use the arithmetic sequence 12,15,18,21...

what is the equation of the nth term of the sequence

Let the number be x

10 - 2x = 14

2x = -4

x = -2

_ _ _                    _ _ _ _ _ _ _   _ _ _

|      |                     |      _ _ _    |    |      |

|      |                     |     |         |   |    |      |

|      |                     |     |         |    |   |      |  

|      |                     |    |          |    |   |      |      

|      | _ _ _ _ _ _  |    | _  _ _|    |  |      | _ _ _ _ _ _

| _ _ _ _ _ _ _ _|  | _ _ _ _ _ _|   | _ _ _ _ _ _ _ _|

The slope is 1/6x

You have to re-arranged the problem

x - 6y = 9 --> 6y = x - 9

6y = x - 9

__   ____    ---->  y = 1/6x - 3/2

6        6

Step-by-step explanation:

because

ST = QR = 16

that means that also the distance from the center point is the same.

in other words :

UC = VC

therefore,

2x = 5x - 9

0 = 3x - 9

9 = 3x

x = 3

The greatest acceleration when the unbalanced force is applied will be experienced by the least weighted box ( i.e., the mass of 2 kg)

Acceleration: it is defined as rate of change of velocity with respect to time.

Unbalanced Force:  it means that the force applied in one direction is greatest than the force applied in the opposite direction.

Given that, F = 8n.

let us assume that the boxes are of 2kg, 4 kg, 6 kg and 8 kg.

According to the 2nd law of motion: the external unbalanced force is directly proportional to rate of change of momentum or Force is equal to the product of mass and acceleration.

                         F = m × a

                 ⇒     a = F/ m

where,  F is Force, m is mass and a is acceleration.

Now, acceleration of the box of 2kg = 8÷2 = 4 m/s²

         acceleration of the box of 4kg = 8÷ 4 = 2 m/m²

         acceleration of the box of 6 kg = 8÷ 6 = 1.34 m/s²

         acceleration of the box of 8kg = 8÷ 8 = 1 m/s²

∴ the box with mass of 2kg experience the greatest acceleration.

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Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.

Suppose we have 2 positive integers, a and b, then:

gcd (a, b) = the greatest common divisor = common prime factors of a and b

lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b

In the given problem:

gcd (a, b) = 15

prime factorization of 15:

15 = 3 x 5

Hence,

a = 3 x 5 x ....

b = 3 x 5 x ....

lcm (a, b) = 90

prime factorization of 90:

90 = 3 x 5 x 2 x 3

Therefore the possible pairs of a and b are:

Combination 1:

a = 3 x 5 = 15

b = 3 x 5 x 2 x 3 = 90

Combination 2:

a = 3 x 5 x 2 = 30

b = 3 x 5 x 3 = 35

We can conclude the two integers are 15 and 90 or 30 and 45.

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 4224 hours   integer represents the average temperature per hour change during the 8 hours.

What is the short definition of temperature?

the temperature dropped  = 528 degrees

total time = 8 hours

the average temperature per hour change during the 8 hours = 528  * 8

                                                                                 =        4224 hours

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The graph of the inequality 3x - 2y > 2 is attached below.

We are given an inequality. The inequality is given below.

3x - 2y > 2

First of all, we will simplify the inequality. We need to keep the variable "y" on one side of the inequality. The inequality is modified as given below.

3x - 2y > 2

3x > 2 + 2y

3x - 2 > 2y

2y < 3x - 2

y < (3x - 2)/2

Now, to draw the graph of the inequality. We will first find the equation of the straight line corresponding to the given inequality.

y = (3x - 2)/2

We will draw a dotted line according to the above equation. Now, we will shade the area that satisfies the inequality. Hence, the graph is obtained.

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The original price for the television is $883.51

A store will discount an item by a percent of the original price.

Given that, a store is having a sale on televisions, all televisions are on sale for 15% off, a customer buys a television for $750.99.

Let the original price be x

x*(100-15)% = 750.99

x = 750.99*100/85

x = 883.51

Hence, the original price for the television is $883.51

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The value of x is when the value of the function f(x) = 7 is x= -24 and x = 16

Function:

A correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to output is known as the function of the relation.

Given,

Here we have the function f(x) = 0.5|x - 4| - 3.

Now, we have to find the value of x when the value of f(x) = 7.

