7. Fill in the bubbles to indicate whether each expression is linear or not linear.
5x Linear or Nonlinear
6x+1 Linear or Nonlinear
10xy Linear or Nonlinear
17 Linear or Nonlinear
4x^2 Linear or Nonlinear
5x is Linear , 6x+1 is Linear , 10xy is Nonlinear , 17 is Linear , 4x² is Nonlinear
what is Nonlinear ?
Nonlinear refers to a function, equation, or expression that does not have a constant rate of change. In other words, the value of the dependent variable does not increase or decrease at a constant rate as the independent variable changes.
In the given question,
5x: Linear. This is a linear expression because it is a first-degree polynomial with a single variable, x. It has a constant rate of change, meaning that the value of y increases or decreases at a constant rate as x increases or decreases.
6x+1: Linear. This is also a linear expression because it is a first-degree polynomial with a single variable, x. It has a constant rate of change, meaning that the value of y increases or decreases at a constant rate as x increases or decreases.
10xy: Nonlinear. This expression is not linear because it contains a product of two variables, x and y. A linear expression can only have terms that involve a single variable raised to the first power. This expression has a degree of 2, which makes it a quadratic expression.
17: Linear. This is a linear expression because it is a constant value. It has a slope of 0, which means that the value of y does not change as x changes.
4x²: Nonlinear. This expression is not linear because it contains a variable, x, raised to the power of 2. A linear expression can only have terms that involve a single variable raised to the first power. This expression has a degree of 2, which makes it a quadratic expression.
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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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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
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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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
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
if m(x)= sin²(x), then m'(x)=? A. cos²x+sin²x. B.sinx²-cos²x C. 2cos²x-sinx D. cos²-sin²x
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:
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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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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if k(x) =3x, then f'(x)=?
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 +
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
what is the quotient of 837 and 26
Answer:
The quotient of 837 divided by 26 is approximately 32.2692 (rounded to four decimal places).
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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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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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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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:
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.
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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.6 In 1 and 2, write the expression using words. 1. (23,000-789) × 19 In 3-4, read the exproccia 2.6+(88×7)
1) the expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."
How to write the expression in words1) The expression (23,000-789) × 19 can be written in words using the following steps:
The expression inside the parentheses is the difference between 23,000 and 789, which is 22,211.
The expression is then multiplied by 19, which means it is being increased by 19 times.
So the final expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."
2) The expression 2.6+(88×7) can be read in words using the following steps:
The expression inside the parentheses, 88×7, means 88 multiplied by 7.
The result of the multiplication is 616.
The expression then becomes 2.6 added to 616.
So the final expression in words can be read as "Two point six plus six hundred and sixteen."
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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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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
Need help please
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
What was the initial mass (in mg) of the sample? --------------
What is the mass 7 weeks after the start?-------------
1. The initial mass of the sample was 32 mg. 2. The mass of the sample 7 weeks after the start is approximately 0.162 mg.
What is radioactive decay?An unstable atomic nucleus releases particles or electromagnetic radiation as it undergoes radioactive decay, changing into a different nucleus. Since this process is unpredictable and spontaneous, the decay's timing cannot be anticipated. The radioactive substance's half-life, or the amount of time it takes for half of its radioactive atoms to decay, is used to calculate the rate of decay. Radiometric dating, nuclear energy production, and medical imaging all employ radioactive decay, which can cause the emission of alpha particles, beta particles, or gamma rays. Understanding the behaviour of matter at the atomic and subatomic level requires knowledge of radioactive decay.
1. The radioactive decay is given by the formula:
[tex]N(t) = N_0 * (1/2)^{(t/T)}[/tex]
Now, for half-life of Palladium-100 is 4 days and t = 16 and N(t) = 2 we have:
[tex]2 = N_0 * (1/2)^{(16/4)}\\2 = N_0 * (1/2)^4\\2 = N_0* 1/16\\N_0 = 2 * 16\\N_0 = 32 mg[/tex]
2. Foe 7 weeks:
7 weeks = 7 * 7 days = 49 days.
[tex]N(49) = N_0 * (1/2)^{(49/4)}\\N(49) = 32 * (1/2)^{(49/4)}\\N(49) = 0.162 mg[/tex]
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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
Please help with #13!!
13.
m
mFP=
mPD=
Answer:
Step-by-step explanation:
36 26 so 36 +26 = 89
The base of the right prism shown is a right triangle.
1. Name two lines parallel to AD.
2. Name a line skew to DE.
3. State the number of base edges.
4. State the number of lateral faces.
5. Find the base area,
6. Find the lateral area.
7. Find the volume.
Two lines parallel to AD are BF and CE.
Two lines skew to DE are EF and DF.
The number of base edges is three: DE, EF, and DF.
The number of lateral faces is three: ABDF, BCEF, and ACDE.
The base area is 6 square units.
The lateral area is 72 square units.
The volume is 36 cubic units.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
1. Name two lines parallel to AD.
BF, CE
2. Name a line skew to DE.
EF, DF
3. State the number of base edges.
DE, EF, DF
4. State the number of lateral faces.
3, Which are ABDF, BCEF, ACDE.
5. Find the base area,
the base of a prism is ΔDEF,
DE = AC = 3,
EF = BC = 4,
DF = 5
A = √(s(s-a)(s-b)(s-c))
s = (3 + 4 + 5)/2 = 6
A = √(s(s-a)(s-b)(s-c))
A = √(6(6-3)(6-4)(6-5))
A = √(6(3)(2)(1))
A = √36
A = 6
6. Find the lateral area.
the lateral area would be the sum of the area of the four rectangular faces.
A = lb
ABDF
A1 = 5* 6 = 30,
BCEF,
A2 = 4 * 6 = 24
ACDE
A3 = 3 *6 = 18
lateral area = 30 + 24 + 18
= 72
7. Find the volume.
The volume of a prism can be calculated by multiplying the area of the base by the height of the prism. Therefore, the formula for the volume of a prism is:
V = Bh
Where V is the volume, B is the area of the base, and h is the height of the prism.
V = 6 * 6 = 36
hence,
Two lines parallel to AD are BF and CE.
Two lines skew to DE are EF and DF.
The number of base edges is three: DE, EF, and DF.
The number of lateral faces is three: ABDF, BCEF, and ACDE.
The base area is 6 square units.
The lateral area is 72 square units.
The volume is 36 cubic units.
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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)
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Camille opened a savings account and deposited $8,063.00 as principal. The account earns 14.69% interest, compounded quarterly. What is the balance after 10 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Save answer
Answer:$26,141.13.
Step-by-step explanation:
Using the formula A = P * (1 + r/n)^(n*t), where A is the balance, P is the principal, r is the interest rate, n is the number of times per year that the interest is compounded, and t is the time in years, we can calculate the balance in the savings account after 10 years:
A = 8,063.00 * (1 + 0.1469/4)^(4*10)
A ≈ 26,141.13
Therefore, the balance in the savings account after 10 years, rounded to the nearest cent, is $26,141.13.