Simplify: (sin θ − cos θ)^2 − (sin θ + cos θ)^2 A) −4sin(θ)cos(θ) B) 2 C) sin^2 θ D) cos^2 θ

Answer:

Step-by-step explanation:

No of people using both gym and pool that is N( gup ) = 25

No of people using both track and pool that is N( tup ) = 30

No of people using both track and gym that is N( tug ) = 17

No of people using all that is N( gutup) = 6

No of people  using two or three facilities

= 25+30+17- 2 x 6

= 60

Total no of people = 125

No of people using only one facility

= 125 - 60

= 65 .

Ratio of people using only one facility

= 65 / 125

.52

Required probability

= .52 .

probability that the person uses exactly one of the facilities

= .52

Answer:208

Step-by-step explanation:

13 x 16 = 208

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Answer:

In this problem, there is multiple choice for every question. The trick is to exclude the answer that unlikely true.

To solve this easier, you need to find the distance of AB first. After that try to match the answer coordinate with the midpoint of AB. 

1.  Answer: Point C(-3.6, -3.4) divides AB in the ratio 2:3

A (-2,-1) and B(-6, -7)The distance between A and B would be:

x= x2-x1 = -6 - (-2)= -4

y= y2-y1 = -7 - (-1)= -6

Since both x and y coordinate of A and B is minus, let's try answer with x and y minus value.

Point C(-3.6, -3.4) divides AB in the ratio 2:3

x3= x1 + AB ratio* AB distance

x3= -2 + (2/2+3)*(-4)= -3.6

y3= y1 + AB ratio* AB distance

y3= -1 + (2/2+3)*(-6)= -1 - 12/5= -3.4

2.  Point C(0, 1) divides AB in the ratio 4:7

A(4,-3) and B(-7,8)

The distance between A and B would be:

x= x2-x1 = -7 - (4)= -11

y= y2-y1 = 8 - (-3)= 11

Since both x and y distance is 11, let's try answer with total ratio 11

Point C(0, 1) divides AB in the ratio 4:7

x3= x1 + AB ratio* AB distance

x3= 4 + (4/4+7)*(-11)= 4- 4=0

y3= y1 + AB ratio* AB distance

y3= -3 + (4/4+7)*(11)= -3 +4= 1

3. Answer: Point C(8, 9) divides AB in the ratio 5:3

A(3,4) and B(11,12)The distance between A and B would be:

x= x2-x1 = 11 - (3)= 8

y= y2-y1 = 12 - (4)= 8

Since both x and y distance is 8, let's try answer with the total ratio 8. Both of x and y also plus, so focus on coordinate with both x and y plus too.

Point C(3.5, -2.5) divides AB in the ratio 1:7-----> total ratio 8,y minus

Point C(-2, 5) divides AB in the ratio 2:6  -----> total ratio 8, x minus

Point C(8, 9) divides AB in the ratio 5:3   -----> total ratio 8, both x and y plus

x3= x1 + AB ratio* AB distance

x3= 3 + (5/5+3)*(8)= 3+ 5=8

y3= y1 + AB ratio* AB distance

y3= 4 + (5/5+3)*(8)= 4 +5= 9

4. Point C(-2, 5) divides AB in the ratio 2:6  

A(-5,2)and B(7, 14)

The distance between A and B would be:

x= x2-x1 = 7 - (-5)= 12

y= y2-y1 = 14 - (2)= 12

Since both x and y distance is 12, it will be hard to use it since 12 has many factors. Both y coordinate is plus, so focus on coordinate with y more than x and plus.

Point C(4, 1.6) divides AB in the ratio 3:2  ----->  x more than y

Point C(-2, 5) divides AB in the ratio 2:6  -------> y plus, y more than xx3= x1 + AB ratio* AB distance

x3= -5 + (2/2+6)*(12)= -5+ 3=-2

y3= y1 + AB ratio* AB distance

y3= 2 + (2/2+6)*(12)= 2 +3= 5

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

This is a parabola.

As the coefficient of x^2 is positive it will open upwards ( shaped like a 'U').

