Part B
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural
numbers, n.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d (k+ 1).

Answers

Answer 1

The inductive step is assuming that the statement is true for some  n = k , where  k  is one of the values we want to prove the statement for, it shows that it is also true for  n = k+1.

How to carry out Mathematical Induction?

Suppose we have the statement 3n > 4n for all positive integers  n.

Now, the statement above is false when n = 1 , since 3 is less than 4. However, it will be true for all other positive integers.

In that case, we can still prove this statement by induction for all integers  n ≥ 2 .

Thus, the inductive step is assuming that the statement is true for some  n = k , where  k  is one of the values we want to prove the statement for, it shows that it is also true for  n = k+1.

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Related Questions

To which subsets of the Real Numbers does square root of 36 belong.

Answers

Answer:

The square root of 36 is a rational number. A rational number is a number that can be written as a fraction, a/b, where a and b are integers.

Answer:

Step-by-step explanation:

Hi, let me help you out.

The square root of 36 is 6.

6 belongs to the following subsets.

Natural Numbers (All numbers greater than 1, except fractions or decimalsWhole Numbers (All Natural Numbers + 0; fractions are still NOT included)Integers (All Whole Numbers + negative numbers; this set includes neither fractions nor decimals, like the two number sets aboveRational Numbers (All integers plus - wait for it - fractions & decimals!)

Overall, 6 belongs to 4 sub-sets.

__________________

Hope I helped! Best wishes.

___________________

A geometric seqerence 1.5, -3, 6, -12 .... How many regative terms in the sequencs greater than
- 6000 ?​

Answers

The total negative terms are 4 which are greater than -6000 if the geometric sequence 1.5, -3, 6, -12 ... with a common ratio -3.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

A geometric sequence 1.5, -3, 6, -12 ....

The common ratio r = -3/1.5 = -2

1.5, -3.6, 6, -12, 36, -108, 324, -972, 2916, -8748

The total negative terms = 4

Thus, the total negative terms are 4 which are greater than -6000 if the geometric sequence 1.5, -3, 6, -12 ... with a common ratio -3.

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Please help whilst I try to solve this as well.

Answers

Answer:

420

Step-by-step explanation:

Answer:

V = 340 cm3

Step-by-step explanation:

Calculate the volume of the prism without the gap, then subtract the volume of the gap.

[tex]V=(5)(10)(8)-(3)(2)(10)=400-60=340cm^{3}[/tex]

Hope this helps

Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros
of -3, -3, 4, and 2.
y(x) =

Answers

The factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)

How to determine the factored form?

The given parameters are:

Leading coefficient, a = 1Zeros = -3, -3, 4, and 2.

Rewrite the zeros as:

x = -3, x = -3, x = 4 and x = 2

Set the zeros to 0

x + 3 = 0, x + 3 = 0, x - 4 = 0 and x - 2 = 0

Multiply the zeros

(x + 3) * (x + 3) * (x - 4) *(x - 2) = 0

Express as a function

y(x) = a(x + 3) * (x + 3) * (x - 4) *(x - 2)

Substitute 1 for a

y(x) = (x + 3)²(x - 4)(x - 2)

Hence, the factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)

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what is the answer please??

Answers

Answer:

See below

Step-by-step explanation:

Area of a circle = pi * r^2

  for this circle  :    Area = 3.142 * 10 * 10 =  314.2 cm^2

The formula for area of a circle is [tex]\pi r^{2}[/tex]

So using pi as 3.142, we can do 3.142 • 100 which is 314.2 when moving place values.

Even though you did not ask, the circumference formula is 2[tex]\pi[/tex]r.

If we were given the same information, where the radius is 10, and we were solving circumference, then we would do 3.14 • 20 = 62.8.

Brainliest if helpful.

Simplify (27-17)^2-80

Answers

Answer:

-60

Step-by-step explanation:

Please help my question is in the attachment!

Answers

Answer:

a = -9

b = -3

c = 11

d = 19

Step-by-step explanation:

a. x = -2

y= + 3x + 1

y= -2²+ 3(-2)+1

y= -4-6+1

y = -9

b. x= -1

y= + 3x+ 1

y= -1² + 3(-1) +1

y= -1 -3 + 1

y = -3

c. x =2

y = + 3x +1

y= 2²+ 3(2) +1

y= 4 +6 +1

y = 11

d. x= 3

y = +3x +1

y = 3² +3(3) +1

y= 9 +9 +1

y = 19

Determine the area of a sector with√20 radius meters, and central angle 30°.
I will mark brainliest!
Answer Options:
20πm²
5π/3m²
30πm²
π/3²

Answers

Answer: [tex]\frac{5\pi}{3}[/tex]

Step-by-step explanation:

[tex]A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}[/tex]

60 milllimeter equals kilograms

Answers

Answer: .00006kg

Step-by-step explanation:

The graph shown below expresses a radical function that can be written in the form F(x) = a(x+ k)^1/n+ C. What does the graph tell you about the value of a in this function?

