we have that
A quadratic equation that will have a solution of only x = 0 is given by the equation
[tex]y=x^2[/tex]A right circular cone has a radius of x+4 and a height 5 units less than its radius. Express the volume of the cone as a polynomial function. The volume of a cone is V=13πr2h for radius r and height h. Enter π as pi.
The equation of the volume function is V(x) = 1/3(x + 4)²(x - 1)
How to determine the volume function?The given parameters are
Radius, r = x + 4
Height, h = 5 units less than the radius
This means that
h = r - 5
So, we have
h = x + 4 - 5
Evaluate
h = x - 1
The volume of a cone is calculated as
V = 1/3πr²h
Substitute the known values in the above equation
V = 1/3 * (x + 4)² * (x - 1)
This gives
V = 1/3(x + 4)²(x - 1)
Express as a function
V(x) = 1/3(x + 4)²(x - 1)
Hence, the function is V(x) = 1/3(x + 4)²(x - 1)
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please help me solve
The co-ordinate of B ( -3 , 2 )
What is the Mid Point of Line Halfway between the two end points is the midway?Its x value lies in the middle of the two x values.
Its y value lies in the middle of the two y values.
To figure it out:
Add the two "x" coordinates, then divide by two.
n order to divide by two, add the two "y" coordinates.
Mid point (X , Y) formula
X = ( x₁ + x₂ ) ÷ 2
Y = ( y₂ + y₂ ) ÷ 2
where ( x₁ , y₁) co- ordinate of A ( 7 , -2 )
(x₂ , y₂ ) co- ordinate of B
2 = ( 7 + x₂ ) ÷ 2
x₂ = -3
0 = ( -2 + y₂ ) ÷ 2
y₂ = 2
co- ordinate of B ( -3 , 2 )
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What is the coefficient of the first term in this expression?
x+9y^3 +4
The coefficient of the first term of the polynomial is 1.
How to find the coefficient of the first term in an expression?
Polynomials are algebraic expressions of the following form:
f = Σ (cₙ · xₙⁿ)
Where:
cₙ - n-th Coefficient of the polynomial.xₙ - n-th Variable associated with the n-th term of the polynomial.The order of the terms of a polynomial is usually from the left to the right. Then, the first term of the polynomial x + 9 · y³ + 4 is x = 1 · x, whose coefficient is equal to 1.
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A. What is the difference in total area of Alaska and Connecticut? Express your answer in scientific notation. Show your work or explain your answer.
3. What is the difference in total population of California and Alaska? Express your answer in scientific notation. Show
your work or explain your answer.
Answer:
A. Total area of Alaska is considerable larger than total area of Connecticut.
B. Population of California is considerably larger that population of Alaska.
Step-by-step explanation:
A. What is the difference in total area of Alaska and Connecticut?
According to the US government, total areas of Alaska and Connecticut are 663,268 square miles and 5,567 square miles, respectively.
The difference between both quantities is:
[tex]x=6.633 \times 10^{5} mi^{2} -5.567 \times 10^{3} mi^2\\x=6.577 \times 10^{5} mi^2[/tex]
Which means that total area of Alaska is considerable larger than total area of Connecticut.
B. What is the difference in total population of California and Alaska?
According to the US government, total populations of California and Alaska are 39,512,223 people and 710,249 people, respectively.
The difference between both quantities is:
[tex]x=3.951 \times 10^7 people - 7.103 \times 10^5 people\\x=3.880 \times 10^7 people[/tex]
Which means that population of California is considerably larger that population of Alaska.
What is the answer to the equation:
1 + 6p = 7(6p -4) -7p
PLEASE HELP ME I NEED ANSWER IN % MINUTES BECAUSE IMA HAVE TO LEAVE SOON< NEED ANSWER ASAP!!!!
Answer:
p = 1
Step-by-step explanation:
1+6p = 7(6p-4)-7p
multiply 7
1 + 6p = 42p - 28 - 7p
simplify
1 + 6p = 35p - 28
p's on one side
-29p = -29
p = 1
A 25-foot ladder is leaning against the side of a house so that the bottom of the ladder is 15 feet from the base of the house. Will the ladder reach a window that is 21.5 feet above the ground?
From the given parameters using Pythagoras theorem, we can say that No, the ladder will not reach a window that is 21.5 feet above the ground.
How to use Pythagoras Theorem?
