Given a convex quadrilateral ABCD with AC⊥BD, prove that
AB2+CD2=BC2+AD2.

750 mL is equivalent to 25.36 oz.

When measuring liquids, the metric system and the US customary system are commonly used. In the metric system, the standard unit of measurement for liquids is milliliters (mL) and in the US customary system, it's ounces (oz).

To convert between these units, you can use a conversion factor.

One way to convert mL to oz is to use the conversion factor of 1 oz = 29.5735 mL. To find the number of ounces in 750 mL, you can use this conversion factor to set up an equation:

750 mL = x oz

Where x is the number of ounces you want to find. To solve for x, you can divide both sides of the equation by the conversion factor:

x = 750 mL / 29.5735 mL/oz

x = 25.36 oz

It's important to note that this is an approximation and for more accurate measurements, you should use an online calculator or consult a chart.

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A) True. The source term in a partial differential equation (PDE) represents a forcing function or external input to the system being modeled.

A) True. The source term in a partial differential equation (PDE) represents a forcing function or external input to the system being modeled. In the finite element method (FEM), the PDE is discretized into a set of algebraic equations, and the source term appears in each of these equations.

Specifically, for each algebraic equation resulting from the discretization of the PDE, the source term contributes to the coefficient of the dependent variable on the left-hand side of the equation, and it is taken to the right-hand side of the equation. The resulting coefficient and right-hand side term are then used to construct the corresponding row of the global coefficient matrix and the right-hand side vector, respectively.

Therefore, the source term affects all algebraic equations in the finite element method and is an essential component of the mathematical model. Changing the source term will affect the solution obtained from the ANSYS solver and can result in a different physical behavior of the system being modeled.

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Answer:30 x 96 feet = 10 x 32 yards

Step-by-step explanation:Convert 30 x 96 feet to yards

To convert length x width dimensions from feet to yards we should multiply each amount by the conversion factor. One foot equals 0.333333 yards, in order to convert 30 x 96 feet to yards we have to multiply each amount of feet by 0.333333 to obtain the length and width in yards. In this case to convert 30 x 96 feet into yards we should multiply the length which is 30 by 0.333333 and the width which is 96 by 0.333333. The result is the following:

30 x 96 feet = 10 x 32 yards

Definition of foot

A foot (symbol: ft) is a unit of length. It is equal to 0.3048 m, and used in the imperial system of units and United States customary units. The unit of foot derived from the human foot. It is subdivided into 12 inches.

Definition of yard

A yard (symbol: yd) is a basic unit of length which is commonly used in United States customary units, Imperial units and the former English units. It is equal to 3 feet or 36 inches, defined as 91.44 centimeters.

Meters to yards formula and conversion factor

To calculate a foot value to the corresponding value in yards, just multiply the quantity in feet by 0.333333 (the conversion factor).

Meters to yards formulae

yards = feet * 0.333333

The factor 0.333333 is the result from the division 1 / 3 (yard definition). Therefore, another way would be:

yards = feet / 3

Using our feet to yards converter you can get answers to questions like:

- How many yards are in 30 x 96 feet?

- 30 x 96 feet is equal to how many yards?

- How to convert 30 x 96 feet to yards?

- What is 30 x 96 feet in yards?

- How many is 30 x 96 feet in yards?

Hope this helped :)

The estimated number of birdhouses with one nest in non-golf locations would depend on the overall number of birdhouses in the non-golf locations if the proportion of nests occupied is the same for golf and non-golf sites.

Let's assume that there are a total of N birdhouses in the non golf locations, and that the proportion of nests occupied in both golf and non golf sites is p. The proportion of birdhouses with one nest in the non-golf locations would likewise be p since the proportions of nests occupied are the same for both locations. 

As a result, the anticipated number of birdhouses with one nest in areas other than golf courses would be:

Expected count = proportion of birdhouses with 1 nest x total number of birdhouses

Expected count = p x N

So, if we know the value of p and N, we can calculate the expected count of birdhouses with 1 nest in nongolf locations.

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Answer:

1

Step-by-step explanation:

1=1

Amy will earn $28.70 + $3.80 = $32.50.