Answers

For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.

Given the value of function  F(x)=[tex]a(x+k)^{1/n}+C[/tex].

We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :

a[tex](x+k)^{1/n}[/tex]+C=0

a[tex](x+k)^{1/n}[/tex]=-C

a=-C/[tex](x+k)^{1/n}[/tex]

Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.

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What is the weighted average cost of capital (WACC) for ABC Limited which has the following capital structure? $5m of equity with a cost of equity of 15%; $2m of mezzanine finance with a cost of 9.5%; $1m of senior debt with a cost of debt of 7%.​

Answers

Answer:

the answer is 13.73 %

The scale on a map shows that 200 miles is represented by 5 inches on a map. Which proportion can be used to find the distance on the map, x, that represents 50 miles? StartFraction 5 over 200 EndFraction = StartFraction x over 50 EndFraction StartFraction 200 over 5 EndFraction = StartFraction x over 50 EndFraction StartFraction 50 over 200 EndFraction = StartFraction 5 over x EndFraction StartFraction 5 over 50 EndFraction = StartFraction x over 200 EndFraction

Answers

The proportion can be used to find the distance on the map (x) that represents 50 miles will be x/50 = 5 / 200. Then the correct option is A.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The scale on a map shows that 200 miles is represented by 5 inches on a map.

Then the proportion can be used to find the distance on the map (x) that represents 50 miles will be

x/50 = 5 / 200

Then  the correct option is A.

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A line passes through the point (5,-11) and has slope of -2.
Find an equation of this line.
y = -2x – 1
y = 5x – 11
y = 5x – 2
y = -2x – 11

Answers

Answer:

y=-2x -1

Step-by-step explanation:

(y-y1) = m(x-x1)

y-(-11) = -2(x-5)

y+11 = -2x + 10

subtract 11 on both sides thus

y = -2x -1

there are 20nstudents in a math class who have brown hair this represent 80 percent of the students in the class with equation can be used to find the total os student in the math

Answers

Answer:

Equation is 20 = 0.8 time x

x=25

Step-by-step explanation:

80% = 0.8

So to find x we 20/8

and we get 25 as the final answer

PLEASE HELP!!

Discussion Topic
Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This
approach follows the teachings of Euclid, in which he describes the relationships between
points, lines, and planes without any numerical measurement. You saw evidence of Euclidean
geometry inside several proofs and geometric constructions.
In contrast, the focus of this unit is understanding geometry using positions of points in a
Cartesian coordinate system. The study of the relationship between algebra and geometry was
pioneered by the French mathematician and philosopher René Descartes. In fact, the
Cartesian coordinate system is named after him. The study of geometry that uses coordinates
in this manner is called analytical geometry.
It's clear that this course teaches a combination of analytical and Euclidean geometry. Based
on your experiences so far, which approach to geometry do you prefer? Why? Which
approach is easier to extend beyond two dimensions? What are some situations in which one
approach to geometry would prove more beneficial Han the other? Describe the situation
and why you think analytical or Euclidean geometry is more applicable.

Answers

Based on my experiences so far, the approach to geometry that I prefer is: Euclidean Geometry. This is because the problems are easy to visualize since they are restricted to two-dimensional planes.

Which approach is easier to extend beyond two dimensions?

The approach that is easier to extend beyond two dimensions is Euclidean Geometry. Again, this is because of how it deals with shapes and visualization of the same.

Take for instance a triangle; it is easy to go from a two-dimensional equilateral triangle  to a square pyramid.

What are some situations in which one approach to geometry would prove more beneficial than the other?

Analytical geometry is a superior technique for discovering objects (points, curves, and planes) based on their qualities in some situations than Euclidean geometry is in others (for example, when employing topography or building charts).

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It has been estimated that 72.7% of alcoholics need professional help to stop drinking. What is the probability that a random alcoholic can kick the habit without professional help? It has been estimated that 72.7 % of alcoholics need professional help to stop drinking . What is the probability that a random alcoholic can kick the habit without professional help ?​

Answers

The probability that a random alcoholic can kick the habit without professional help is 0.273 .

What is Probability ?

Probability is the study of likeliness of an event to happen.

It has a range of 0 to 1 , where 0 indicates uncertainty and 1 indicates certainty.

It is given that

The alcoholics that need professional help to stop drinking is 72.7 %

Therefore the probability of this is 72.7 /100 = 0.727

The probability that they will not need professional help is given by

q = 1 - p

q = 1 -0.727

q = 0.273

Therefore the probability that a random alcoholic can kick the habit without professional help is 0.273 .

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Find the average rate of change of the function f(x) - 2x² + 6x + 6, from x=-3 to x=-1. Note, the directions are equivalent to "Find the average rate of change over the interval [-3,-1]".​

Answers

Answer: -2

Step-by-step explanation:

I will assume you meant [tex]f(x)=2x^{2}+6x+6[/tex].

[tex]f(-3)=2(-3)^2 + 6(-3)+6=6\\\\f(-1)=2(-1)^2 + 6(-1)+6=2\\\\\therefore \frac{f(-3)-f(-1)}{-3-(-1)}=\frac{6-2}{-2}=\boxed{-2}[/tex]

A line intersects the points (8, 2) and (12, -10). What is the slope of the line in simplest form? m = [?]​

Answers

Answer:  m = -3

Work Shown:

[tex](x_1,y_1) = (8,2) \text{ and } (x_2,y_2) = (12,-10)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-10 - 2}{12 - 8}\\\\m = \frac{-12}{4}\\\\m = -3\\\\[/tex]

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

Answer:  [tex]\textsf{y = -3}[/tex]

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

Given: [tex]\textsf{Goes through (8, 2) and (12, -10)}[/tex]

Find:  [tex]\textsf{The slope of the line}[/tex]

Solution: In order to determine the slope of the line we need to use the slope formula where we just plug in the values and simplify.

Plug in the values

[tex]\textsf{y = }\frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]\textsf{y = }\frac{-10 - 2}{12 - 8}[/tex]

Simplify the expression

[tex]\textsf{y = }\frac{-12}{12 - 8}[/tex][tex]\textsf{y = }\frac{-12}{4}[/tex][tex]\textsf{y = -3}[/tex]

Therefore, the slope of the line that fits the description that was provided in the problem statement is -3.


1. Henry is working in a pack room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35
lbs. His tolerance is +/-5 lbs. Which of the following weights are allowable? Circle all allowable weights.
a. 34
b. 36
C. 29
d. 40

Answers

The allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

Henry is working in a packed room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35

lbs. His tolerance is +/-5 lbs.

Weight of the bag = 35 lbs

Tolerance = ± 5 lbs

Allowable weights = 35 ± 5

= 35 + 5 = 40 lbs

= 35 - 5 = 30 lbs

Thus, the allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.

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A motorboat moves across a lake at a constant speed. When it begins, it is 64 km from the shore. After 17 minutes, it is 30 km from the shore. Which function describes the motorboat's distance from the shore?

A. y=-17x+30
B. y=2x+64
C. y=-17x+64
D. y=-2x+64

Please solve fast!
I am giving a lot of points!

Answers

Answer:

y = -2x + 64

Explanation:

The x represents the time in minutes and y represents distance in km.

Determine coordinates: (0, 64), (17, 30)

Find slope:

[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) : \dfrac{30-64}{17-0} = -2[/tex]

Find equation:

[tex]\sf y- y_1 = m(x - x_1)[/tex]

[tex]\sf y - 64 = -2(x - 0)[/tex]

[tex]\sf y = -2x + 64[/tex]

please help! I need this quickly

write an equation in standard form of the line passing through the points (12,6) and (-3,11)​

Answers

Answer:

x + 3y = 30

Step-by-step explanation:

We are given that a line contains the points (12,6) and (-3,11)​.

We want to write the equation of this line in standard form.

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.

Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

So first, let's find the slope of the line.
The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.

[tex]x_1=12\\y_1=6\\x_2=-3\\y_2=11[/tex]

Now substitute these values into the formula.

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

m=[tex]\frac{11-6}{-3-12}[/tex]

Subtract

m=[tex]\frac{5}{-15}[/tex]

Simplify

m=[tex]-\frac{1}{3}[/tex]

The slope is -1/3

Here is the equation of the line so far in slope-intercept form:

[tex]y=-\frac{1}{3} x + b[/tex]

We need to solve for b.

As the equation passes through (12,6) and (-3,11)​, we can use either one to help solve for b.

Taking (12, 6) for example:

[tex]6=-\frac{1}{3}(12) + b[/tex]

Multiply

[tex]6=-\frac{12}{3} + b[/tex]

Divide

6 = -4 + b

Add 4 to both sides.

10 = b

Substitute 10 as b in the equation.

[tex]y = -\frac{1}{3} x + 10[/tex]

Here is the equation in slope-intercept form, but remember, we want it in standard form.

In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.

[tex]\frac{1}{3} x + y = 10[/tex]

Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.

So, let's multiply both sides by 3 to clear the fraction.

[tex]3(\frac{1}{3} x + y) = 3(10)[/tex]
Multiply.

x + 3y = 30

Topic: finding the equation of the line (standard form)

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find the y-component of this vector
leave an explanation for brainlest

Answers

The y- component of the vector is 18.31728 m

What is Vector?

A quantity that has both magnitude and direction but not position.

The y- component is

Dy = 18.6* sin80

Dy = 18.6* 0.9848

Dy= 18.31728 m

Hence, the y- component of the vector is 18.31728 m.

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Factorise and evaluate

50 × 11 + 50 × 9

Answers

Answer:

1000

Step-by-step explanation:

50 × 11 + 50 × 9 ← factor out 50 from each term

= 50(11 + 9)

= 50(20)

= 1000

....................

Answers

..................................


What single transformation was applied to triangle A to get triangle B?

Choose 1 answer:
Translation
Rotation
Reflection
Dilation

Answers

The answer is Reflection

help pls i jusiot jiojfgnio43nfginfmowenfviowngognior3

Answers

Answer:

i dont know

Step-by-step explanation:

sorry please be a bit more clear on what help you would like

An expression is shown below:

4ck2 + 10k2 − 16ck − 40k

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Answers

Part A:

The greatest common factor is 2k

2k(2ck + 5k - 8c - 20)

Part B:

factor by grouping

2k (k(2c + 5) - 4(2c + 5))2k(k - 4)(2c + 5)

2k(k - 4)(2c + 5) is the final factored form

Over which interval is the graph of the parent absolute value function decreasing?

(–∞, ∞)
(–∞, 0)
(–6, 0)
(0, ∞)

Answers

The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.

What is the parent absolute value function?

An absolute value function is defined as a function that contains an algebraic expression within absolute value symbols.

The absolute value function is f(x) = |x| is defined as,

f(x )

x = x < x = 0 < x = -x

Observe that the graph is V-shaped.

The vertex of the graph is (0,0).

The domain is the set of all real numbers.

The x-intercept and the y-intercept are both 0.

Hence, The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.

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Two cars leave Chicago to go to a town in that suit up north. One car is traveling 13 mph faster in it arrived in four hours the other car took five hours to get there find the speed of each car

Answers

The speeds of the two cars will be 52 mph and 64 mph.

How to find the speed of an object?

If the object is going linearly, and at constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.

If the object traveled D distance in T units time, then that object's speed is S = D/T

Two cars leave Chicago to go to a town in that suit up north.

One car is traveling 13 mph faster in it arrived in four hours the other car took five hours to get there.

Let the distance traveled by both cars is x.

Speed of the first car = x/5

Speed of the second car = x/4

So, the equation form will be

x/5 + 13 = x/4

(65 + x )/ 5 = x /4

4(65 +x ) = 5x

260  + 4x =5x

x = 260

Speed of the first car = x/5 = 52mph

Speed of the second car = 52 + 13 = 65 mph

The speeds of the two cars will be 52 mph and 64 mph.

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What is the value of n in the equation 2n² + 4n = 0? What is the value of n in the equation 2n² + 4n = 0 ?​

Answers

N = 0

2(0)² + 4(0) = 0

0 + 0 = 0

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Select two options.Things turn into geographical features of the Earth, such as the Himalayas, when the Eldest Magician blows on them.The Eldest Magician and the animals engage in conversations using language, which is an example of personification.The animals engage in activities that are typical of their species, such as the cow chewing its cud and the beaver building a dam.The author repeats foreign expressions such as "Kun" and "Payah kun" in the conversations between the Magician and the animals Explain how cache (SRAM) can support CPU pipelining. Gerald is constructing a line parallel to line l through point P. He begins by drawing line m through points P and Q. He then draws a circle centered at Q, which intersects line l at point N and line m at point S. Keeping the compass measure, he draws a congruent circle centered at point P, which intersects line m at point T.Which next step will create point R, such that when a line is drawn through points P and R, the line will be parallel to line l?Lines m and n intersect at point Q. A circle is drawn around point Q and forms point S on line m and forms point N on line l. Point P is also on line m. A circle is drawn around point P and forms point T on line m.Use the compass to construct a circle centered at Q through point P.Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.Using the compass measure between points S and N, draw an arc above line l, centered at N, intersecting the edge of circle Q. Use the compass to construct a circle centered at P through point Q.Mark this and return 2.how are the amino acids formed from the codon in mutation #2 different from those formed from the original codon pattern. Which of the following is not a constitutional role of the president? (3 points) Which of these will complete the simple sentence?Mee Younga. was a great math student, but she did notenjoy her English classes as muchb. and Henry practiced for their duet for hoursAc. got sick right before the performance;however, she was able to complete her solonone of thesePlease select the best answer from the choices providedBd. none of these If 1 < a x , then the minimum value of [tex] \rm log_{a}(x) + log_{x}(x) [/tex] is ?PLEASE HELP!!!!