Sums of terms with the pattern k.[tex]x^{n}[/tex]—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5.
What is polynomial?A polynomial is a mathematical expression made up of coefficients multiplied by the sum of powers in one or more variables.A polynomial is a mathematical statement made up of coefficients and indeterminates that uses solely the operations addition, subtraction, multiplication, and powers of positive-integer variables. x2 4x + 7 is an illustration of a polynomial of a single indeterminate x. A polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation, such as the quadratic equation, cubic equation, etc. As an illustration, the polynomial 2x+5 has an exponent of 1. A polynomial is described as an expression made up of variables, constants, and exponents that are joined using mathematical operations like addition, subtraction, and multiplication.To learn more about polynomial refer to:
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Juan claims the function y =3+2 exponent 3 square root x-1
Need answer to question down below :)
y = 3 + 2[tex](3\sqrt{x} -1)[/tex] is a quadratic function.This function represents a real-valued function that maps a real number x to the real number y.
What is a quadratic function?The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph
A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
The function y = 3 + 2[tex](3\sqrt{x} -1)[/tex] can be explained as follows:
The first part of the function, "3" is a constant that is added to the result of the next part of the function.The next part of the function, "2[tex](3\sqrt{x} -1)[/tex]," represents an exponential expression. Here, the base is "2" and the exponent is "3√x - 1."The exponent, "3√x - 1," represents the square root of x, multiplied by 3 and then subtracted by 1. This means that the value of x is first evaluated under the square root, then multiplied by 3, and finally subtracted by 1.So, the entire function "y = 3 + 2[tex](3\sqrt{x} -1)[/tex]" can be read as: "y is equal to 3, plus 2 raised to the power of 3 times the square root of x, minus 1."To learn more about quadratic function refers to:
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The manager of a store orders swing sets that cost $350 and sells them for $560. What is the mark-up percentage?
The required mark-up percentage of the manager is 60%.
What is Mark-up percent?The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %. The markup percentage, which is computed as (12 - 8) / 8, is 50% for an item that costs the business $8 to produce but is priced at $12.
According to question:We have,
Cost price of the Unit = $350
Selling price of the unit = $560
Then,
Mark-up percentage = ($560 - $350)/$350 × 100
Mark-up percentage = $210/$350 × 100
Mark-up percentage = 0.6 × 100
Mark-up percentage = 60%
Thus, required mark-up percent is 60%.
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Ms. Lee is shopping for a new electric water heater. Brand A costs $575 and uses 442 kilowatt-hours per month. Brand B
costs $651 and uses 397 kilowatt-hours per month. If electricity costs $0.17 per kilowatt-hour, how much would Ms. Lee save
on electricity per month by buying Brand B?
Ms. Lee would save $ per month.
Ms. Lee would save $40.19 per month by buying Brand B. To calculate this, we must first find out how much each brand costs to operate each month.
What is brand cost?Brand cost is the amount of money invested in a brand or product in order to create, maintain, and grow its value. This includes the costs associated with advertising and promotion, research and development, marketing, and product design. Brand cost also includes activities such as creating and maintaining a good corporate image, creating brand loyalty, and expanding the customer base.
For Brand A, this would be $75.54 (442 kW x $0.17/kW).
For Brand B, this would be $67.35 (397 kW x $0.17/kW).
We can then subtract the cost for Brand B from the cost for Brand A to get the amount of money Ms. Lee would save each month.
This would be $40.19 ($75.54 - $67.35).
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a glass of water is $\dfrac{3}{7}$ full and $\dfrac{4}{7}$ empty. it has 6 ounces of water in it. how many ounces of water can the glass hold?
The glass can hold up to 9 ounces of water.
Given that the glass is [tex]$\dfrac{3}{7}$[/tex] full, there must be [tex]$\dfrac{4}{7}$[/tex] a glass that is empty. If the glass has 6 ounces of water in it, then we can able to find the total volume of the glass by dividing the amount of water in the glass by the fraction that is full.
Here is the calculation of the total volume of the glass:
[tex]$\text{Volume of glass}[/tex] =[tex]\dfrac{\text{Amount of water}}{\text{Fraction full}}[/tex] =[tex]\dfrac{6}{\dfrac{3}{7}}[/tex] = [tex]9$[/tex] ounces
By calculating the volume of the glass we came to know that the glass can hold 9 ounces of water in total.
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What is the quotient of
7.584
×
1
0
6
7.584×10
6
and
7.9
×
1
0
2
7.9×10
2
expressed in scientific notation?
0.96×10⁴ is the quotient of 7.584×10⁶ and 7.9×10²
What is Division?A division is a process of splitting a specific amount into equal parts.
We need to find the quotient of
7.584×10⁶ and 7.9×10²
Dividend is the number that is to be divided by the divisor.
Divisor is the number by which the dividend is to be divided is called the divisor.
The resultant of the division is called the quotient.
7.584×10⁶/7.9×10²
0.96×10⁶⁻²
0.96×10⁴
Hence, 0.96×10⁴ is the quotient of 7.584×10⁶ and 7.9×10²
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Enter the correct answer in the box.
A delivery company uses cars, cargo vans, and semitrailers. The company uses its cargo vans to deliver packages to locations at a 75-mile radius from the warehouse. If the distance to the delivery location is 8 miles or less from the delivery boundary, a cargo van will still be used. The company uses the other vehicles for any distance outside this range.
Write an inequality to represent the instances when a vehicle other than a cargo van is used, where x is the distance of a location from the warehouse.
The inequality to represent the instances when a vehicle other than a cargo van is used, where x is the distance of a location from the warehouse is given as follows:
x ≤ 8.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.Distances of 8 miles or less are of at most 8 miles, hence the inequality is defined as follows:
x ≤ 8.
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After the GCFs are factored out, what is the common binomial factor for x2 + 3x + 5x + 15?
The common binomial factor for the given expression is[tex]$x+3$[/tex].
What is binomial factor?Polynomial factors known as binomial factors contain two terms only. Because binomials are simple to solve and the roots of the binomial factors are the same as the roots of the polynomial, binomial factors are intriguing. The first step in locating a polynomial's roots is to factor it.Consider factoring by grouping if your set of four words lacks a GCF. Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each individual binomial. 3. Factor the common binomial out.We are given the expression[tex]$x^2+3 x+5 x+15$.[/tex]
We wish to find the common binomial factor for the given expression. So, we have:
Solution:
Factoring by grouping, we have:
[tex]x^2+3 x+5 x+15 & =x(x+3)+5(x+3) \\[/tex]
[tex]& =(x+3)(x+5)[/tex]
Therefore, we can see that the common binomial factor for the given expression is[tex]$x+3$[/tex].
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Please help:
I think of a number. If I subtract 10 from my number, then square the result, I get the same answer as if I square my number, then subtract 10 from the result.
What is my number?
You must show an algebraic method ( use letter x in your working).
The number you think is 5.5
How to find the number?
An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
Let x represent the number you think. Thus, we can write:
(x - 10)² = x²-10
x² - 20x + 100 = x²-10
-20x + 100 = -10
20x = 100 + 10
20x = 110
x = 110/20
x = 5.5
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To indirectly measure the distance across a river, Francisco stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Francisco draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
Francisco uses the method of similar triangles to find the distance across the river, and the distance across the river is 372 feet.
What is a Triangle?A triangle is a polygon with three sides and three vertices. The triangle's total number of angles comes to 180°. The distances between the formed the sight-lines are;
RB = 210 feet
OC = 275 feet
The distance between the point close to the river and the next point further from the river = is 115 feet
In triangles ΔPRB and ΔPOC,
we have;
∠PRE = ∠POC = 90°
Given;
∠PER ≅ ∠PCO
By the corresponding angle formed between two parallel lines and a common transversal.
Using angle-angle similarity theorem;
ΔPRE is similar to ΔPOC Which gives;
PR / PO = RE / OC
Let x represent the distance across the river,
we have;
PR = x
PO = 115 + x
Which gives;
x / (115+x) = 210 / 275
275x = 210 × (115 + x)
275x = 24150 + 210x
275x - 210x = 24150
65x = 24150
x = 371. 54
Therefore, the distance across the river is 372 feet.
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The lines shown below are parallel. If the green line has a slope of -1/2, what is the slope of the red line?
The slope of the red line is -1/2
What is a slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Here, we have
Two lines are parallel. Two lines are shown by the color green and red line.
As we know if lines are parallel then their slope is equal.
W are given a green line parallel to the red line.
The slope of the green line is -1/2
But The slope of the red line = slope of the green line.
The slope of the red line = -1/2
Hence, The slope of the red line is -1/2.
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consider the following differential equation y'' - 8y αy = 0 for which value(s) of α does the characteristic equation have 2 distinct real solutions? 2 complex solutions? 1 repeated real solution?
The characteristic equation has 2 distinct real solutions if α > 16, 2 complex solutions if α < 16, and 1 repeated real solution if α = 16.
The characteristic equation of the differential equation y'' - 8y + αy = 0 is given by:
r^2 - 8r + α = 0
For 2 distinct real solutions, the discriminant of the characteristic equation must be positive, which leads to the condition:
(8)^2 - 4α > 0
64 - 4α > 0
-4α < -64
α > 16
For 2 complex solutions, the discriminant must be negative, which leads to the condition:
(8)^2 - 4α < 0
64 - 4α < 0
-4α > -64
α < 16
For 1 repeated real solution, the discriminant must be zero, which leads to the condition:
(8)^2 - 4α = 0
64 - 4α = 0
α = 16
For 2 distinct real solutions α > 16, For 2 complex solutions α < 16 and For 1 repeated real solution α = 16.
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what is the end behavior?
Answer:
the answer is a. -2
Step-by-step explanation:
i hope that helps you
thanku
Please help me with this problem
The given graph represents a quadratic function with negative leading coefficient, hence it opens down.
c) Its vertex is its maximum and the function is increasing before reaching vertex and decreasing after it.
The vertex is at (-2, 8) so the domain on which the function is increasing is:
x < - 2d) The x-intercepts of the graph are x = - 6 and x = 2. The function is positive between the x-intercepts and negative outside, so:
f(x) < 0 when x < - 6 and x > 2equation for parabola if the point is (3,0)
Answer:
[tex]y=(x-3)^{2}[/tex]
Step-by-step explanation:
First, it should be noted that the parabola shown is just the parent parabola translated over 3 units to the right. To shift the parent parabola over to the right 3 units, we need to square x-3. So, the equation for the parabola shown is [tex]y=(x-3)^{2}[/tex].
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Have a GREAT day!!!
I want to be done already :(
Answer: 4/D
Step-by-step explanation: going through the options one by one.
for the first point, the first statement is true since both lines intersect at (4,5)
for the second point, this is also true because since (4,5) is on both functions, x=4 and y=5 will be a solution for both
for the third point, this is also true since the point of intersection is (4,5), this is the solution for the system
for the fourth point, this is untrue. since we don't know what f and g are and the only solution to the system is (4,5), what works for f may not necessarily work for g. so 4/d is the answer.
ps. you got this :) you'll be done before you know it
how to report statistical power apa
Following APA criteria, statistical power should be stated along with effect magnitude, sample size, and alpha level.
Following the recommendations of the American Psychological Association (APA), statistical power should be stated. This includes stating the sample size that was utilised, the estimated effect size, and the alpha level that was chosen for the analysis. The degree of the difference between two groups is measured by the effect size, which should be stated together with the accompanying confidence interval. The sample size, which represents the number of observations used in the study, is also crucial. The degree of significance, commonly known as the alpha level, should also be given. This shows the likelihood of a false-positive finding and can be used to assess the accuracy of the findings. Researchers are able to accurately assess the trustworthiness of the results when statistical power is reported in accordance with APA recommendations.
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Ravindra' monthly income i rupee 90000. After pending on variou expenditure, he manage to ave rupee 40000 per month. What percentage of hi income doe he ave?
The percentage of his income he saved is 44.4%.
Percentage is a way of expressing a number as a fraction of 100. It is commonly used to represent a proportion or share of a whole, such as a percentage of a total amount, a percentage of a target or goal, a percentage of a population, etc.
In mathematical terms, a percentage can be represented as a decimal or a fraction, and is expressed as a symbol, such as "%".
If Ravindra's monthly income is rupee 90000 and saves rupee 40000 per month, then the percentage can be calculated as:
percentage = (40,000/90,000) x 100% = 44.4%
Hence, she saves 44.4% of his income per month.
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an account earns simple intrest find the interest earned and the balance of the account 200 at 3 % for 5 years
The interest earned and the balance of the account 200 at 3 % for 5 years is 30.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that an account earns simple intrest
We have to find the interest earned
the balance of the account 200 at 3 % for 5 years
I=PRT
P is the principal amount
t is the time
r is the rate of interest
I=200×0.03×5
I=30
Hence, the interest earned and the balance of the account 200 at 3 % for 5 years is 30.
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What is the slope of a line that passes through the points (9,8) and (2,3)?
The slope of the line that passes through the points (9,8) and (2,3) is 5/7.
What is a slope in a graph?The slope of a line in a graph is a measure of its steepness or slant. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical terms, the slope of a line can be represented as the difference in the y-coordinates of two points on the line divided by the difference in the x-coordinates of the same two points.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the given points, we get:
slope = (3 - 8) / (2 - 9) = -5 / -7 = 5/7
So, the slope of the line that passes through the points (9,8) and (2,3) is 5/7.
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Can someone help with 17-20 please
When the figure is rotated around the line, a cylinder is created.
Find the volume of the solid?The perimeter of the 2-D figure is 20 units.The volume of the solid is 40π units.Two dimensional shapes created by the cross sections of the solid are circles and rectangles.When this figure is rotated around the line, a solid called a right circular cylinder is created.A right circular cylinder is a three-dimensional object that has two parallel circular bases connected by a curved surface.The perimeter of the 2-D figure is the sum of the lengths of the sides, which is 20 + 8 + 20 + 8 = 56.The volume of the solid is the area of the base times the height, which is π(5)² x 10 = 250π.Two two-dimensional shapes created by cross sections of the solid are circles and rectangles.A circle is created when the cross section is perpendicular to the axis of rotation.A rectangle is created when the cross section is parallel to the axis of rotation.The circles will have a radius of 5 and the rectangles will have length and width of 10 and 8, respectively.To learn more about right circular cone refer to:
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This afternoon Dan left school, rode the bus 1/4 of a mile, and then walked 1/8 of a mile to get home. How much farther did Dan ride than walk?
Answer:
0.125 miles
Explanation:
1/4 of a mile is 440 yards and 1/8 of a mile is 220. 440-220=220.
6. if f(x) =2x - 6 and g(x)=3x+9, find (f+g)(x)
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2012, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1171.
Regression equation:
Final answer:
The linear regression model is expressed as y = -25.31x + 1017.075.
What is linear regression?The best-fit line is given by:
y = bx + a
The slope is as follows:
b = Σ(x - X) ( y - Y)/Σ(x - X)²
After determining the slope using the means for x and y, the coefficient an is calculated.
The means are provided by:
X = (0 + 1 + 2 + 3 + 4 + 5)/ 6 = 2.5
Y= (904 + 924 + 938 + 957 + 977 + 1023)/6
= 953.83
The figures are as follows:
Σ(x - X) = (0 - 2.5) +(1 - 2.5) + ---------+ (5 - 2.5)
Σ( y - Y) = ( 904 - 953.83) + (924 - 953.83) + ---------- + ( 1023 - 953.83)
Making use of a calculator:
Σ(x - X) ( y - Y) = -443
Σ(x - X)² = 17.5
As a result, the slope is:
b = -443/17.5
= -25.31
y = -25.31x + a
Using the means to locate a:
953.83 = -25.31 x 2.5 + a
a = 1017.075
As a result, the linear regression model is:
y = -25.31x + 1017.075
After 2012, the number of cases would reach 1171 in x years, and x is found when y = 1171. Thus:
1171 = -25.31x + 1017.075
1171 - 1017.075 = -25.31x
x = 6
2012 + 6 = 2018
The number of reported cases is expected to reach 1171 by 2018.
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Please Help me with numbers 1 2 and 3!!!! I dont know!!!
Step-by-step explanation:
it says it in the headline : the cube root function.
1.
it goes through (0, 0) and (1, 1) and (-1, -1).
so,
f(x) = cubic root(x)
domain = (-infinity, +infinity)
range = (-infinity, +infinity)
x-intercept = 0
y-intercept = 0
2.
the function is y = cubic root(x + 2)
compared to
y = cubic root(x)
the domain is x >= -2
wrong !
this is not a square root. for the square root that domain would be correct (there are no real number square roots for negative values). but cubic roots are possible also for negative values. this function has the same domain and range as the basic y = cubic root(x) : (-infinity, +infinity).
the function is a vertical translation of g(x) = cubic root(x).
wrong !
vertical means up/down.
but it is a horizontal (left/right) translation of that g(x). by 2 units to the left, actually.
