Which of the following options represents a logical first step that can be used
to prove the trigonometric identity
cos(x)/ cos(x)+sin(x)tan(x)=cos^2(x)?

Answer:   Z²+ 9Z + 8

Step-by-step explanation:

You take the two z's and times them to get Z² then you do the Z times 1 to get  1Z then you do the Z times 8  to get 8Z then you take the 8 times 1 and get 8 so then you add the like terms. You add 1Z and 8Z and you get 9Z.  The you put it in standard form to get Z²+9Z+8

Answer:

Infinitely many solutions

Step-by-step explanation:

Since you already have y isolated in one equation, you can plug it in and use it in the other equation

2y = 8x + 12

2(4x + 6) = 8x + 12

8x + 12 = 8x + 12

Get the x's to one side

12 = 12

Meaning you have infinitely many solutions.

Try plugging in any x value you can think of and the left side will always equal the right side. so

x = 0 --> 8(0) + 12 = 8(0) + 12

12 =12

x = 1 --> 8(1) + 12 = 8(1) + 12

20 = 20

and so on.

I graphed it here for you and the 2 functions are on top of each other which means at every x value y = 4x + 6 is equal to 2y = 8x + 12

Answer:

The answer is B.

Step-by-step explanation:

You have to apply gradient formula by using coordinates :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Let (x1,y1) be (-14,-13),

L3t (x2,y2) be (7,0),

[tex]m = \frac{0 - ( - 13)}{7 - ( - 14)} [/tex]

[tex]m = \frac{13}{21} [/tex]

Answer:

1232

Step-by-step explanation:

13/91= 176/x

1/7=176/x

x= 176*7

x= 1232 bass

True if the lines were not vertical this would be false.

Answer:

d) [tex](\sqrt[8]{(10} )^{3 x}[/tex]

Step-by-step explanation:

Step(i):-

Given   [tex](\sqrt{10} )^{\frac{3 x}{4} }[/tex]

we will use formula

  [tex](a)^{m n} = (a^{m} )^{n}[/tex]

[tex](\sqrt{10} )^{\frac{3 x}{4} } =( (10)^{\frac{1}{2} } )^{\frac{3 x}{4} }[/tex]

              = [tex]( (10)^{\frac{1}{2} X\frac{3 x}{4} } )[/tex]

             = [tex]( (10)^{\frac{3 x}{8} } )[/tex]

            = [tex]((10)^{\frac{1}{8} } )^{3x}[/tex]

Step(ii):-

  we will  apply [tex](a)^{\frac{1}{n} } = \sqrt[n]{a}[/tex]

           = [tex](\sqrt[8]{(10} )^{3 x}[/tex]

Answer:

3x^2+12x+12

Step-by-step explanation:

i think you just sub in x+2 into 3x^2

Answer:

1. A

2. B

3. B

Step-by-step explanation:

1. 180+57-94= 29

2. 4x + 7 + 97 + 180 - 17x - 13 = 180

-13x = -91

x = 7

3. 180 - 64-38 = 78

180-78 =. 102

Answer:

A) 29°

B) 7°

B) 102°

Step-by-step explanation:

1. ------------------------

2.  ------------------------

3.  ------------------------

Answer:

Step-by-step explanation

Cluster- a group of points that close together

symmetry- data is balanced on opposite sides of  a point or line

spread- how close or far apart the values are in  a data set

center- the middle of a data set

gap- a space between data values

Answer:

$468

Step-by-step explanation:

I = P*R*T

I = 300*0.04*14

I = 168

168 + 300 = 468

Answer:

Step-by-step explanation:

Total cake shared=1/2

Pete share=x

Bill= twice as much as Pete

=2x

Pete's share+ Bill's share=total share

x+2x=1/2

3x=1/2

x=1/2÷3

x=1/2×1/3

=1/6

Pete's share=x=1/6

Bill's share=2x

=2(1/6)

=2/6

=1/3

Answer:

m<B = 44

Step-by-step explanation:

Since AB is a diameter, then angle C is a right angle.

That makes angles A and B complementary angles.

m<A + m<B = 90

46 + m<B = 90

m<B = 44

Answer:

B = 44

Step-by-step explanation:

The sum of the angles of a triangle is 180

A + B+ C = 180

<C = 90 since it is 1/2 of the intercepted arc which is 180

46+ B + 90 = 180

136 + B = 180

B = 180-136

B =44

Answer:

The values of F will be "16.58 i + 11.18 j".

