The correct answer is c: Initial value: 1, rate of change 5 over 3. In this case, the change in y is 3 (from 1 to 4) and the change in x is 5 (from 0 to 5).
What is a linear equation?A linear equation is an equation that describes a straight line when it is graphed. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept. Linear equations are used to describe many real-world situations, such as the height of a ball thrown in the air, the distance traveled by a car, or the height of a person over time.
This question is asking for the initial value and rate of change for a linear equation. The initial value is the y-intercept, which is the point at which the line crosses the y-axis. In this case, the y-intercept is 1, so the initial value is 1. The rate of change is the slope of the line, which can be found by calculating the change in y over the change in x. In this case, the change in y is 3 (from 1 to 4) and the change in x is 5 (from 0 to 5). Therefore, the rate of change is 5 over 3, so the correct answer is c: Initial value: 1, rate of change 5 over 3.
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According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide. What is the approximate area of the park? Show your work.
The approximate area of Central Park is about 450 square blocks.
What is the approximate area of the park?The given dimensions of the park stated in the question are
Length of Central Park = 50 blocks
Width of Central Park = 9 blocks
The approximate area of Central Park is the product of its length and width:
So, we have
Area of Central Park = Length x Width
When the given values are substituted into the the equation mentioned above, we obtain the subsequent expression
Area = 50 * 9
Evaluate
Area = 450
Hence, the approximate area is about 450 square blocks.
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From the sum of 2x –2 y - 24 and 2 y + 24, subtract -4x –2 y + 12
The final expression after the subtraction is -6x + 4y + 12.
The given expression is:
(2x - 2y - 24 + 2y + 24) - (-4x - 2y + 12)
Simplifying the expression inside the parentheses, we get:
2x - 2y + 2y + 24 - 4x + 2y - 12
Combining like terms, we get:
(-2x + 2y + 2y) + (24 - 12) - 4x
Simplifying further, we get:
-2x + 4y + 12 - 4x
Combining like terms, we get:
-6x + 4y + 12
Therefore, the final expression after the subtraction is -6x + 4y + 12.
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Hellppppp me with mathh
Answer:
20.50 + 10m
Step-by-step explanation:
Basic expression:
8.50 + 12 + 6.25m + 3.75m
First, let's add the base payments which are 8.50 and 12.
8.50 + 12 = 20.50.
Now we have 20.50 + 6.25m + 3.75m
Next we have to add the monthly payments.
Assuming she's paying these all at the same time, 6.25m + 3.75m = 10m
Our finalized expression is:
20.50 + 10m = Club costs
Gavin wants to buy a skateboard that sells for $49. 99. An advertisement says that next week the skateboard will be on sale for $42. 50 how much will Gavin save if he waits until next week to buy the skateboard
Answer:$7.49
Step-by-step explanation:
just subtract 42.50 from 49.99
49.99-42.50=7.49
If x has a remainder of 5 when divide by 6 and x>10, what is the smallest possible value of x ?
The smallest possible value of x is 11.
To find the smallest possible value of x, we can use the formula x = 6n + 5, where n is an integer. This formula represents the fact that x has a remainder of 5 when divided by 6.
If we plug in different values for n, we can find the smallest possible value of x that is greater than 10.
When n = 1, x = 6(1) + 5 = 11
When n = 2, x = 6(2) + 5 = 17
When n = 3, x = 6(3) + 5 = 23
Therefore, the smallest possible value of x that is greater than 10 is 11, so the answer is 11.
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(5)/(x-5)=5+(x)/(x-5) Is the equation an identity, a conditional equation, or an inconsistent equation?
The given equation (5)/(x - 5) = 5 + (x)/(x - 5) is a conditional equation.
We can simplify the equation as follows:
(5)/(x - 5) - (x)/(x - 5) = 5
(5 - x)/(x - 5) = 5
Now, we can cross-multiply to get rid of the fraction:
5 - x = 5(x - 5)
Distributing the 5 on the right side of the equation gives us:
5 - x = 5x - 25
Adding x to both sides and adding 25 to both sides gives us:
30 = 6x
Dividing both sides by 6 gives us:
x = 5
Since the equation has a solution, it is a conditional equation. Therefore, the answer is a conditional equation.