3.
for 1 <= x <= 4 we have already the average rate of change :
about 0.197
for 4 <= x <= 7 we get
(f(7) - f(4))/(7 - 4) ≈ (1.91 - 1.59)/3 ≈ 0.109
so, the interval [1, 4] has a greater average of change.
which is also clear when looking at the graph : the function increases stronger for the lower x-values than for the larger x-values.
6. Matthew and Toby went back to school shopping. Matthew bought 5 shirts and 2
pairs of pants for $165. Toby bought 3 shirts and 5 pairs of pants for $251. Each shirt
and each pair of pants cost the same amount.
What is the cost of one pair of pants?
A. $17
B. $23
C. $57
D. $40
Therefore , the solution of the given problem of equation comes out to be cost of one pair of pants is $40.
What is equation ?The similar symbol (=) is used in mathematical equations to variables denote equality between two propositions. Mathematical formulae, which are abstractions of reality, are used to demonstrate how different numerical factors can be compared. For instance, the equal sign splits the integer 12 or perhaps the equation y + 6 = 12 to two separate halves. One can compute how so many characters each side of the a character has. Contradictory meanings are common in symbols.
Here,
Given :
Mathew bought 5 shirts and 2 pairs of pairs is $165.
Toby bought 3 shirts and 5 pairs of pants for $251.
x is the shirt of price ,
y is the pants of price .
Thus,
=> 5x + 2y = 165
=> 3x + 5y = 251
So,
=> x = 165 -2y/5
=> 3(165 - 2y/5) + 5y = 251
=> 3(165 - 2y /5) + 5y = 251
=> 495 - 6y + 25y = 251 *5
=> 495 + 19y = 1255
=> 19y = 1255 - 495
=> 19 y = 760
=> y =760/19
=> y = 40
and
=> x = 165 - 2*40 /5
=> x = 165-80/5
=> x = 85/5
=> x =17
Thus , cost of one pair of pants is $40.
Therefore , the solution of the given problem of equation comes out to be cost of one pair of pants is $40.
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A car traveled a distance of 600.15 km in 7.5 hours. How many kilometers did the car travel per hour on the average?
Answer:
Step-by-step explanation:
600.15/ 7.5 = 80.02
Graph the function y=|x|-3
Question 13, Will mark brainliest for the RIGHT answer! NO need to show work :)
The value of the trigonometric relation tan θ = 0.25819889
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin (-θ) = -sin (θ)
csc (-θ) = -csc (θ)
cos (-θ) = cos (θ)
sec (-θ) = sec (θ)
tan (-θ) = -tan (θ)
cot (-θ) = -cot (θ)
In the first quadrant, sin, cos and tan are all positive.
In the second quadrant going anti-clockwise, only sin is positive.
In the third quadrant going anti-clockwise, only tan is positive.
In the fourth quadrant going anti-clockwise, only cos is positive
Given data ,
Let the angle be represented as θ
Now , the measure of sin θ = - ( 1/4 )
So , the value of θ lies in the 3rd quadrant
Taking inverse on both sides of the equation , we get
θ = sin⁻¹ ( - ( 1/4 ) )
θ = 194.47751218° + 2πn
Now , In the third quadrant going anti-clockwise, only tan is positive.
So , tan θ = tan ( 194.47751218 )
On simplifying the equation , we get
tan ( 194.47751218 ) = 0.25819889
Hence , the value of tan ( 194.47751218 ) is 0.25819889
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A bank says you can double your money in 10
10
years if you put $1,000
$
1
,
000
in a simple interest account. What annual interest rate does the bank pay?
Divide the principal by the time, interest rate, and time period to calculate simple interest.Annual interest rate is 0.02.
What rate of interest does the bank charge annually?
Divide the principal by the time, interest rate, and time period to calculate simple interest.The equation is expressed as "Simple Interest = Principal x Interest Rate x Time."It is easiest to calculate interest using this equation.
I, or the interest earned or charged on a loan, can be calculated using the straightforward interest formula.
I = Prt, where P is the principal, r is the yearly interest rate stated in decimal form, and t is the loan term expressed in years, gives the amount of interest.
It is necessary to transform the rate r from percentage to decimal form.
Then, 2,000 = 1,000 * r * 10 ;
Finally, r = 2 ÷ 10 = 20 ÷ 100 = 0.02
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Pls show work and answer the question
Answer:
Step-by-step explanation:
