Find the eighth term of each geometric sequence. -30,7.5,-1.875, . . . . .

Explicit formulas for arithmetic sequences are derived from terms in arithmetic sequences. It helps to find each term in arithmetic progression easily. The arithmetic progression is a1, a2, a3, ..., an. where the first term is denoted as 'a', we have a = a1, and the tolerance is denoted as 'd'. The tolerance formula is d = a2 - a1 = a3 - a2 = an - an - 1. The nth term of the arithmetic progression represents the explicit formula for the arithmetic progression.

Explicit formula: an= a + (n − 1) d

Explicit formula: Sn = n/2 [2a+(n-1) d]

Where,

nth term in the arithmetic sequence

a = first term in the arithmetic sequence

d = difference (each term and its term difference) previous term, i.e., d = an-an-1

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We can conclude that BC ≅ DA is congruent under corresponding parts of congruent triangles.

So,

Given: BA ≅ DC, ∠ B A C ≅ ∠ D C A

To Prove: BC ≅ DA

First, we'll prove the △BAC ≅ △DAC

So, △BAC ≅ △DAC under SAS conditions.

Therefore, we can conclude that BC ≅ DA is congruent under corresponding parts of congruent triangles.

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Answer: (1, 34) and (2, 17)

Step-by-step explanation:

Step 1: Divide 34 by the smallest prime factor.

34/2 = 17

Step 2: Since 17 itself is a prime number, therefore, it is divisible by 17 only.

17/17 = 1

Step 3: Now further division is not possible. Thus, we will consider 2 and 7 as the prime factors of 34.

The required solution for the given arithmetic problems are,
A) 2/5
B) 72 / 125
C) 6, 3/4, 12/5, and 3/10
D) 4, 1/6 and 6

A) 12/25 times 15/18.
Division of two fractions performed as multiplication of numerator of one fraction with a denominator of another function over a denominator of one function with a numerator of another function.
= 12 / 25  * 15 / 18 = 2 / 5

Similarly

b) 12/25 divided by 15/18.
= [12 / 25 ] / 15 / 18
= 12 / 25 * 18 / 15
= 72 / 125

C) 6 and 3/4 times 1 and 2/5
 6 * 1 = 6
3 / 4 * 1 = 3/4
6 * 2/5 = 12/5
3/4 * 2/5 = 3 / 10

D) 4 and 1/6 divided by 1 and 2/3.
= 4 / 1 = 4
= 1/6  / 1 = 1/6
= 4 / 2/3 = 6
= 1/6 / 2/3 = 1/4

Thus, the required solution for the given arithmetic problems is mentioned above.

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Step-by-step explanation:

when x increases by 1. y decreases by 7.

e.g. from (-4, 7) to (-3, 0).

the slope is therefore -7/1 = -7.

the slope is always the factor of x in the equation.

y = -7x + b

b is the y-intercept (the y value when x = 0).

let's use e.g. (-3, 0) to get b :

0 = -7×-3 + b = 21 + b

b = - 21

so, the full equation is

y = -7x - 21

Answer:

true

Step-by-step explanation:

The quadrilateral with vertices (2 , 5), (4 , 8), (7 , 6), and (5 , 3) is a rectangle.

The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

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

In a rectangle, each pair of adjacent side/line is perpendicular with each other, thus, the slope is negative reciprocal of one another. Also, opposite sides are parallel, thus their slopes are equal.

let A = (2 , 5)

B = (4 , 8)

C = (7 , 6)

D = (5 , 3)

(8 - 5)/(4 - 2) = (3 - 6)/(5 - 7)

3/2 = -3/-2

3/2 = 3/2

(6 - 8)/(7 - 4) = (3 - 5)/(5 - 2)

-2/3 = -2/3

(8 - 5)/(4 - 2) = (6 - 8)/(7 - 4)

3/2 = -2/3

(6 - 8)/(7 - 4) = (3 - 6)/(5 - 7)

-2/3 = 3/2

(3 - 6)/(5 - 7) = (3 - 5)/(5 - 2)

3/2 = -2/3

(3 - 5)/(5 - 2) = (8 - 5)/(4 - 2)

-2/3 = 3/2

Using the slope of the line connecting the vertices, we have proved that the quadrilateral with vertices (2 , 5), (4 , 8), (7 , 6), and (5 , 3) is a rectangle.

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Answer:

Hope this helps :)

24.263 = 24.3

341.276 = 341.28

299.61 = 300

4,123.499 = 4,123

5.246 = 5.25

Step-by-step explanation:

When rounding first look at the number next to the place that is told to rounded to (for example, they tell you to round to nearest tenth, then look at the place value next to it). If that number is 1, 2, 3, or 4 then round down, and if that number is 5, 6, 7, 8, or 9 then round up.