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Kyle’s handful of trail mix has 2 almonds, 4 peanuts, 3 raisins, and 5 sunflower seeds. If he picks one item from the handful of trail mix at random, what is the probability that the item is a peanut?
StartFraction 1 over 14 EndFraction
StartFraction 1 over 7 EndFraction
StartFraction 2 over 7 EndFraction
Two-fifths
The answer is Start Fractiοn 2 οver 7 End Fractiοn.
What is Algebraic expressiοn ?Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.
Kyle's handful οf trail mix cοntains a tοtal οf 2 + 4 + 3 + 5 = 14 items.
The prοbability οf picking a peanut is the number οf peanuts in the handful divided by the tοtal number οf items in the handful:
prοbability οf picking a peanut = number οf peanuts / tοtal number οf items
prοbability οf picking a peanut = 4 / 14
Simplifying the fractiοn by dividing bοth the numeratοr and denοminatοr by 2, we get:
prοbability οf picking a peanut = 2 / 7
Therefοre, the answer is StartFractiοn 2 οver 7 EndFractiοn.
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4. Let X be uniformly distributed on [10, 100). Calculate Tx (a) by using Risk Adjusted Premium Principle with risk index p = 2 (b) by using Risk Adjusted Premium Principle with risk index p = 10
Let X be uniformly distributed on [10, 100). By using Risk Adjusted Premium Principle
(a) Tx = 106.9615242
(b) Tx = 314.8076211
We can calculate Tx using the formula:
Tx = E[X] + p * σ[X]Where E[X] is the expected value of X, p is the risk index, and σ[X] is the standard deviation of X.For a uniformly distributed random variable X on the interval [a, b), the expected value is:
E[X] = (a + b) / 2And the standard deviation is:
σ[X] = √((b - a)² / 12)For X uniformly distributed on [10, 100), we have:
a = 10b = 100
So:
E[X] = (10 + 100) / 2 = 55σ[X] = √((100 - 10)² / 12) = 25.98076211
Now we can calculate Tx for each risk index:
(a) For p = 2:Tx = 55 + 2 * 25.98076211 = 106.9615242
(b) For p = 10:Tx = 55 + 10 * 25.98076211 = 314.8076211
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Much of Ann's investments are in Cilla Shipping. Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626. Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share. Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share. Which of Ann's investments has increased in value more, and by how much?
Ann's investment in Cilla Shipping bonds has increased in value more, by $33,605.41
What is purchase price?
The complete cost of purchasing an asset is known as the original cost. The whole costs associated with purchasing and using an asset are taken into account when calculating its initial cost.
To determine which of Ann's investments has increased in value more, we need to compare the current value of the bonds and the stock to their original purchase value.
First, let's calculate the purchase price of the bonds:
7 bonds x $500 par value x 0.95626 market rate = $3,349.82
So, Ann initially invested $3,349.82 in the Cilla Shipping bonds.
Next, let's calculate the purchase price of the stock:
125 shares x $28.00 per share = $3,500.00
So, Ann initially invested $3,500.00 in the Cilla Shipping stock.
Now, let's calculate the current value of the bonds:
7 bonds x $500 par value x 1.06384 market rate = $37,286.48
So, the current value of the bonds is $37,286.48.
Let's also calculate the current value of the stock:
125 shares x $30.65 per share = $3,831.25
So, the current value of the stock is $3,831.25.
To determine which investment has increased in value more, we can calculate the percentage increase for each investment:
Percentage increase in bonds = [(current value - purchase price) / purchase price] x 100%
= [(37,286.48 - 3,349.82) / 3,349.82] x 100%
= 1010.46%
Percentage increase in stock = [(current value - purchase price) / purchase price] x 100%
= [(3,831.25 - 3,500.00) / 3,500.00] x 100%
= 9.48%
So, we can see that the bonds have increased in value more than the stock, by a significant amount.
The bonds have increased in value by 1,010.46%, while the stock has increased in value by only 9.48%. The bonds have increased in value by a total of $33,936.66 ($37,286.48 - $3,349.82), while the stock has increased in value by a total of $331.25 ($3,831.25 - $3,500.00).
