In a rhombus, all the side lengths are $10,$ and one of the angles is equal to $120^\circ. $ Find the area of the rhombus

Answer:

Q11: x = 3

Q12: x = -4

Step-by-step explanation:

Q11
We have the equation as
[tex]\:64^{2x\:+\:4}=16^{5x}[/tex]

Convert the bases in terms of the common base 4

64 = 16 x 4 = 4 x 4 x 4  = 4³

16 = 4 x 4 = 4²

Therefore the original equation becomes:
[tex]\mbox {\large 4^{3\left(2x+4\right)}=4^{2\cdot \:5x}}[/tex]

Since the bases are the same in this equation, the exponents must also be the same

Equation the two exponents we get

3(2x + 4) = 2·5x

==> 6x + 12 = 10x

Move 12 to the right side

6x = -12 + 10x

Move 10x to the left:

6x - 10x = -12

-4x = -12

x = -12/-4 = 3

Answer to Q11

-------------------------------------------------------------

Q12

We can solve this in a similar manner to Q12

27 = 3 x 3 x = 3³

9 = 3 x 3 = 3²

Plugging these in we get

[tex]\mbox {\large 27^x = 3^{3(x)} = 3^{3x}}[/tex]

[tex]\mbox {\large 9^ {(x - 2)} = 3^{2(x-2)} = 3^{2x -4} }\\\\[/tex]

Thus we get

[tex]\mbox {\large 3^{3x} = 3^{2x -4} }\\\\[/tex]

Equating the exponents we get

[tex]3x = 2x - 4\\\\3x - 2x = -4\\\\x = -4[/tex]

ANSWER to 12

For the function f(x) = -5(4)x - 10, the end behaviour signifies that [x→∞,f(x)→-∞] and [x→-∞,f(x)→∞].

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given function is f(x) = -5(4)x - 10

On solving the function it gives -

f(x) = -20x - 10

The graph for the function is plotted.

The end behavior of a function f(x) describes the behavior of the function as x approaches +∞ and as x approaches -∞.

Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is -20x, the degree is 1, i.e. odd, and the leading coefficient is -20, i.e. negative.

This means that function f(x) approaches ∞ as x approaches -∞, and f(x) approaches -∞, as x approaches ∞.

Therefore, the end behaviour is [x→∞,f(x)→-∞] and [x→-∞,f(x)→∞].

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The Volume of the cell with an edge length of 10 Angstroms is 1×10⁻²¹cm³.

The volume of a cube with edge length of "L" is calculated as "L³" .

In order to find the volume of a cube with edge length = 10 angstroms (A) , we first need to convert the units to cm.

we know that 1 Angstrom = 1×10⁻⁸ cm,

So, 10 angstroms = 10×10⁻⁸ cm ;

The volume of a cell with an edge length of 10 Angstroms can be calculated as follows:

The volume of the cube in cm³ is =  (10×10⁻⁸ cm)³

⇒ 10³×10⁻²⁴ cm³

⇒ 1×10⁻²¹ cm³ .

Therefore , the volume of the cell is 1×10⁻²¹ cm³ .

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Technetium-99m has a half-life of 6 hours. After 21 hours, the remaining radioactive material  in the patient's blood stream is 0.053 mL.

The formula for half life is given by:

P(t) = Po (1/2)^(t/T)

Where:

P(t) = the remaining quantity of the substance at period t

Po = initial quantity

T = half life

Information available in the problem:

Po = 0.6 mL

T = 6 hours

t = 21 hours

Plug these parameters into the formula:

P(21) = 0.6 x (1/2)^(21/6)

P(21) =  0.6 x (1/2)^(3.5)

P(21) = 0.053

Hence, the remaining radioactive material  in the bloodstream is 0.053 mL

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The distance from A to B is 355.42 feet.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

Tan 4 = PQ/853

PQ = tan 4 x 853

PQ = 0.07 x 853 _____(1)

Tan 7 = PQ/(853 - x)

PQ = tan 7 x (853 - x)

PQ = 0.12 x (853 - x) ______(2)

Now,

From (1) and (2) we get,

0.07 x 853 = 0.12 x (853 - x)

59.71 = 102.36 - 0.12x

0.12x = 102.36  - 59.71

0.12x = 42.65

x = 355.42 feet

Thus,

A to B distance is 355.42 feet.

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Answer:

Step-by-step explanation: This equation only contains enough information to define a line in a  Koordinates system as far as i can tell. One point on this line would be y=3 and x=0 another one y=0 and x=15:4

i think xD

Answer: The correct option is, (B) SAS.

Step-by-step explanation: The SAS Postulate says that triangles are congruent if any pair of corresponding sides and their included angle are congruent.

A patent is a form of intellectual property that gives an individual or organization the exclusive right to manufacture, use, and/or sell an invention for a set period of time.

The length of a patent varies by country, but generally lasts for 20 years from the date the patent is filed with the government. This period can be extended in certain cases if the patent office grants a patent term extension.

The formula for calculating the length of a patent is: Length of Patent = Initial 20 Year Period + Extension. The initial 20 year period starts from the filing date of the patent application and is the same for all countries. However, the length of the extension varies depending on the country and the circumstances of the patent. For example, some countries may offer a 5-year extension, while others may offer a 10-year extension.

The length of a patent must be carefully calculated so that the patent owner can maximize the benefits of the patent. By calculating the patent length and extension, the patent owner can ensure that they are able to take advantage of their exclusive right to the invention for the maximum amount of time possible.

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y = C1e^(kx) is a valid solution to the equation.

To check that the given y is a solution to the equation, we must first substitute the given y into the given equation. We can do this by substituting the constants C1, C2, and k into the equation. We then move each side of the equation to the same side and simplify. This will result in an equation of 0 = 0, which confirms that the given y is a solution to the equation. In this case, the general solution to the second order differential equation dy dx + ky is yx) C1 cos(kx) + C2 sin(kx) or yx = D1 cosh(kx) + D2 sinh(kx). As such, the given y is a solution to the equation.

For the given equation, dy/dx = Py, with a constant k > 0, the given solution is y = C1e^(kx) or y = D1 cosh(kx) + D2 sinh(kx). To check that this is a valid solution, we can substitute the given solution into the equation and calculate dy/dx. If the result is equal to Py, then we can be sure that the given solution is a valid solution to the equation. For example, if we take the first solution y = C1e^(kx), then we can calculate dy/dx as dy/dx = C1ke^(kx) which is equal to Py = kC1e^(kx). We can see that the two sides are equal, so we can confirm that y = C1e^(kx) is a valid solution to the equation.

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Answer:

obtuse

Step-by-step explanation:

or acute triangle

is the answer

An increase in demand would result in a shift of line two to the right (option b).

The lines shown are known as demand and supply curves. The demand curve is a curve that shows the relationship between price and quantity demanded.

The demand curve has a negative slope.  This means that the higher the price, the lower the quantity demanded. This is in line with the law of demand.

When there is a change in demand, the demand curve would shift either to the left or to the right. If demand increases, the demand curve would shift to the right.

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Answer:

the answer is 20

Step-by-step explanation:

formulate the given
2/10%
rewrite the fraction
2/0.1  (then multiply both the numerator and denominator with the same integer)

= 20/1 (then simplify)
= 20
FA: 20

Answer:

Step-by-step explanation:

The ratio of the volume of the cylinder to the volume of the prism is 4/π.

The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm3, m3, in3, etc.

The volume of a square prism is referred to as the amount of space occupied by a 3-dimensional prism that has two congruent square bases and four rectangular faces are known as the volume of square prism. It is measured in cubic units. The volume of a prism is the product of the cross-sectional area and its length. The cross-sectional area is also known as the base area of the square prism.

We are given that a certain cylinder and square prism have equal lateral surface area.

Lateral surface area of cylinder = 2πrh

Lateral surface area of square prism = 4sH

So, 2πrh = 4sH

Also, the height of the cylinder is equal to the height of the prism.

So, h=H

Put in above equation:

2πrh = 4sh

⇒ πr = 2s

⇒ r/s = 2/π

The ratio of the volume of the cylinder to the volume of the prism

⇒ Volume of cylinder/ Volume of prism

⇒ πr²h/s²h

⇒ π(r/s)²

⇒ π(2/π)² ---- (From above)

⇒ 4/π

Thus, the ratio of the volume of the cylinder to the volume of the prism is 4/π.

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The time that Llyr arrives at Nuneaton, given that it is 6 minutes late, is 10 34.

Llyr's journey from Preston to Nuneaton took 114 minutes.

Kathy would not catch the 10 28 train to Milton Keynes.

Llyr is meant to arrive in Nuneaton at 10 28 but arrived 6 minutes later which is:

= 10 28 + 6

= 10 34

The time that the trip took is therefore:

= Arrival at Nuneaton - Departure at Llyr

= 10 34 - 08 40

= 1 hour 54 minutes

= 114 minutes

The time that Kathy would get back to the station is:

= Arrival time at Nuneaton + 1 hour 50 minutes

= 08 52 + 1 hour 50

= 10 42

This is too late for the 10 28 train to Milton Keynes.

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The experimental mass percent of barium in the sample is 55.526.

percentage, a relative value indicating hundredth parts of any quantity.

Given that the Barium metal was quantitatively precipitated from a 1.52 g sample of BaCl₂∙2H₂O.

The mass of the barium that was collected was 0.844 g.

We need to find the experimental mass percent of barium in the sample.

Let x/100 is the percentage of Barium.

x/100×1.52=0.844

0.0152x=0.844

x=55.526

Hence, the experimental mass percent of barium in the sample is 55.526.

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By using the tangent property of a circle, it has been proved that  ABC is isosceles

<BAY = 72°

< ABC = 54°

What is a circle's tangent?

First, it's crucial to understand circles.

Every point on a circle keeps a set distance from the center point in a two-dimensional, rounded form known as a circle. The circle's radius is the fixed separation.

The tangent to a circle is the straight line that intersects the circle at any point.

Then Now

<ACB = <BAY = 72° ( angles in alternate segments)

<ABC + <ACB + < CAB = 180° { being sum of angles of triangle }

54° + 72° + <CAB = 180°

<CAB = 180° - 126°

<CAB = 54°

Hence

ABC is an isosceles triangle

(being <CAB = <ABC)

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20×3=60

the present age of shirsha

Answer:

Let Shrisha's present age be x

According to question ,

After 20 years ,

Shrisha's age will be 3 times her present age.

[tex]\therefore \: 20 + x = 3x \\ \longrightarrow \: 3x - x = 20 \\ \longrightarrow \: 2x = 20 \\ dividing \: both \: sides \: by \: 2 \\ \\ \longrightarrow \: \cancel \frac{2x}{2} = \cancel \frac{20}{2} \\ \\ \longrightarrow \:\boxed{ x = 10}[/tex]

hence , Shrisha's present age is 10 years.

hope helpful! :)

Point (2, 1) is not the solution of the inequality y ≥ (1/2)x + 3.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

y ≥ (1/2)x + 3

Check whether point (2, 1) is the solution or not. Then we have

1 ≥ (1/2)(2) + 3

1 ≥ 1 + 3

Point (2, 1) is not the solution of the inequality y ≥ (1/2)x + 3.

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Answer:

x = 15

Step-by-step explanation:

We take x as the variable that replicates the number

When we put it into a equation we get

x + 15 = 2x

x = 15

When we check

15 + 15 = 2(15)

30 = 30

The sum of angles is 360 degrees is the required graph which represents the translation.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

Given,

x , y and z are exterior angles of triangle ABC.

So,

By angle sum property of triangle

Angles of

1 + 2 + 3 = 180

1 + z = 180

3 + y = 180

2 + x = 180

z + 180 = 1

y + 180 = 3

x + 180 = 2

So,

by substituting we get ,

180 - z + 180 - y + 180 - x = 180

x + y + z = 180 +180 + 180 - 180

x+ y +z = 360

Therefore, The sum of angles is 360 degrees is the required graph which represents the translation.

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If A limousine service has 15 cars available for rides: then the number of different collections C of 5 limousines are possible is 3003 .

To find the number of different collections C of five limousines, we can use combinations. A combination is a way to choose a subset of items from a larger set, without regard to order.

Let the number of Cadillac models n.

Then, 15 - 8 = 7 cars are Cadillacs. So, n = 7.

The number of different collections of 5 limousines from the 15 cars is given by the number of combinations of 5 items taken from a set of 15 items:

⇒ ¹⁵C₅ = 15!/(5!×(15 - 5)!) = 15!/(5!×10!) = 3003.

Therefore , there are 3003 different collections C of five limousines that the event organizer can choose from the limousine service's fleet of 15 cars.

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The mood of this sestet in Sonnet XIX by John Milton is hopeful.

This quote is from John Milton's Sonnet XIX and speaks about the idea that serving God does not necessarily mean doing physical work for him, but rather bearing his "mild yoke" with devotion.

The line "They also serve who only stand and wait" suggests that waiting for God's will with patience and humility is a form of service in itself. This sonnet explains how a devotee must be. The state of God is described as "kingly" and those who serve him well are said to speed at his bidding, without rest.

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The question for the answer is

That murmur, soon replies, “God doth not need

Either man’s work or his own gifts; who best

Bear his mild yoke, they serve him best. His state

Is kingly. Thousands at his bidding speed

And post o’er land and ocean without rest:

They also serve who only stand and wait.”

What is the mood of this sestet in Sonnet XIX by John Milton?

grim

hopeful

detached

somber

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To calculate the number of ways to arrange the books on a shelf, we can use the formula for permutations.

The formula for permutations is  [tex]\frac{n!}{(n-r)!}[/tex]  

where:  n is the total number of items

              r is the number of items being selected.

a. In this case, there are 8 books total (3 blue + 3 green + 2 red), and we are arranging all of them.

so n= 8 and r = 8, the number of arrangements is

[tex]\frac{8!}{(8-8)!}[/tex] = 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =  40320

So the answer to (a) is 40320.

b. To calculate the number of arrangements if the books of the same color are grouped, we can consider each group as one item.

There are 3 groups (blue, green, red), and we are arranging those

so n = 8 and r = 3.

Hence, the number of arrangements is

[tex]\frac{8!}{(8-3)!}[/tex] = [tex]\frac{8!}{5!}[/tex] = [tex]\frac{8x7x6x5x4x3x2x1}{5x4x3x2x1}[/tex] = 336

So the answer to (b) is 336.

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The difference is that in an observational study, the researchers do not control treatment, and in an experiment, they do.

An experiment is a method used to verify or disprove a theory, as well as to determine something's effectiveness or likelihood.

An experiment vs an observational research differs fundamentally in that:

Members of a sample are measured or surveyed during an observational study without any attempt to manipulate them.

In an experiment, decisions are made under controlled conditions, subjects are divided into groups, and one group is given therapy while the other is left untreated. The main distinction between well-executed observational studies and experimental designs is that the replies of participants are unaffected, whereas in experiments, at least some participants are subjected to a treatment condition at random.

As a result, the researchers in an experiment control the therapy, but they do not in an observational study.

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The Mustang is worth $24,320 after one year.

Compound interest is computed on the principal as well as the interest accumulated over the preceding period. It differs from simple interest in that interest is not added to the principal when computing interest for the next month.

Compound annual growth rate (CAGR) is the average yearly growth rate of an investment over a time period greater than one year. It is one of the most reliable methods for calculating and determining returns for individual assets, investment portfolios, and anything else whose value might grow or decline over time.

The formula to calculate the value of the Mustang after one year is:

value_after_one_year = value_initial * (1 - 0.24)

Plugging in the given values:

value_after_one_year = $32,000 * (1 - 0.24)

= $32,000 * 0.76

= $24,320

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Examples of categorical variables are race, sex, age group, and educational level.

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Answer:

Below

Step-by-step explanation:

I believe your equation is incorrect ( perhaps a typo)

probably it is   x^2 - 17x +16

  then you could choose factors 16 and 1

     to get this    (x-1)(x-16)

Answer:

x = 0

y = -2

Step-by-step explanation:

1. 6x+2y = -4

2. x - 2y = 4

in our second equation lets isolate x

x = 2y + 4

now lets plug this into our first equation

6(2y+4) + 2y = -4

12y + 24 + 2y =-4

14y +24 = -4

14y = -28

y = -2

lets plug in y into the second equation to find x

x = 2(-2)+4

x = -4+4

x = 0

The total number of bars which were sold Online = 14816

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer.

The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers.

Multiplication is used to make repetitive adding of the same number easier.

The number of cases of Essence soap sold is one-third as many as the number of Zing soap,

So:

Essence soap = 72 cases / 3 = 24 cases

The total number of cases sold will be:

72 cases + 24 cases = 96 cases.

And the total number of bars sold is:

96 cases * 156 bars/case = 14816 bars.

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The 2-digit number that is a multiple of 9 and the sum of it digits is 1/5 of the number itself is 45.

A 2-digit number can be written as:

a*10 + b

Where a and b are single digit numbers.

We know that the number is a multiple of 9, and we also know that:

a + b = (1/5)*(a*10 + b)

We can isolate one of the variables:

a + b = 2a + (1/5)b

b - (1/5)b = 2a - a

(4/5)b  = a

So, now we need to find values of b such that:

a is also a whole number.

10a + b is a multiple of 9.

if b = 5 we will get:

(4/5)*5 = a

4 = a

Then the number is 45, which is 5*9, so it is a multiple of 9.

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