We are told that the ladder is 25 ft and leans against the wall and so this will be the hypotenuse of the right angle triangle formed with the building.
The horizontal distance from the base of the ladder to the building is 15 ft. Thus, this will be the base or adjacent side of the triangle.
I have drawn a triangle to show this measurements and so we can use Pythagoras theorem to find the vertical height from the top of the ladder to the ground.
BC² = AB² + AC²
25² = 15² + AC²
AC² = 25² - 15²
AC = √(25² - 15²)
AC = 20 feet
Since the ladder is a vertical height of 20 ft from the ground which is less than the height of the window from the ground then we cans ay that the ladder will not reach the window.
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For any line, if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? why or why not?
For any line, if you draw two right triangles using the line as the hypotenuse, we can say that; Yes, the triangles have to be similar because the sides of both triangles will have the same ratio.
How to interpret congruent triangles?From the attached diagram, we will assume any two right triangles are drawn on the line OP, and AB and A'B' as the hypotenuse on the same line OP.
Now, due to the fact that the slope of the line OP is constant and assume that it makes x° with the positive x-axis, then we can say that;
tan x = AC/BC = A'C'/B'C'
Thus;
AC/A'C' = BC/B'C'
Therefore, we can say that the sides of the two right triangles are in the same ratio and as such, Δ ABC and Δ A'B'C' are similar.
Therefore, all the right triangles will be similar.
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The teachers at a middle school voted on one of two locations for the school party.
There were 30 votes for the skating rink and 13 votes for the bowling alley.
What is the ratio of the number of votes for skating to the number of votes for bowling?
3043
1343
1330
3013
Based on the number of teachers who voted for the skating rink and those who voted for the bowling alley, the ratio of votes for skating to bowling is 30 : 13
How to find the ratio?The ratio can be found by taking a ratio of those who voted for the skating rink against those who voted for the bowling alley. This ratio should then be taken to its simplest form.
Number of votes for bowling alley = 13 votes
Number of votes for skating rink = 30 votes
The ratio of votes for the skating rink to those of the bowling alley is:
30 : 13
This is the simplest form.
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1.Charles wants to invest $20,000. The investment firm is offering 8% interest compounded monthly. How much money will he have made if he leaves his money with the bank for 40 years?2.Lisa’s grandmother left her a $100,000 inheritance. She wants to invest themoney in an account paying 7.2% interest compounded continuously. How muchmoney will be in the account after 30 years?3.John saved $50,000. and wants to put the money into an Index Annuity that paysan average of 8.4% per year, compounded semi-annually. How long will it takehim to reach his goal of $1,000,000?4.Susie needs to make $100,000 to pay her home mortgage and has $10,000 toinvest. How much interest will she need if her bank compounds the interestannually to reach her goal?5.Betty wants to retire in 45 years. She needs $2,000,000. If she’s able to find aMutual Fund that offers 9.5% interest and compounds quarterly, how much willshe need for a deposit?
Apply the compound interest formula:
A= P (1+r/n)^nt
Where:
A: future value of the investment
P: Principal amount
r: interest rate (in decimal form)
n: number of compounding periods in each year
t: years
Replacing:
A= 20,000 (1+0.08/12)^12x40
A = 20,000 (1.0067)^480
A= 485,467.7116
HCF of 220 and 8?? I need the answer quick I’m just doing my homework right now
Answer:
4
Step-by-step explanation:
the prime factors for each is
220 = 2 ×2×5×11
8 = 2×2×2
so the HCF =2×2 = 4
what is slope from (6,-10),(-15,15)
Write an equation that represents a reflection in the x -axis of the graph of g(x)=|x| .h(x)=
The equation that represents a reflection in the x -axis of the graph of g(x) is y = -|x|.
We are given a function g(x). The function g(x) is defined as the modulus of x. The equation is : g(x) = |x|.
We need to find the equation that represents the reflection of the graph of g(x). The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point but leave the x-value the same.
Let h(x) be the function that represents the reflection of the function g(x).
h(x) = -g(x)
h(x) = -|x|
The equation can be written as y = -|x|. The graph of the reflection is attached below.
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Could someone tell me the y intercept for the tables in questions 2 and 3
Using it's concept, the y-intercept for each table in this problem is given as follows:
2) y = 4.
3) y = -3.
What are the intercepts of a function?The x-intercept of a function is given by solutions of x to the equation f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis, also called f(0).In the context of this problem, we are given two tables with pairs of values (x,y), hence the y-intercept for each case is given by the value of y when x = 0.
