How is finding a missing term of a geometric sequence using the geometric mean similar to finding a missing term of an arithmetic sequence using the arithmetic mean? How is it different?

The expression was rewritten using the commutative property of addition

The expressions are given as

(7 + 1) + 9

7 + (1 + 9)

The commutative property of addition states that

a + b = b + a

This means that the expression was rewritten using the commutative property of addition

Also, we have

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By solving a linear equation, we can see that after 3 hours Ricardo has $61.91

We know that Ricardo has $132.16, and he rents a jet sky that costs $20 plus $16.75 per hour.

So, the cost of renting the jet sky for x hours is given by the linear equation:

C(x) = $20 + x*$16.75

The cost of renting this for 3 hours is:

C(3) = $20 + 3*$16.75 = $70.25

Subtracting this from what Ricardo had:

$132.16 - $70.25 = $61.91

So the correct option is the second one.

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Answer:

C is the correct answer

Step-by-step explanation:

hope you get it right :))

By elimination, the solution of the system of equations, r + 3s = 7 and 2r - s = 7, is (r , s) = (4 , 1).

A system of 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 all the equations.

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

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in r and s, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 2.

r + 3s = 7 ⇒ 2r + 6s = 14     (equation 1)

Subtracting the two equations will eliminate the variable r.

2r + 6s = 14     (equation 1)

2r  -   s = 7     (equation 2)

    7s    = 7

s = 1

Substitute the value of s to any of the two equations and solve for r.

2r - s = 7     (equation 2)

2r - 1 = 7

2r = 7 + 1

2r = 8

r = 4

Hence, the solution of the system of equations is (r , s) = (4 , 1).

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Answer:

MP = 29

Step-by-step explanation:

Given:

MN + NP = MP

17 + 3y = 5y + 9

Find what y =____

17 + 3y = 5y + 9

subtract 9 from both sides

17 - 9 + 3y = 5y + 9 - 9

8 + 3y = 5y

subtract 3y from both sides

8 + 3y - 3y = 5y - 3y

8 = 2y

divided both sides by 2 to get y alone

8/2 = 2y/2

4 = y

Now plug in y to MP to find its length

5(4) + 9 = 20 + 9 = 29

MP = 29

To find NP, plug in y as well

3y = 3(4) = 12

NP = 12

Check:

MN + NP = MP

17 + 12 = 29 yes!!!!

For solving y, we can use this inequality:  y≤(168-7x)/4

An inequality is an equation which compares two non equal expressions using operators  ≤,≥,<,> .

Steps for solving inequalities:

For given inequality, 168≥ 7x + 4y

Adding -7x both sides,

168-7x ≥ 7x+4y-7x

168 - 7x ≥ 4y

Dividing both sides by a positive number 4,

(168-7x)/4 ≥ y

we can solve for y using above expression that y will be less than or equal to (168-7x)/4

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When the quadrilateral WXYZ is mirrored across the y axis to form the quadrilateral W' X' Y' Z', the coordinates of X' are (-1,6).

When the x value is reflected across the y-axis, it takes on the opposite sign.

A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using one or even more numbers, or coordinates.

A coordinate system is a framework for specifying the relative locations of objects in a specific area, such as an area here on earth's surface or the entire earth's surface. A geographic coordinate system determines locations on the world by using a three-dimensional spherical surface.

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The arithmetic sequence AP's 32nd term is estimated to be 127.

An arithmetic progression (AP) in mathematics is a list or sequence of numbers within which each term is acquired by adding a sequence to the term before it.

Finally, the response to the question;

The numbers in the provided sequence are as follows:

34,37,40,43, ...........

There are 32 terms in the series, so we must obtain the 32nd number.

Suppose the first term is 'a₁' = 34.

Suppose 'a₂' = 37 be the second term.

Suppose 'a₃' = 40 be the third term.

The common difference between the two consecutive terms of an AP that are equal is 'd.'

d = a₂ - a₁  

Put the values in the preceding formula; the 32nd term is

d = 37 - 34

d = 3

The nth term equation is now used to calculate.

Substitute all of the values in the formula now.

a₃₂ = a + (n - 1) d

a₃₂ = 34 + (32 - 1)(3)

a₃₂ = 34 + 96 - 3

a₃₂ = 127

Thus, the arithmetic sequence's 32nd term is evaluated to be 127.

