MATHEMATICS HIGH SCHOOL

Use angle difference identity to find the exact value.1. tan 15 degrees

2. tan -105 degrees

Answers

Answer 1
Answer: Hello,

1)
tan (a-b)=(tan a - tan b)/(1+tan a tan b)

15=45-30
tan 45°= (√2/2)/(√2/2)=1
tan 30°=(1/2)/(√3/2)=√3/3
tan (45°-30°)= (1-√3/3)/(1+1*√3/3)=(3-√3)/(3+√3)=(3-√3)²/6=2-√3

tan (-105°)=tan (75°)= tan (60°+15°)=(tan 60+tan15°)/(1-tan 60°*tan 15°)

tan 15°=2-√3
tan 60°=√3°
tan (-105°)=(√3+2-√3)/(1-√3*(2-√3))=2/(1-2√3+3)=1/(2-√3)=2+√3

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Katalin drove 210 miles on her vacation. She drove an average of 1.4 times faster on the second 105 miles of her trip than she did on the first 105 miles of her trip. Which expression represents the time she spent driving? Let x = her speed on the first half of the trip.A. 180x B. 360 divided by x. C. 252 divided by x. D. 180 divided by x.
What is the solution to 3!

Trying to figure out this for a long time. Please help!!!​

Answers

Answer:

One solution to this question could be that g(xl=x^2 and f(x)=sqrt{x+1}

Step-by-step explanation:

If g(x)=x^2, f(g(x))=f(x^2)=sqrt{x^2+1}

Evaluate [(30 + 6) − 32] ÷ 9 ⋅ 2.

Answers

Use PEMDAS:

[(30+6) -3^2] / 9* 2
= (36 -9)/ 9* 2
= 27/9* 2
= 3*2
= 6

The final answer is 6~

Answer: just use PEMDAS

[(30+6) -3'2] / 9'2

= (36 -9)/ 9'2

= 27/9'2

= 3'2

= 6

Step-by-step explanation:

Select all statements that are true about the graph of ordered pair (5, −1) . The point is 5 units below the x-axis. The point is 1 unit below the x-axis. The point is 1 unit to the left of the y-axis. The point is in the fourth quadrant. The point is on the x-axis.

Answers

The statements (B) and (D) are "true" about the graph of ordered pair (5, −1).

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The graph of the ordered pair (5, -1). The point (5, -1) is located 5 units to the right of the y-axis and 1 unit below the x-axis.

So statement A is false. It is not 5 units below the x-axis.

So, statement B is true.

The fourth quadrant is the region where x > 0 and y < 0, so it lies in the fourth quadrant.

Thus, statements (B) and (D) are "true" about the given graph.

Learn more about graphs here:

brainly.com/question/16608196

#SPJ2

Answer:

The point is below the x-axis and The point is in the fourth quadrant.

Step-by-step explanation:

Need help... will mark brainliestWhat is the average daily temperature for all ten years? ____degrees

Answers

Answer:

53.6°

Step-by-step explanation:

Pretty much just add all the (y)s together then divide by 10.

50+52+51+54+53+57+54+54+55+56=536

536/10 =53.6

the average temperature is 53.6°

I know that y=20 and x=50 but will someone explain how to get them. Thanks!

Answers

given that A and B are parallel, you can conclude that 30 = x - y since they are corresponding angles. Also you can conclude that 5y = 2x since they are alternate interior angles. At this point, there is a solvable system of equations set up

30 = x - y

5y = 2x


Now, you must isolate a variable so let's isolate x from the 1st equation. so u just need to add y to both sides, getting x = 30 + y. Now you plug that into the 2nd equation and solve for y. 5y = 60 + 2y. Subtract 2y from both sides. 3y = 60. Divide by 3, y = 20.

Now with your y value, just plug back into original equation (the 1st one). 30 = x - 20. Solve for x by adding 20. X = 50

A gourment shop wants to mix coffe beans that cost $3.00 per pound with coffe beans that cost $4.25 per pound to create 25 pounds of a new blend that cost $3.50 per pound. Find the number of pounds of each nerded to produce the new blend

Answers

If the gourmet shopkeeper mix 15 pounds of coffee beans which costs 3.0$ per pound with 10 pounds of coffee beans costing 4.25$ per pound.
The mixture of 25 pounds will cost 3.5$ per pound.

It can be found using 
3*x + 4.25*(25 -x) = 25*3.50
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