Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. -12, 24, -48, ...​

Answer:

Absolute, relative, absolute, relative, relative

Step-by-step explanation:

Absolute location is the coordinates or address of something- it is exact.

Relative location is the location in reference to something else. For example, Mexico is south of the US compares the location of Mexico to the location of the US.

Answer:

1st: absolute

2nd: relative

3rd: absolute

4th: relative

5th: relative

Step-by-step explanation:

Absolute location provides a deeper, more drawn out description, while relative tends to usually use other buildings, landmarks, or other interesting things to point out the direction.

Absolute: (44 degrees N, 19 degrees W), 104 Lovers Lane.

Relative: East off the street of Mcdonalds, Across the street from the Cinema.

Step-by-step explanation:

This is an equation, where we need to find the value of x.

To solve this equation, we can first use the distributive property to expand 3.4(x + 7) which gives 3.4x + 3.4 * 7 = 3.4x + 23.8

Now we have the equation:

3.4x + 23.8 - 2.1 = 35.5

Next, we can add 2.1 to both sides of the equation:

3.4x + 23.8 = 37.6

Then, we can subtract 23.8 from both sides of the equation:

3.4x = 13.8

Finally, we can divide both sides of the equation by 3.4 to find the value of x:

x = 4

Therefore, the value of x that solves the equation is 4.

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Answer:

k

Step-by-step explanation:

Answer:

28/4 - 2x^3 = 7- 2x^3

Hope this helps!

Answer:

1

Step-by-step explanation:

This is the answer because:

You can use PEMDAS or GEMS to help you remember the order of operations.

PEMDAS: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction

GEMS: Grouping (Parenthesis), Exponents, Multiplication and Division (whichever comes first from left to right), Addition and Subtraction (whichever comes first from left to right).

1) We have to use the order of operations in order to solve this.

2) First, we have to divide because it's the first thing there is, 28/4 = 7

3) Next, we have to multiply since we cannot subtract before multiplying because you have to follow the rules of Order of Operations. 2 x 3 = 6

4) Finally, 7 - 6 = 1

Hope this helps!

Answer:

34791112

Step-by-step explanation:

Please check the attached for the explanation.

The next number for given sequence is 34791112.

The given sequence is 2,2,5,12,62,749,46450,......

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

Each number in the sequence is of the form Number3 × Number2 + Number1 = Number4

5×2+2=12

12×5+2=62

62×12+5=749

749×62+12=46450

So, the required number is

46450×749+62=34791112

Therefore, the next number for given sequence is 34791112.

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The algebraic expression after combining the like terms is

c² - 6c + 4cx - 7x + 1 .

An algebraic expression is a combination of constants, variable and coefficients in such a way that they form several terms in the form of a multi-variable polynomial.

A simple algebraic expression is given by :

3x+4y+2xy-9.

This algebraic expression contains four separate terms where x and y are variables , 3 and 4 and 2 are coefficients and 9 is a constant.

The given algebraic expression is:

-6c+c²-6x+4cx-x+1

To combine all the like terms we separate the variables and the constants.

or, c² - 6c + 4cx - 6x - x + 1

or, c² - 6c + 4cx - 7x + 1

Hence the required simplified expression is given by  :

c² - 6c + 4cx - 7x + 1

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The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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Answer:

might be four

not sure

good luck!

Answer:

20 hours Have a nice day

\(-21x^{2}-588\)

let me know if anything is unclear, I'm happy to help!

Answer:

$15.69

Step-by-step explanation:

multiply the retail price by 1.06 to get the price after taxes.

find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer

Answer:

c; 30

Step-by-step explanation:

the tens place is the second to last unit in a whole number

that number is 3

because there is one number after it you add one 0 to the end

30

Answer: -13

Step-by-step explanation:

The total distance from Duncan's start on the diving board to his lowest point beneath the surface of the pool will be 12 feet.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Duncan is excited to begin diving lessons. He starts on the diving board, 5 feet above the surface of the pool. Then, Duncan dives off the board and ends up 7 feet below the surface of the pool.

Distance = 7 + 5
Distance = 12 feet

Therefore, the total distance from Duncan's start on the diving board to his lowest point beneath the surface of the pool will be 12 feet.

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Step-by-step explanation:

By Pythagoras' theorem,

12^2 = 11^2 + height^2

height = ±√12^2 - 11^2 (rej -ve value since height > 0)

height = 16.279 (5sf) = 16.3 (nearest tenth place)

Topic: Pythagoras theorem

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Answer:

C(min)  =  277.95 $

Container dimensions:

x = 2.822 m

y = 1.411 m

h = 3.52 m

Step-by-step explanation:

Let´s call x  and  y the sides of the rectangular base.

