this is my question.please help QUICK​

Very quickly: since tan(30°) = 1/√3,

(1 + tan(30°)) / (1 - tan(30°)) = (1 + 1/√3) / (1 - 1/√3)

… = (√3 + 1) / (√3 - 1)

… = (√3 + 1)² / ((√3)² - 1²)

… = ((√3)² + 2√3 + 1²) / (3 - 1)

… = (3 + 2√3 + 1) / 2

… = (4 + 2√3) / 2

… = 2 + √3

On the other side, we have sin(30°) = 1/2 and sin(60°) = √3/2, so

(1 + sin(60°)) / (1 - sin(30°)) = (1 + √3/2) / (1 - 1/2)

… = (1 + √3/2) / (1/2)

… = 2 (1 + √3/2)

… = 2 + √3

and we're done, both sides are equal.

We can also prove this algebraically:

Force the denominator on the left side into a difference of squares:

(1 + tan(30°)) / (1 - tan(30°)) × (1 + tan(30°)) / (1 + tan(30°))

… = (1 + tan(30°))² / (1 - tan²(30°))

Expand the numerator:

… = (1 + 2 tan(30°) + tan²(30°)) / (1 - tan²(30°))

Recall that 1 + tan²(x) = sec²(x) :

… = (sec²(30°) + 2 tan(30°)) / (1 - tan²(30°))

Since sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x), multiply through every term by cos²(30°) :

… = (sec²(30°) + 2 tan(30°)) / (1 - tan²(30°)) × cos²(30°) / cos²(30°)

… = (1 + 2 sin(30°) cos(30°)) / (cos²(30°) - sin²(30°))

Recall that sin(2x) = 2 sin(x) cos(x) and cos(2x) = cos²(x) - sin²(x) :

… = (1 + sin(2×30°)) / cos(2×30°)

… = (1 + sin(60°)) / cos(60°)

Finally, recall that cos(90° - x) = sin(x), so cos(60°) = sin(30°) = 1/2, and we can write 1/2 = 1 - 1/2, so

… = (1 + sin(60°)) / (1 - sin(30°))

as required.

Answer:

D) 22

Step-by-step explanation:

Since it gives you two rays just set them equal and solve for X.

6x - 14 = 3x +4

      +14        +14

6x = 3x + 18

-3x   -3x

3x = 18

/3    /3

x = 6

Then plug x into either one of the equations

6(6) - 14

36 - 14

22

Answer:

D. 22

Step-by-step explanation:

Answer:

-1, -2, and -3

Step-by-step explanation:

-1 + -2 + -3 = -6

Answer:

Step-by-step explanation:

1) r = 5mm; d = 10 mm

2) r = 6 cm; d = 12 cm

3) r = 9 m; d = 18 m

4) r = 8 km; d = 16 km

5) r = 11 m; d = 22 m

6) r = 15 mm; d = 30 mm

7) r = 13 km; d = 26 km

8) r = 7 cm; 14 cm

Answer:

6 feet per minute

Step-by-step explanation:

Answer:

6 feet per minute.

Step-by-step explanation:

5ft + 1ft = 6ft per minute.

Answer:

≥

..................................................

Answer:

3. D

4. A

5. B

Step-by-step explanation:

Answer:

They are all positive because you must go right.

They are all negative because you must go down.

Step-by-step explanation:

Example. (1,-4)

You go over one.

Down 4

Step-by-step explanation:

2*22/7*48=301.714 .This the answer

Answer:

Yeah, what they said above.

Step-by-step explanation:

Answer:

-1 and 4/3

Step-by-step explanation:

Given the quadratic equation;

f(x) = 3x^2-x-4

To get all potential roots, we will equate f(x) = 0

3x^2-x-4 = 0

3x^2-4x+3x-4 = 0

x(3x-4)+1(3x-4) = 0

(x+1)(3x-4) = 0

x+1= 0 and 3x-4 = 0

x = -1 and 3x = 4

x = -1 and x= 4/3

Hence the potential roots are -1 and 4/3

Answer:

1.

(x+1)(x+2)>x(x+3)

x^2+2x+x+2>x^2+3x

x^2+3x+2>x+3x

2>0

2.

(x+2)^2>x(x+4)

x^2+4x+4>x^2+4x

4>0

Step-by-step explanation:

1.

Suppose x is the lowest number in the set of 4 consecutive numbers, then x+1, x+2, and x+3 are then the next numbers in the sequence since they are the next whole numbers.

Then, to follow the conditions of the problem, we make the equation:

(x+1)(x+2)>x(x+3)

Using the formula of (a+b)(c+d)=ac+ad+bc+bd, we can expand both sides of the equation into this:

x^2+2x+x+2>x^2+3x

=x^2+3x+2>x^2+3x

We can then cancel x^2+2x from both sides and we are left with 2>0.

2.

Again, suppose x is the lowest value in the set of consecutive numbers. In this case, odd numbers increase by 2 each time so the series of numbers are:

x, x+2, x+4

Therefore, to follow the conditions of the problem, we make the equation:

(x+2)^2>x(x+4)=

(x+2)(x+2)>x(x+4)

Using the same formula of (a+b)(c+d)=ac+ad+bc+bd, we get:

x^2+4x+4>x^2+4x

Cancel x^2+4x from both sides and we are left with 4>0

Hope this helps!

Answer:

1234567890

Step-by-step explanation:

?

Answer:

3. 15 baskets

4. 16 tries

Step-by-step explanation:

3.

