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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60 milllimeter equals kilograms
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?
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 value of n in the equation 2n² + 4n = 0? What is the value of n in the equation 2n² + 4n = 0 ?
N = 0
2(0)² + 4(0) = 0
0 + 0 = 0
A geometric seqerence 1.5, -3, 6, -12 .... How many regative terms in the sequencs greater than
- 6000 ?
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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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%.
Answer:
the answer is 13.73 %
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]".
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]
Over which interval is the graph of the parent absolute value function decreasing?
(–∞, ∞)
(–∞, 0)
(–6, 0)
(0, ∞)
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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Please help whilst I try to solve this as well.
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
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
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
A line intersects the points (8, 2) and (12, -10). What is the slope of the line in simplest form? m = [?]
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]
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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.
To which subsets of the Real Numbers does square root of 36 belong.
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.
___________________
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
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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Simplify (27-17)^2-80
Answer:
-60
Step-by-step explanation:
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!
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]
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
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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help pls i jusiot jiojfgnio43nfginfmowenfviowngognior3
Answer:
i dont know
Step-by-step explanation:
sorry please be a bit more clear on what help you would like
find the y-component of this vector
leave an explanation for brainlest
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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Please help my question is in the attachment!
Answer:
a = -9
b = -3
c = 11
d = 19
Step-by-step explanation:
a. x = -2
y= x² + 3x + 1
y= -2²+ 3(-2)+1
y= -4-6+1
y = -9
b. x= -1
y= x² + 3x+ 1
y= -1² + 3(-1) +1
y= -1 -3 + 1
y = -3
c. x =2
y = x² + 3x +1
y= 2²+ 3(2) +1
y= 4 +6 +1
y = 11
d. x= 3
y = x² +3x +1
y = 3² +3(3) +1
y= 9 +9 +1
y = 19
....................
..................................
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) =
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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Factorise and evaluate
50 × 11 + 50 × 9
Answer:
1000
Step-by-step explanation:
50 × 11 + 50 × 9 ← factor out 50 from each term
= 50(11 + 9)
= 50(20)
= 1000
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
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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what is the answer please??
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.
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
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]
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.
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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What single transformation was applied to triangle A to get triangle B?
Choose 1 answer:
Translation
Rotation
Reflection
Dilation
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)
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
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
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
please help! I need this quickly
write an equation in standard form of the line passing through the points (12,6) and (-3,11)
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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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 ?
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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