In item 2, when x = 0, y = 4, hence the y-intercept is of y = 4.In item 3, when x = 0, y = -3, hence the y-intercept is of y = -3.More can be learned about the y-intercept of a function at https://brainly.com/question/26249361
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problem 4: Solve for x
The variable x has a value of 3 in the triangle
How to determine the solution of x?The given parameter represents the triangle(s) in the figure
In the triangle, we can see that:
There are two trianglesThe pair of triangles have parallel sidesAlso, the triangles are similar trianglesThe above means that:
The sides of the triangle are in equivalent ratio
This is represented as
4 : 5x - 4 = 4 : 3x + 2
This also means that
5x - 4 = 3x + 2
Collect the like terms
5x - 3x = 4 + 2
Evaluae
2x = 6
Divide
x = 3
Hence, the value of x is 3
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Por el punto a(-3,-6) pasa una línea recta con pendiente m=2 obtén
a) la ecuación de la recta en su forma ordinaria
b) la ecuación de la recta en su forma general
Equation of line in ordinary form: y = 2x+0
Equation of line in standard (general) form: 2x - y = 3
What is Slope?
The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
a) Ordinary form =>
Slope Intercept Form:
y = mx+b
where m is the slope of the line
(Δy/Δx)
and b is the y-intercept.
For a line with slope 2 and point (-3,-6), plug 2 in for m, -3 for x, -6 for y, and solve for b.
-6 = 2(-3) + b
-6 = -6 + b
6 - 6 = b
b = 0
The equation in slope intercept form is
y = 2x+0
b) Standard form =>
Point Slope Form:
(y - y1) = m(x - x1)
Where m is the slope of the line
(Δy/Δx), y1 is the y coordinate of a point, and x1 is the x coordinate of a point.
For a line with slope 2 and point (-3,-6), plug 2 in for m, -3 for x1, -6for y1,
(y - (-6)) = 2(x - (-3))
Standard Form:
Ax + By = C
Where A, B, and C are integers. To write an equation in standard form, rewrite the equation in point slope form so that it fits the formula for standard form.
(y - (-6)) = 2(x - (-3))
(y + 6) = 2(x + 3)
y + 6 = 2x + 3
2x - y = 6 - 3
2x - y = 3
Hence, Equation of line in ordinary form is y = 2x+0
Equation of line in standard (general) form is 2x - y = 3
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calculate y-7 when y=20
The value of the expression is 13 that is formed by subtraction .
A mathematical expression that uses integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).
However, transcendental numbers like such and e are not algebraic because they are not created by employing integer constants and algebraic processes.Although the definition of e necessitates an infinite number of algebraic operations, the generation of is frequently expressed as a geometric expression.Using the properties of arithmetic operations, an expression can be reduced to a rational fraction ( associative properties and commutative properties of addition and multiplication, distributive property and rules for the various operations on the given fractions).now we use subtraction:
y-7
= 20-7
= 13
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what is the the slope of (20,15) (30,35)
Slope = 2
The slope of coordinates ( 20 , 15 ) and (30 , 35) = 2
What is slope?The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).The slope is defined as the ratio of the vertical change between two points, known as the rise, to the horizontal change between those same two points, known as the run.Determine the coordinates of two points on the line. Calculate the difference in y-coordinates between these two points (rise).Determine the x-coordinate difference between these two points (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).Here given two points (20, 15) and (30 , 35)
Formula to find slope = y2 - y1 / x2 - x1
= 35 - 15 / 30 - 20
= 20 / 10
= 2 / 1
= 2
∴ Slope of (20 , 15) (30 , 35) = 2 .
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Find each of the missing sides of the right triangles using Pythagorean Theorem.
We need to apply the Pythagorean Theorem, which says that the square of the Hypothenuse is equal to the sum of the squares of the cathetus. So we have:
[tex]\begin{gathered} 41^2=x^2+9^2 \\ 1681=x^2+81 \\ x^2=1681-81 \\ x^2=1600 \\ x=\sqrt[]{1600} \\ x=40 \end{gathered}[/tex]The missing side is equal to 40.
What is the domain/range of a parabola with the equation [tex]x=-2(y-2)^2+2[/tex]?
The quadratic function's domain for a given function is -2<x>2.
What is the Domain of a quadratic function?