Answer:

A

Step-by-step explanation:

x² - 14x

using the method of completing the square

add ( half the coefficient of the x- term )² to x² - 14x

x² +2(- 7)x + (- 7)²

= x² - 14x + 49

= (x - 7)² ← perfect square

Step-by-step explanation:

12 degres below 0 is -12°C ..so the temperature rose from -12°C to 24°C

The difference now from Morning to afternoon is

=24°C-(-12°C)

=24°C+12°C

=36°C

Answer:

Mean:  76

Median:  69

Mode:  63

Range: 46

Standard deviation: 15.5

Step-by-step explanation:

Given:

If each value in the data set is increased by a constant k, the mean, median, and mode will be increased by k.  

The range and standard deviation will remain unchanged.

Therefore, if each value in the data set is increased by 14:

The fraction equivalent to 24 /56 is  6/14.

A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.

Given:

Scale the numerator and the denominator down by a factor of 4.

According to given question we have

Down by a factor of 4 means divide  by 4.

when you scale the numerator and denominator down by 4, you just divide both of them by 4.

So since 24 divided by 4 is 6 and 56 divided by 4 is 14,

The answer is 6/14.

Therefore, the fraction equivalent to 24 /56 is  6/14.

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the order of titles according to the correct description boxes is  (0, 4.9), (-3,10), (-9, -3) and then (4.9, 10) respectively.

We first look at the graph, and then, we analyze it, completing the tiles.

From the graph, the function is increasing in two intervals (-10,-9) and (4.9,10). The function is increasing over two interval, (-10, -9) and (4.9,10) , so the corresponding tile is (4.9, 10) for increasing in two intervals.

Between -9 and 4.9 the function is decreasing, so the corresponding tile is (0, 4.9).

An interval where the function is above the x-axis, so between -9 and -3, and then above 10, so the corresponding tile is (-9,-3) for interval over which the difference is positive.

Interval over which the difference is negative is when an interval where the function is below the x-axis, so before -10, and then between -3 and 10. Thus the corresponding tile is (-3,10).

Therefore, we can conclude the following relations

interval in which difference of the number of sales is decreasing→ (0, 4.9)

interval over which difference of the number of sales is negative→ (-3,10)

interval over which difference of the number of sales is positive→  (-9, -3)

interval in which difference of the number of sales is increasing→ (4.9, 10)

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By substitution, the solution of the system of equations,  x + 6y = 2 and 5x + 4y = 36, is (8 , -1).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 6y = 2     (equation 1)

5x + 4y = 36     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

x + 6y = 2     (equation 1)

x = 2 - 6y

Substitute the value of x to the second equation.

5x + 4y = 36     (equation 2)

5(2 - 6y) + 4y = 36

10 - 30y + 4y = 36

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

10 - 30y + 4y = 36

-30y + 4y = 36 - 10

-26y = 26

y = -1

Substitute the value of y in the equation of x.

x = 2 - 6y

x = 2 - 6(-1)

x = 2 + 6

x = 8

Hence, the solution of the given system of equations is (8 , -1).

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The equation of the line 2x - y = 9 expressed in slope-intercept form is y = 2x - 9 with a slope equal to 2.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the equation of the line 2x - y = 9, which is in standard form, transform it into slope-intercept form by isolating the variable y in one side.

2x - y = 9

y = 2x - 9

Hence, the equation of the line in slope-intercept form is y = 2x - 9 where the slope is equal to m = 2.

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The explicit formula can be found in three easy steps. Find the first term and the common difference of the arithmetic sequence first. Replace the values in the explicit formula's nth term.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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The amount that Jared needs before taxes for his new computer is $606.19

What does before-tax price mean?

The before-tax price means the amount that Nick needs to acquire the laptop before considering the sales  tax of 7.25%, but after having factored in the layway fee of 1.2%

before-tax price=cost of computer*(1+layway fee %)

cost of computer=$599

layway fee=1.20%

before-tax price=$599*(1+1.2%)

before-tax price=$ 606.19

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The word “quantity” indicate to use a variable

The phrase is given as:

quantity

In an algebraic expression, phrases are used to indicate variables

So, anywhere the word is used, it implies that we make use of a variable

Take for instance:

A quantity is more than 2 means x > 2

Hence, the word “quantity” indicate to use a variable

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The slope-intercept equation of the line with a slope of -13 that goes

through (5, 7)

y = -13x + 72

point slope form:  y = MX + b

m = slope, b = y-intercept

y = -13x + b  through (5,7)

Use the given point as (x,y) to find b

7 = -13(5) + b

7 = -65 + b

b = 72

y = -13x + 72

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.  the web change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx. Where “m”  is the slope of a line. So, tan θ to be the slope of a line. Pick two points on the road and determine their coordinates.

Determine the difference in y-coordinates of those two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope). Whenever the equation of a line is written within the form y = MX + b,  

it's called the slope-intercept form of the equation. The m  is the slope of the line. And b  is that the b in the point that is the y-intercept (0, b).  for instance, for the equation y = 3x – 7, the slope is 3,  and therefore the y-intercept is (0, −7).