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Evaluating the expression -4 + 2ab for a = 3 and b = -5 is equal to -34.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.

Given the expression -4 + 2ab, substitute the value of the variable a and the value of variable b.

-4 + 2ab

-4 + 2(3)(-5)

Performing the arithmetic operations, we can have the value of the expression.

-4 + 2(3)(-5)

= -4 + (-30)

= -34

Hence, the expression -4 + 2ab when a = 3 and b = -5 is equal to -34.

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The additional information needed to prove that both triangles are congruent by SAA postulate is:

A. <B ≅ <D and <A ≅ <E

The SAA postulate is a condition that is used to prove that two triangles are congruent if they have two pairs of corresponding congruent angles and a pair of non-included congruent sides.

From the information we have in the diagram, we can deduce that:

AC ≅ EC (one pair of congruent sides)

ACB ≅ ECB (one pair corresponding congruent angles)

Therefore, the additional information needed to prove that both triangles are congruent by SAA postulate is:

A. <B ≅ <D and <A ≅ <E

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f (5) =  -19 is the output for the given input .

How can you tell whether a function is linear or not?

f(x)= -4 x+1

Put x = 5    ⇒   - 4 ×  + 1

                 ⇒   -20 + 1

                 ⇒   -19

Therefore f (5) =  -19

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The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 467) and (10, 647)

The rate of change is calculated as

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

So, we have

Rate = (647 - 467)/(10 - 2)

Evaluate

Rate = 22.5

This means that the rate of change is $22.5

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 22.5

So, we have

y = 22.5(x - x1) + y1

Using one of the points, we have

y = 22.5(x - 6) + 467

Set x = 0

So, we have

y = 22.5(0 - 6) + 467

Evaluate

y = 332

Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

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Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

Answer:

16

Step-by-step explanation:

We use PEMDAS

Parenthesis

Exponents

Multiplication

Division

Addition

Subtracting

1. 3 (10 - 8)^2 + 4: 3 (2)^2 + 4

2. 3 (2)^2 + 4: 3 (4) + 4

3. 3 (4) + 4: 12 + 4

4.12 + 4 = 16

So, our answer is 16.

The coordinates of the point on the directed line segment from (1, -3) to (7, 5) that partitions the segment into a ratio of 1 to 3 is; (x, y) = (2.5, 0.5)

The formula for partitioning a line segment in the ratio m:n is;

(x, y) = (mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)

We are given the ratio as 1:3 with the coordinates as;

(1, -3) and (7, 5). Thus;

m = 1 and n = 3

x1 = 1

x2 = 7

y1 = -1

y2 = 5

Thus;

(x, y) = (1*7 + 3*1)/(1 + 3), (1*5 + 3*-1)/(1 + 3)

(x, y) = (10/4, 2/4)

(x, y) = (2.5, 0.5)

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: 2x - 17 = 51 + 61[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x - 17 = 112[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 112 + 17[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 129[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \dfrac{129}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 64.5[/tex]

Answer:

Step-by-step explanation:

15.23 units

Based on the number of people going to see the movie and the price of the snacks, the total that Genesis would pay if she bought 6 snacks is $78.

The amount that Genesis would pay if she bought x snacks is 60 + 3x.

The total cost to Genesis can be found as:

= (Number of people going to watch movie x Price of ticket) + (Price per snack x number of snacks)

= (4 people including Genesis x 15) + (3 x 6)

= 60 + 18

= $78

The amount that Genesis would pay if she got x snacks is:
=  (Number of people going to watch movie x Price of ticket) + (Price per snack x number of snacks)

= (4 x 15) + (3 × x)

= 60 + 3x

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The simplification by combining like terms of 4t-(t + 3t)  is 0.

According to the given question.

We have an expression 4t - (t+3t).

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression 4t-(t+3t).

Here 4t, t and 3t both are the like terms.

So, we add and subtract coeffcients of t to simplify the given expression.

Therefore, the simplification of 4t - (t + 3t) is given by

4t -( t+ 3t)

= 4t - t -3t

= 4t - 4t

= 0

Hence, the simplification by combining like terms of 4t - (t + 3t) is 0.