If we convert to vertex form we can find the line of symmetry  and the coordinates of the vertex:

f(x) = 3x^2 - 2x + 1

f(x) = 3(x^2 - 2/3 x) + 1

f(x) = 3[(x - 1/3)^2 - (1/3)^2] + 1

f(x) = 3(x - 1/3)^2 - 1/3 + 1

f(x) = 3(x - 1/3)^2 + 2/3

So the line of symmetry is  x = 1/3 and

the vertex ( the minimum of the curve) is at (1/3, 2/3).

Answer:

B. 8

Step-by-step explanation:

Step 1: Find g(-2)

g(-2) = (-2)² + 1

g(-2) = 4 + 1

g(-2) = 5

Step 2: Find f(5)

f(5) = 2(5) - 2

f(5) = 10 - 2

f(5) = 8

Answer:

x=12

Step-by-step explanation:

Intersecting Chords Formula:

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

10 * x =  ( 3+x) *8

10x = 24+8x

Subtract 8x

10x-8x = 24+8x-8x

2x= 24

Divide by 2

2x/2 =24/2

x = 12

Answer:

the answer you are looking for is the letter B. 33

Answer:

3  CUPS pints

Step-by-step explanation:

Multiple to get it by doing this (1/2) US pint x 3 = 1.5 US pints *2= 3 cups

Answer:

Step-by-step explanation:

Use the Pythagorean theorem to find the altitude.

h^2 = 9^2 - 6.4^2

h^2 = 40.04

h = 6.328

area = base * height/2

area = (2 * 6.4) * 6.328/2

area = 40.5 square units

Answer:

arrow 4

Step-by-step explanation:

The amount of energy needed in the transformation from liquid to gas is equal to the gas to liquid transition.

Boiling is the mechanism by which a substance passes from the liquid phase to the gaseous form.

Like water diagram in phase:

Evaporisation is a method of phase shift in which the water transitions from a liquid to a gas (water vapour).

Condensation is the process of phase shift in which water transitions from a gas to a liquid, and the vapour becomes a cloud.

Answer:

4

Step-by-step explanation:

ya boy did the test

Answer:

9.7 , 310.4

Step-by-step explanation:

length of each side = 64/8=8

using theorem Pythagoras

A²=10.5² – (8/2)²

A=9.7 ft

area of triangle

1/2×8×9.7=38.8

area of octagon

38.8×8=310.4

The Length of the octagon  is 9.7 and the area of octagon is 310.4.

Length of octagon

Length of each side = 64/8

Length of each side =8

Pythagoras theorems

A²=√10.5² – (8/2)²

A²=√110.25 – 16

A²=√94.25

A=9.7 ft

Area of octagon

Area of triangle=1/2×8×9.7

Area of triangle=38.8

Area of octagon=38.8×8

Area of octagon=310.4

Therefore the Length of the octagon  is 9.7 and the area of octagon is 310.4.

Learn more about Length and  area of octagon here:https://brainly.com/question/358118

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Answer:

Hey there!

We have the equation: y2-y1/x2-x1.

So, we have: 8-2/8-6.

6/2, or 3.

Hope this helps!

Answer:

x = 63

Step-by-step explanation:

We can find the value of x by multiplying the difference of large arc to small arc with 1/2

if a = 117° then the large arc would be 243

1/2 × (243 - 117) = 63

Answer:

5x-8

Step-by-step explanation:

Answer:

35cm

Step-by-step explanation:

The net of a regular pentagon has 10 sides.

Since each of the faces are equilateral triangles, the side lengths are equal.

Therefore:

Length of each side of the net = 70/10 =7cm

Therefore, the base is a regular pentagon of side length 7cm.

The perimeter of the base of the pyramid = 5 X 7

=35cm

The perimeter of the base of the pyramid is 35cm.

Answer:

3

Step-by-step explanation:

1/2 is 3 times 1/6, because 3/1  [tex]\frac{3}{1} * \frac{1}{6} = \frac{3}{6}[/tex] and 3/6 is the same as 1/2.  Thus, he can make 3 bowls of granola.

Answer:

Step-by-step explanation:

Q1: <B = 150 °

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

8x-10 = 3x+90

5x=100 (subtract 3 from both sides)

x=20   (divide both sides by 5)

x = 20

<B= 3x +90

<B = 3 (20) +90

<B = 60 + 90

<B = 150

Q2: 62

An angles complement (not compliment, haha) is what the number that added to the angle equals 90°.