The surface area for  a rectangular container is:

S = Area of the base (A₁) +  2 * area of a lateral side x (A₂) + 2 * area lateral y (A₃)

Area of the base is :

A₁ =  x*y       we assume, according to problem statement that

x  =  2*y      y  = x/2

A₁  =  x²/2

Area lateral on side x

A₂  = x*h           ( h  is the height of the box )

Area lateral on side y

A₃ = y*h        ( h  is the height of the box )

s = x²/2  + 2*x*h + 2*y*h

Cost  =  Cost of the base + cost of area lateral on x + cost of area lateral on y

C = 10*x²/2  + 8* 2*x*h  + 8*2*y*h

C as function of x is:

The volume of the box is:

V(b) = 14 m³  = (x²/2)*h       28 = x²h      h = 28/x²

C(x) = 10*x²/2  + 16*x*28/x² + 16*(x/2)*28/x²

C(x)  =  5*x²  +  448/x  + 224/x

Taking derivatives on both sides of the equation we get:

C´(x)  =  10*x  -  448/x² - 224/x²

C´(x)  =  0             10x  -  448/x² - 224/x² = 0     ( 10*x³ - 448 - 224 )/x² = 0

10*x³ - 448 - 224 = 0       10*x³ = 224

x³  =22.4

x = ∛ 22.4

x = 2.822 m

y = x/2  =  1.411 m

h = 28/x²  =  28 /7.96

h =  3.52 m

To find out if the container of such dimension is the cheapest container we look to the second derivative of C

C´´(x) = 10 + 224*2*x/x⁴

C´´(x)  =  10 + 448/x³    is positive then C has a minimum for x = 2.82

And the cost of the container is:

C = 10*(x²/2) +  16*x*h + 16*y*h

C = 39.82 +  158.75  + 79.38

C =  277.95 $

\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

Here's the solution ~

The Radius of the circle is 1 ft

now, use the given formula to find the Area of circle ~

\(\qquad \sf  \dashrightarrow \: \pi {r}^{2} \)

\(\qquad \sf  \dashrightarrow \:3 ( {1})^{2} \)

\(\qquad \sf  \dashrightarrow \: 3 (1)\)

\(\qquad \sf  \dashrightarrow \: 3 \: \: ft {}^{2} \)

The area of given circle is 3 ft²

Answer:

3ft 2

Step-by-step explanation:

The graph of the two given system of inequalities y > 2x - 5

y < -3x is; Attached below

We are given two inequalities;

y > 2x - 5

y < -3x

The graph that represents the 2 inequalities has been attached and from the graph, we see that;

The solution of the system of inequalities is the shaded pink area between the two dotted lines.

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Answer: 1.72%

Step-by-step explanation:

16300-16020/16300 = 1.72%

Answer:

25 %

Step-by-step explanation:

75 - 20% = 60

60 + 60 (x) = 75      where x = tax rate  

   x = .25   or 25 %

The kinetic energy of the safe increases the force exerted by the concrete

to several times the weight of the safe.

Reasons:

First part

The mass of the steel safe, m = 2,200 kg

Velocity of the safe just before it hits the concrete, v = 40 m/s

The amount by which the safe was compressed, d = 0.06 m

The kinetic energy, K.E., of the safe just before it hits the round is therefore;

\(\displaystyle K.E. = \mathbf{\frac{1}{2} \cdot m \cdot v^2}\)

\(\displaystyle K.E._{safe} = \frac{1}{2} \times 2,200 \times 40^2 = 1,760,000 \ Joules\)

Work done by concrete, W = Force, F × Distance, d

By the law of conservation of energy, we have;

The work done by the concrete, W = The kinetic energy, K.E. given by the safe

W = K.E. = 1,760,000 J

The effect of the work = The change in the height of the safe

Therefore;

The distance, d, over which the force of the concrete is exerted = The change in the height of the safe = 0.06 m

d = 0.06 m

Therefore;

\(\displaystyle The \ force \ of \ the \ concrete, \, F = \frac{1,760,000\, J}{0.06 \, m} = 29,333,333. \overline 3 \, N = 29.\overline 3 \ MN\)

Second part:

The gravitational force of the Earth on the safe, W = The weight of the safe

W = Mass, m × Acceleration due to gravity, g

W = 2,200 kg × 9.81 m/s² ≈ 21,582 N

The ratio of the force exerted by the concrete to the weight of the safe is found as follows;

\(\displaystyle Ratio \ of \ forces = \frac{29.\overline 3 \times 10^6 \, N}{21,582 \, N} = \frac{4,000,000}{2,943} \approx \mathbf{1359.16}\)

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The coordinates of p which divides the line AB in ratio 3:1 is (3.75, 3.5).

The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.

P ( x , y ) = ( c ⋅ m + a ⋅ n m + n , d ⋅ m + b ⋅ n m + n ) .

Ratio of line = 3:2

m and n represents the ratios 3:2

let the coordinates of p(x, y).

using Section formula

= [ (3(4) + 1(3) / (3+1), 3(3) + 1(5) / 3+ 1]

= (15/ 4, 14/4)

= (3.75, 3.5)

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Answer:

b

Step-by-step explanation:

Answer:

The answer is b

Step-by-step explanation:

100 represents a whole amount so the numerator would be 3 over 100 because it is 3% out of a total of 100.

The values of a and b are a = -3 and b = 42. The solutions for x can be written as:

x = -3 - √42

x = -3 + √42

To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:

Step 1: Move the constant term to the right side:

2x² + 12x - 66 = 0

Step 2: Divide the equation by the leading coefficient (2):

x² + 6x - 33 = 0

Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:

x² + 6x + (6/2)² = 33 + (6/2)²

x² + 6x + 9 = 33 + 9

x² + 6x + 9 = 42

Step 4: Rewrite the left side as a perfect square:

(x + 3)² = 42

Step 5: Take the square root of both sides:

√(x + 3)² = ±√42

x + 3 = ±√42

Step 6: Solve for x:

x = -3 ± √42.

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