Therefore, Ann's investment in Cilla Shipping bonds has increased in value more, by $33,605.41 ($33,936.66 - $331.25).
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help a girl out ??? :)
We can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.What is exponential function?The exponential function is of the form -
f(x) = eˣ
Given is to write the exponential growth and exponential decay equation.
{ 1 } -
The general exponential growth equation is -
[tex]$f(x)=a(1+r)^{x}[/tex]
{ 2 } -
The general exponential decay equation is -
[tex]$\frac {dN}{dt}= -\lambda N[/tex]
Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.
Therefore, we can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.To solve more questions on functions, visit the link-
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Determine the possible number of positive real zeros and negative real zeros for the polynomial function P(x)=6x^(4)-x^(3)+5x^(2)-x+9 given by Descartes' Rule of Signs.
According to Descartes' Rule of Signs, the possible number of positive real zeros for a polynomial function is determined by the number of sign changes in the coefficients of the terms in the function.
Similarly, the possible number of negative real zeros is determined by the number of sign changes in the coefficients of the terms in the function when x is replaced with -x.
For the polynomial function P(x)=6x^(4)-x^(3)+5x^(2)-x+9, there are 2 sign changes in the coefficients of the terms: from 6 to -1, and from 5 to -1. Therefore, the possible number of positive real zeros is 2 or 0.
For the polynomial function P(-x)=6(-x)^(4)-(-x)^(3)+5(-x)^(2)-(-x)+9, there are 0 sign changes in the coefficients of the terms. Therefore, the possible number of negative real zeros is 0.
In conclusion, the possible number of positive real zeros for the polynomial function P(x)=6x^(4)-x^(3)+5x^(2)-x+9 is 2 or 0, and the possible number of negative real zeros is 0.
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Rowan is training to run in a race. He runs 15 miles in the first week, and each week following, he runs 3% more than the week before. Using a
geometric series formula, find the total number of miles Rowan runs over the first ten weeks of training, rounded to the nearest thousandth.
The total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.
Explain about the geometric series?In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred as the common ratio.
In the question:
Rowan is preparing for a race by running. He runs 15 miles the first week, and then he runs 3% more each week after that.Let 'x' be the miles that Rowan runs in 1st week.
Xn for the nth week.
x1 = 15 (given)
x2 = 15*(1 + 3%) = 15*1.03
Xn = 15*(1 + 3%0ⁿ⁻¹ = 15*(1.03ⁿ⁻¹)
Let 'S' be the total miles.
S = x1 + x2+ .....+ xn
S = 15 + 15 *1.03 + 15*1.03² + ...+ 15*1.03⁹
On solving the series:
S = 15 × 1.(1.03¹⁰ - 1)/0.03
S = 57.31
S = 58
Thus, the total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.
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here Given Cost and Revenue functions C(a) = q^3 - 11q^2 +56q + 5000 and R(a)=- 3q^2 + 2600q, what is the marginal profit at a production level of 40 items? The marginal profit is ____ dollars per item.
The marginal profit at a production level of 40 items is 2064.
To find the marginal profit at a production level of 40 items, we need to first find the marginal cost and marginal revenue at this production level. The marginal cost and marginal revenue are the derivatives of the cost and revenue functions, respectively.
The marginal cost function is:
C'(q) = 3q^2 - 22q + 56
The marginal revenue function is:
R'(q) = -6q + 2600
At a production level of 40 items, the marginal cost is:
C'(40) = 3(40)^2 - 22(40) + 56 = 296
The marginal revenue at this production level is:
R'(40) = -6(40) + 2600 = 2360
The marginal profit is the difference between the marginal revenue and marginal cost:
Marginal profit = 2360 - 296 = 2064
Therefore, the marginal profit at a production level of 40 items is 2064.
Answer :[tex]\boxed{2064}[/tex].
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Which relationship has a zero slope?
a.A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2.
b.A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3.
c. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5)
d.A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
The relationship that has a zero slope is option a, he first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2.
What is the slope of a horizontal line?Positive slopes and negative slopes are absent from horizontal lines. A horizontal line's slope is always zero. This is due to the fact that it has a constant height—if we use the rise over run technique, rise will always be 0 regardless of what run is.
Option A is the connection with a zero slope.
Regardless of the x-values, option A's y-values are all fixed at (2). This implies that for any change in x (run), the change in y (rise) is always zero, resulting in a slope of zero.
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Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,6)(1,6) and (-9,-2)(−9,−2).
The equation of the perpendicular bisector of the line segment with endpoints (1,6) and (-9,-2) is y = (-5/4)x - 3.
What is the perpendicular bisector?Any location on the perpendicular bisector is equally spaced from the line segment's terminal points, according to the perpendicular bisector theorem.
These procedures must be taken in order to determine the equation of a line segment's perpendicular bisector:
Determine the line segment's midway.
Determine the line segment's slope.
In order to determine the slope of the perpendicular bisector, calculate the negative reciprocal of the slope.
To determine the equation of the perpendicular bisector, use a line's point-slope form.
These procedures allow us to determine the equation for the perpendicular bisector of the line segment with ends (1, 6) and (-9, -2), which is as follows:
Midpoint: The midpoint of the line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates:
Midpoint = ((1 + (-9))/2, (6 + (-2))/2)
= (-4, 2)
Slope: The slope of the line segment can be found using the formula:
slope = (change in y) / (change in x)
slope = (6 - (-2)) / (1 - (-9))
= 8/10
= 4/5
Negative reciprocal: The slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment:
slope of perpendicular bisector = -1 / slope
= -1 / (4/5)
= -5/4
Equation: We can now use the point-slope form of a line to find the equation of the perpendicular bisector. We will use the midpoint of the line segment as the point on the line:
y - y1 = m(x - x1)
where m is the slope of the perpendicular bisector, and (x1, y1) is the midpoint of the line segment. Substituting the values we found, we get:
y - 2 = (-5/4)(x + 4)
Simplifying, we can write the equation in slope-intercept form:
y = (-5/4)x - 3
Hence, the equation of the perpendicular bisector of the line segment with endpoints (1,6) and (-9,-2) is y = (-5/4)x - 3.
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Find the solution to the following equation: 4(x + 3) = 44
Answer:
x = 8
Step-by-step explanation:
4(x + 3) = 44 ( divide both sides by 4 )
x + 3 = 11 ( subtract 3 from both sides )
x = 8
4x-22<-6 on a number line
By answering the above question, we may state that Shade the region to line the left of the open circle, since x is less than 4.
what is a line?A line is a geometric object that is infinitely long and has no width, depth, or curvature. A line, which can also exist in two-, three-, and more-dimensional spaces, is therefore a one-dimensional object. A line is often used to refer to a line segment with two points as its endpoints. A line is a flat, one-dimensional object that may extend indefinitely in both directions and has no thickness. The terms "straight line" or "old correct line" are sometimes used to describe a line that has no "wobble" anywhere along its length.
plot the inequality 4x-22<-6 on a number line,
4x - 22 + 22 < -6 + 22
4x < 16
4x/4 < 16/4
x < 4
Plot an open circle at 4 on the number line to indicate that x is not included in the solution set.
Shade the region to the left of the open circle, since x is less than 4.
The resulting graph should look like this:
○----------------->
| | | | | | |
-∞ -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Grayson bought snacks for his team's practice. He bought a bag of popcorn for $3.50 and a 5-pack of juice bottles. The total cost before tax was $11.05. Write and solve an equation which can be used to determine
Answer:
7.55
Step-by-step explanation:
3.50 + x = 11.05, x = 11.05 - 3.50, x = 7.55
Answer:
Step-by-step explanation:
Let [tex]x[/tex] be the cost of a juice bottle. Then
[tex]3.50+5x=11.05[/tex]
Solve this:
[tex]5x=7.55[/tex] (subtracted 3.50 from both sides)
[tex]x=7.55/5=1.51[/tex] (divided both sides by 5)
So juice bottles cost $1.51
Alex has kept within his budget during this 4-week period! He also earned an extra $12 one week for cleaning his neighbor’s garage. If Alex wants to save the $10 he has left over every 4-week period, how much less time will it take for him to earn enough money for the shoes? Remember, the shoes cost $45.99 plus tax.
The time it will take for Alex to earn enough money to purchase his shoes is given as follows:
13.6 weeks.
How to obtain the time needed to earn the money?The time needed to obtain enough money to purchase the shoes is obtained applying the proportions in the context of the problem.
Alex saves $10 every 4 weeks. He earned an extra $12 for cleaning his neighbor’s garage, hence the amount he must save is of:
45.99 - 12 = $33.99.
Considering that he saves $10 each week, and he must save $33.99 to purchase the shoes, the number of periods of four weeks that he needs is of:
33.99/10 = 3.399 periods of four weeks.
As each period is composed by four weeks, the number of weeks that he needs to save enough money is obtained as follows:
4 x 3.399 = 13.6 weeks.
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Given F(-9,-4), E(-7,a) G(-2,5), and H(-6,-1) find the value of a so that EF is parallel to GH
If F(-9,-4), E(-7, a) G(-2,5), and H(-6,-1) then the value of a is equal to -1, then EF is parallel to GH.
What are the parallel lines?
Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.
To determine if EF is parallel to GH, we need to compare the slopes of the two lines.
The slope of line EF can be found using the coordinates of points E and F:
slope of EF = (y2 - y1)/(x2 - x1) = (a - (-4))/(-7 - (-9)) = (a + 4)/2
The slope of line GH can be found using the coordinates of points G and H:
slope of GH = (y2 - y1)/(x2 - x1) = (5 - (-1))/(-2 - (-6)) = 6/4 = 3/2
For EF to be parallel to GH, their slopes must be equal. Therefore, we can set the slope of EF equal to the slope of GH and solve for a:
(a + 4)/2 = 3/2
Multiplying both sides by 2, we get:
a + 4 = 3
Subtracting 4 from both sides, we get:
a = -1
Therefore, if a is equal to -1, then EF is parallel to GH.
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find (gof)(x) if f(x)=X^2-3, and g(x)=2x-1,
The composite result function ( g o f )(x) in the functions f(x) = x² - 3 and g(x) = 2x - 1 is 2x² - 7.
What is the function operation ( g o f )(x) in the given functions?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f(x) = x² - 3g(x) = 2x - 1(g o f)(x) = ?First, set up the composite result function (g o f)(x).
(g o f)(x) = g( f(x) )
g( x ) = 2x - 1
g( f(x) ) = 2( f(x) ) - 1
g( f(x) ) = 2( x² - 3 ) - 1
Now, simplify the function by applying distributive property.
g( f(x) ) = 2( x² - 3 ) - 1
g( f(x) ) = 2 × x² - 2 × 3 - 1
g( f(x) ) = 2x² - 6 - 1
Add -6 and -1
g( f(x) ) = 2x² - 7
Therefore, the function operation ( g o f ) is 2x² - 7.
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We know that (2 + 3) + 5 = 2 + (3 + 5) and 2 * (3 * 5) = (2 * 3) * 5. The
grouping with parentheses does not affect the value of the expression.
Is this true for exponents? That is, are the numbers below equal?
2(34) and (23)5
If not, which is bigger? Which of the two would you choose as the meaning of the following expression?
235
Explain your reasoning.
Answer:
Step-by-step explanation:
Find the volume of a cone whose depth is 14 cm and base radius is 9/2cm
The volume of the cone is approximately 94.25π cubic cm.
To find the volume of a cone, we use the formula V = 1/3πr²h, where V is the volume, r is the radius of the base, and h is the height or depth of the cone. In this case, we know that the depth of the cone is 14 cm and the base radius is 9/2 cm.
First, we need to calculate the radius of the base in terms of cm, since the formula requires it. We are given that the base radius is 9/2 cm, so we can substitute this value for r:
r = 9/2 cm
Next, we need to calculate the volume of the cone using the formula. We know that the depth of the cone is 14 cm, so we can substitute this value for h:
V = 1/3πr²h
V = 1/3π(9/2)²(14)
V = 1/3π(81/4)(14)
V = 1/3π(1134/4)
V = 1/3π(283.5)
V = 94.25π
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LetP(x)=10x5−35x4+22x3+13x2+4x+4. (a) Use the Rational Roots Theorem to find all possible rational roots ofP(x). LetP(x)=10x5−35x4+22x3+13x2+4x+4. (b) Find all roots ofP(x)
The Rational Roots Theorem states that the possible rational roots of a polynomial equation are the factors of the constant term divided by the factors of the leading coefficient. Therefore, the possible rational roots of P(x) are ±1, ±2, ±4, and ±4.
To find the exact roots of P(x), we can use synthetic division. Synthetic division is an efficient way of dividing a polynomial by a number. Using this method, we can determine that there are three roots for P(x): 1, -2, and -3. To verify this, we can evaluate P(x) for each of the three roots and confirm that the result is zero.
We can also use the quadratic formula to find the remaining two roots. Since P(x) is a 5th degree polynomial, the two remaining roots are complex and can be found using the quadratic formula. The complex roots of P(x) are -0.5 ± 0.5i.
In conclusion, the roots of P(x) are 1, -2, -3, -0.5 ± 0.5i. All of these results can be verified by evaluating P(x) and confirming that the result is zero.
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What is the common denominator of 7/9 and 6/7
Answer: 126
Step-by-step explanation: I belive that is the answer
Does someone mind helping me with this problem? Thank you!
Starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To find the future amount of the investment after 40 years, we can use the formula for compound interest:
Future Amount = Present Value x (1 + Interest Rate/Compounding Frequency)^(Compounding Frequency x Time)
In this case, the present value (PV) is $500, the interest rate (r) is 15%,
the compounding frequency (n) is 1 (since the interest is compounded every 2 years).
The time (t) is 40 years.
Plugging in the values, we get:
Future Amount = [tex]500 \times (1 + 0.15/1)^{(1 \times 40/2)}[/tex]
Future Amount = [tex]500 \times (1.15)^{20}[/tex]
Future Amount = [tex]500 \times 13.591409[/tex]
Future Amount = $6,795.70 (rounded to the nearest cent)
Therefore, starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.
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Determine the LCM of the given polynomials: Enter your answer in factored form. \[ \begin{array}{l} x^{2}+8 x y+12 y^{2} \\ x^{2}-36 y^{2} \end{array} \]
The LCM of the given polynomials is \[ (x+6y)(x+2y)(x-6y) \].
The LCM (Least Common Multiple) of two polynomials is the smallest polynomial that is a multiple of both of the given polynomials. To find the LCM, we need to factor the given polynomials and then take the product of the highest power of each factor.
Factoring the first polynomial: \[ x^{2}+8 x y+12 y^{2} = (x+6y)(x+2y) \]
Factoring the second polynomial: \[ x^{2}-36 y^{2} = (x+6y)(x-6y) \]
Now, we can take the product of the highest power of each factor to find the LCM:
\[ LCM = (x+6y)(x+2y)(x-6y) \]
So, the LCM of the given polynomials in factored form is \[ (x+6y)(x+2y)(x-6y) \].
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Find the equation of the line shown. 10 9 8 6 5 4 3 2 1 1 23 4 5 67 8 9 10
The equation of the line shown is y = 2x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/1 = 4/2
Constant of proportionality, k = 2.
Therefore, the required equation is given by:
y = kx
y = 2x
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The customer service company for an online retailer wants to rate the effectiveness of their support. At the end of the service phone call, customers are asked to answer questions about the friendliness and helpfulness of the customer service agent. What type of sampling method is this?
A. Cluster Sampling
B. Convenience Sampling
C. Stratified Random Sampling
D. Systematic Sampling
please answer quick i will give u free branliest.
The expression when simplified is (d)
How to determine the expressionFrom the question, we have the following representation that can be used in our computation:
Black triangle = -xWhite triangle = xBlack square = -1White square = 1Using the above as a guide, we have the following:
The given expression is
3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square
This gives
-3x + 2x - 2 + 1
Evaluate the like terms
-x - 1
This means
1 Black triangle and 1 Black square
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