Step-by-step explanation:

The given values are:

Force, F = 20 N

Angle, Ф = 33°

The formula use in the given scenario will be:

⇒  [tex]x=a \ Cos\theta[/tex]

⇒  [tex]y=a \ Sin\theta[/tex]

Now,

For Force, [tex]F=ai+bj[/tex]

⇒  [tex]a=F \ Cos\theta[/tex]

⇒     [tex]=20 \ Cos(34^{\circ})[/tex]

⇒     [tex]=20\times .829[/tex]

⇒     [tex]=16.58[/tex]

and,

⇒  [tex]b=F \ Sin\theta[/tex]

⇒     [tex]=20 \ Sin(34^{\circ})[/tex]

⇒     [tex]=20\times .55[/tex]

⇒     [tex]=11.18[/tex]

So that,

⇒  [tex]F=16.58 \ i+11.18 \ j[/tex]

Answer:  C

Step-by-step explanation:

Reflection across x = -1

The simplest way to calculate the new coordinates is to draw x = -1, count how many units away the point is from x = -1, then count the same number of units from x = -1 in the OPPOSITE direction to find the reflection. (see attachment)

J = (0, 0) is 1 unit to the right of x = -1

J' = (-2, 0) is 1 unit to the left of x = -1

K = (1, 4) is 2 units to the right of x = -1

K' = (-3, 4) is 2 units to the left of x = -1

L = (3, 3) is 4 units to the right of x = -1

L' = (-5, 3) is 4 units to the left of x = -1

Reflection across x-axis

Change the sign of the y-value:  (x, y) → (x, -y)

J' = (-2, 0)           J'' = (-2, 0)

K' = (-3, 4)           K'' = (-3, -4)  

L' = (-5, 3)            L' = (-5, -3)

Answer:

" Expected Payoff " = $ 6.70

Step-by-step explanation:

Consider the steps below;

[tex]Probability of Winning the 550 Dollar Prize - 1 / 200,\\Probability * Money Won = " Expected Payoff " For The 550 Dollar Prize,\\\\1 / 200 * 550,\\" Expected Payoff " - 2.75 Dollars,\\\\Probability of Winning the 510 Dollar Prize - 1 / 200,\\\\1 / 200 * 510,\\" Expected Payoff " - 2.55 Dollars,\\\\Probability of Winning the 280 Dollar Prize - 1 / 200,\\\\1 / 200 * 280,\\" Expected Payoff " - 1.4 Dollars,\\\\[/tex]

[tex]Conclusion ; Expected Payoff = 6.70 Dollars[/tex]

Answer:

37

Step-by-step explanation:

If this is a regular hexagon, the sides have the same length

3y +19 = 6y+1

Subtract 3y from each side

3y+19-3y = 6y-3y+1

19 = 3y+1

Subtract 1 from each side

19-1 = 3y+1-1

18 = 3y

Divide each side by 3

18/3 = 3y/3

6 =y

ST = 6y+1

     =6*6+1

     =36+1

     = 37

Answer:

37 units

Step-by-step explanation:

sides are equal

3y+19=6y+1

3y= 18

y= 6

3y+19= 3*6+19= 37

QR=ST= 37 units

Answer:

Step-by-step explanation:

The words "two iles a month" tells us that the expression represened by those words is the "2x" part of the equation. x represents the number of months. The .5 part tells us that he began this process with a half mile.

Answer:

1500 grams

Step-by-step explanation:

A= P(0.5)^t

A=3000(0.5)^1

A=1500

Answer:

D

Step-by-step explanation:

A line parallel to the y- axis is a vertical line with equation

x = c

where c is the value of the x- coordinates the line passes through, thus

x = 4 is the equation of a line parallel to the y- axis → D

Answer:

A) KJ AND JH

Step-by-step explanation:

EF = JH  The three lines indicate they are equal

EK = GH  The one line indicates they are equal

KJ = FG  The two lines indicates they are equal

Answer:

A) KJ and JH

Step-by-step explanation:

[tex]answer \\ \sqrt{208} \\ solution \\ hypotenuse = c \\ perpendicular = 8 \\ base = 12 \\ using \: pythagoras \: theorem \\ {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {c}^{2} = {8}^{2} + {12}^{2} \\ or \: {c }^{2} = 64 + 144 \\ or \: {c}^{2} = 208 \\ c = \sqrt{208} \\ hope \: it \: helps[/tex]

Step-by-step explanation:

Given that the formula of gradient is :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

So you have to try for every coordinates :

Option A,

[tex] \frac{6-(-2)}{-1-4} = - \frac{8}{5} (incorrect) [/tex]

Option B,

[tex] \frac{8-(-2)}{-1-4} = -2 (correct) [/tex]

Option C,

[tex] \frac{10-(-2)}{-1-4} = - \frac{12}{5} (incorrect) [/tex]

Option D,

[tex] \frac{12-(-2)}{-1-4} = - \frac{14}{5} (incorrect) [/tex]

Answer:

[tex]y = \frac{5}{2} x^{2}[/tex]

Step-by-step explanation:

When you scale a parabola vertically, you multiply the [tex]x^{2}[/tex] by what you are scaling it vertically by.