In order to find the value of x as have to equate the give function with the value of f(x), that is 7,

So, when we apply these on the function then we get,

=> 7 = 0.5|x - 4|-3

Now, we have to move all the numbers instead of x, then we get,

=> 7 + 3 = 0.5|x - 4|

=> 10 = 0.5 |x - 4|

=> 10/0.5 = |x - 4|

=> 20 = |x - 4|

So in this place we can get the following forms,

=> x - 4 = 20 and

=> x - 4 = - 20

Because we get two values being an absolute value function.

Now, we have to add 4 on both sides

Then we get

=> x - 4 + 4 = 20 + 4 and

=> x - 4 + 4 = - 20 + 4

So, the value of x is

=> x = 24 and x = - 16

Therefore, for the given function the values of x are 24 and - 16.

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Answer:

672

Step-by-step explanation:

600+ .12(600)

600 + 72 = 672

Answer:

$24.27

Step-by-step explanation:

Original price: $

34.99

Discount percentage:

25

%

Results

Discount:

$8.75

Final Price:

$26.24

Details

Discount = Original Price x Discount %/100

Discount = 34.99 × 25/100

Discount = 34.99 x 0.25

You save = $8.75

Final Price = Original Price - Discount

Final Price = 34.99 - 8.7475

Final Price = $26.24

- 7.5% = $24.27

The cost of the sweater after a 25% of discount and 7.5% of sales tax will be 28.21.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A sweater priced at 34.99 is on sale for 25% off. Then the cost after the discount is calculated as,

⇒ (1 - 0.25) x 34.99

⇒ 26.24

If the sales tax is 7.5%. Then the cost after the sales tax is given as,

⇒ (1 + 0.075) x 26.2425

⇒ 28.21

The cost of the sweater after a 25% of discount and 7.5% of sales tax will be 28.21.

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Many solutions for a = c and b = 8.

No solution for a = c and b ≠ 8.

One solution for a ≠ c, b can be anything.

What is solution of equations?

Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is considered a solution to the problem. Finding the solution or solutions to an equation is known as solving it.

The two sides of the equation must be identical for all values of x if

ax + b = cx + 8 has an unlimited number of solutions. This suggests that

a = c and b = 8.

The two sides of the equation cannot be equal for any value of x if

ax + b = cx + 8 has no solutions. The only way this is possible is if

a = c and b ≠ 8, therefore b can be anything other than 8.

If there is exactly one solution to the equation ax + b = cx + 8, then a ≠ c, meaning that 'a' can be anything other than c. In this situation, 'b' is not constrained in any way (b can be anything).

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For the given triangles , developing proof is not possible due to following reasons:

First triangle : 21 + 25 < 48 not true.

Second triangle : Interior angle 130° > Exterior angle 125°

As given in the question,

For the given triangles developing proof is not possible due to following reasons:

First triangle:

Measure of three sides are given as 21, 25 , and 48.

As per the property to form a triangle : Sum of two sides is always greater than the third side.

Here, 21 + 25 < 48 .

Above mention property does not satisfied by given triangle.

Second triangle:

In a triangle, measure of exterior angle is always greater the opposite interior angles.

Here, measure of interior angle 130° > measure of exterior angle 125°

Does not satisfy the relation of exterior angles with interior angle.

Therefore, for the given triangles , developing proof is not possible due to following reasons:

First triangle : 21 + 25 < 48 not true.

Second triangle : Interior angle 130° > Exterior angle 125°.

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The instance has a mean of 1834 and a standard deviation of 231.2, respectively.

Given data;

A comparison of typical earnings for different professions can be found in the international average salary income database. The information is acquired from publications and reports that were obtained directly from governmental organizations, like the US Bureau of Labor Statistics or the ILO. Consider being informed that the standard deviation of the income of computer programmers in Canada is $458.60 and that a computer programmer in Canada making $2,063.30 has a z-score of 0.50 in comparison to other programmers in Canada. Consequently, the typical pay for computer programmers in Canada is. Assume you are also informed that the mean wage for computer programmers in Portugal is $1,387.40 and that a computer programmer in Portugal who earns $1,387.40 has a z-core of 2.00 in comparison to other computer programmers in Portugal is $925.

Since, the salaries are relative and we know that the z-score is given by;

z = X - μ / σ

0.50 = 2063.30 - μ / 458.60

μ = 2063.30 - 229.3

μ = 1834

As, the salaries are relevant so;

2 = 1387.40 - 925 / σ

σ = 462.4/2

σ = 231.2

Hence, the mean and standard deviation of the case is 1834 and 231.2 respectively.

