Answer:
9/16 of a square inch
Step-by-step explanation:
[tex] \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} [/tex]
Answer:
9 /16 inches^2
Step-by-step explanation:
To find the area of the tile, multiply the length by the width
A = 3/4 * 3/4
A = 9 /16 inches^2
if k(x) =3x, then f'(x)=?
solve for the unknown to find the unit rate
1/5 ?
----- = -----
1/20 1
Answer: 4
Step-by-step explanation:
To find the unit rate, we can cross-multiply the fractions.
Multiplying the numerator of the first fraction by the denominator of the second fraction, we get 1/5.
Multiplying the numerator of the second fraction by the denominator of the first fraction, we get 1/20.
Now we have the equation 1/5 = 1/20.
To solve for the unknown, we can cross-multiply again, which gives us 20 * 1/5 = 4.
Therefore, the unit rate is 4.
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = [tex]\frac{168}{7}[/tex] = 24
Triangle PQR is drawn with coordinates P(0, 2), Q(0, 5), R(1, 4). Determine the translation direction and number of units if R′(−7, 4).
8 units down
8 units up
8 units to the right
8 units to the left
It follows that the translation direction is 8 units to the left and 0 units up or down.
Describe translation?A translation is a geometric change in Euclidean geometry where each point in a figure, shape, or space is moved uniformly in one direction. A translation can either be thought of as moving the origin of the coordinate system or as adding a constant vector to each point
The new vertices of a triangle with vertex locations of (0,0), (1,0), and (0,1), for instance, would be (2,3, (3,3), and (2,4) if the triangle were translated 2 units to the right and 3 units up.
We can use the following procedures to get the translation direction and number of units for R′(7, 4):
1. Determine the difference between R and R′'s x-coordinates: −7 − 1 = 8
2. Determine the difference between R and R′'s y coordinates: 4 − 4 = 0
It follows that the translation direction is 8 units to the left and 0 units up or down.
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Write an equation in point-slope form. Part I: Create an equation of a line in point-slope form. Be sure to identify all parts of the equation before writing the equation. (3 points) Part II: Using the equation of the line you wrote in Part I, write an equation of a line that is perpendicular to this line. Show your work. (3 points)
The line's equation in point-slope form is shown here. Point (2, 5) is the given point on the line, and slope 2 is the given slope of the line. The slope of this line is -1/2, which is the negative reciprocal of the slope.
How do you formulate an equation in point-slope form?A line's point slope form equation is [tex]y - y_1 = m(x - x_1)[/tex]. Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.
We require a point on the line and the slope of the line in order to create a line equation in point-slope form. In point-slope form,
[tex]y - y1 = m(x - x1)[/tex]
As an illustration, suppose we want to formulate the equation of the line passing through the coordinates (2, 5) and having a slope of 2. The values can be entered into the point-slope form as follows:
y - 5 = 2(x - 2)Let's say the given line has the equation [tex]y - y1 = m(x - x1)[/tex], where (x1, y1) is a point on the line and m is the slope of the line.
we can use the given point (2, 5). Then we can plug in the values into the point-slope form:
[tex]y - 5 = (-1/2)(x - 2).[/tex]
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solve the equation
a) y''-2y'-3y= e^4x
b) y''+y'-2y=3x*e^x
c) y"-9y'+20y=(x^2)*(e^4x)
Answer:
a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:
r^2 - 2r - 3 = 0
Factoring, we get:
(r - 3)(r + 1) = 0
So the roots are r = 3 and r = -1.
The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:
y_h = c1e^3x + c2e^(-x)
To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = Ae^4x
Taking the first and second derivatives of y_p, we get:
y_p' = 4Ae^4x
y_p'' = 16Ae^4x
Substituting these into the original differential equation, we get:
16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x
Simplifying, we get:
5Ae^4x = e^4x
So:
A = 1/5
Therefore, the particular solution is:
y_p = (1/5)*e^4x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^3x + c2e^(-x) + (1/5)*e^4x
b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:
r^2 + r - 2 = 0
Factoring, we get:
(r + 2)(r - 1) = 0
So the roots are r = -2 and r = 1.
