Which double-angle or half-angle identity would you use to verify that 1+cos2a=2/1+tan2a?

straight line = 180 degrees

180-92 = 88

 so angle 1 = 88 degrees

Answer: [tex]-3^x +4[/tex]

Step-by-step explanation:

The equation for the vertical reflection of a function f(x) across the x-axis is given by :-

[tex]y=-f(x) [/tex]

The vertical shift of 'k'  units of a function g(x) is given by :-

 [tex]y=g(x)+k [/tex]

Now, the equation for the vertical reflection of a function [tex]f(x)=3^x[/tex] across the x-axis is given by :-

[tex]-f(x)=-3^x [/tex]

Then , the equation for the vertical shift of 4 units of function [tex]-3^x[/tex] is given by :-

[tex]y=-3^x +4[/tex]

Hence, the function represents transforming [tex]f(x)=3^x[/tex] with a reflection over the x-axis and a vertical shift of 4 units

[tex]y=-3^x +4[/tex]

To cover 50 windows with coverings that are 15 windows long, at least 4 window coverings are needed to span all the windows.

The question asks how many window coverings are necessary to span 50 windows, given that each window covering is 15 windows long. To find out how many window coverings are required, you divide the total number of windows by the length of one window covering. So, we do 50 ÷ 15 which equals approximately 3.33. Since you can't have a fraction of a window covering, you'll need at least 4 full window coverings to span all 50 windows.

[tex]4(x+2)=2(x+3)+2(x-1)\\\\use\ the\ distributive\ property:\ a(b\pm c)=ab\pm ac\\\\(4)(x)+(4)(2)=(2)(x)+(2)(3)+(2)(x)-(2)(1)\\\\4x+8=2x+6+2x-2\ \ \ \ |simplify\\\\4x+8=(2x+2x)+(6-2)\\\\4x+8=4x+4\ \ \ \ |-4x\\\\8=4\ FALSE!!!\\\\Answer:\ NO\ SOLUTION\ (x\in\O)[/tex]

perimeter = 4s

56=4s

s=56/4 = 14

diagonal = sqrt (s^2 x 2)= sqrt(14^2 x 2) = sqrt(392) = 19.7989 cm

round answer as needed

Answer:

The approximate length of diagonal is:

19.796 cm.

Step-by-step explanation:

We are given the perimeter of a square as 56 cm.

Let 's' be the side of the square.

We know that the perimeter of square is given as:

[tex]Perimeter=4\times s\\\\56=4s\\\\s=\dfrac{56}{4}\\\\s=14[/tex]

Hence, the side of square is 14 cm.

Now, the length of a diagonal(D) is given as:[tex]D=\sqrt{2}s[/tex]

( Since it could be proved with the help of Pythagorean Theorem )

Hence, as s=14 cm

Hence, the length of diagonal is:

[tex]D=\sqrt{2}\times 12\\\\D=1.414\times 14\\\\D=19.796\ cm[/tex]

Hence, the approximate length of diagonal is:

19.796 cm.

The value of x is 13.

The problem at hand has a quadrilateral shape. The problem depicts four angles and sides, with the only known angle being X.

The graphic depicts four sides (quad), and the stick drawn in the center of each side explains the length relationship.

One stick is equal to two sticks, and two sticks are equal to one stick.

Angles Assumed:

X=102 deg

W=(7x+4) deg

Y=(5x-4) deg

Because angle X is 102 degrees, angle Z must also be 102 degrees. A quadrilateral has a total angle of 360 degrees.

So, to find x, do the following:

102 + 102 + 7x + 4 + 5x - 4 = 360

Add the constant terms: 102 + 102 + 4 - 4 = 204

Combine x terms: 7x + 5x = 12x

Substitute the combined terms:

204 + 12x = 360

Isolate x:

12x = 360 - 204

12x = 156

x = 156 / 12

Simplify:

x = 13

Therefore, the solution is x = 13.

L = lemon drops

J = jelly beans

L +J = 100

L=100-J

1.90L + 1.20J=1.48*100

1.90(100-j) +1.20J =148

190-1.90J+1.20J=148

190-0.7J=148

-0.7J=-42

J = 60

L=100-60 = 40

40 pounds of Lemon Drops are needed

Final answer:

40 pounds of lemon drops are needed.

