The zero of the function f(x) = 2x² - 8 is ± 2.
Zeros of the function
Zero of the function means the values of x when f(x) is equal to 0. Which means that when f(x) = 0, x is a zero of the function.
Given,
Here we have the function f(x) = 2x² - 8.
Here we need to find the zero of the function.
As per the definition of the zeros of the function,
We have to apply the value of f(x) = 0, then we get,
2x² - 8 = 0
Now, we need the value of x only, so we have to move the other numbers to the other side , then we get,
2x² = 8
Now, move the number 2 to the right hand side then it will be dividing the number 8,
x² = 8/2
x² = 4
x = √4
Therefore, the value of x is ± 2.
So, the zeros of the function is either +2 or -2.
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Mathematical induction
Yes this question can be proven by mathematical induction
What do you mean by induction in mathematics?
For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.
Here, n ≥ 1
1/1.2 + 1/2.3 + 1/3.4 + .............. + 1/n(n +1)
We employ the idea of Sigma here.
S/1/r(r + 1) { r = 1 to n }
Sigma [1/(r + 1) - 1/(1/r)] { r = 1 to n }
put r = 1 \s1/1 - 1/(1 + 1) = 1 - 1/2
put r = 2 \s1/2 - 1/(2 +1) = 1/2 - 1/3
put r = 3 \s1/3 - 1/(3 +1) = 1/3 - 1/4
........................................................... put r = n 1/n - 1/(n + 1)
after adding
Sigma = [1/(r+1) - 1/(1/r)] {r = 1 to n } = 1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + ............1/n - 1/(n +1)
= 1 - 1/( n +1) = n/( n +1)
Consequently, 1/1.2 + 1/2.3 + 1/3.4 +... 1/n(n + 1) = n/(n + 1).
so it proved
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Michael is dressing up as maggie this year. he is making his costume. michael needs 8.6 yards of furry fabric. if the fabric costs $1.82 per yard, how much will michael be spending on fabric?
Michael will be spending the cost of $ 15.652 on the Furry Fabric.
Given, that Michael is dressing up as Maggie,
He is making his costume and he needs 8.6 yards of furry fabric
The fabric costs $1.82 per yard.
So, as he needs 8.6 yards of fabric and each yard of that fabric costs him $1.82.
1 yard of Furry Fabric = $1.82
8.6 yards of Furry Fabric = $1.82 × 8.6
8.6 yards of Furry Fabric = $ 15.652
Hence, Michael will be spending the cost of $ 15.652 on the fabric.
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A share of Southside stock sold for $37. The annual dividend is $1.85. Three years later the stock has increased 17% in value and the dividend has increased 5%.
What is the dividend 3 years later? Round to the nearest cent.
The price of the share 3 years later, given the increase in value, can be found to be $43.29
How to find the price per share?The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.
This means that the price of the share 3 years later would be:
= Share price currently x ( 1 + increase in value)
= 37 x ( 1 + 17 % )
= 37 x 1. 17
= $ 43. 29
The price is $43.29
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What is the name of the bolded part of this shape?
Answer:
A right-angled triangle
you need to construct a fence around an area of 1600ft2 . what are the dimensions of the rectangular pen to minimize the amount of material needed?
The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.
What is the meaning of minimum dimension?The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.
With regard to the above problem,
let us say L is the lenght of the rectangle and W is the width
Based on the formula for the area of a rectangle,
L x W = 1600ft
To minimize the perimeter, of the rectangle, we must assume that:
L = W
that is L² = 1600
If we applied square root to both sides of the equation, we'd have
L = 40
Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.
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A biker travels down the street at 15 m/s. It
takes 60 seconds to travel to the end of the
street. How long was the street?
The street was 900m long when the speed is 15m/s and, the time is 60 seconds.
What is meant by distance, speed, and time?To calculate speed, divide the distance traveled by the time it took to complete the voyage, so speed = distance divided by time. To determine the distance, multiply the speed by the passage of time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.
Distance divided by time equals speed. Distance = time * speed
To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.
Given,
Speed of the biker who travels down the street=15m/s
Time taken=60seconds
Distance=?