3: 4 is ratio so 3:4=x:20, 3/4=x/20, and you get x=15

4. ratio is still 3:4, 3:4=12:x, 3/4=12/x, x=16, so 16 tries

Answer:

4*s= 520

s= 130

area=s*s=130*130=16900m^2

Step-by-step explanation:

Answer:

7 cars

Step-by-step explanation:

The computation of the number of cars to be filled is shown below:

A car that is 90% full and the total people is 20 so 90% would be

= (.90)(20)

= 18

A car that is 65% full and the total people is 20 so 65% would be

= (.65)(20)

= 13

Now

Total number of people = (5)(18) + (3)(13).

= 129

Now the number of cars to be filled is

= 129 ÷ 20

= 6.45

= 7 cars

Answer:

6

Step-by-step explanation:

Answer:

Width = 16 m

Length = 4 m

Step-by-step explanation:

The area of rectangular is 64m² the length of the pool is 12 m less that the width . The situation can be represented by the equation x

Area of a rectangle = Length × Width

L = W - 12

Hence:

64 = (W - 12) × W

64 = W² - 12W

W² - 12W - 64 = 0

Factor using

(W + 4)(W - 16) = 0

Width = 16m

Length = W - 12

Length = 16 m - 12 m

= 4 m

Answer:

Use PEMDAS

(Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

18 - 3 (5) + 2

18 - 15 + 2

3 +2

5

Answer:

5

Step-by-step explanation:

Answer:

∠1 = 42°

∠2 = 48°

∠4 = 48°

∠3 = 21°

∠5 = 21°

Step-by-step explanation:

Given:

∠WZY = 138°

Find:

∠1

∠2

∠3

∠4

∠5

Computation:

WZ = ZY

So,

∠3 = ∠5

So,

∠3 + ∠5 + 138 = 180

2∠3 = 42

∠3 = 21°

∠5 = 21°

∠1 = 180 - 138

∠1 = 42°

∠W = ∠Y

∠X + ∠Y + ∠W = 180

42 + ∠Y + ∠W = 180

∠Y = 69

∠2 = 69 - 21

∠2 = 48°

∠4 = 48°

Answer:

true

Step-by-step explanation:

first find the median of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Answer:

(1,-3.7)

Step-by-step explanation:

subtract the y axis to go down

5 - 8.7 = -3.7

The solution is B ( 1 , -3.7 )

The coordinates of the zombie is given by B ( 1 , -3.7 )

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the initial point of the man be A

The value of A = A ( 1 , 5 )

Let the coordinates of the zombie be B

The value of B = B ( x , y )

The zombie is 8.7 units below

So , it is a vertical shift by 8.7 units

Therefore , the y coordinate will decrease by 8.7 units

Substituting the values in the equation , we get

B = A ( 1 , 5 - 8.7 )

B = B ( 1 , -3.7 )

Therefore , the value of B is B ( 1 , -3.7 )

Hence , the coordinates of B is B ( 1 , -3.7 )

To learn more about transformation of function click :

https://brainly.com/question/26896273

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1) Power of a Product

2) Power Rule (or Power of a Power)

Answer:

-Number 1 is Power of a Power Property, I think

-Number 2 is Power of a Power Property

Answer:

120

Step-by-step explanation:

Blue marbles = 2

Red marbles = 3

Total marbles = 2 + 3 = 5

If a marble is drawn 300 times ;prediction for the number of times a blue marble will be drawn :

P(drawing a blue marble) = number of blue marbles / total number of marbles

= 2 /5 = 0.4

Predicted number of times blue is drawn in 300 selections :

300 * 0.4 = 120

Approximately 120 times

Answer:

The Graph of a Quadratic Function

A quadratic function is a polynomial function of degree 2 which can be written in the general form.

Step-by-step explanation:

Example: Graph: f(x)=−x2−2x+3.

Solution:

Step 1: Determine the y-intercept. To do this, set x=0 and find f(0).

f(x)f(0)===−x2−2x+3−(0)2−2(0)+33

The y-intercept is (0,3).

Step 2: Determine the x-intercepts if any. To do this, set f(x)=0 and solve for x.

f(x)000x+3x======−x2−2x+3−x2−2x+3x2+2x−3(x+3)(x−1)0−3orx−1x==Set f(x)=0.Multiply both sides by −1.Factor.Set each factor equal to zero.01

Here where f(x)=0, we obtain two solutions. Hence, there are two x-intercepts, (−3,0) and (1,0).

Step 3: Determine the vertex. One way to do this is to first use x=−b2a to find the x-value of the vertex and then substitute this value in the function to find the corresponding y-value. In this example, a=−1 and b=−2.

x====−b2a−(−2)2(−1)2−2−1

Substitute −1 into the original function to find the corresponding y-value.

f(x)f(−1)====−x2−2x+3−(−1)2−2(−1)+3−1+2+34

The vertex is (−1,4).

Step 4: Determine extra points so that we have at least five points to plot. Ensure a good sampling on either side of the line of symmetry. In this example, one other point will suffice. Choose x=−2 and find the corresponding y-value.

x −2  y 3f(−2)=−(−2)2−2(−2)+3=−4+4+3=3Point(−2,3)

Our fifth point is (−2,3).

Step 5: Plot the points and sketch the graph. To recap, the points that we have found are

y−intercept:x−intercepts:Vertex:Extra point:(0,3)(−3,0) and (1,0)(−1,4)(−2,3)

Answer: