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I really don't know how to calculate this question.

(3 tan 45°)(4 sin 60°)-(2 cos 30°)(3 sin 30°)
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Answers

Answer 1
Answer:

Answer:

9\,\sin(60^\circ), which is equal to \displaystyle (9√(3))/(2).

Step-by-step explanation:

An angle of 45^\circ corresponds to an isosceles right triangle: the length of the two legs (adjacent and opposite) would be equal. Accordingly:

\displaystyle \tan(45^\circ) = \frac{\text{Opposite Leg}}{\text{Adjacent Leg}} = 1.

Let A denote the measure of an angle. Double-angle identity for sine:

2\, \sin(A) \cdot \cos(A) = \sin(2\, A).

By this identity:

\begin{aligned}& (2\, \cos(30^\circ)) \cdot (3\, \sin(30^\circ)) \n &= 3\, (2\, \cos(30^\circ) \cdot \sin(30^\circ)) \n &= 3\, \sin(2 * 30^\circ) \n &= 3\, \sin(60^\circ)\end{aligned}.

(A = 30^\circ in this instance.)

Hence:

\begin{aligned}&(3\, \tan(45^\circ)) \cdot (4\, \sin(60^\circ)) - (2\, \cos(30^\circ)) \cdot (3\, \sin(30^\circ)) \n &= 12\, \sin(60^\circ) - 3\, \sin(60^\circ) \n &= 9\, \sin(60^\circ)\end{aligned}.

\displaystyle \sin(60^\circ) = (√(3))/(2). Therefore, \displaystyle 9\, \sin(60^\circ) = (9 √(3))/(2).

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The number 3456 is divisible by wich single-digit number?

Answers

I'm assuming what you mean is what can you divide 3456 by to get a natural number.

First of all every number is divisible by 1.  

Every even number is divisible by 2, so since 3456 is an even number, it can be divided by 2.  That would equal 1728.

2456 can also be divided by 3, to get 1782.  

You can also divide it by 4, to get 865.

Divided by 6, it's 576.

Divided by 8, it's 432.

And lastly, 3456 divided by 9 is 384.

So, there isn't just one single-digit number you can divide 3456 by to get a natural number.  You can divide it by 1,2,3,4,6,8, and 9.

Hope that helps!

PLEASE HELP ASAP!!! :)Using the remainder theorem, what is the remainder of the quotient of x^3– 6x^2 + 4x– 5 and 1 - 3?

A.88
B. -20
c.-74
D. 34

Answers

The remainder of the quotient is -20.

Option B is the correct answer.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x³ - 6x² + 4x - 5 and x - 3

Now,

x - 3 ) x³ - 6x² + 4x - 5 ( x² - 3x - 5

         x³ - 3x²

       (-)    (+)

             -3x² + 4x

             -3x² + 9x

          (+)      (-)

                    -5x - 5

                    -5x + 15

                (+)      (-)

                          -20

Thus,

The remainder is -20.

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Answer:

The correct answer is B. -20.

Step-by-step explanation:

I got it right on the Edmentum test.

I need help quick A student is cutting a square out of a piece of poster board. The area of the poster board can be represented as (4x ^ 2 + 14x - 8) in ^ 2 The area of the square can be represented as (x ^ 2 + 8x + 16) in^2 Write an expression to represent the area of the poster board left over after the student cuts out the square

Answers

Answer:

area left = (3x² + 6x - 24) in²

Step-by-step explanation:

the area of poster board left

= area of poster board - area of square cut out

= 4x² + 14x - 8 - (x² + 8x + 16) ← distribute parenthesis by - 1

= 4x² + 14x - 8 - x² - 8x - 16 ← collect like terms

= (4x² - x² ) + (14x - 8x) + (- 8 - 16)

= 3x² + 6x + (- 24)

= (3x² + 6x - 24) in²

From 1985 to 2007, the number B B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 B(t)=-329.4t+13747 where t is the year and t=0 corresponds to 1985. How many federally insured banks were there in 1990?

Answers

The number of federally insured banks in the year 1990 was 12,100.

Given data:

To find the number of federally insured banks in the year 1990, you need to substitute the value of t = 1990 into the given function B(t):

B(t) = -329.4t + 13747

Since t corresponds to the year and t = 0 corresponds to 1985, we need to calculate for t = 1990 - 1985.

t = 5.

Substitute t = 5 into the function:

B(5) = -329.4 * 5 + 13747

Now, perform the calculations:

B(5) = -1647 + 13747

B(5) = 12100

Hence, there were approximately 12,100 federally insured banks in the year 1990.

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Final answer:

Using the given equation and by substituting t with 5 (for the year 1990, five years after 1985) in that equation, we find that there were 13363 federally insured banks in 1990.

Explanation:

The question is asking how many federally insured banks there were in 1990, given that the number of banks in any given year from 1985 to 2007 is given by the equation

B(t) = -329.4t + 13747

. In this equation,

t

is the year with t=0 corresponding to 1985. To find the answer, we should substitute in the appropriate value of t, which would be 5 because 1990 is five years after 1985. Thus, the equation becomes B(5) = -329.4*5 + 13747. This simplifies to 15010 - 1647, which equals

13363

. Therefore, there were 13363 federally insured banks in 1990.

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1/2(x-6.5) = 3.16 what is x?

Answers

Answer:

x =12.82

Step-by-step explanation:

1/2(x-6.5) = 3.16

Multiply each side by 2

1/2(x-6.5) *2 = 3.16 *2

(x-6.5) = 6.32

Add 6.5 to each side

(x-6.5+6.5) = 6.32+ 6.5

x =12.82

Answer: 12.82

Step-by-step explanation:

1/2(x-6.5)= 3.16

x=12.82

How much of a 3/4 of cup serving is in a 2/3 cup of yogurt?

Answers

Answer:

8/9

Step-by-step explanation:

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