Answer:
[tex] p(x) = k[ x^2-4x-104] [/tex]
Step-by-step explanation:
Say if alpha and beta are the zeroes of the quadratic polynomial then the quadratic polynomial is given by ,
[tex]\implies p(x) = k[x^2-(\alpha+ \beta)x +\alpha\beta ] [/tex]
where k is a constant[tex]\implies p(x) = k[ x^2 - [ (2+6\sqrt3)+(2-6\sqrt3)x] + \{ (2+6\sqrt3)(2-6\sqrt3)\} ] \\\\\implies p(x) = k[ x^2 - 4x + \{ (2)^2-(6\sqrt3)^2\}] \\\\\implies p(x) = k[ x^2 -4x \{ 4-108\} ] \\\\\implies\boxed{\boxed{ p(x) = k[ x^2-4x-104] }}[/tex]
This is the required answer !
The graph below represents the number of miles, y, that the satellite Space Explorer
flies in a hours. Find the rate of change.
Miles
90,000
85,000
80,000
75,000
70,000
65,000
60,000
55,000
50,000
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
Answer:
0
Space Explorer
Seve
(10,10000)
(5.5000)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Hours
miles per hour
Submit Answer
Answer:
1000
Step-by-step explanation:
answer is 1000 miles per hour
using the standard From of the quadratic Function y=-3x²-12x-9
The standard From of the quadratic Function is (−2,3).
What is the standard From?y=-3x²-12x-9
Find the given parabola's characteristics.
To continue, tap...
Opens down in the direction of ( 2, 3), with
( -2, 35 /12) as the focus.
x = 2 is the symmetry axis.
The directrix is y = 37 /12
By entering a few x values into the equation, you may get the associated y values. You should choose the x values close to the vertex.
To continue, tap...
x y − 4 − 9 − 3 0 − 2 3 − 1 0 0 − 9
Using the chosen points and the parabola's attributes, draw the curve.
Opens downward in direction
Focus: ( 2, 35 12) Vertex: ( 2, 3)
x = 2 is the symmetry axis.
The following directrix: y = 37 12 x y 4 9 3 0 2 3 1 0 0 9.
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(b)
(i) Factorise 1000x³-y³ completely.
(ii) Hence, without using a calculator, show that 124 is a factor of 992.
Answer:
i. (10-y)(100x^2 +10xy + y^2)
ii. See the explanation
Step-by-step explanation:
i. 1000x³-y³ =
10³x³ - y³ =
(10x)³ - y³ = ==> use formula: x³ - y³ = (x-y)(x^2+yx+y^2)
(10-y)((10x)^2 +10xy + y^2) =
(10-y)(10^2 * x^2 +10xy + y^2) = ==> simplify
(10-y)(100x^2 +10xy + y^2)
ii. 992/124=
(992-192)/(124-24)=
800/100 = 8
As a result, 8*124=992.
Hence, 124 (and 8) is a factor of 992
Which expression is equivalent to 18-(8* q) ? .
A (8q) - 18
B (18 - q) * 8
C (18 - 8) * c
D 18 - (0 * 8)
Answer:
the way you typed that is kinda confusing but the answer is
[tex]18 - 8q[/tex]
Are the whole numbers closed under division justify with example?
The division of the whole numbers is not closed under property as the division of whole number is not always a whole number.
A set has the closure property under a particular operation if the result of the operation is always an element in the set. If a set has the closure property under a particular operation then we say that the set is “closed under the operation.” The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division that is a ÷ b is not always a whole number.
For example, 5 and 8 are whole numbers, but 5÷8 is not a whole number.
Therefore, closure property does not exist for division of whole numbers.
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The ratio in the table for ditance covered in meter to time taken in hour i contant. Let d = ditance covered in 15 hr. Let t = time taken to cover 8 m. Which table how the correct value for t and d? A. B. C. D
The table that shows the correct t and d values is
Distance Covered (m) Time Taken (hr)
8 6
32 15
How to determine the correct values for t and d
The table of values is given as:
Distance Covered (m) Time Taken (hr)
8 6
16 12
32 15
48 18
The distance covered in 15 hours is 32 m and the time taken to cover 8 m is 6 hours
When these values are extracted, we have:
Distance Covered (m) Time Taken (hr)
8 6
32 15
The above represents the table that shows the correct t and d values
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Create a formula without a function that adds 14 days to the date the client was last contacted.
The Excel formula to enter in cell H4 is = (G4 + 14)
Excel formulas are expressions used to perform computation.
To determine the formula:
From the question,
The date the client was last contacted is in cell G4
14 days is to be added to the content of cell G4
So, the formula is:
G4 + 14
Add bracket
(G4 + 14)
Excel formulas begin with the equality (=) sign
So, we have:
= (G4 + 14)
Hence, the formula to enter the cell H4 is = (G4 + 14)
Complete question:
In the cell, H4 creates a formula without a function that adds 14 days to the date the client was last contacted cell G4
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Excel formulas are expressions used to perform computation.
The date the client was last contacted is in cell G4
14 days is to be added to the content of cell G4
So, the formula is:
G4 + 14
Add bracket
(G4 + 14)
Hence, the formula to enter the cell H4 is = (G4 + 14)
In the cell, H4 creates a formula without a function that adds 14 days to the date the client was last contacted cell G4
A power company serves 17,000
customer's homes in a town. The
population of the town is decreasing by
about 3% every year. Which function
would represent the number of
homes,"H", the company will serve after
"n" years.
Answer:
2nd
Step-by-step explanation:
p=17000
r = -0.03
Hn)= p×(1+r)^n
H(n)= 17000(1+-0.03)^n
What does congruent mean square?
Answer:
All the sides of the square are equalso the squares are congruent.. Are congruent shapes? Two shapes that are the same size and the same shape are congruent.
hope this helps
mark me brainliest
Step-by-step explanation:
40 POINTS!
A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
A. (6, 0)
B. (0, 5)
C. (1, 4)
D. (1, 5)
The best estimate of the solution to the system of equations will be (1, 4). Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the equations is given below.
2x + 3y = 12 ...1
4x + 2y = 10 ...2
Divide the equation 2 by 2, then we have
2x + y = 5 ...3
Subtract equation 3 from equation 2, then we have
2x + 3y - 2x - y = 12 - 5
2y = 7
y = 3.5
y ≈ 4
Then the value of 'x' is calculated as,
2x + 3.5 = 5
2x = 1.5
x = 0.75
x ≈ 1
The best gauge of the answer for the arrangement of conditions will be (1, 4). Then, at that point, the right choice is C.
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Someone please help!! (screenshot attached)
The number of CDs that can be bought are { 5, 4, 3, 2, 1 }.
What is an inequality ?
A relationship between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. So inequality emerges from an imbalance.
Given, No. of CDs = x
A CD costs $11 and He has total $60.
So, According to the question,
No. of CDs × Cost of each CD ≤ 60
x × 11 ≤ 60
11x ≤ 60
x ≤ 60/11
Since the number of CDs can't be in fraction and The maximum CDs can be bought is 5.
So, The possible No. of CDs that can be purchased are { 5, 4, 3, 2, 1 }
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It reflects off the mirror and strikes a wall 9.5m away at point P. By what distance does the laser spot on the wall move if the mirror is rotated by 10??
As per the tangent formula, the distance does the laser spot on the wall move if the mirror is rotated by 10 is 2.9m
While we looking into the given question we have identified the following values,
Previous distance = 9.5
And the angle = 30 degrees
Rotated angle = 10 degrees
And the distance is considered as x.
Then as per the tangent formula, it can be written like the following,
=> tan 30/9.5 = tan 10/x
When we apply the tangent value, then we get,
=> 0.5773/9.5 = 0.1763/x
When we perform the cross multiplication, then we get,
=> 0.5773x = 9.5 x 0.1763
=> 0.5773x = 1.6749
Then the value of x is obtained as,
=> x = 1.6749/0.5773
=> x = 2.9012
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What are the factors of x³ 4x² 11x 30?
( x+2) , ( x-3 ) and ( x+ 5 ) are the roots of the equation .The function's zeros are frequently referred to as the function's roots, solutions, or x-intercepts.
what are roots in a equation ?The function's zeros are frequently referred to as the function's roots, solutions, or x-intercepts. These are all used across mathematics and have the same meaning as the zero concept. As a result, when a function y= or f(x)= is supplied, the zeros of the function are function values where y=0 or f(x)=0 f (x) = 0.
here ,
Since the sum of the coefficients is not zero , 1 is not a root
let x = -2
= -8 + 16 + 22 - 30 = 0
= -2 is a factor
dividing [tex]x^{3} + 4x^{2} -11x -30[/tex] by ( x + 2)
quotient = [tex]x^{2} + 2x -15[/tex]
= [tex]x^{2} +5x - 3x -15 =0[/tex]
= x(x + 5) - 3 ( x+ 5 ) =0
= ( x -3 ) ( x + 5 ) =0
other factors are ( x -3 ) and ( x+5 )
So , ( x+2) , ( x-3 ) and ( x+ 5 ) are the roots of the equation .
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keegan bought 5 T-shirts and 2 pairs of shoets for $49.50. Each pair of shorts, s, cost twice as much as each T-shirt, t.
Part A
Which system ot equations can vevused to find the price of the shorts and t-shirts?
(use attachment)
Part B
how much did keegan pay for each t-shirt and each pair of shorts?
Part A
Adding the costs, [tex]2s+5t=49.50[/tex].
Since a pair of shorts costs twice as much as a T-shirt, [tex]s=2t[/tex].
The correct answer is option 3.
Part B
[tex]2(2t)+5t=49.50 \\ \\ 9t=49.50 \\ \\ \boxed{t=5.50} \imploes \boxed{s=11}[/tex]
I need help describing this, I forgot how to find all of it
The (a) Hole in the expression is x, (b) The vertical assumption is -10 and (c) the horizontal assumption is that the denominator is greater than the numerator.
How to find Hole, vertical and horizontal assumptions?You should know that a hole occurs if there is a common term between the the numeration and the denominator when factorized, For vertical assumption, the denominator must be equal to zero and horizontal assumption, numerator will be equal to denominator
The given expression is:
[tex]\frac{x^{2}-2x }{x^{3}-9x^{2} -10x }[/tex]
The Hole is
Factorize the numerator= x²-2x
x is common in the expression
x(x-2)
Factorize the denominator= x³-9x²-10x
x(x²-9x-10)
= [x²-10x+x-10]
x[(x²-10x)+(x-10)]
Simplify further to get
x[x(x-10)+1(x-10)]
=x[(x+1)(x-10)]
Combine numerator and denominator to see the hole
[tex]\frac{x(x-2)}{x(x+1)(x-10)}[/tex]
From the expression the hole is x
b. vertical assumption
The denominator =0
x³+9x²-10x=0
Differentiate to have
dy/dx= 3x²-18x-10
2nd order derivative is
d2y/d2x=6x-18
Applying limit as x approaches 0
6x-10
Therefore x=-10
c. horizontal assumption the numerator is less than the denominator
x²-2x<x³-9x²-10x
In conclusion, the Hole in the expression is x, The vertical assumption is -10 and the horizontal assumption is that the denominator is greater than the numerator.
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What is 2.66666666667 as a fraction?
The fraction 2.666666666667 equals [tex]\frac{8}{3}[/tex] .
A fraction is used to represent a portion/part of something larger. It symbolises the equal parts of the whole. A fraction is comprised of two components the numerator and the denominator. The top number is referred to as that of the numerator, and the bottom number is known as the denominator. The denominator specifies the total number of equal parts in a whole, whereas the numerator describes the number of equal parts taken.
2.666667 to fraction conversion:1. Assume that x = 2.666667 (1)
2. Six is the repeating digit.
To the left of the decimal point, put the repeating digit.
In this instance, multiply the decimal point by 10 to move it one place to the right.
Thus,
(x = 2.666667) * 10
Equation 10x = 26.66667 (2)
4. Take Eq. (1) away from Eq (2)
10x - x = 26.66667 - 2.666667
9x = 24
9 divided by both sides
x = [tex]\frac{24}{9}[/tex] or [tex]\frac{8}{3}[/tex]
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What is the nth root theorem?
Answer:
The nth root theorem is a mathematical principle that states that, for any positive integer, it will have n nth roots!
An nth root of x is equivalent to saying [tex]\sqrt[n]{x}[/tex]. To elaborate, if you want to know how many 2nd roots that 1 has, through this theorem you will know it has 2 of these roots (-1 and 1). This applies for all numbers!
hope this helps :)
What is a function example equation?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Example of Function is f(x) = 2x + 5.
What is a function ?A formula, rule, or legislation that specifies how one variable (the independent variable) and another variable are related (the dependent variable).
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Based on Elements
One One FunctionMany One FunctionOnto FunctionOne One and Onto FunctionInto FunctionConstant FunctionBased on Equation
Identity FunctionLinear FunctionQuadratic FunctionCubic FunctionPolynomial FunctionsBased on the Range
Modulus FunctionRational FunctionSignum FunctionEven and Odd FunctionsPeriodic FunctionsGreatest Integer FunctionInverse FunctionComposite FunctionsBased on the Domain
Algebraic FunctionsTrigonometric FunctionsLogarithmic FunctionsExample of Function is f(x) = 2x + 5.
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What is a zero measurement?
The quantity or complete absence of the thing being measured is represented by the zero point.
Ex. Because the zero point is set arbitrarily and does not indicate the complete absence of temperature, the Fahrenheit scale is an interval scale.
What exactly is a random zero point?Zero degrees on either scale is not a "true" zero because it is an arbitrary number. The absence of temperature does not occur at the zero point; It's just a random number on the scale. Other examples of common interval scales include: Age and SAT scores (one is culturally determined).
Which scale has a point at zero?In addition, on a ratio scale, the distance between two variables is also the same. Furthermore, a proportion scale has a genuine zero point, meaning the worth of zero isn't erratic.
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Write two inequalities to compare a and b how do you know?
To compare two numbers, a, and b, we can write two inequalities:
a < b when a is less than b
a > b when a is greater than b.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We may write two inequalities to compare two numbers, a and b:
a < b
a > b
If a is less than b, then the first inequality is true and the second is false. If a is greater than b, then the first inequality is false and the second is true. Otherwise, if a and b are equal, then both inequalities are false.
We can determine which inequality is true by comparing the values of a and b and using the rules of inequality.
For example, if a=3 and b=5, then we can determine that a < b is true and a > b is false because 3 is less than 5.
On the other hand, if a=8 and b=2, then we can determine that a < b is false and a > b is true because 8 is greater than 2.
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does someone mind helping me with this? Thank you!
Answer:
[tex]y = 2x - 3[/tex]
Step-by-step explanation:
❗ The way I solved this problem doesn't involve me using point-slope form like the problem tells you to use❗
⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to
⭐What does "opposite reciprocal" mean?
Opposite reciprocal: the slope of the perpendicular line is the reciprocal of the slope of the line it is perpendicular to and it has the opposite sign of the slope of the line it is perpendicular to.⭐What is slope-intercept form?
One way to write the equation of a line[tex]y = mx + b[/tex]m = the slopeb = the y-interceptWe can find the equation of the perpendicular line by:
Substituting the slope of the perpendicular line into the point-slope form equation using the opposite reciprocalSubstituting the given coordinate into the point-slope form equation to solve for b1. Substituting the slope into the point-slope form equation:
⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to
The slope of the line the perpendicular like is perpendicular to is [tex]\frac{-1}{2}[/tex].
Therefore, the slope of the perpendicular line is [tex]2[/tex]
Substitute the slope into the point-slope form equation.
[tex]y = 2x + b[/tex]
Now, all we have to do is solve for b.
2. Substituting the given coordinate into the point-slope form equation:
We are given the coordinate (6,9).
[tex]y = 2x + b[/tex]
[tex]9 = 2(6) + b[/tex]
[tex]9 = 12 + b[/tex][tex]-3 = b[/tex]
Substitute "b" into the point-slope form equation.
[tex]y = 2x + 3[/tex]
How do you solve two parallel lines crossed by a transversal?
When two lines are crossed by a transversal, a number of angle pairs are formed. The sum of the measures of these angle pairs can be used to solve for unknown angles in the diagram.
Here are some of the angle pair relationships that hold for two lines crossed by a transversal:
Alternate Interior Angles: Alternate interior angles are pairs of angles on opposite sides of the transversal, but inside the two lines. These angles are congruent (have the same measure).Alternate Exterior Angles: Alternate exterior angles are pairs of angles on opposite sides of the transversal, but outside the two lines. These angles are congruent.Corresponding Angles: Corresponding angles are pairs of angles on the same side of the transversal, but on opposite sides of the two lines. These angles are congruent.Using these relationships, you can set up equations to solve for unknown angles in the diagram. For example, if you are trying to find the measure of angle A, you might use the fact that corresponding angles are congruent to set up the equation "m<A = m<D". Then, you can use other angle pairs to find the measures of the other angles, and solve the system of equations to find the measure of angle A.
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What kind of sequence is 6 12 24?
As there is a common ratio between each term so this is a geometric sequence.
How geometric sequence is applied in real life?The idea of geometric progression can be used to determine how much money you will have in your account after a particular number of years if you deposit money in a bank that offers a fixed annual rate of interest.
What is the important property of geometric sequence?In a geometric progression or series, each term is equal to the one before it times the common factor, which is a fixed non-zero multiplier. The number of terms in a geometric series might be either finite or infinite.
Since in 6 12 and 24 the common ratio r=2. That is if we multiply the previous term by 2 we will get the next term so the given sequence is geometric sequence.
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How do I find a unique number in an array?
The simplest way to get unique number from an array is by putting all numbers of the array into hashmap's key and then print the keySet
How do we find a unique number in an array?an array is a collection of elements or numbers of the same data type.There are more than one way to find unique elements or number from an array:
1.By using hashing
2. By using nested loop
3. By using sorting
4. By putting all the elements in the hashmap's key
But the simplest way to get unique number from an array is the fourth method. And this is done by putting all the number from the array into the hashmap's key, we then print the key set.
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your class collected more than 410 cans of food for th eannual food drive in the first week, 185 cans were collected.how many cans c of food were colected in the second week?
The number of cans collected in the second week would be 225 cans.
A can of food is a container that holds a prepared food product, such as vegetables, fruits, beans, or soups. Canned foods are shelf-stable, meaning they can be stored for long periods of time without spoiling. They are often used as a convenient and easy-to-store source of food, especially in emergency situations.
To find out how many cans of food were collected in the second week, you need to subtract the number of cans collected in the first week from the total number of cans collected. In this case, the number of cans collected in the second week would be:
410 cans - 185 cans = <<410-185=225>>225 cans.
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Find the values of X and y in the diagram.
What form is used to inform the SSS of your illness or injury?
A sickness Notification Form is used to inform the SSS loan of your illness or injury.
The sickness benefit, according to SSS President and Chief Executive Officer Aurora C. Ignacio, is a daily cash payment made for each day a member is unable to work as a result of illness or accident.
In order to be eligible for the program, a member must have made at least three monthly contributions in the twelve months prior to the semester of illness or injury, be confined for at least four days in a hospital or at home, have used all of their current company sick days for the current year, and have informed their employer of their illness or injury.
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The formula for the area of a trapezoid is A = ½h(b₁ + b₂), where h is the height
and b₁ and b2 are the two bases. Rewrite the formula to solve for h in terms of A, b₁
and b₂.
Step-by-step explanation:
that means that we need to transform the equation so that we get a form
h = ...
A = ½h(b1 + b2) | multiply both sides by 2
2A = h(b1 + b2) | divide both sides by (b1 + b2)
2A/(b1 + b2) = h
that's it.
3 3/8 T = ? lb
math question
Answer:
6,750 pounds
Step-by-step explanation:
3 3/8 tons = ? pounds
there are 2,000 pounds in 1 ton so:
3 3/8 * 2,000 = 6,750 pounds
Four transformations of the function f(x) are given below. For each transformation, drag the graph that shows the result of that transformation into the box under it.
Answer:
g(x) = f(x) + 4 → Graph #5
h(x) = f(x + 4) → Graph #6
k(x) = f(x) - 4 → Graph #4
m(x) = f(x - 4) → Graph #3
Step-by-step explanation:
g(x) = f(x) + 4 → Graph #5
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) up by 4.
⭐ Graph #5 exhibits this transformation because I took the point (0,1) and shifted it up 4 units to get (0,5). Graph #5 is the only graph that showed point (0,5).
h(x) = f(x + 4) → Graph #6
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the x-values of f(x) by -4.
⭐ Graph #6 exhibits this transformation because I took point (0,1) and shifted it left 4 units to get (-4,1). Graph #6 is the only graph that showed point (-4,1).
k(x) = f(x) - 4 → Graph #4
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) down by 4.
⭐ Graph #4 exhibits this transformation because I took point (0,1) and shifted it down 4 units to get (0,-3). Graph #4 is the only graph that showed point (0,-3)
m(x) = f(x - 4) → Graph #3
⭐ This transformation of f(x) means that to get to g(x), you have to shift all of the x-values of f(x) right by +4.
⭐ Graph #3 exhibits this transformation because I took point (0,1) and shifted it right 4 units to get (4,1). Graph #3 is the only graph that showed point (4,1).