We know that,
Distance=Speed× Time
Distance=15×60
Distance=900m
Therefore, the street was 900m long
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Which expression represents "10 subtracted from the quotient of 3 and a number"?
A 3n - 10
B 10 - 3n
C 10 - 3 over n
D 3 over n - 10
The expression that represents "10 subtracted from the quotient of 3 and a number" is D. 3 over n - 10.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Let the number be n
The expression will be:
= 3/n - 10
Therefore, the correct option is D.
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Drag the red and blue dots along the x-axis and y-
Answer:
Put one dot at (0,3) and the other dot at (1,0)
Step-by-step explanation:
Let x = 0
6x + 2y = 6
6(0) + 2y = 6
2y = 6 Divide both sides by 2
y = 3
(0,3)
Let y = 0
6x + 2y = 6
6x + 2(0) = 6
6x = 6 Divide both sides by 6
x = 1
(1, 0)
The local craft fair charges the vendors a flat rate of $15 plus $10 for each hour that they splend at the fair. If the vendor owed $65, how many hours did he remain at the craft fair?
Answer:
5 hours
Step-by-step explanation:
$65 - $15 = $50
$50/$10 = 5
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, -6) and (-8, 2)
The distance between the two points is 8.25 units
What is meant by the distance between two points?The distance between two points in a plane is the length of the line segment separating the two locations. Typically, the equation d=((x2 - x1)2 + (y2 - y1)2) is used to calculate the distance between two locations. You may use this formula to get the separation between any two points on an x-y plane or coordinate plane.
The following is the formula for the separation between two points:
d= √(x₁-x₂)²+(y₁-y₂)²
Points (x1, Y1) and (x2, Y2)
As given in the question, the points are (-6, -6) and (-8, 2)
The distance between the two points is,
d= √(-6+8)²+(-6-2)²
d=√4+64
d=√68 units= 8.25 units
Therefore, the distance between the two points is 8.25 units
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Conrad read a 180180180-page book cover to cover in a single session, at a constant rate. It took him 666 hours.
Let yyy represent the number of pages left to read after ttt hours.
Which of the following information about the graph of the relationship is given?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Slope and xxx-intercept
(Choice B)
B
Slope and yyy-intercept
(Choice C)
C
Slope and a point that is not an intercept
(Choice D)
D
xxx-intercept and yyy-intercept
(Choice E)
E
yyy-intercept and a point that is not an intercept
(Choice F)
F
Two points that are not intercepts
The information about the graph of the relationship that is given is: E. y-intercept and a point that is not an intercept.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear, quadratic, trigonometric function, generally occurs at the point where the value of "x" is equal to zero (x = 0).
What is the slope-intercept form?Mathematically, the slope-intercept form of a straight line is generally modeled or represented by this mathematical expression;
y = mx + c
Where:
x represents a data point i.e the number of hours.y represents a data point i.e the number of pagesm represents the slope.c represents the y-intercept i.e total number of pages.In this context, we can reasonably infer and logically deduce that the total number of pages (y-intercept) which is equal to 180 is an information that was provided, as well as the number of hours (666 hours), which represents a data point on the x-coordinate of the graph.
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a 39-inch by 104-inch piece of cardboard is used to make an open-top container by removing a square from each corner of the cardboard and folding up the flaps on each side. what size square should be cut from each corner to get a container with the maximum volume? enter the area of the square and do not include any units in your answer.
According to the solving the area of the square is 68.0625.
What's a square's area?As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.
According to the given data:The box formed after cutting the square from each corner will have the dimensions as,
length = 104 - 2x, width = 39 - 2x, height = x.
∴ volume of the box = length × width × height
∴ v = (104 - 2x)(39 - 2x)(x) -----(i)
∴ v = (104 - 2x) (39x - 2[tex]x^{2}[/tex])
∴ v = 104(39x - 2[tex]x^{2}[/tex]) -2x(39x - 2[tex]x^{2}[/tex])
∴ v = 4056x - 208[tex]x^{2}[/tex] - 78[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]
∴ v = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
let f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x -----(ii)
To, find x for which f(x) is maximum,
⇒we should apply second derivative test ,
According to this test, first we should find critical points at which f'(x) = 0.
then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.
∴ let us consider, f'(x) = 0.
now, f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
⇒ f'(x) = 12[tex]x^{2}[/tex] - 572x + 4056. -----(iii)
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014)
⇒ f'(x) = 0.
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014) = 0
⇒ x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/2a ; where a = 3, b = -143, c = 1014.
∴ x = (-(-143) ± [tex]\sqrt{(-143)^{2} -4(3)(1014)}[/tex])/2×3
∴ x = (143 ± [tex]\sqrt{8281}[/tex])/6.
∴ x = [tex]\frac{143 + 91}{6}[/tex] , x = [tex]\frac{143 - 91}{6}[/tex]
⇒ x = 39, 8.25
the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.
Area of the square is = [tex]x^{2}[/tex] = [tex]8.25^{2}[/tex]
∴ Area = 68.0625
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400 kilometers in 8 hours at a constant speed
Write an equivalent ratio for each ratio
Answer:2/5=4/10 and 1/4=2/8
Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.
I need help asap please now please !!!!!!!!!!!
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{1}{6}[/tex] x + 9
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (6, 10) ← 2 points on the line
m = [tex]\frac{10-9}{6-0}[/tex] = [tex]\frac{1}{6}[/tex]
the line crosses the y- axis at (0, 9 ) ⇒ c = 9
y = [tex]\frac{1}{6}[/tex] x + 9 ← equation of line
- is slightly variable - and follows a nearly normal distribution - with a mean of 25 square feet - and a standard deviation of 3 square feet. (a) what is the probability that - the area covered by a can of spray paint - is more than 27 square feet?
The probability that the area covered by a can of spray paint is 0.251
The variable of interest is:
X: are objects that can be painted with a single can of spray paint.
This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.
Symbolically:
P(X≥27)
To calculate the probability, use the standard normal distribution, so first standardize the value of X using:
Z= (X-μ)/σ
P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)
Now, because the Z-table contains cumulative probability information:
P(Zα≤Z₀)=1-α
you must perform the following conversion to calculate the requested probability:
1 - P(Z<0.67)= 1 - 0.749= 0.251
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What is an
equation of the line that passes through the points (6, 0) and (3, 4)?
The equation that passes (6,0) and (3,4) is -3y=4(x-6)
What are the different forms of straight lines ?
The following information about the straight line is required if we wish to obtain the equation for it.
1. The y-intercept and slope
2. Two-point and slope
3. Two things.
4. the intersection of the x- and y-axes
the straight line that passes through (6,0) and (3,4).
The equation can be expressed in a point-slope form which is ,
y/x-6=4/-3
∵ -3y=4(x-6)
Hence,
The equation that passes (6,0) and (3,4) is -3y=4(x-6)
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Write a system of equations with the solution (4, -3).
The system of equations with the solution (4, -3) is y = x - 7 and y = 2x - 11.
We are given a point. The coordinates of the point are (4, -3). We need to find a system of equations such that they pass through the given point.
We will use the slope-point form of a line. Let the slope of the equation of the straight line be "m". We need two equations. The general equation of a line using the slope-point form is given below.
(y - y1) = m(x - x1)
We know that both equations must pass through the given point for the solution to exist.
(y - (-3)) = m(x - 4)
(y + 3) = m(x - 4)
We just need to take any two values of the slope of the line.
First, we take m = 1. The corresponding equation is given below.
(y + 3) = m(x - 4)
(y + 3) = 1*(x - 4)
y + 3 = x - 4
y = x - 7
Next, we take m = 2. The corresponding equation is given below.
(y + 3) = m(x - 4)
(y + 3) = 2*(x - 4)
y + 3 = 2x - 8
y = 2x - 11
Hence, the system of equations is y = x - 7 and y = 2x - 11.
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Solve each system by substitution.
4x + y = 19
6x + 7y=1
Step-by-step explanation:
that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.
finally we use one of the original equations to solve for the second variable.
4x + y = 19
so, that gives us
y = 19 - 4x
we use that now in the second equation :
6x + 7(19 - 4x) = 1
6x + 133 - 28x = 1
-22x + 133 = 1
-22x = -132
22x = 132
x = 6
now, let's use e.g.
4x + y = 19
4×6 + y = 19
24 + y = 19
y = -5
At a real estate agency, an agent sold a house for $307,000. The commission rate is 5.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The commission that thereal estate agency gets is $16885.
The commission that the agent gets is $76750
How to calculate the commission?The selling price for a house = $ 307,000
The commission rate for real estate agency = 5.5 %
The commission rate for the agent = 25 %
So, the commission which real estate agency gets:
= 5.5 % of $307,000
= 0.055 × $ 307,000
= $16885
The commission which agent get:
= 25% of $ 382,000
= 0.25 × $ 307,000
= $76750
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Gabriella is going back to school shopping.each notebook she buys costs $3 and each pack of markers costs $3.she buys 4 packs of markers and n notebooks.she writes the follwing expression represent how much shr spend
Answer:
$24
Step-by-step explanation:
3(4) + 3(4) = x (the total cost)
12 + 12 = x
x = $24
marrisa bought 3 packages of balloons and 4 packages of party favors for a total of 14.63. Ray bought 2 packs of balloons and 4 packs of party favors for a total of 16.03. find the price of a pack of balloons and the price of a pack of party favors
The price of a pack of balloons is 4. 39
The price of a pack of party favors is 0. 36
How to determine the valuesWe have that;
Let the cost of balloons be x
Let the cost of party favors by y
From the information given, we have that;
3x + 4y = 14. 63 (1)
2x + 4y = 16. 03 (2)
Now, let's make 'x' the subject from equation (1)
x = 14. 63 - 4y/ 3 (3)
Substitute in equation (2)
3( 14. 63 - 4y/ 3) = 16. 03
expand the bracket
43. 69 - 12y /3 = 16. 03
cross multiply
43. 69 - 12y = 48. 09
collect like terms
- 12y = - 4. 4
make 'y' the subject
y = 0. 36
substitute in equation (3)
x = 14. 63 - 4(0. 36)/ 3
x = 13. 1/ 3
x = 4. 39
Hence, the prices are 4. 39 and 0. 36 respectively.
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State the value of the two square numbers closest to 55. Hence, show that 55 is not a square number.
Answer:
7.416 is the answer
Help Please!!!
Direct and Inverse Variations
aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given sequence is 5,9,13,17,21
Five comma nine comma thirteen comma seventeen comma twenty one.
We need to find the nth term of the sequence.
Firstly we need to find the sequence is AP or GP.
An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.
so 9-5=4,
13-9=4
Hence the sequence is a Aritmetic sequence.
In arithmetic sequence the nth term can be find by using the formula
aₙ=a+(n-1)d
where a is first term and d is common difference.
Hence aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.
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Solve. −1 − 10x < −1
The solution to the inequality is x > 0
What is Inequality?Inequality in mathematics differentiate two values, if one is less than, greater than, or not equal to another value
Evaluate the equation by letting the unknow to be on one side
−1 − 10x < −1
-10x < -1+1
Add +1 to both sides
= -1-10x+1 < -1+1
= -10x < 0
Divide both sides by -10 same factor and flip the relation because of negative factor
= -10x /-10 > 0/-10
= x > 0
Therefore the solution to the inequality is x>0
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Expand and simplify (2x + 5)2
Answer: 4x+10
simplified: 2x+5
Step-by-step explanation:
Answer: 4x+10
You multiply 2 by (2x) = 4x
You multiply 2 by (5) = 10
please help me with this
Answer: final answer = 3/8
Step-by-step explanation:
it says 1/8 + 1/4. before you can add them you have to make sure that both fractions have the same denominator first you have to make both of the bottom denominators the same so its 1/8+2/8.
1/8+2/8=3/8
what are the coefficients in 4x + 8y - 5
Answer:
Step-by-step explanation:
A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.
The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).
the sum of the number of factors of n and n2 is 34. how many such distinct numbers such that n<150 exist?
The total 18 numbers such that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34
Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.
Factors in total (2+1)*(1+1)=6
It will have 2- 4 times and 3-2 times for 122.
15 total factors of 5*3
Situation 1: N = xy
attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.
Regarding N-x-2 and Y-3 timings.
There are a total of (2+1)*(3+1)=12 factors.
Situation 2
Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.
Consequently, 17+1 = 18 factors in total.
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