Profit and loss:

A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.

Amy will earn $28.70 from selling 7 large necklaces (7 x $4.10 = $28.70) and $3.80 from selling 1 small necklace, so in total, she will earn $28.70 + $3.80 = $32.50.

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This is just here for the 20 character limit but the answer is in the picture.

Answer:

1,251 miles

Step-by-step explanation:

if 1/3 inch is 417 miles then one inch would be 3/3 so

417 x 3= 1,251 miles.

I hope this helps!

i get 11/2 is this wright answer??

Answer:

24 square millimeters

Step-by-step explanation:

Area of a triangle is half of the base times the height.

\(\frac{1}{2} bh\)

Here, that means

\(\frac{1}{2}\)(8)(6) = 24 square millimeters

Answer:

Mean, median, mode is 7 and the range is 4

Step-by-step explanation:

The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .

To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.

The scale factor is:

= 31 / 8

= 3. 875

Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :

= 13. 7 x 3. 875

= 53. 09 units

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Answer:

7.5 litres

Step-by-step explanation:

Let the amount of orange juice ve 3x litres and amount of grapefruit juice be 1x. (As they are in ratio of 3:1.)

Now, according to the question,

So,

⇒ Amount of orange juice + Amount of grape fruit juice = 10 litres

⇒ 3x + x = 10

⇒ 4x = 10

⇒ x = 10 ÷ 4

⇒ x = 2.5

Now,

⇒ Amount of orange juice he used= 3x litres

⇒ Amount of orange juice he used= 3(2.5) litres

⇒ Amount of orange juice he used= 7.5 litres

∴ He used 7.5 litres of orange juice.

Answer:

Given :

The length of a rectangle is 4 cm more than its width

The area of the rectangle is 96 cm²

To Find :

Width of the rectangle.

Solution :

Let the length of the rectangle be x cm.

Let the breadth of the rectangle be y cm.

Case 1:

➣

➣  _____(1)

Case 2 :

We have the formula for area of the rectangle as follows :

Where,

l = length → x cm

b = breadth → y cm.

➣

➣

Substitute, x = 96/y in equation 1,

➣

➣

➣

➣

➣

Divide by minus sign,

➣

➣

➣

➣

➣

➣

➣

As per assumption, y = breadth of the rectangle.

•°• y = -12 is not acceptable.

Substitute, y = 8 in equation 1,

➣

➣

➣

➣

Step-by-step explanation:

The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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Answer:

8.1

Step-by-step explanation:

The distance between Points M and N is 8.062258

so to round it to the nearest tenth will be to first look at the second decimal, if it is higher then 5 then it crosses over to the first decimal in this case that is zero so it then becomes 1.

You should deposit approximately $340.84 monthly to reach $293,000 in 28 years at a 4.4% annual interest rate compounded monthly.

To calculate the monthly deposit required for an investment plan paying 4.4% interest compounded monthly to reach $293,000 in 28 years, we use the future value of an annuity formula:

FV = P * (((1 + r)^n - 1) / r)

Here, FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of payments. First, convert the annual interest rate (4.4%) to a monthly rate by dividing by 12, which gives 0.0367 (4.4%/12) or 0.00367 as a decimal. The number of payments (n) is 28 years * 12 months/year = 336.

We want to find P, so rearrange the formula:

P = FV / (((1 + r)^n - 1) / r)

Substitute the values:

P = $293,000 / (((1 + 0.00367)^336 - 1) / 0.00367)

P ≈ $340.84

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The rational expressions below are given by:

Considering these concepts, the rational numbers for this problem are given by:

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9514 1404 393

Answer:

  12. (x, D, E, F) = (8, 38°, 75°, 67°)

  13. (x, P, Q, R) = (13, 126°, 30°, 24°)

Step-by-step explanation:

The sum of angles in a triangle is 180°. We choose to write the equations assuming all measures are degrees.

12. (5x -2) +(9x +3) +(11x -21) = 180

  25x = 200 . . . . . . . add 20, simplify

  x = 8 . . . . . . . . . divide by 25

Then the angle measures are ...