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Answer:

-54

Step-by-step explanation:

8(-9)=-72

6(-3)=-18

-72+(-18)=-54

-Hope this helped

A line passes through the points (0, 0) and (–17, –11). The equation in the slope-intercept form will be y=9/5x+0

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the line passes through the points (0, 0) and (–17, –11).

The slope of the line is,

m = (5+4)/(5-0)

m= 9/5

The equation of the line passes through the point as,

(y-y₁)=m(x-x₁)

(y-0)=9/5(x-0)

5(y-0)=9(x-0)

5y=9x+0

y=9/5x+0

Thus, a line passes through the points (0, 0) and (–17, –11). The equation in the slope-intercept form will be y=9/5x+0

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Answer:

  (a)  (-26, -34)

Step-by-step explanation:

You want the solution to the system of equations ...

apparently using inverse matrices.

The system can be represented by the matrix equation ...

  AX = B

where A is the 2×2 matrix of coefficients, X is the 2×1 variable vector, and B is the 2×1 matrix of constants.

The solution to this system is found by multiplying on the left by the inverse of A:

  A⁻¹·AX = A⁻¹·B

  X = A⁻¹·B

The attachment shows the result of making this calculation:

  [tex]\boxed{X=\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}-26\\-34\end{array}\right]}[/tex]

The function, g(x), has a constant rate of change and will increase at a faster rate than the function f(x) for all the values of x.  

Given:

g(x) = 5/2 x -3 ..... (1)

f(x) = - 3.5 at x = 0

So, putting the value of x=0 in equation (1) for comparison. We get,

g(x) at x = 0

=> g(x) = 5/2 x (0) - 3

=> g(x) = -3

In this value of x function g(x) is faster than function f(x) having a value equal to -3.5.

Similarly, put x = 1 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (1) - 3

=> g(x) = (5-6)/2

=> g(x) = -1/2

In this value of x function g(x) is faster than function f(x) having a value equal to -1.

Similarly, put x = 2 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (2) - 3

=> g(x) = (5-3)

=> g(x) = 2

In this value of x function g(x) is faster than function f(x) having a value equal to 1.5.

Similarly, put x = 3 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (3) - 3

=> g(x) = (15/2 - 3)

=> g(x) = 7.5 - 3

=> g(x) = 4.5

In this value of x function g(x) is faster than function f(x) having a value equal to 4.

Therefore, for all values of x function g(x) is faster than function f(x).

function f(x).

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The relationship has a constant of proportionality of 38/39

From the question, the given parameters are

Variable 1 = 9/6

Variable 2 = 19/13

The above parameters can be represented as the following points

(x, y) = (9/6, 19/13)

The constant of proportionality of the points is then calculated as

k = y/x

Substitute the known values in the above equation

So, we have the following equation

k = (19/13)/(9/6)

Evaluate the quotient

So, we have

k = 38/39

Hence, the constant of proportionality is 38/39

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Answer:

D) Alan was farther away from Madison when he started driving

F) Alan and Andrew started the same distance from Madison

Step-by-step explanation:

Hopefully I got them all!!!

Answer:

A)

[tex]\sf -2x+7=-x+9[/tex]

[tex]\sf -2x+7-7=-x+9-7[/tex]

[tex]\sf -2x=-x+2[/tex]

[tex]\sf -2x+x=-x+2+x[/tex]

[tex]\sf -x=2[/tex]

[tex]\sf \cfrac{-x}{-1}=\cfrac{2}{-1}[/tex]

[tex]\boxed{\sf x=-2}[/tex]

____________________

B)

[tex]\sf 4x +15=2x+6[/tex]

[tex]\sf 4x+15-15=2x+6-15[/tex]

[tex]\sf 4x=2x-9[/tex]

[tex]\sf 4x-2x=2x-9-2x[/tex]

[tex]\sf 2x=-9[/tex]

[tex]\sf \cfrac{2x}{2}=\cfrac{-9}{2}[/tex]

[tex]\boxed{\sf x=-\cfrac{9}{2}}[/tex]

____________________

C)

[tex]\sf 8x+26=5x+14[/tex]

[tex]\sf 8x+26-26=5x+14-26[/tex]

[tex]\sf 8x=5x-12[/tex]

[tex]\sf 8x-5x=5x-12-5x[/tex]