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The sum of the given finite series is -5050

The summation notation is used to expressed a long summation into a single formula.

Expand the sum of the given finite series:

[tex]\sum\limits^{100}_{n=0} {(-1)n} =0-1-2-3-...-100[/tex]

The right side is an arithmetic series. We can ignore the 0 in the first term, so the arithmetic series is:

-1 -2 - 3 -4 - ... - 100

We get:

a(1) = -1

d = -2 - (-1) = -1

a(n) = -100

n = 100

Substitute these parameters into the sum formula:

S(n) = n/2 [a(1) + a(2)]

S(100) = 100/2  [-1 + (-100)]

S(100) = 50 . (-101) = -5050

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Using the converse of same-side interior angle theorem, the complete proof that shows why lines l and m are parallel is explained below.

According to the converse of same-side interior angle theorem, if two same-side interior angles that are formed on two lines that are intersected by a transversal are supplementary, then the two lines are parallel to each other.

To prove that lines l and m are parallel to each other, the following proof with statements and reasons that justify each are given below:

Statement                                                 Reasons                                        

1. <2 and <5 are supplementary             1. Given

2. <3 ≅ <2                                                 2. Vertical angles theorem

3. <3 and <5 are supplementary            3. Transitive property

4. l║m                                                        4. converse of same-side interior        

                                                                     angle theorem

Thus, using the converse of same-side interior angle theorem, the complete proof that shows why lines l and m are parallel is given above.

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The missing terms are 1.4, 0.8, 0.2

The series is ,

2, __, __, __, -0.4,...

To find the missing terms of the arithmetic sequence , we need to find the the common difference (d).

So formula to find the value of d

[tex]t_{n}[/tex] = a+ (n-1)d

Where [tex]t_{n}[/tex]= nth term of the series

           a = first value of the sequence

           n = number of terms

Here

          [tex]t_{5}[/tex]= -0.4

          a = 2

          n = 5

-0.4= 2 + 4d

d = -0.6

Now we will add -0.6 from the first number of the series, so we get

[tex]t_{2}[/tex] = 2+(-0.6)

   =2-0.6

   = 1.4

[tex]t_{3}[/tex] = 1.4 - 0.6

   = 0.8

[tex]t_{4}[/tex] = 0.8 - 0.6

    0.2

Therefore the Missing terms of the series = 1.4, 0.8, 0.2

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The point-slope form be y - 7= 0.4(x - 6) then 0.4x - y = -4.6 be the standard form.

Given:

(x1, y1) = (6, 7)

The value of m = 2/5

The point-slope form is given by, y - y1 = m(x - x1)

substitute the values in the above equation, we get

y - 7 = 2/5(x - 6)

simplifying the equation,

y - 7 = 0.4(x - 6)

Therefore, the point-slope form is y - 7= 0.4(x - 6)

Standard form is Ax + By = C

Since, slope-intercept form is y = 0.4x + 4.6

⇒ 0.4x - y = -4.6

Therefore, 0.4x - y = -4.6 is the standard form.

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Finding the equation of the parabola, it is found that the height of the diving board is of 24 feet.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

From the maximum height, it is found that the vertex is at (1,25), hence:

h = 1, k = 25.

Hence:

y = a(x - 1)² + 25.

You hit the water 6 feet from the diving board, hence y(6) = 0, meaning that we use it to find a as follows:

0 = a(6 - 1)² + 25

25a = -25.

a = -1.

Hence:

y = -(x - 1)² + 25.

The height of the diving board is y(0), hence:

y = -(0 - 1)² + 25 = -1 + 25 = 24 feet.

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For the given inequality 6 x+9<7 x, x is greater than 9

Inequality is the relation between two expressions linked by the arithmetic expression other than equal sign. Such as less than (<), greater than (>), less than equal to (<=) and greater than equal to (>=).

Let's solve the inequality

6 x+9<7 x

Separate the variables and constants by moving them on the same side. Such as

9<7x-6x

9<x

We want to keep the variable on the left side. Then, just interchange the positions.

x>9

Therefore, it is clear that x is greater than 9.

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Answer:

Step-by-step explanation:

x = number of math problems left to do

x + 8 = 17

    x = 17 -8

    x = 9

Kamyle needs to do 9 more math problems

Answer:

40, 28

Step-by-step explanation:

Let the numbers be x and y. The sum of two numbers is 68 and the difference is 12.

[Assuming x > y]

Now add these equations,

[tex]\Rightarrow[/tex] x + y + x - y = 68 + 12

[tex]\Rightarrow[/tex] 2x = 80

[tex]\Rightarrow[/tex] x = 40

Then, y = 68 - 40 = 28

Hence,

The required numbers are:

Some tips:

Answer:

[tex]x = 1 + \frac23c[/tex]

Step-by-step explanation:

Hello!

Solve for x by isolating the variable.

The solution for x is [tex]x = 1 + \frac23c[/tex].