  ∠D = 5(8) -2 = 38°

  ∠E = 9(8) +3 = 75°

  ∠F = 11(8) -21 = 67°

__

13. (10x -4) +(4x -22) +(x +11) = 180

  15x = 195 . . . . . . . . . . add 15, simplify

  x = 13 . . . . . . . . . divide by 15

Then the angle measures are ...

  ∠P = 10(13) -4 = 126°

  ∠Q = 4(13) -22 = 30°

  ∠R = 13 +11 = 24°

to tiny submit closer picture

Answer:

When x = 4 and -4

Step-by-step explanation:

  x² = (4)² = 16

x² = (-4) =16

Answer:

.39 a cupcake

Step-by-step explanation:

to find the unit price, take 9.36 divided by 24

The quotient of (x^3 + 3x^2 - 4x - 12)/(x^2 + 5x + 6) is (x - 2).

To find the quotient of (x^3+3x^2-4x-12)/(x^2+5x+6) we can use polynomial long division method.

First, divide x^3 by x^2 and write down the quotient (x)

To find the remainder :

(x^3 + 3x^2 - 4x - 12) - x(x^2 + 5x + 6)

= x^3 + 3x^2 - 4x - 12 - x^3 - 5x^2 - 6x

= -2x^2 - 10x - 12

Now divide -2x^2 by x^2 and get the quotient (-2)

Then the remainder is :

(-2x^2 - 10x - 12) - (-2)(x^2 + 5x + 6)

= -2x^2 - 10x - 12 + 2x^2 + 10x + 12

= 0

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By permutation without repetition, there are 524160 possible different special pizzas.

The possible special pizzas can be calculated with permutation without repetition. The formula of permutation without repetition can be written as

P = n! / (n - k)!

where P is all of the possible combinations, n is the number of objects or elements, and k is how many numbers should be chosen.

From the question above, we know that :

n = 16

k = 5

By substituting the parameters, we can determine all of the possible different pizzas

P = n! / (n - k)!

P = 16! / (16 - 5)!

P = 16! / 11!

P = 16 x 15 x 14 x 13 x 12 x 11! / 11!

P = 524160

Hence, there are 524160 possible different special pizzas

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Answer:

1

Step-by-step explanation:

The required number to be added on both sides of the equation is 1.

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

The given quadratic equation is x² - 2x - 1 = 0.

In order to solve it using completing square method, the steps are as follows,

x² - 2x - 1 = 0.

=> x² - 2 × 1 × x - 1 = 0.

Add 1 on both sides to get,

=> (x² - 2 × 1 × x + 1) - 1 = 1

=> (x² - 2 × 1 × x + 1²) - 1 = 1

=> (x - 1)² - 1 = 1

=> (x - 1)² = 2

Hence, the number that has to be added to complete the square is 1.

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Answer:

Keep flip change as

4/1 / 1/3=4/1 *3/1=12

4/1 / 2/3 = 4/1*3/2= 12/2=6

Answer:

true

Step-by-step explanation:

it's in the correct order

Answer:

The answer is true.

Step-by-step explanation:

because when the exponent is an odd number a negative number stays negative

and when the exponent is an even number the sign changes and a negative number becomes positive

Step-by-step explanation:

the middle one has to be the same for both part ratios.

the best here is to bring the ratio element of B in the first part ratio to 10. we need to double the B element there

for that (as a ratio is a fraction) we also have to adapt the A element in the same way.

so, we get

4×2 : 5×2 : 9 =

= 8 : 10 : 9

and that is also shown in the graphic.

Answer:

X:Y:Z= 8:10:9

Step-by-step explanation:

Let x be the number of students in class A

Let y be the number of students in class B

Let z be the number of students in class C

x:y = 4:5

y:z= 10: 9

x:y:z = ?

Find the LCM of the y terms (5 and 10 ) which is 10

Divide 10 by the first y term (5) = 2

Divide 10 by the second y term(10) = 1

X: y = (4 x 2) :(5 x 2)= 8:10

y:z =(10 x 1) : (9:1)= 10:9

x:y:z= 8:10:9