Add: x 5 - 4x 4 + 7x 3 + 8, 9x 3 + 7x 2 - 10, and -2x 5 + 7x 4 - 3x + 8.

Answer:

Step-by-step explanation:

Answer:

z= -2

Step-by-step explanation:

5z-2= -12

5z= -10

z= -2

The complete question is

"Using the segment addition postulate, which is true?

AB + BC = AD

AB + BC = CD

BC + CD = AD

BC + CD = BD"

Using the segment addition postulate, the true option is D; BC + CD = BD.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

We have been given the number line and four points A, B, C, and D on the line with coordinates -6, -1, 2, and 8 respectively.

(a) L.H.S. = AB + BC = 5 + 3 = 8,

   R.H.S = AD = 14 ≠ 8.

So, this option is incorrect.

(b) L.H.S. = AB + BC = 5 + 3 = 8,

   R.H.S = CD = 6 ≠ 8.

So, this option is incorrect.

(c) L.H.S. = BC + CD = 3 + 6 = 9,

   R.H.S = AD = 14 ≠ 9.

So, this option is incorrect.

(d) L.H.S. = BC + CD = 3 + 6 = 9,

   R.H.S = BD = 9.

So, this option is correct.

Hence, the correct option is (d).

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a) Using the Euclidean algorithm, we can find gcd (707,413) as follows:707 = 1 · 413 + 294413 = 1 · 294 + 119294 = 2 · 119 + 562119 = 2 · 56 + 71356 = 4 · 71 + 12 71 = 5 · 12 + 11 12 = 1 · 11 + 1

Thus, gcd (707,413) = 1.

We can find the coefficients s and t that solve the equation 707s + 413t

= 1 as follows:1 = 12 - 11 = 12 - (71 - 5 · 12) = 6 · 12 - 71 = 6 · (119 - 2 · 56) - 71

= - 12 · 56 + 6 · 119 - 71

= - 12 · 56 + 6 · (294 - 2 · 119) - 71 = 18 · 119 - 12 · 294 - 71

= 18 · 119 - 12 · (413 - 294) - 71 = 30 · 119 - 12 · 413 - 71

= 30 · (707 - 1 · 413) - 12 · 413 - 71 = 30 · 707 - 42 · 413 - 71

Thus, s = 30, t = -42. So we have found that 707(30) + 413(−42) = 1.

b) Since 707s + 413t = 1 and 9 does not divide 1, the equation 707x + 413y = 9 has no integer solutions. Therefore, we can conclude that there are no such integers x and y.

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Answer:

$228

Explanation:

Given data

Total electricity consumption = 2400 kWh

Rate of consumption = 9.5 cent per kWh

converting cent to dollar we have. 9.5/100= $0.095

hence the bill is 2400*0.095= $228

The cost of the bill would be:$228
The formula to calculate the bill is as follows: Cost of Bill = Total kWh x Rate

The above formula can be used to determine the cost of the electricity bill based on the number of kilowatts per hour and the rate per kilowatt-hour.2400 kWh represents the total kilowatt-hours in a month.
Rate = $0.095
Therefore, the cost of the electricity bill is as follows:
Cost of the bill = 2400 x $0.095= $228
Hence, the correct answer is option C. $228.

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Answer:

\(8x^{2} +14x+6\)

Step-by-step explanation:

The formula for the area of rectangle is length times width:

\((2x+2)(4x+3)\\\)

Use FOIL method:

\(8x^{2} +6x+8x+6\\8x^{2} +4x+6\)

Answer:

14 dollars

Step-by-step explanation:

To find the price, you multiply 3.50 with 400% or 4.00

3.50 x 4 = 14.00

Answer:

I don't know the answer sorr

The solution to the system of equations is:

x1 = -1/2
x2 = 7/2
x3 = 0

To solve this system of equations, we need to first identify the given equations:

1. x3 = 0
2. 3x1 + x2 + x3 = 2
3. -x1 + x2 + 2x3 = 3

Now let's solve step-by-step:

Step 1: Substitute x3 from equation 1 into equations 2 and 3:

2. 3x1 + x2 = 2
3. -x1 + x2 = 3

Step 2: Solve equation 2 for x1:

x1 = (2 - x2) / 3

Step 3: Substitute x1 from step 2 into equation 3:

-((2 - x2) / 3) + x2 = 3

Step 4: Solve for x2:

(2 - x2) / 3 + x2 = 3
2 - x2 + 3x2 = 9
2x2 = 7
x2 = 7/2

Step 5: Substitute x2 back into the expression for x1 from step 2:

x1 = (2 - (7/2)) / 3
x1 = (-3/2) / 3
x1 = -1/2

So, the solution to the system of equations is:

x1 = -1/2
x2 = 7/2
x3 = 0

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it is not a universal rule that the sum of two repeating decimals will always be a repeating decimal. There are instances where their sum can result in a terminating decimal or an integer, as demonstrated in the examples above.

It is not always true that the sum of two repeating decimals must be a repeating decimal.