When all of the x-values in the domain are assessed into the function, which is what is often referred to by the y-values, the range of a function is just the range of output values. This suggests that in order to clarify the range, the domain has to be determined.The domain of this quadratic function includes always all x values. This was very simple.The provided parabola, y = ax2 + bx + c, is in the Standard Form. Therefore, we should simplify the process by converting it to vertex form.Function given [tex]x=-2(y-2)^2+2[/tex]
The vertices are represented by the vertex form, y = an (x-h)^2+ k, and (h,k).
h=-2
k=+2
It is clear that this parabola has a minimum value of y = -2 and a maximum value of y=+2.
The quadratic function's domain for a given function is -2<x>2.
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Eddie needs 2 \displaystyle \frac{2}{3} 3 2 cups of flour for one batch of pancakes. How much flour does he need for 2 \frac{1}{2}2 2 1 batches? Make sure to put cups at the end of your answer.
The cups of flour that is needed for 2 1/2 cups of flour is 6 2/3 cups.
How much flour is needed?A mixed number is a fraction that has a whole number, a numerator and a denominator. The numerator usually has a smaller value when compared with the denominator. An example of a mixed number is 2 1/2.
In order to determine the cups of flour that is needed for 2 1/2 batches of pancakes, multiply 2 1/2 by 2 2/3. Multiplication is the mathematical operation that is used to determine the product of a number. The sign that represents multiplication is x.
Flour needed = batches to be made x amount of flour needed for one batch
2 2/3 x 2 1/2
8/3 x 5/2 = 20 / 3 = 6 2/3 cups
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What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places.
The equation of the line of best fit for the following data is ŷ = 1.16393X + 0.88525
Option A
This is further explained below.
What is a regression equation?Generally, Y is represented by the equation Y = a + bX + e, which represents the regression equation. The value of the dependent variable, which is referred to as Y, is what is being explained or predicted.
a, also known as Alpha, is a constant; it is equal to the value of Y when the value of X is equal to 0. b, also known as Beta, is the coefficient of X; it is the slope of the regression line.
In conclusion,
Sum of X = 34
Sum of Y = 44
Mean X = 6.8
Mean Y = 8.8
Sum of squares (SSX) = 48.8
Sum of products (SP) = 56.8
Regression Equation = ŷ = bX + a
b = SP/SSX = 56.8/48.8 = 1.16393
a = MY - bMX = 8.8 - (1.16*6.8) = 0.88525
ŷ = 1.16393X + 0.88525
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explain why the researchers used data from ten trials and averaged them, rather than data from a single trial.
Answer:
It meant that the results were more reliable and the average makes it more reliable.
Step-by-step explanation:
The researchers used data from ten trials and averaged them, rather than data from a single trial because the data from single trials are more likely to include errors.
What is the research?Research the issue utilizing data from a number of sources. It is critical to understand what one is attempting to achieve while designing an experiment.
The first method is to average identical successive trials, in which the researcher simply compares mean values across groups of patients or treatment effects. Averaging, to some extent, presume that the behavior is random. This premise is often ignored. If there is something systematic going on, such as a trial-by-trial change in response owing to adaptation/learning or weariness, this is potentially highly significant clinical information that is lost when the trials are averaged.
Thus, the data from single trials are more likely to include errors
Hence, the researchers used data from ten trials and averaged them, rather than data from a single trial.
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What is the unit rate for a relationship A (the table)? (do not include units for this one)
PLEASE ANSWER ASAP
Answer:
it is per 1
Step-by-step explanation:
math help for homework
Answer:
[tex]f(x)=x+2[/tex]
Step-by-step explanation:
Given parameters:
f(0) = 2f(2) = 4Therefore, there are two points on the line:
(0, 2) and (2, 4)The linear relationship between the x and y values is:
The y-value is 2 more than the x-value.[tex]\implies f(x)=x+2[/tex]
To prove this algebraically, define the points:
(x₁, y₁) = (0, 2)(x₂, y₂) = (2, 4)Find the slope of the linear function by substituting the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-2}{2-0}=\dfrac{2}{2}=1[/tex]
Substitute the found slope and one of the points into the point-slope formula to create a linear function that satisfies the given parameters:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=1(x-0)[/tex]
[tex]\implies y-2=x[/tex]
[tex]\implies y=x+2[/tex]
Hence proving that the linear function is:
[tex]f(x)=x+2[/tex]
Question 11(Multiple Choice)(05.06 MC)Using the graph of the function g(x) = log3 (x-4), what are the x-intercept and asymptote of g(x)?The x-intercept is 3, and the asymptote is located at x = 4.The x-intercept is 5, and the asymptote is located at x = 4.The x-intercept is 4, and the asymptote is located at y = 5.The x-intercept is 5, and the asymptote is located at y = 3.
Graph:
x intercept = where it crosses the x axis = 5
asymptote = never touches it = 4
Answer:
The x-intercept is 5, and the asymptote is located at x = 4.
Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function:Vertex = (-4,2)Point = (-4,0)F( x )= Answer for coordinate 1 (x- Answer for coordinate 2 )^2 +Answer for coordinate 3
In order to find the quadratic equation, let's use the vertex form below:
[tex]y=a(x-h)^2+k[/tex]Where the vertex is located at (h, k).
So, if the vertex is (h, k) = (-4, 2) and using the point (x, y) = (-4, 0), we have:
[tex]\begin{gathered} y=a(x+4)^2+2 \\ 0=a(-4+4)^2+2 \\ 0=a\cdot0^2+2 \\ 0=2 \end{gathered}[/tex]Since the final statement is false, it's not possible to have a quadratic function with vertex (-4, 2) and with the point (-4, 0).
If we use the point (4, 0) instead, we would have:
[tex]\begin{gathered} y=a(x+4)^2+2 \\ 0=a(4+4)^2+2 \\ 0=a\cdot64+2 \\ 64a=-2 \\ a=-\frac{2}{64} \\ a=-\frac{1}{32} \end{gathered}[/tex]So the equation in this case would be:
[tex]y=(-\frac{1}{32})(x-(-4))^2+2[/tex]The empty spaces would be filled with the values -1/32, -4 and 2.
Aaron invested $740 in an account paying an interest rate of 5%
compounded continuously. Justin invested $740 in an account paying an interest rate of 5% compounded daily. After 18 years, how much more
money would Justin have in his account than Aaron, to the nearest dollar?
The amount of money Justin would have in his account than Aaron, to the nearest dollar is $0
What is the future value formula for continuous compounding cash flow?
The future value, which is used to determine the worth of this investment of $740 made now in 18 years is as shown below:
FV=PV*e^(rt)
FV=the worth of the investment in 18 years=unknown
PV=the amount invested today=$740
e=mathematical exponential value=2.7182818
r=rate of interest which compounded continuously=5%
t=time of investment in years=18
FV=$740*2.7182818^(5%*18)
FV=$740*2.7182818^(0.90)
FV=$740*2.459603087981220
FV=$1,820.11
Justin:
FV=PV*(1+r/m)^(n*m)
PV=$740
r=5%
m=number of times in a year that interest is compounded=365
m=number of years=18
FV=$740*(1+5%/365)^(18*365)
FV=$1,819.99
difference=$1,820.11-$1,819.99
difference=$0.12($0 to the nearest dollar)
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ackie deposited a $865.98 paycheck, a $623 stock dividend check, a $60 rebate check, and $130 cash into her checking account. Her original account balance was $278.91. Assuming the checks clear, how much will be in her account after deposits are made?
for a singles match, a tennis court is 78 feet long and 27 feet wide. Which calculation would give the perimeter of a tennis court for a singles match?
Answer: 3 miles
Step-by-step explanation:
15840 feet
= 15840 ÷ 5280 miles
= 3 miles
Find the elapsed time Start 5:15am End time 12:04pm
Given that the start time is 5:15 am. It can be represented as,
[tex]S=5\colon15[/tex]Also given that the end time is 12:04 pm. It can be represented as.
[tex]E=12\colon04[/tex]The elapsed time (e) is equal to the difference between the end time and start time as given below,
[tex]e=E-S[/tex]Substitute the values,
[tex]e=12\colon04-5\colon15[/tex]Note that 04 minutes is greater than 15 minutes, so we have to borrow 1 hour from 12 hours and add it to the minutes,
[tex]12\colon04\equiv11\colon64[/tex]Replace the value and perform the subtraction,
[tex]\begin{gathered} e=11\colon64-5\colon15 \\ e=(11-5)\colon(64-15)_{} \\ e=6\colon49 \end{gathered}[/tex]Thus, the required elapsed time is 6:49, that is, 6 hours and 49 minutes.
