If the lengths of two adjacent sides of a parallelogram area a and b, and if the acute angle formed by these two sides is theta, show that the product of the lengths of the two diagonals is given by the expression (a^2 + b^2)^2 - 4a^2b^2cos^2theta

Answer: A

Step-by-step explanation:

Well when we use a calculator to determine the square root of 158 we get= 12.56980509.

And so option A woud be closest, smallest difference between all.

Answer: A

Step-by-step explanation: Square root of 158 simplified is 12.5698

Answer:

charged with providing of three types of clients

The measure of angle x of the quadrilateral inscribed in a circle is x = 31°

Given data ,

Let the quadrilateral be ABCD inscribed in a circle

Now , the measure of angles of the quadrilateral are

Opposite angles are supplementary: A + C = 180° and B + D = 180°.

Adjacent angles are supplementary: A + B = 180°, B + C = 180°, C + D = 180°, and D + A = 180°

And , the sum of opposite angles is always equal to 180°

So , the measure of 118° + 2x° = 180°

On simplifying , we get

2x = 62

Divide by 2 on both sides , we get

x = 31

Hence , the angle is solved and x = 31

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Answer:

I am pretty sure it's 0.2

Answer:

5/24

Step-by-step explanation:

To find 5/12 divided by 2, we do keep change and flip

Therefore we keep 5/12 change the division sign and flip the 2

We will get

5/12 * 1/2, this would give us 5/24

I guess this can help you, you're welcome in advance

The solution is, the simplification of the equation is :

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

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

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

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Answer:

First, you find the volume of each box

Volume = Length * Width * Height

Box A

V = 13 * 40 * 5

V = 2600 cm^3

Box B

V = 8 * 10 * 25

V = 2000 cm ^3

Box C

V = 11 * 20 * 30

V = 6600 cm ^3

Since 7400, the cubes trying to be packed, is bigger than any of the volumes of the boxes, 2 boxes must be used

The boxes with volumes that add up to a number greater than 7400 are Box C with Box A or B (either works, as long as C is one of them)

The total volume of the boxes together can be found with simple addition

2600 + 2000 + 6600 = 11200 cm ^3

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

The arithmetic mean of the returns is 7.06%.

The geometric mean of the returns is 6.77%.

Arithmetic mean is the sum of the returns divided by the total years of return.

Arithmetic mean = sum of  returns / number of years

Arithmetic mean = (12.6 + 16.9 + 4.4 - 5.8 + 7.2)% / 5

Arithmetic mean = 35.3% / 5

Arithmetic mean = 7.06%

Geometric mean is the average of a set of numbers that is determined by finding the product of the numbers.

Geometric mean = [(100 + 12.6) x (100 + 16.9) + (100 + 4.4) + (100 - 5.8) + (100 + 7.2)]^(1 / 5) - 1

Geometric mean = [112.6% x 116.9 x 104.4 x 94.2 x 107.2]^(1/5) - 1

Geometric mean = [1.126 x 1.169 x 1.042 x 0.942 x 1.072]^(1/5) - 1

Geometric mean = 1.377^(1/5)  - 1 = 0.0677 = 6.77%

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Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

Answer:

B

Step-by-step explanation:

When you flip over the y-axis you the x is multiplied by -1

Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

Answer:

D

Step-by-step explanation:

x^2 - 7x + 12 +  (x - 3)^2             Add (x - 3)^2 after it has been expanded.

x^2 - 7x + 12 + x^2 - 6x + 9        Combine like terms

2x^2 -7x - 6x + 21

2x^2 - 13x + 21                           Factor

(2x - 7)(x - 3)

Which is exactly what D says.

Answer:

supplementary

linear

Step-by-step explanation:

Answer: 13.7ft (1 decimal place)

Step-by-step explanation:

For this question you will have to use Pythagoras theorem.

The formula for the short side is x²=c²-b² and when you put the numbers from this question into it you get x²=15²-6²

15²=225

6²=36

x²=225-36

x²=189

Then, as you want to find x on its own, you would have to square root 189 which is 13.7 (1 decimal place).

Hope this helps :)

As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.

The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:

Number of Heads / Total Number of Flips = Experimental Probability of Heads

The number of heads in this case is 48, and the total number of flips is 100. Therefore,

Heads Experimental Probability = 48 / 100 = 0.48

We can multiply this by 100 to get a percentage:

Heads Experimental Probability = 0.48 * 100 = 48%

As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.

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Answer:

₱ 248,452.51

Step-by-step explanation:

₱ 248,452.51

Answer:

1. 10/7, 2/1, 1,5

2. 5/8 * 3/2

Step-by-step explanation:

(:

Answer:

Which part exactly.. Or which number exactly

Answer:

-4 and 1

Step-by-step explanation:

-4 times 1 equals -4 and then -4 plus 1 equals 3

The two numbers that satisfy the given conditions are 4 and -1. They multiply to -4 and add up to 3.

To find two numbers that satisfy the given conditions, we can set up a system of equations.

Let's assume the two numbers are represented by 'x' and 'y'. We know that their product is -4 and their sum is 3, so we can write the following equations:

xy = -4 (Equation 1)

x + y = 3 (Equation 2)

To solve this system of equations, we can use the substitution or elimination method. Let's use the substitution method.

From Equation 2, we can express y in terms of x: y = 3 - x.

Substituting this into Equation 1, we get:

x(3 - x) = -4

Expanding and rearranging the equation, we have:

3x - x² = -4

Rearranging again, we get a quadratic equation:

x² - 3x - 4 = 0

We can factor this equation:

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

Setting each factor to zero, we find two possible solutions for x:

x - 4 = 0 --> x = 4

x + 1 = 0 --> x = -1

Now, we can substitute these values of x back into Equation 2 to find the corresponding values of y:

For x = 4: y = 3 - 4 = -1

For x = -1: y = 3 - (-1) = 4

Therefore, the two numbers that satisfy the given conditions are 4 and -1. They multiply to -4 and add up to 3.

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Answer:

1.  8

2.  24

Step-by-step explanation:

The number of persons that drink grape milk only :

18 - 10 = 8

The number of persons that drink coffee :

42 - 8 = 34

The number of persons that drink coffee only :

34 - 10 = 24

The complement is 10%

The proportion is given as:

p = 90%

The complement is calculated as:

Complement = 100% - p

This gives

Complement = 100% - 90%

Evaluate the difference

Complement = 10%

Hence, the complement is 10%

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Answer:

-5y

Step-by-step explanation:

Since there is a common term (z) both in the numerator and in the denominator, i cancelled it from them.

Then, I divided the numerator by - 2 because it is a factor both of the numerator and denominator.

Answer:

16 gallons

Step-by-step explanation:

We need to find 4/5 of 20 gallons.

To do this, simply multiply 4/5 by 20.

\(\implies \dfrac{4}{5} \times 20=\dfrac{4 \times 20}{5}=\dfrac{80}{5}=16\)

The loss on selling 50 shares of stock would be 87.50.

To calculate the loss on selling 50 shares of stock originally bought at

\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.

First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.

Next, we calculate the difference between the purchase price and the selling price:

\(13.75 - 12 = 1.75.\)

Finally, we multiply the difference by the number of shares sold:

\(1.75 \times50 = 87.50.\)

Therefore, the loss on selling 50 shares of stock would be 87.50.

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Since the triangle is a right isosceles triangle and each leg measures x, its area is given by:

Now, let's use the given area and solve it for x:

Since the "path" already has fence, the amount of fence needed is 2x: