what is the common ratio for the geometric sequence? 54,36,24,16...

Answer:500

explanchion: 1000/50=500

Sea level starts at 0m

Since we start at 0 and it is 20m above sea level, we can add.

0 + 20 = 20m

Therefore, the elevation is 20m

Best of Luck!

A system of inequalities to describe this situation are as follows;

x + y ≤ 16

20x + 12y ≥ 240.

The system of inequalities has been solved graphically and one possible solution is (6, 10).

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hours tutoring purchased and number of hours clearing tables respectively, and then translate the word problem into algebraic equation as follows:

In Mathematics, the inequality symbol for "no more than" is ≤ while the inequality symbol for "at least" is ≥.

Since Morgan makes $20 per hour tutoring and $12 per hour clearing tables and can work no more than 16 total hours and must earn at least $240, the system of linear inequalities that are required to model this situation include the following:

x + y ≤ 16

20x + 12y ≥ 240

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (6, 10).

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W satisfies all the three conditions of being a subspace of V. So, W is a subspace of V.

W is the set of all 3 x 2 matrices of the form [a,b; (a + b),0; 0,c]. It needs to be verified that W is a subspace of V, which has standard operations. Let us check whether W satisfies the three conditions to be a subspace of V or not:

Closure under addition: If X, Y are any two elements of W, then X + Y is also in

W.[a₁, b₁; (a₁ + b₁), 0; 0,c₁] + [a₂, b₂; (a₂ + b₂), 0; 0,c₂] = [a₁ + a₂, b₁ + b₂; (a₁ + b₁ + a₂ + b₂), 0; 0,c₁ + c₂]

The resulting matrix has the same form as W. So, W is closed under addition.

Closure under scalar multiplication: If X is any element of W and k is any scalar, then k

X is also in W.k[a, b; (a + b), 0; 0,c] = [ka, kb; k(a + b), 0; 0,kc]

This is of the same form as W. So, W is closed under scalar multiplication.

Contains zero vector: The zero vector is [0,0; 0,0; 0,0], which is of the same form as W. So, W contains the zero vector.

Therefore, W satisfies all the three conditions of being a subspace of V. So, W is a subspace of V.

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A≈50.27cm²

Using the formulas

A=πr2

d=2r

Solving forA

A=1

4πd2=1

4·π·82≈50.26548cm²

Answer:

16π cm^2

Step-by-step explanation:

The formula for the area of a circle is \(\pi r^{2}\), r being the radius. The radius is always half of the diameter, so in this case, the radius is 4. \(4^{2}\) is just 4 * 4 which is 16. Multiply that by π and you get 16π. Or, approximately 50.27 cm^2

To perform the operation \(\(\frac{7x}{5} + \frac{5x}{7}\)\), we need to find a common denominator and then add the fractions. The result is \(\(\frac{49x}{35} + \frac{25x}{35} = \frac{74x}{35}\).\)

To add the fractions \(\(\frac{7x}{5}\)\) and \(\(\frac{5x}{7}\)\), we first need to find a common denominator. The least common multiple of 5 and 7 is 35.

Now, we can rewrite the fractions with the common denominator:

\(\(\frac{7x}{5} = \frac{7x}{5} \cdot \frac{7}{7} \\\\ = \frac{49x}{35}\)\)

\(\(\frac{5x}{7} = \frac{5x}{7} \cdot \frac{5}{5} \\\\ = \frac{25x}{35}\)\)

Adding the fractions together, we get:

\(\(\frac{49x}{35} + \frac{25x}{35} = \frac{49x + 25x}{35} \\\\ = \frac{74x}{35}\)\)

Therefore, the sum of \(\(\frac{7x}{5} + \frac{5x}{7}\) is \(\frac{74x}{35}\)\).

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Option B is correct -The value of x is 15/2

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

the given expression is,

7( 2x - 5) -2(2x - 5) = 4(x + 5)

now ,open all the brackets of the equation,

14x - 35 - 4x + 10 = 4x + 20

now , add all the like terms of this expression,

10x -25 = 4x + 20

arrange all the like terms on one side and rest on the other side,

10x - 4x = 20 +25

6x = 45

x = 45/6

x =  15/2

so, 15/2 is the value of x in this expression.

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The linear function rule that models the total cost y​ for any number of sweatshirts x would be: y = 9.50x

What is Algebraic expression ?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.

To write a linear function rule that models the total cost y​ (in dollars) for any number of sweatshirts x, we can use the equation of a line which is given as:

y = mx + b

where m is the slope of the line and b is the y-intercept.

In this case, the slope represents the cost per sweatshirt, which is $7.00, and the y-intercept represents the fixed cost, which is the shipping charge of $2.50. Therefore, the linear function rule that models the total cost y​ for any number of sweatshirts x can be written as:

y = 7x + 2.50

If the shipping charge applied to each sweatshirt, the linear function rule would change. In this case, the cost per sweatshirt would be the sum of the base cost of $7.00 and the shipping charge of $2.50, which is $9.50. Therefore, the linear function rule that models the total cost y​ for any number of sweatshirts x would be: y = 9.50x

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Answer: B

Step-by-step explanation:

Answer:

10% of 100,000 = 10,000

Step-by-step explanation:

100,000 x 0.10 = 10,000

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Answer:

10,000

Step-by-step explanation:

10%=0.10

Of=Multiplication

0.10 x 100,000

10,000

Answer:

He should use 1/2 of a teaspoon of pepper.

Step-by-step explanation:

From the question, the soup recipe requires 1/4 of a teaspoon of pepper for every 1/2 of a teaspoon of dried basil.

Now, to determine how much pepper Terrell should use if he uses 1 teaspoon of dried basil for the huge pot of soup,

Let the quantity be x

If 1/4 of a teaspoon of pepper requires 1/2 of a teaspoon of dried basil,

then, x teaspoon of pepper will require 1 teaspoon of dried basil

x = (1/4 × 1) ÷ (1/2)

x = 1/4 ÷ 1/2

x = 1/4 × 2/1

x = 2/4

x = 1/2

∴ 1/2 of a teaspoon of pepper is required for 1 teaspoon of dried basil.

Hence, he should use 1/2 of a teaspoon of pepper.

Answer:

40% = 0.40

800 / 0.40 = 2000 total tickets were sold

Step-by-step explanation:

Answer: x^6+6x^4+8x^2+2

Step-by-step explanation:

Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in

(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2

Answer: Greatest common factor is x.

Step-by-step explanation:

(\(x^2\)) (4x)

Both terms share x.  x is the Greatest Common factor, and the only factor in this manner.

If you were to simplify and take out the x, you would have:

x  (x)*(4)

Answer:

7x-2+5x-10+4x=180°

16x-12=180

16x=192

x=192/16

x=12

Answer:

B

Step-by-step explanation:

Sin x°= opposite ÷ hypotenuse

Cos x°= adjacent ÷ hypotenuse

Tan x°= opposite ÷ adjacent

Ctg x°= adjacent ÷ opposite

The correct will bet cot x = adjacent ÷ opposite

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Using trigonometric properties we have

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Answer: y=5(x+15)2−26 5

Answer:

padlet        com     /vpena20241    

/sv1blyklvnvfbcdw

Step-by-step explanation:

The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.

For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".

Using quantifiers and logical connectives, we can express the given fact as follows:

∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))

Explanation:

- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r

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The functions e^x/2 and xe^x/2 form a fundamental set of solutions of the differential equation on the interval (-[infinity],[infinity]). The general solution of the differential equation is

y(x) = c1 e^x/2 + c2 xe^x/2.

The differential equation

4y"-4y'+y

=0

can be solved using the method of characteristic equation. It is given that the fundamental set of solutions of the differential equation on the interval (-[infinity], [infinity]) are

e^x/2 and

xe^x/2.

The Wronskian of the given differential equation is given as:

w(e^x/2, xe^x/2) - _

= e^x/2 * d/dx (xe^x/2) - xe^x/2 * d/dx (e^x/2)

= e^x/2 * e^x/2 - xe^x/2 * e^x/2

= e^x

Therefore, since Wronskian is never zero, the given fundamental set of solutions are linearly independent.Let's form the general solution of the differential equation

4y"-4y'+y

=0 as:

y(x)

= c1 e^x/2 + c2 xe^x/2

Here, c1 and c2 are arbitrary constants.

Therefore, the answer is:

The functions e^x/2 and xe^x/2 form a fundamental set of solutions of the differential equation on the interval (-[infinity],[infinity]). The general solution of the differential equation is

y(x)

= c1 e^x/2 + c2 xe^x/2.

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The Laplace transforms for the given functions (a) through (f):

a. we have

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{\cos(3t)u(t)\} = \frac{s}{s^2 + 9}\)\)

b. we have:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{e^{-10t}u(t)\} = \frac{1}{s + 10}\)\)

c. we can split the transform into two parts:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{e^{-10t}\cos(3t)u(t)\} = \frac{1}{(s + 10)^2 + 9}\)\)

d. we can obtain the transform as follows:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{-10t\cos(3t)u(t)\} = -\frac{d}{ds}\left(\frac{s}{s^2+9}\right)\)\)

e. we can write the transform as follows:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{[2-2e^{-4t}]u(t)\} = \frac{2}{s} - \frac{2}{s+4}\)\)

f. we can express the transform as follows:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{[15 + 15\cos(500t)]u(t)\} = \frac{15}{s} + \frac{15s}{s^2+250000}\)\)

A well-known mathematical method for resolving a differential equation is the Laplace transform. Transformations are used to solve a variety of mathematical issues. The goal is to change the issue into one that is simpler to handle.

To find the Laplace transforms of the given functions, we'll use the standard Laplace transform formulas. Here are the Laplace transforms for each function:

(a) \(\(x(t) = \cos(3t)u(t)\)\)

Using the formula for the Laplace transform of cosine, we have:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{\cos(3t)u(t)\} = \frac{s}{s^2 + 9}\)\)

(b) \(\(x(t) = e^{-10t}u(t)\)\)

Using the formula for the Laplace transform of exponential functions, we have:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{e^{-10t}u(t)\} = \frac{1}{s + 10}\)\)

(c) \(\(x(t) = e^{-10t}\cos(3t)u(t)\)\)

Using the properties of the Laplace transform and the formulas for exponential and cosine functions, we can split the transform into two parts:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{e^{-10t}\cos(3t)u(t)\} = \frac{1}{(s + 10)^2 + 9}\)\)

(d) \(\(x(t) = -10t\cos(3t)u(t)\)\)

Using the properties of the Laplace transform and the formulas for multiplication by (t) and cosine functions, we can obtain the transform as follows:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{-10t\cos(3t)u(t)\} = -\frac{d}{ds}\left(\frac{s}{s^2+9}\right)\)\)

(e) \(\(x(t) = [2-2e^{-4t}]u(t)\)\)

Using the properties of the Laplace transform and the formulas for constant multiplication, subtraction, and exponential functions, we can write the transform as follows:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{[2-2e^{-4t}]u(t)\} = \frac{2}{s} - \frac{2}{s+4}\)\)

(f) \(\(x(t) = [15 + 15\cos(500t)]u(t)\)\)

Using the properties of the Laplace transform and the formulas for constant multiplication and cosine functions, we can express the transform as follows:

\(\(\mathcal{L}\{x(t)\} = \mathcal{L}\{[15 + 15\cos(500t)]u(t)\} = \frac{15}{s} + \frac{15s}{s^2+250000}\)\)

These are the Laplace transforms for the given functions (a) through (f).

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Answer:

pentagon

Step-by-step explanation:

540 / 5 = 108

The domain of the function C(m) = 0.05m + 20 is (0, ∞) and the range of the function C(m) = 0.05m + 20 is (20, ∞).

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

Haley pays a monthly fee of $20 for her cell phone and then pays 5 cents per minute used. The total cost of Haley’s monthly cell phone bill can be expressed by the function

\(\rm C(m) = 0.05\ m + 20\)

The domain of the function is from zero to infinity because time can never be negative.

Then the range of the function will be

At m = 0, the value of C(m) will be

C(m) = 0.05(0) + 20

C(m) = 20

At m = ∞, the value of C(m) will be

C(m) = 0.05(∞) + 20

C(m) = ∞

Thus, the domain of the function is (0, ∞) and the range of the function is (20, ∞).

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To evaluate the indefinite integral ∫x³cos(x³) dx as an infinite series, we can use the power series expansion of the cosine function.

The power series expansion of cos(x) is given by:

cos(x) = 1 - (x²/2!) + (x⁴/4!) - (x⁶/6!) + ...

Now, let's substitute u = x³, then du = 3x² dx, and rearrange to obtain dx = (1/3x²) du.

Substituting these values into the integral, we get:

∫x³cos(x³) dx = ∫u(1/3x²) cos(u) du

= (1/3) ∫u cos(u) du

Now, we can apply the power series expansion of cos(u) into the integral:

= (1/3) ∫u [1 - (u²/2!) + (u⁴/4!) - (u⁶/6!) + ...] du

= (1/3) [∫u du - (1/2!) ∫u³ du + (1/4!) ∫u⁵ du - (1/6!) ∫u⁷ du + ...]

Integrating each term separately, we can express the indefinite integral as an infinite series.

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Option (c) 26.7% of the global oceans are Marine Protected Areas (MPAs). Marine Protected Areas (MPAs) are designated areas in the oceans that are set aside for conservation and management purposes.

They are intended to protect and preserve marine ecosystems, biodiversity, and various species. MPAs can have different levels of restrictions and regulations, depending on their specific objectives and conservation goals.

As of the current knowledge cutoff in September 2021, approximately 26.7% of the global oceans are designated as Marine Protected Areas. This means that a significant portion of the world's oceans has some form of protection and management in place to safeguard marine life and habitats. The establishment and expansion of MPAs have been driven by international agreements and initiatives, as well as national efforts by individual countries to conserve marine resources and promote sustainable practices.

It is worth noting that the percentage of MPAs in the global oceans may change over time as new areas are designated or existing MPAs are expanded. Therefore, it is important to refer to the most up-to-date data and reports from reputable sources to get the most accurate and current information on the extent of Marine Protected Areas worldwide.

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To find the integer value of n that results in exactly 560 lattice points strictly in the interior of the triangle, use the equation: n = (560 + 2)/8.

This equation is derived by counting the lattice points on each side of the triangle, starting with the side between points (1,1) and (9,1). This side has a length of 8, so it contains 8 lattice points, including the two endpoints. The remaining sides have lengths of 8 + n and 8 + n, which combined have 8 + 2n lattice points. The total number of lattice points in the triangle is then 8 + 8 + 2n = 16 + 2n.  

Solving for n when the total number of lattice points is 560 gives us n = (560 + 2)/8. Therefore, the integer value of n is 70.

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Answer:

5 cups

Step-by-step explanation:

To do this simply, we can just count up how many cups we can buy.

starting balance=

$12.50

after cup 1=

12.5−2.5=$10.00

after cup 2=

10−2.5=$7.50

after cup 3=

7.5−2.5=$5.00

after cup 4=

5−2.5=$2.50

after cup 5=

2.5−2.5=$0.00

From this, we can see that after buying the 5th

cup, the buyer is out of money, so that means that you can buy

5 cups of food to feed the animals before running out of money.

The number of cups is 2 cups

The equation is y = 2x + 10 where the slope of the equation x is the number of cups and y is the total amount

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the total number of cups be = x

The total amount y = $ 14

The cost of entering the zoo = $ 10

The cost of of feeding the animals per cup = $ 2

So , the equation will be

Total amount y = cost of entering the zoo + ( total number of cups x cost of of feeding the animals per cup )

Substituting the values in the equation , we get

y = 2x + 10   be equation (1)

On simplifying the equation , we get

14 = 2x + 10

Subtracting 10 on both sides of the equation , we get

2x = 4

Divide by 2 on both sides of the equation , we get

x = 2 cups

Therefore , the value of x is 2 cups

Hence , the number of cups is 2 cups

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Answer:

25%

Step-by-step explanation:

The figure is a right-angled triangle so we can use trigonometric ratios to solve for E.

Side DE is adjacent to That is

Since \(\begin{gathered}

Important notice:

/\2 = Power 2

Answer:

D. 1,047.2

Step-by-step explanation:

The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed.

The silo is made up of a cylinder with the height of 10 feet and base radius of 5 feet and two cones, each having the height of 5 feet and base radius of 5 feet.

The formulas volume of cylinder πr /\2 h and volume of cone 1/3  πr/\2h can be used to determine the tatol volume of the silo.

Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is:

V = π(5)/\2 (10) + (2) ( 1/3) π(5) /\2 (5)

= ( 4/3 ) (250)π

= 1,047.2 cubic feet.