Explanation:

To find out how many pounds of lemon drops are needed to make a 100-pound mix that costs $1.48 per pound, we can set up a system of equations. Let L represent the number of pounds of lemon drops and J represent the number of pounds of jelly beans.

Since the total weight of the mix is 100 pounds:

L + J = 100

Given the cost of lemon drops is $1.90 per pound and jelly beans cost $1.20 per pound, and the entire mix should cost $1.48 per pound:

1.90L + 1.20J = 100 * 1.48

We already have that L + J = 100, so J can be expressed as 100 - L. Substituting J in the second equation we get:

1.90L + 1.20(100 - L) = 148

Solving for L:

1.90L + 120 - 1.20L = 148

0.70L = 28

L = 28 / 0.70

L = 40

Therefore, 40 pounds of lemon drops are needed for the mix.

Answer: Volume of cylinder is 1152.38 m³.

Step-by-step explanation:

Since we have given that

Radius of cylinder = 10 m

Height of cylinder = 11 m

Using Cavalieri's principle , volume of an oblique cylinder is equal to volume of cone.

So, Volume of an oblique cylinder is given by

[tex]V=\frac{1}{3}\pi r^2h\\\\V=\frac{1}{3}\frac{22}{7}\times 10\times 10\times 11\\\\V=1152.38\ m^3[/tex]

Hence, Volume of cylinder is 1152.38 m³.

Answer:

f(-2 ) =2

f(0) = 3

f(4) = -1

Step-by-step explanation:

Clearly by looking at the graph of the given function f(x) we could observe that the function f(x) is increasing in the interval (-∞,0] and then decreasing in the interval (0,∞).

Also, the function is discontinuous at x=0.

( Since, there is a break in a graph and also the left and right hand limit of the function are not equal at x=0)

Hence, from the graph we could directly say that:

                 f(-2 ) =2

                 f(0) = 3

                  f(4) = -1

The values of the function values are:

f(-2 ) =2, f(0) = 3 and f(4) = -1

On the graph, the value of the function when x = -2 is 2

Hence, the value of f(-2) is 2

On the graph, the values of the function when x = 0 are 1 and 3.

However, the line that has a closed circle (i.e f(0) = 3) will take precedence over the line that has an open circle (i.e f(0) = 1)

Hence, the value of f(0) is 3

On the graph, the value of the function when x = 4 is -1

Hence, the value of f(4) is -1

Read more about functions and graphs at:

https://brainly.com/question/13136492

there are 5 ways for 1st place, then there would be 4 ways for 2nd place, then 3 ways for third

5*4*3 = 60 different ways

Answer:  The required number of ways is 60.

Step-by-step explanation:  Given that there are five automobiles entered in a race and there are no ties.

We are to find the number of ways in which the first three finishers come in.

Since there are 5 automobiles entered in the race, so the number of ways in which first finisher come in is 5.

Now, there are no ties, so the number of ways in which second and third finisher come in are 4 and 3 respectively.

Therefore, the total number of ways in which the first three finishers come in is

[tex]n=5\times4\times3=60.[/tex]

Thus, the required number of ways is 60.

The true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.

Let's analyze each statement:

1. The graph of [tex]\(y - \log(x-4)\)[/tex] is the graph of [tex]\(y - \log(x)\)[/tex] translated 4 units down.

  This statement is incorrect. The function [tex]\(y - \log(x-4)\)[/tex] is the result of shifting the graph of [tex]\(y = \log(x)\) 4[/tex] units to the right, not down.

2. The graph of [tex]\(y = \log(x) - 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units down.

  This statement is incorrect. The function [tex]\(y = \log(x) - 4\)[/tex] represents a vertical translation of 4 units down from the graph of [tex]\(y = \log(x)\)[/tex], not left.

3. The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units up.

  This statement is true. Adding a constant term to a function vertically shifts the graph of the function by that amount. So, adding 4 to [tex]\(y = \log(x)\)[/tex] shifts it 4 units up.