There are cases where their sum can result in a terminating decimal or even an integer.
Let me provide you with a step-by-step explanation:
Firstly, understand what a repeating decimal is. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point, such as 0.333... or 0.272727...
Now, let's consider two repeating decimals as examples: 0.333... and 0.666...
Add these two repeating decimals together:
  0.333...
+ 0.666...
---------
= 0.999...
Observe that the result, 0.999..., is also a repeating decimal. In fact, it is mathematically equal to the integer 1. This demonstrates that the sum of two repeating decimals can be an integer.
Let's consider another example: 0.333... and 0.467467...
Add these two repeating decimals together:
  0.333...
+ 0.467467...
------------
= 0.800467...
In this case, the sum of the two repeating decimals is a mixed decimal with a terminating part (0.800) and a repeating part (467).

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The total number of vertices a full 5-ary tree with 100 internal vertices have is 501.

A tree with m or less offspring at each node is known as an m-ary tree. When m = 2, a binary tree is the particular case, and a ternary tree, which has m = 3 and a maximum of three offspring, is another special case.

A m-ary tree with just a root node has a height of 0, as the height h of an m-ary tree does not include the root node. The maximum depth D of any tree node determines the height of the tree.

In computer science, a collection of nodes often represented hierarchically in the following way is referred to as a "m-ary tree." At the root node, the tree is initiated. A list of pointers to each node's child nodes is kept by each node in the tree. There are less than or as many child nodes as m.

It is given the m-ary tree as 5-ary tree (m)

And the number of Intervals = 100(i)

We can calculate the number of vertices by using

n = m*i + 1 = 100*5 + 1 = 501

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Answer:

It is A) -4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer C is correct.  The absolute value of 10 is 10 and that of -10 is 10.  Same result.

To win the Ohio Classic Lotto, you need to match all six numbers drawn. In this lottery game, players choose six numbers from a set range, typically from 1 to 49.

The winning combination is determined by a random drawing of six numbers, usually conducted by a lottery machine or ball-drawing mechanism.

For a chance to win the jackpot prize, you must have all six numbers on your ticket match the six numbers drawn in the official drawing. This means that every number on your ticket must exactly correspond to the numbers selected in the drawing, and in the same order.

Matching fewer than all six numbers does not result in winning the jackpot prize. However, depending on the specific rules of the Ohio Classic Lotto, there may be secondary prizes for matching a subset of the drawn numbers, such as matching five, four, or three numbers correctly. These secondary prizes are typically of smaller value than the jackpot prize.

In summary, to win the Ohio Classic Lotto, you need to match all six numbers in the drawing.

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Answer:

x = 10    y = 5

Step-by-step explanation:

-4x + 11y = 15

-4(2y) + 11y = 15

-8y + 11y = 15

3y = 15

y = 5

x = 2y

x = 2(5)

= 10

He should compare frequencies because it allows for clearer comparison of groups of each size.

What do you mean by frequency?

The frequency of a repeated event is its number of instances per unit of time. [1] In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively. The quantity of times a specific data value occurs is known as its frequency. We use f to represent a data value's frequency.

We analyze categorical data by recording percentages of cases occuring in  each category.

Therefore, he should compare frequencies because it allows for clearer comparison of groups of each size.

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The points on the x-axis where the electric potential is zero are approximately 2.8 cm and 7.0 cm.

To find the point or points on the x-axis where the electric potential is zero, we need to consider the contributions of the two charges at different locations.

The electric potential at a point due to a point charge can be calculated using the formula:

V = k * (q / r)

where V is the electric potential, k is the electrostatic constant \((k = 8.99 x 10^9 N m^2/C^2)\) , q is the charge, and r is the distance from the charge to the point where the potential is being calculated.

Let's consider the contributions of the two charges individually:

1. Positive charge (13.5 nC) at x = 0 cm:

The electric potential due to this charge at a point on the x-axis (x ≠ 0) can be calculated as:

V1 = k * (q1 / r1)

where q1 = 13.5 nC and r1 is the distance from the point on the x-axis to the positive charge at x = 0 cm.

2. Negative charge (-1.2 nC) at x = 7 cm:

The electric potential due to this charge at a point on the x-axis (x ≠ 7 cm) can be calculated as:

V2 = k * (q2 / r2)

where q2 = -1.2 nC and r2 is the distance from the point on the x-axis to the negative charge at x = 7 cm.

The total electric potential at a point on the x-axis, where both charges contribute, is given by the sum of V1 and V2:

V_total = V1 + V2

To find the point or points where the electric potential is zero, we need to solve the equation V_total = 0.

Let's calculate the distances (r1 and r2) for a general point on the x-axis and then solve for the values of x that satisfy V_total = 0.

For a general point (x, 0) on the x-axis:

r1 = x cm

r2 = |x - 7| cm

Substituting these values into the equation V_total = V1 + V2 and setting it to zero:

0 = k * (q1 / x) + k * (q2 / |x - 7|)

Simplifying further:

(q1 / x) = - (q2 / |x - 7|)

We can now solve this equation to find the points on the x-axis where the electric potential is zero. However, the solution is not straightforward and requires numerical methods or graphing techniques.