An angle is 34 more than its complement.

Let x represent the angle.

Let y represent its complement.

x= 34 +(90-x)

y= (90-x)

x + y = 90

34 + (90-x) + (90-x) =90

x= 62

Check the answer.

x= 34 more than complement.

62-34=28

62+28=90

Checked!

Words of encouragement:

Good luck!

Answer:

x = 76 roses

Step-by-step explanation:

Step 1: Define variables

x = # of roses

y = # of tulips

Step 2: Write systems of equations

x = 4y + 8

5x + 2y = 414

Step 3: Use Substitution

5(4y + 8) + 2y = 414

20y + 40 + 2y = 414

22y = 374

y = 17

Step 4: Plug in y to find x

x = 4(17) + 8

x = 68 + 8

x = 76

Answer:

x = 76

Step-by-step explanation:

x = Roses

y = Tulips

x = 4y + 8

5x + 2y = 414

5(4y + 8) + 2y = 414

20y + 40 + 2y = 414

22y = 374

y = 17

x = 4(17) + 8

x = 68 + 8

x = 76

Complete question:

Dr. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?

Answer:

Here,

Independent variable (IV) is: the color of the light produced by the lamp (red, orange, yellow, green, or blue)

We are also told only 10 participants are available.

All 10 participants are being exposed to all five levels of the color variable in the same order.

Counterbalancing is said to be a technique used when establishing task order. It helps prevent introduction if cofounding variables.

Dr. Lyte will need to use counterbalancing technique in this scenario because some of the participants may be unable to understand difference in similar colours. Example some participants may not be able to differentiate between orange and red when the red colour comes after orange.

But using counterbalancing technique, Dr. Lyte can avoid such an error.

Answer:

2. -3, 1.

3. -2, 0.

4. 6, 8.

5. 20.

Step-by-step explanation:

2. x - 3y + 6 = 0

-3y = -x -6

y = 1/3x + 2

y + 4 = -5/4(x - 1)

y + 4 = -5/4x + 5/4

y = -5/4x + 5/4 - 16/4

y = -5/4x - 11/4

If you sketch these two lines on paper (or draw them on a graphing calculator), you will find that they intersect at (-3, 1).

So, the values you enter on the response would be -3, 1.

3. x + 3y = -2

x = -3y - 2

-3x + 5y = 6

-3(-3y - 2) + 5y = 6

9y + 6 + 5y = 6

14y + 6 = 6

14y = 0

y = 0

x + 3 * 0 = -2

x + 0 = -2

x = -2

-3 * -2 + 5 * 0 = 6

Since everything works out, the solution to the two equations is (-2, 0).

So, the values you enter on the response would be -2, 0.

4. 3x - 4y = -14

2x + 5y = 52

2(3x - 4y = -14)

3(2x + 5y = 52)

6x - 8y = -28

6x + 15y = 156

6x + 15y = 156

-6x + 8y = 28

23y = 184

y = 8

3x - 4 * 8 = -14

3x - 32 = -14

3x = 18

x = 6

2 * 6 + 5 * 8 = 12 + 40 = 52

Everything works out, so your solution is (6, 8).

Your answer will be (6, 8).

5. For a system of equations to have no solution, the y's and the x's must have the same coefficients.

5x - Ky - 10 = 0

y = 1/4x + 6

-Ky = -5x + 10

Ky = 5x - 10

1/5Ky = x - 2

1/20Ky = 1/4x - 1/2

1/20K = 1

K = 20

y = 1/4x - 1/2

y = 1/4x + 6

1/4x - 1/2 = 1/4x + 6

1/4x - 1/4x = 6 + 1/2

0 = 6.5

There is no solution, so K = 20.

Hope this helps!!

If the plane is flying at an altitude of 21,000 feet, it is perpendicular to the observer's horizontal line of sight. Thus, I concluded that the given information be assigned to the attachment below.