The general solution to the homogeneous equation y'' + y' - 2y = 0 is:
y_h = c1e^(-2x) + c2e^x
To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax + B)e^x
Taking the first and second derivatives of y_p, we get:
y_p' = Ae^x + (Ax + B)e^x
y_p'' = 2Ae^x + (Ax + B)e^x
Substituting these into the original differential equation, we get:
2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x
Simplifying, we get:
3Ae^x = 3xe^x
So:
A = 1
Therefore, the particular solution is:
y_p = (x + B)e^x
Taking the derivative of y_p, we get:
y_p' = (x + 2 + B)e^x
Substituting back into the original differential equation, we get:
(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x
Simplifying, we get:
-xe^x - Be^x = 0
So:
B = -x
Therefore, the particular solution is:
y_p = xe^x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^(-2x) + c2e^x + xe^x
c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:
r^2 - 9r + 20 = 0
Factoring, we get:
(r - 5)(r - 4) = 0
So the roots are r = 5 and r = 4.
The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:
y_h = c1e^4x + c2e^5x
To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax^2 + Bx + C)e^4x
Taking the first and second derivatives of y_p, we get:
y_p' = (2Ax + B)e^4x + 4Axe^4x
y_p'' = 2Ae^4x +
How much money would an investment of 300 at rate of 12 percent compound monthly be after 4 years
Answer:
data given
principal 300
rate12%
time 4 years
Step-by-step explanation:
from
A=P[1+r/100]^n
where
A is amount
p is principal
r is rate
n is interest period
now,
A= 300[1+12/(100×12)]^(12×4)
A=300×1.01^48
A=483.67
: .would be 483.67
Find the surface area. Round to the nearest hundredth
Answer:
122.30 cm²
Step-by-step explanation:
Divide the polyhedron into shapes:
+) 2 triangles with the same area.
The area of the triangle is
(4.3×11)÷2 = 23.65 cm².
And with two triangles of the same area we take the sum of both areas
23.65 + 23.65 = 47.3 cm²
+) 3 rectangles with different areas.
(3×6) + (3×8) + (3×11) = 75 cm²
So the surface area is the sum of areas of the triangles and rectangles
47.3 + 75 = 122.3 = 122.30 cm²
how am i supposed to prove that theyre collinear
Answer:
They are collinear if they are on the same line
If you have a standard score of Z = 1, what percentage of the population has scores less than you?
Step-by-step explanation:
From a z-score table
z-score = 1 corresponds to .8413 or 84.13 percentile
meaning 84 .13 % have a lesser score than you
A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 10 feet. The slant height is 12 feet. What is the height of the heater? Round to the nearest tenth of a foot.
The height of the heater is approximately 6.6 feet.
What is Pythagoras theorem?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.
We can use the Pythagorean theorem to find the height of the pyramid. Let's call the height "h". Then, the slant height is the hypotenuse of a right triangle with base and height both equal to 10 feet, so we have:
h² + 10² = 12²
Simplifying and solving for h, we get:
h² + 100 = 144
h² = 44
h ≈ 6.6 feet
Therefore, the height of the heater is approximately 6.6 feet.
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La Suma delos cuadrados de dos números naturales consecutivos es 181 halla dichos numeros
The two consecutive natural numbers whose sum of squares is 181 are 9 and 10
Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:
x² + (x+1)² = 181
Expanding the equation:
x² + x² + 2x + 1 = 181
Combining like terms:
2x² + 2x - 180 = 0
Dividing both sides by 2:
x² + x - 90 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -90
x = (-1 ± √(1 + 360)) / 2
x = (-1 ± √(361)) / 2
x = (-1 ± 19) / 2
We discard the negative value, as it does not correspond to a natural number:
x = 9
Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.
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Please help with #13!!
13.
m
mFP=
mPD=
Answer:
Step-by-step explanation:
36 26 so 36 +26 = 89
For each of the following three scenarios, state which hypothesis test you would use from among the four introduced so far: the z test, the single-sample t test, the paired-samples t test, and the independent-samples t test. (Note: In the actual studies described, the researchers did not always use one of these tests, often because the actual experiment had additional variables.) Explain your answer. (20pts) a. A study of 40 children who had survived a brain tumor revealed that the children were more likely to have behavioral and emotional difficulties than were children who had not experienced such a trauma (Upton & Eiser, 2006). Parents rated children’s difficulties, and the ratings data were compared with known means from published population norms. b. Talarico and Rubin (2003) recorded the memories of 54 students just after the terrorist attacks in the United States on September 11, 2001—some memories related to the terrorist attacks on that day (called flashbulb memoriesfor their vividness and emotional content) and some everyday memories. They found that flashbulb memories were no more consistent over time than everyday memories, even though they were perceived to be more accurate. c. The HOPE VI Panel Study (Popkin & Woodley, 2002) was initiated to test a U.S. program aimed at improving troubled public housing developments. Residents of five HOPE VI developments were examined at the beginning of the study so researchers could later ascertain whether their quality of life had improved. Means at the beginning of the study were compared to known national data sources (e.g., the U.S. Census, the American Housing Survey) that had summary statistics, including means and standard deviations.
Answer:
a. For the study of 40 children who had survived a brain tumor, the appropriate hypothesis test would be a single-sample t test. This is because the study involves comparing the ratings data from the parents with known means from published population norms. A single-sample t test is used to determine whether a sample mean is statistically different from a known population mean. In this case, the sample mean is the ratings data from the parents, and the population mean is the known means from published population norms.
b. For Talarico and Rubin's study of memories, the appropriate hypothesis test would be a paired-samples t test. This is because the study involves comparing the consistency of flashbulb memories and everyday memories over time, for the same group of individuals. A paired-samples t test is used to determine whether there is a statistically significant difference between two related samples, such as before and after measurements for the same group of individuals.
c. For the HOPE VI Panel Study, the appropriate hypothesis test would be an independent-samples t test. This is because the study involves comparing the means of residents in the five HOPE VI developments at the beginning of the study with known national data sources that had summary statistics, including means and standard deviations. An independent-samples t test is used to determine whether there is a statistically significant difference between the means of two independent groups. In this case, the two independent groups are the residents in the HOPE VI developments and the known national data sources.
Step-by-step explanation:
The circle graph below shows the number of animals in Mushu's farm. Sheep Donkeys Camels Goats Cows If there were 24 goats, how many cows are there in the farm?
By assuming that the farmer has goat and cows in the ratio 3:4, the number of cows in the farm will be 32 cows.
If there were 24 goats, how many cows are there in the farm?To find out how many cows are in the farm, we need to know the total number of animals in the farm. Assuming the ratio of goats to cows is 3:4, we can write this as: [tex]3x : 4x[/tex]
Where 3x represents the number of goats, and 4x represents the number of cows. If we know that there are 24 goats, we can set up an equation to solve for x:
3x = 24
Dividing both sides by 3, we get:
x = 8
Now that we know the value of x, we can find the number of cows:
= 4x
= 4(8)
= 32
Therefore, there are 32 cows in the farm.
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Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).
The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:
A B (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0
0 1 0
1 0 0
1 1 0
The truth table is what?A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.
The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.
To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.
A B A ⋁ B A ⋀ B ~(A ⋀ B) (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0 0 1 0
0 1 1 0 1 0
1 0 1 0 1 0
1 1 1 1 0 0
So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.
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See the photo below
This problem involves integration and algebraic manipulation, and belongs to the subject of calculus. The solutions are:
[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]
[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]
[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]
This is a problem that asks us to find the values of some definite integrals using given values of other definite integrals. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.
The problem involves some algebraic manipulation and the use of the linearity of the integral.
It also involves finding the constant "a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.
See the attached for the full solution.
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Given the expression 3x+2 evaluate the expression for the given values of x when x=(-2)
Answer:
...............................
Use the graph to answer the questions for the questions
The vertex is (50, 630). The vertex is the peak and correspond with the coordinates of he maximum height of the arch.
The solutions is the base of the arch and this (20, 0) and (80, 0)
vertex form, y = -0.7(x - 50)² + 630
Quadratic equation factored form, y = -0.7 (x - 80) (x - 20)
The equations are the same when plotted on a graph and examined mathematically. physically it looks different.
the domain is (-∞, ∞)
The height of the monument 15 feet from the left side is 472.5 feet
How to find the quadratic equationsince the zeroes of the quadratic equation is (20, 0) and (80, 0), hence we have that
y = a(x - 20)(x - 80) and the equation pass points (50, 630)
630 = a(50 - 20)(50 - 80)
630 = a * 30 * -30
630 = -900a
a = -0.7
Quadratic equation has a standard vertex form, y = a(x - h)² + k
y = a(x - h)² + k
vertex (h, k) = (50, 630) and a = -0.7
plugging the values
y = -0.7(x - 50)² + 630
Quadratic equation has a standard factored form, y = a(x - h)² + k
y = a(x - r2)(x - r1)
where r2 and r1 are the roots r1 = 20 r2 = 80 an a = -0.7
plugging the values
y = -0.7 (x - 80)(x - 20)
The height of the monument 15 feet from the left side is gotten from the graph
this is 15 feet from 20 hence x = 35 feet
from the graph it can traced to be 472.5 feet
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Which geometric term describes ∠ T A G ?
Answer:
angle
Step-by-step explanation:
since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!
Answer: i know it is acute
PLEASE HELP
Find the Area
2cm
___cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
1. Find radius:
If diameter is 2, divide it by 2 to get radius = 1
2. Find formula:
A=πr^2
3. Plug in:
A = π(1)^2
4. Solve (multiply):
A = π(1)^2:
3.14159265359
Or
3.14 cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
A=[tex]\pi[/tex]r^2
r=2
2/2=1
A=[tex]\pi[/tex](1)^2
=[tex]\pi[/tex]1
≈3.14x1
≈3.14cm^2
Given that sin 0 = 20/29 and that angle terminates in quadrant III, then what is the value of tan 0?
The value of Tanθ is 20/21.
What is Pythagorean Theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given: sinθ = -20/29 and that angle terminates in quadrant III.
We have to find the value of tanθ.
Using the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Sinθ = Perpendicular/hypotenuse
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Adjacent = - √Hypotenuse² - perpenducualr²
Replace the known values in the equation.
Adjacent = -√29² - (-20)²
Adjacent = -21
Find the value of tangent.
Tanθ = Perpendicular/base
Tanθ = -20/(-21)
Hence, the value of Tanθ is 20/21.
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Consider the verbal phrase.
Two and nineteen hundredths times a number g, plus fifty-nine hundredths
Part A
Enter an expression to represent the verbal phrase.
g +
Part B
Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93
verbal phrase can be represented by 7.16.
What is the verbal phrase?Part A:
The verbal phrase can be represented by the following expression:
[tex]2.19g + 0.59[/tex]
Here, "Two and nineteen hundredths times a number g" can be written as 2.19g, and "plus fifty-nine hundredths" can be written as [tex]0.59[/tex] .
Part B:
To evaluate the expression when [tex]g = 3[/tex], we substitute 3 for g in the expression and simplify:
[tex]2.19g + 0.59[/tex]
[tex]= 2.19(3) + 0.59 [\ Substitute g = 3][/tex]
[tex]= 6.57 + 0.59[/tex]
[tex]= 7.16[/tex]
Therefore, the correct answer is [tex]7.16.[/tex]
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The given question is incomplete. the complete question is given below:
Consider the verbal phrase.
Two and nineteen hundredths times a number g, plus fifty-nine hundredths
Part A
Enter an expression to represent the verbal phrase.
g +
Part B
Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93
Find each arc length. Round to the nearest tenth.
If FG = 27 yd, find the length of FED.
mFED= yards
(30 points) will give brainiest for effort
The length of arc FED is approximately 51.1 yards, rounded to the nearest tenth.
What is an arc length?The length of a section of a circle's circumference is known as an arc length.
The radius of the circle and the angle the arc subtends at the centre of the circle are two variables that affect an arc's length.
To find the length of FED, we need to first find the measure of the arc EGD. Since a circle has 360 degrees, we can find the measure of arc EGD by subtracting the measures of arcs DGC, CGF, and FGE from 360:
m(EGD) = 360° - m(DGC) - m(CGF) - m(FGE)
m(EGD) = 360° - 80° - 47° - 90°
m(EGD) = 143°
The formula for arc length is:
Arc length = (central angle / 360) x (2πr)
We can use this information to find the radius of the circle:
FG = 2r
27 yd = 2r
r = 13.5 yd
Now we can use the formula for arc length to find the length of arc FED:
Arc length FED = ((∠FED) / 360) x (2πr)
We know that ∠(EGD) + ∠(FED) = 360, so we can solve for ∠(FED):
∠(FED) = 360° - ∠(EGD)
∠(FED) = 360° - 143°
∠(FED) = 217°
Plugging in the values, we get:
Arc length FED = (217° / 360) x (2π x 13.5 yd)
Arc length FED = (0.6028) x (84.78 yd)
Arc length FED = 51.11 yd
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find the radius of a cylinder if the volume is 2,035.75 in^3 and the height is 3 times the radius. use the formula V= pi r^2h
The radius of the cylinder is approximately 6.75 inches.
How to calculate volume of cylinder?We can use the formula for the volume of a cylinder to solve this problem:
[tex]V = \pi r^2h[/tex]
We know that the volume V is 2,035.75 [tex]in^3[/tex], and the height h is 3 times the radius r. So we can write:
[tex]V = \pi r^2(3r)[/tex]
Simplifying this expression, we get:
V = 3π[tex]r^3[/tex]
To solve for r, we can divide both sides of the equation by 3π[tex]r^2[/tex]:
V/(3π[tex]r^2[/tex]) = r
Substituting the given value for V, we have:
2,035.75/(3π[tex]r^2[/tex]) = r
Multiplying both sides by 3πr^2, we get:
2,035.75 = 3π[tex]r^3[/tex]
Dividing both sides by 3π, we have:
[tex]r^3[/tex] = 2,035.75 / (3π)
Taking the cube root of both sides, we get:
r = [tex](2,035.75 / (3\pi ))^{1/3[/tex]
Using a calculator, we find that:
r ≈ 6.75 inches
Therefore, The cylinder has a radius of about 6.75 inches.
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Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
+
X
Ś
The required graph of the function given; h (x) has been attached.
Define a graph?In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.
Here as per the question the graph of the function, h (x) has been attached.
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Help me pleas whith this
The diameter of a circle is 38 feet.what is the circles circumfrence. Use 3.14 for pi
Answer:
The circumference of the circle is 119.32 ft.
Step-by-step explanation:
The circumference of a circle can be solved through the formula:
C = πd
where d is the diameter
Given: d = 38 ft
π = 3.14
Solve:
C = πd
C = 3.14 (38 ft)
C = 119.32 ft
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 35 minutes of calls is $16.83 and the monthly cost for 52 minutes is $18.87. What is the monthly cost for 39 minutes of calls?
Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.
Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:
(x1, y1) = (35, 16.83)
(x2, y2) = (52, 18.87)
The slope of the line passing through these two points is:
m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27
Using point-slope form with the first point, we get:
y - y1 = m(x - x1)
y - 16.83 = 0.27(x - 35)
Simplifying, we get:
y = 0.27x + 7.74
Therefore, the monthly cost for 39 minutes of calls is:
y = 0.27(39) + 7.74 = $18.21
Step-by-step explanation:
Write an equation for the polynomial graphed below
The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).
How to derive the equation of the polynomial
In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:
y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.Then, by direct inspection we get the following information:
y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3
First, determine the lead coefficient:
- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)
- 3 = a · 3 · 1 · (- 2) · (- 3)
- 3 = 18 · a
a = - 1 / 6
Second, write the complete expression:
y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)
To learn more on polynomials: https://brainly.com/question/29260355
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