[tex]\sf 3x=-12[/tex]

[tex]\sf \cfrac{3x}{3}=\cfrac{-12}{3}[/tex]

[tex]\boxed{\sf x=-4}[/tex]

____________________

D)

[tex]\sf 7x+31=16x+17[/tex]

[tex]\sf 7x+31-31=16x+17-31[/tex]

[tex]\sf 7x=16x-14[/tex]

[tex]\sf 7x-16x=16x-14-16x[/tex]

[tex]\sf -9x=-14[/tex]

[tex]\sf \cfrac{-9x}{-9}=\cfrac{-14}{-9}[/tex]

[tex]\boxed{\sf x=\cfrac{14}{9}}[/tex]

The angle between the two vectors < 8, 3 > and < 4, −3 > is 57.43°

Given: vectors < 8, 3 > and < 4, −3 >

To find the angle between two vectors, we can use the dot product method:

First, you will compute the dot product and magnitudes of both vectors. Thus,

Let a = < 8, 3 > and b = < 4, −3 >

a · b = <8, 3> ·<4, -3> = 8(4) + (3)(-3) =  32-9 = 23

|a| = √(8² + 3²) = √(64+9) = √73

|b| = √(4² + (-3)²) = √(16 + 9) = √25 = 5

By using the angle between two vectors formula using dot product,

θ = cos⁻¹ [ (a · b) / (|a| |b|) ]

θ = cos⁻¹ (23 / √73 · 5)

θ  = cos⁻¹ (23/42.72) = 57.43°

Therefore, the angle between the following two vectors is 57.43°

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After multiplying the simplified expression is   [tex]\frac{-x+5}{2x + 6}[/tex] ; x  ≠ -3 , 3 , -2 , -5  , the correct option is (b) .

In the question ,

it is given that ,

the expression is (x²-25)/(2x²+10x+12) × (-x²+x+6)/(x²+2x-15)

we need to find the value of the expression after multiplication .

= (x²-25)/(2x²+10x+12) × (-x²+x+6)/(x²+2x-15)

On splitting the given quadratic equation into factors , we get  

= (x+5)(x-5)/2(x+3)(x+2) × -(x+2)(x-3)/(x-3)(x+5)

= [tex]\frac{(x+5)(x-5)}{2(x+3)(x+2)}[/tex] × [tex]\frac{-(x+2)(x-3)}{(x-3)(x+5)}[/tex]

After cancelling out the common factors , we get

= -(x - 5)/2(x + 3)

= -x+5 / 2x + 6

= [tex]\frac{-x+5}{2x + 6}[/tex]    : x  ≠ -3 , 3 , -2 , -5

Therefore  , After multiplying the simplified expression is   [tex]\frac{-x+5}{2x + 6}[/tex] ; x  ≠ -3 , 3 , -2 , -5  .

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The area of the trapezoid formed is equal to 12 square meters.

The area of the trapezium is calculated by using the formula.

A =(a + b) × h / 2

In the given trapezium the length of the parallel sides are:

2 m and 4 meters.

The distance between the parallel sides is 4 m

Area of the trapezium = (2+4) × 4÷2 = 12 square meters

A trapezoid is a quadrilateral that has at least one pair of parallel sides.

A trapezoid is a convex quadrilateral by definition in Euclidean geometry. The parallel sides serve as the trapezoid's bases. The remaining two sides are referred to as the lateral sides or the legs if they are parallel; otherwise, the trapezoid appears to be a parallelogram, with two pairs of bases.

Therefore the area of the trapezium is 12 square meters .

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Answer: Carol's Thrift shop rate of change = $4.99/item

Wilma's Child Care rate of change is $7.50/hr

Step-by-step explanation:

Carol's Shop: equation of the line is in y=mx + b form, where m = slope = rate of change = $4.99/item

Wilma's slope = (y2 - y1) / (x2 - x1) = (15-0)/ (2-0) = $7.5/hr

Wilma's has the greater rate of change

The conversion of 41.98km to centimeters is gotten as; 4198000 cm

We are dealing with units conversion here and in this concept it involves converting from unit to the other using a standard conversion ratio.

Now, we are given the value as 41.98 km. However, we want to convert this value from kilometers to centimeters. The conversion ratio is;

1 kilometer = 100000 centimeters

Thus, using the conversion ratio above, we can say that;

41.98 km = (41.98 * 100000)/1

= 4198000 cm

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