For example, say you have  [tex]y = 8x^{2}[/tex]. That means that  [tex]y = x^{2}[/tex] was scaled vertically by a factor of 8.

I hope this helps!

Answer: yes

Step-by-step explanation: A translation is a transformation that slides a figure to a new position.

So in this problem, notice that we can slide the triangle on the top to the position of the triangle on the bottom.

So, this represents a translation.

Answer:

C. u^2 + 5u – 6 = 0 where u = (x + 2)

Step-by-step explanation:

(x + 2)^2 + 5(x + 2) – 6 = 0

Let u = x+2

(u)^2 + 5(u) – 6 = 0

Answer:

C.u^2+5u-6=0

Step-by-step explanation:

By comparing (x+2)^2+5(x+2)-6=0 to answer C,that is u^2+5u-6=0,u=(x+2).

By sustituting (x+2)into answer C,we get;

(x+2)^2+5(x+2)-6=0 which is the same as the quadriatic equation given in the question.

Answer:

64.89£

Step-by-step explanation:

Given:

Theater ticket costs £63

Booking fee: 3% of original price

Solve for:

Total price of ticket

Solution:

Step 1: Select relevant procedure

The total price including the booking fee, then before working out the total price, the booking fee should be calculated.

Step 2: Perform the calculation

The booking fee of ticket is calculated by:

BF = 3% of £63 or (3/100) x 63 = 1.89

Adding up the ticket price and booking fee to get total price:

Total price = ticket price + booking fee = 63 + 1.89 = 64.89£

Hope this helps!

:)

Answer: 12 child tickets

Step-by-step explanation:

We can use system of equations to find how many child tickets were sold. Let's say x is adult and y is child.

Equation 1

5.25x+3.05y=498.6

This equation comes from the cost of tickets.

Equation 2

x+y=100

This equation comes from the number of tickets.

We can use elimination method to solve for y.

5.25x+3.05y=498.6

5.25x+5.25y=525

Now, we can subtract the equations for x to cancel out and to solve for y.

-2.2y=-26.4

y=12

Answer:

First number:15

Second number: 7

Step-by-step explanation:

To find the 2 numbers, we can use system of equations.

Let's use x for the first number and y for the second number. Our first equation would be:

x-y=8

This equation comes from the first sentence: the difference of the 2 numbers is 8. The second equation would be

2x+3y=51

This equation comes from the second part of the question.

We can use elimination method to find x and y.

x-y=8

2x+3y=51

Let's eliminate x. To do so, the x in both equations must be equal to each other. Since one is x and another is 2x, we must multiply the first equation by 2 to get the same x.

2x-2y=16

2x+3y=51

Now that the x are the same, we can subtract the equations.

-5y=-35

y=7

With our y value, we can find x by plugging y into any of the equations.

x-7=8

x=15

Since we found our x and y, the first number is 15 and the second number is 7.

Answer:

y = x + 2

Step-by-step explanation:

slope = 1

y = mx + b

4 = 1(2) + b

2 = b

y = x + 2

Answer:

10 pi

Step-by-step explanation:

25 pi

20 pi

10 pi

5 pi

C is the answer

The area of the shaded sector of the circle will be 10π units².

Area of a sector of a circle = θ/360 × πr², where r is the radius of the circle and θ is the central angle.

As per the question, QR = 5 and m∠RQS = 4π/5 = 144°.

As per the given question given data:

θ = 4π/5

r = QR = 5

Substitute the values in the formula to get:

Area of sector of a circle = 144/360 × π(5)²

Area of sector of a circle = 1/4 × π(25)

Apply the multiplication operation, and we get

Area of a sector of a circle = 10π units²

Thus, the area of the shaded sector of the circle is 10π units².

Learn more about the area of a sector here:

brainly.com/question/22972014

#SPJ2

The question seems to be incomplete the correct question would be:

In circle Q, QR = 5 and m∠RQS = 4π/5. Find the area of the shaded sector.

Express your answer as a fraction times pi.