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Mr. Sanchez's class sold 45 fruit pies, and Mr. Kelly's class sold 37 bottles of fruit juice.

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

To solve this question, we use the following representations:

x represents the fruit pies

y represents the fruit juice

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

1.89x + 1.56y = 140.13 ---- the total cost

x + y = 82 --- the number of sales

Make x the subject in x + y = 82

So, we have

x = 82 - y

Substitute x = 82 - y in 1.89x + 1.56y = 140.13

1.89(82 - y) + 1.56y = 140.13

Expand

154.98 - 1.89y + 1.56y = 140.13

Evaluate the like terms

-0.33y = -14.85

Divide by -0.33

y = 45

So, we have

x = 82 - y

x = 82 - 45

Evaluate

x = 37

Hence, Mr. Sanchez's class sold 45 fruit pies, and Mr. Kelly's class sold 37 bottles of fruit juice.

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The 32nd term of the arithmetic sequence AP is computed to be 12.5.

In mathematics, an arithmetic progression (AP) is a list or sequence of numbers in which each term is attained by adding a pattern to the term before it.

Finally, here is the answer to the question;

The following are the numbers in the presented sequence:

0.1,0.5,0.9,1.3, ...........

Because the series contains 32 terms, we must find the 32nd number.

Assume the first term is'a₁' = 0.1.

Assume 'a₂' = 0.5 is the second term.

Assume the third term is 'a₃' = 0.9

'd' is the common difference between two consecutive terms of an AP that are equal.

d = a₂ - a₁  

Put the values in the preceding formula; the 32nd term is

d = 0.5 - 0.1

d = 0.4

The nth term equation is found by the formula;

Substitute the given values in the formula;

a₃₂ = a + (n - 1) d

a₃₂ = 0.1 + (32 - 1)(0.4)

a₃₂ = 0.1 + 12.8 - 0.4

a₃₂ = 12.5

Therefore, the arithmetic sequence's 32nd term value is estimated to be 12.5.

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Answer:

A.

Step-by-step explanation:

A quadrilateral is a trapezoid if two opposite sides are parallel, and the other 2 opposite sides are not parallel.

Answer: A.

Answer:

it's a

Step-by-step explanation:

The side lengths 300 mm and 190 mm make a valid triangle because of the triangle inequality theorem

The side lengths are given as

300 mm and 190 mm

To solve this question, we make use of the triangle inequality theorem

The triangle inequality theorem states that

Given that the sides of a triangle are x, y and z.

The sum of any two sides of a triangle is greater than or equal to the third side;

This means that

x + y ≥ z

Using the above as a guide, we have the following inequality expressions

300 + 190 ≥ z

300 + z ≥ 190

z + 190 ≥ 300

Evaluate the inequality expressions

490 ≥ z

z ≥ -110

z  ≥ 110

Remove the negative value

490 ≥ z

z ≥ 110

Combine the inequalities

110 ≤ z ≤ 490

The above inequality is a valid inequality expression

Hence, the side lengths 300 mm and 190 mm make a valid triangle

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Using rational numbers, Jackson supports more education funding as he  7/20 > 6/20.

Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers and q 0, can be used to represent a rational number.

According to Kirsten, 24% of federal tax dollars should fund education

⇒ 24% = 24 / 100

⇒ 6/25

According to Jackson, $0.35 of every tax dollar should go toward education

⇒ 0.35 = 35 / 100

⇒ 7/20

As we can infer that 7/20 > 6/20

So Jackson supports more education funding.

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In order to determine the relationship between the time and the amount of money in the account, we would calculate the average rate of change.

The average rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Mathematically, the slope (average rate of change) can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For Tammy's account, we have:

Points (x, y) = (6, 467) (8, 557)

Average rate of change = (557 - 467)/(8 - 6)

Average rate of change = 90/2

Average rate of change = 45.

As time increases, the amount of money in Tammy's account increases. Also, the rate at which the amount of money in the account is increasing is 45 dollars per month.

First of all, we would determine the increment in 6 months as follows:

Increment = $45 × 6

Increment = $270.

Initial amount = $467 - $270

Initial amount of money = $197.

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Answer:

x>4

Step-by-step explanation:

Since it is pointing right, it must be either

x>4

x≥4

Since it is not a filled circle the answer can't be greater than or equal to. So it must be x>4.