Using numerical methods or a graphing calculator, we find that there are two points on the x-axis where the electric potential is zero, given to two significant figures:

x ≈ 2.8 cm

x ≈ 7.0 cm

Therefore, the points on the x-axis where the electric potential is zero are approximately 2.8 cm and 7.0 cm.

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Answer:

10

Step-by-step explanation:

19-17=2

10+2=12-2 =10

Answer:

6/1 or just 6

Step-by-step explanation:

Answer:

6 over 1 is the slope

Step-by-step explanation:

to find the slope of a line you have to find two points on the line and do rise over run

so for example for this problem I looked at the tho points and starting from the bottom one I went up (rise) six and over (run) one and got 6 over 1  

your welcome : )

130 :DDDDDDDDDDDDddddddddddd

Answer:

2a+c+140

or

(2a)+(c)+140

The city planners can expect a population of 68,666 in the year 2000.

Exponential growth is a concept in mathematics that is used to describe an increase that follows a certain pattern. In the given problem, the city's population is said to be increasing exponentially. It means that the population growth of the city will follow an exponential function.
The general formula for an exponential function is given by y = a*b^x where a and b are constants and x is the variable. Here, a represents the initial population, b is the constant growth rate and x is the number of years from the initial population.

Using the given information, we can find the value of the constant growth rate as follows: b = (Final Population / Initial Population)^(1/Time)where Time is the duration in years between the two given populations. b = (30000/25000)^(1/10)b = 1.01995 (rounded to five decimal places)

Therefore, the population of the city in the year 2000 (which is 40 years from 1960) can be calculated as follows:y = a*b^x where a = 25000, b = 1.01995, and x = 40y = 25000*(1.01995)^40y = 68,666 (rounded to the nearest whole number)

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The sample is a stratified sample.

A stratified sample is a sampling method in which a population is separated into distinct, non-overlapping subpopulations, or strata, and a random sample is taken from each stratum.

This is frequently utilized when the population contains subpopulations with distinct characteristics, and the researcher wants to guarantee that these subpopulations are adequately represented in the sample.

Likewise, in the provided scenario of the electronics store, the store will first separate the customers who purchased a computer over the past two years and then take 100 receipts through a random number generator to question customers about high-speed Internet rates.

This way, it can ensure that all customers are adequately represented in the sample and the information it receives is not biased.

A stratified sample is a sampling technique used in statistics and research to ensure that the sample accurately represents the different subgroups or strata within a population. It involves dividing the population into distinct subgroups or strata based on certain characteristics or variables and then selecting a sample from each stratum.

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The term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.

To find the limit of the given sequence, we can use the ratio test:

StartFraction
(9(n+1)+1)! / (9(n+1))!
Over
(9n+1)! / (9n)!
EndFraction

Simplifying the expression, we get:

StartFraction
(9n+10)(9n+9)(9n+8)...(9n+2)(9n+1)
Over
(9n+1)(9n)(9n-1)...(2)(1)
EndFraction

The terms cancel out and we are left with:

StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction

Taking the limit as n approaches infinity, we get:

lim (n → ∞) StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction

= lim (n → ∞) StartFraction
81n² + 81n + 90
Over
81n² + 9n
EndFraction

= lim (n → ∞) StartFraction
n² + n + 10 / n² + n / 9
EndFraction

As n approaches infinity, the higher order terms dominate, so we can ignore the constants and simplify the expression to:

lim (n → ∞) StartFraction
n² / n²
EndFraction

= 1

Since the limit exists and is finite, the sequence converges. Therefore, the limit of the sequence is 1.

To find the limit of the given sequence or determine if it diverges, consider the sequence:

a_n = (9n+1)! / (9n)!

We can rewrite the sequence using the properties of factorials:

a_n = [(9n+1)(9n)(9n-1)...(9n-(9n-1))] / (9n)!

a_n = (9n+1)

Now, we'll examine the limit as n approaches infinity:

lim (n -> ∞) a_n = lim (n -> ∞) (9n+1)

Since the term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.

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Answer:

22.14

Step-by-step explanation:

Since perimeter is all around the easy part will be adding the trapazoids sides which add up as

11 + 4 + 4 = 19

when it comes to the semi circle you have to figure out the circumfrence

circumfrence = πd = π2

however because it is a semi circle you will need half of the circumfrence

π2 / 2 = π

so then you add the total to get

11 + 4 + 4 + 3.14 = 22.14

Answer:

240 m³

Step-by-step explanation:

Triangular base = 1/2bh=

1/2(5)(12)=30

30x8=240m³

(Volume is in cubic units, not square units, so I’m not sure why the question says that.)

Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.

The function F(x) is a cubic function.

Here, we have,

given function is:

F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x

To determine the algebraic degree of the given (7,7)-function F(x), we need to find the highest exponent of x in the function.

F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x

The algebraic degree of a polynomial function corresponds to the highest exponent of the variable in the function.

Linear functions have an algebraic degree of 1, affine functions have an algebraic degree of 1 or 0, quadratic functions have an algebraic degree of 2, and cubic functions have an algebraic degree of 3.

so, we get,

The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.

Therefore, the function F(x) is a cubic function.

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