4. The graph of [tex]\(y = \log(x+4)\)[/tex] is the graph of [tex]\(y = \log_2(x)\)[/tex] translated 4 units right.

  This statement is incorrect. The function [tex]\(y = \log(x+4)\)[/tex] represents a horizontal translation of 4 units to the left from the graph of [tex]\(y = \log(x)\).[/tex]

Therefore, the true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.

Question

Which statement is true?

The graph of Y - log(x-4) is the graph of y-log,(x) translated 4 units down.

The graph of Y = log: (x)-4 is the graph of y = log. (x) translated 4 units left.

The graph of y = log,(x)+4 is the graph of Y=log.(x) translated 4 units up.

The graph of y = log. (x+4) is the graph of y = log2 (x) translated 4 units right.

It is given that:

The bag contains 5 gold marbles, 25 silver marbles, and 70 red marbles.

Ques 1)

We are asked to find the probability that the second player will also win a small prize given that the first player wins a small prize.

That is we need to find the conditional probability.

Let A denote the event that first player wins the small prize.

B denote the vent that the second player wins the small prize.

A∩B denote the event that both the player wins the small prize.

Let P denote the probability of an event.

We are asked to find:

P(B|A)

[tex]P(B|A)=\dfrac{P(B\bigcap A)}{P(A)}[/tex]

Now we know that:

[tex]P(A)=\dfrac{25}{100}[/tex]

( Since out of 100 marbles 25 are silver)

Also,

[tex]P(A\bigcap B)=\dfrac{25_C_2}{100_C_2}\\\\\\P(A\bigcap B)=\dfrac{25\times 24}{100\times 99}[/tex]

Hence,

[tex]P(B|A)=\dfrac{24}{99}[/tex]

Hence, the probability that the second player will also win a small prize is:

0.242424

Ques 2)

The probability that the first player will win a large prize is:

5/100

( But the first player draws a silver marble and wins)

The probability that the second player will win a large prize is:

5/99

( Since one marble has been taken out by the first player so the second player is left with 99 choices and here also the second player draws a silver and wins the game)

Similarly,

The probability that the third player will win a large prize is:

5/98

( Since one more marble has been taken out by the second player so the third player is left with 98 choices and here also the third player draws a silver and wins the game)

The probability that the fourth player will win a large prize is:

5/97

Hence, the greatest probability of winning a gold marble is by:

Player 4. ( Since, 5/97 is greater than the rest three probabilities)

Ques 3)

The game can be made fair for each player if all have the equal choices of drawing a marble and this can be done by replacing the marbles that have been drawn out by the previous player.

Answer:

The value of k is 4.

Step-by-step explanation:

Given,

f of x equals 1 over 3 x minus 3,

[tex]\implies f(x)=\frac{1}{3}x-3[/tex]

Also, g of x equals 1 over 3 x plus 1,

[tex]\implies g(x)=\frac{1}{3}x+1[/tex]

Since, g(x) = f(x) + k,

By substituting the values,

[tex]\frac{1}{3}x+1=\frac{1}{3}x-3+k[/tex]

[tex]1=k-3[/tex]

[tex]\implies k = 1+3 = 4[/tex]

Hence, the value of k is 4.

x = 50 * tan(60) = 50sqrt(3) =86.6 feet

tower is 93.6 feet tall

Answer:

a

Step-by-step explanation:

Because C is the centroid, therefore:

Segments PZ = ZR;  RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer:      PC = 20      PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer:      ZC = 5        ZQ = 15

C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:      PQ = 40

Answer:

35.5 mph

Step-by-step explanation:

We are given that Sally Leadfoot was pulled over on her way from Syracuse to Ithaca by an officer claiming she was speeding.

Speed limit =65 mph

Sally traveled distance  97 km in 102 minutes

We have to find the Sally's average speed in mph

Time =102 minutes

We know that 1 hour =60 minutes

[tex]102 minutes=\frac{102}{60}=1.7 [/tex]hours

We know that 1 km=0.621371

97 km=[tex]0.621371 \times 97=60.272987[/tex]miles

Average speed =[tex]\frac{60.272987}{1.7}=35.45 mph[/tex]

Average speed  of Sally's =35.5 mph

Hence, average speed of Sally is less than 65 mph .Therefore, she was not fast speeding and she deserves a ticket.