Given -

( Observer at point O, plane flying at point P

( Plane at 55° angle to horizontal line of sight, altitude of 21,000 feet

The distance ( x ), is represented by the line segment OP, with which we have to determine the length of. Therefore we can conclude the following -

[tex]Sin( 55 ) = Altitude / Distance,\\Sin( 55 ) = 21,000 / x,\\----------------\\x = \frac{21,000}{Sin( 55 )},\\x = 21,000 / 0.81915204428\\\\x = ( About ) 25636 feet\\[/tex]

As you can see, the distance from the plane to the observer is about 25,636 ft!

Answer:

25,636 feet

Step-by-step explanation:

I took the test on FLVS and got 100%

Answer:

there's only one equation listed, and it has one solution, which is 0

Step-by-step explanation:

Answer: There is only one equation here...

Anyway it's ans is 0

Step-by-step explanation:

Feel pleasure to help u

Answer:

(D) [tex]f^{-1}{(x$) has an x-intercept of (-36, 0).[/tex]

(E)[tex]f^{-1}{(x)[/tex] has a range of all real numbers.

Step-by-step explanation:

Given the function: [tex]f(x)= -\dfrac23x-24[/tex]

[tex]f(x)+24= -\dfrac23x\\$Multiply both sides by $ -\dfrac32\\x=-\dfrac32(f(x)+24)\\f^{-1}(x)=-\dfrac32f(x)-36[/tex]

When y=f(x)=0

[tex]f^{-1}(x)=-\dfrac32(0)-36\\f^{-1}(x)=-36[/tex]

Therefore, [tex]f^{-1}(x)$ has a x-intercept of -36[/tex]

Also, [tex]f^{-1}(x)[/tex] has a range of all real numbers.

Therefore, Options D and E are correct.

Answer:

4 and 5

Step-by-step explanation:

EDGE

Answer:

47

Step-by-step explanation:

It's just aligning each number / line to each matching one.

Answer:

47 degrees

Step-by-step explanation:

The angle that matches the angle U is angle C

The measure of angle U is 47 degrees

Answer:

The value of a is 50°.

Step-by-step explanation:

In an isosceles triangle, 2 sides have the same lengths and same angles so we can assume that the other side of the triangle is 65°.

Given that the total angle of a triangle is 180°, so have to subtract it :

[tex]a = 180 - 65 - 65[/tex]

[tex]a = 180 - 130[/tex]

[tex]a = 50[/tex]

Answer:

1/7

Step-by-step explanation:

x/y

Plug in the values.

(2)/(14)

Simplify.

1/7

Answer:

1/7

Step-by-step explanation:

=> x/y

Given that x = 2, y = 14

=> (2)/(14)

=> 1/7

Answer:

The train travelled x + 200 km

Answer:

The number of kilometres traveled by the bus is x kilometres. The train travels 200 kilometres farther than the bus, meaning that the train traveled x kilometres, and an additional 200 kilometres.

So, the number of kilometres traveled by the train would be the x km traveled by bus, plus 200 km; or x + 200 km.

Hope this helps!

Answer:

Option D is the correct option.

Explanation:

Since, there is a solid circle(blue) at X=4 which implies the value '4' is included in the inequality solution.

Hope this helps...

Good luck on your assignment...

Answer:

$110

Step-by-step explanation:

we know

selling price = cost price + profit.

given

selling price of TV = $121

profit = 10%of cost

selling price of TV = cost of TV + 10%cost of TV

121 = cost of TV + 10/100 cost of TV

=> 121 = (100 cost of TV + 10 cost of TV)/100

=> 121*100 = 110 cost of TV

=> cost of TV = 121*100/110 = 110

Thus, cost price of TV is $110(option A)

Answer:

m∠A ≈ 43°

m∠B ≈ 55°

mBC ≈ 20

Step-by-step explanation:

Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

Step 1: Find m∠B

[tex]\frac{29}{sin82} =\frac{24}{sinB}[/tex]

Step 2: Solve for ∠B

29sinB = 24sin82°

sinB = 24sin82°/29

B = sin⁻¹(24sin82°/29)

B = 55.038°

Step 3: Find m∠A

180 - (55.038 + 82)

180 - 137.038

m∠A = 42.962°

Step 4: Find BC

[tex]\frac{29}{sin82} =\frac{BC}{sin42.962}[/tex]

Step 5: Solve for BC

29sin42.962° = BCsin82°

BC = 29sin42.962°/sin82°

BC = 19.9581