans at a discount warehouse.

The cost for x number of merchandise under plan A, which offers an annual membership fee of $120 and you pay 80% of the manufacturer's. Therefore, the cost will be,

Cost = 120 + 0.8x

The cost for x number of merchandise under plan B, which offers an annual membership fee of $40 and you pay 90% of the manufacturer's recommended list price. Therefore, the cost will be,

Cost = 40 + 0.9x

Now, in order to find the number of merchandise that you would have to purchase in a year to pay the same amount under both plans, you need to equate the two equations together. Therefore,

Cost from Plan A = Cost from Plan B

120 + 0.8x = 40 + 0.9x

120 - 40 = 0.9x - 0.8x

80 = 0.1x

x = 80 / 0.1

x = 800

Hence, the number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.

Further, the cost for each plan for 800 merchandise can be written as,

PlanA,

Cost = 120 + 0.8(800)

        = $760

Plan B,

Cost = 40 + 0.9(800)

        = $760

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Answer:

Option b , c and d are the part of the expression .

Step-by-step explanation:

We are given that the number of pages she has left to read is 276 - 35d

d represents the number of days she has been reading.

276 denotes the total number of pages

35 pages denotes the number of pages read per day

35 d represents the number of pages she has read during d days

276 - 35d represents teh reamining pages

So, Option b , c and d are the part of the expression .