Answers
Answer:
A
Step-by-step explanation:
B: would lead to g being in the same spot
C: would still be missing the rotation
D:It would be the flipped version of H
Related Questions
Find the value of V.
Answers
From the diagram the value of v is √6
How to solve for the value of v?You should recall that Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.
Using the trigonometrical ratios, we have
Tangent = opposite /adjacent
This implies that
√2/1 = 2√3/v
cross and multiplying to have
v√2 = 2√3
Rationalizing the denominator and making v the subject of the formular we have
v = 2√3/√2 *√2/√2
v = 2√2/2
Therefore the value of v is √6
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Which answer choice gives the correct classification(s) of the number 1,256?
integer
natural, whole
integer, rational
natural, whole, integer, rational
Answers
Answer:
natural, whole, integer, rational
Step-by-step explanation:
Natural Number:
All the numbers in the set {1, 2, 3, …} are natural numbers, 1256 lies in this set.
Whole Number:
All the numbers in the set {0, 1, 2, 3, …} are whole numbers, 1256 lies in this set.
Integer:
All the numbers in the set {… ,-1, 0, 1, 2 …} are integers, 1256 lies in this set.
Rational Number:
1256 can be represented as [tex]\dfrac{1256}{1}[/tex] or [tex]\dfrac{2512}{2}[/tex] etc., which is in the rational form (division of two non zero integers). therefore 1256 is also a rational number.
Hopefully this answer helped you!!
The sides of a triangle are x cm, (x − 4) cm and (x - 8) cm, respectively. If the cosine of the largest angle is, calculate the angles of the triangle.
Answers
the angles of the triangle are approximately 38.24 degrees, 67.53 degrees, and 74.23 degrees.
Step-by-step explanation:
Let's use the Law of Cosines to solve this problem. According to this law, in any triangle with sides of lengths a, b, and c, and angles opposite those sides denoted by A, B, and C, respectively, the following equation holds:
c^2 = a^2 + b^2 - 2ab*cos(C)
We can use this equation to find the cosine of the largest angle, which will allow us to determine the angles of the triangle.
In this case, the largest angle is opposite the longest side, which has a length of (x - 8) cm. So, let's rewrite the Law of Cosines equation in terms of x:
(x - 8)^2 = x^2 + (x - 4)^2 - 2x(x - 4)*cos(C)
Expanding and simplifying this equation gives:
x^2 - 16x + 64 = 2x^2 - 16x + 16 + 2x(x - 4)*cos(C)
Canceling out the common terms and rearranging, we get:
cos(C) = (x^2 + (x - 4)^2 - (x - 8)^2)/(2x(x - 4))
Simplifying the numerator and denominator gives:
cos(C) = (5x - 24)/(2x(x - 4))
Now, we can use a calculator to evaluate the cosine for different values of x and find the values that satisfy the given condition. Specifically, we want the cosine to be negative, since the largest angle of a triangle is always obtuse (greater than 90 degrees).
For example, if we try x = 10, we get:
cos(C) = (5(10) - 24)/(2(10)(6)) = -0.25
This satisfies the condition, so we can use this value of x to find the angles of the triangle:
Angle opposite x cm side = cos^-1((x^2 + (x - 4)^2 - (x - 8)^2)/(2x(x - 4)))
= cos^-1((10^2 + (10 - 4)^2 - (10 - 8)^2)/(210(10 - 4)))
= cos^-1(7/8)
≈ 38.24 degrees
Angle opposite (x - 4) cm side = cos^-1((x^2 + (x - 8)^2 - (x - 4)^2)/(2x(x - 8)))
= cos^-1((10^2 + (10 - 8)^2 - (10 - 4)^2)/(210(10 - 8)))
= cos^-1(3/8)
≈ 67.53 degrees
Angle opposite (x - 8) cm side = 180 - angle opposite x cm side - angle opposite (x - 4) cm side
= 180 - 38.24 - 67.53
≈ 74.23 degrees
Therefore, the angles of the triangle are approximately 38.24 degrees, 67.53 degrees, an the angles of the triangle are approximately 38.24 degrees, 67.53 degrees, and 74.23 degrees.
I hope this helped
The salaries did not rise with inflation. The butter is now 25% costlier. By what percentage should a housewife reduce the consumption, so that her expenditure stays the same
Answers
The percentage of reduction in consumption required to keep the same expenditure is 25%.
What is Inflation?Inflation is an economic phenomenon that occurs when the prices of goods and services increase over time.
To find out the percentage of reduction in consumption, we need to calculate the difference between the current and the original prices of the butter.
This can be done by subtracting the original price of the butter from the current price of the butter (25% costlier).
The difference can be expressed as a percentage by dividing the difference by the original price.
Therefore, the percentage of reduction in consumption required to keep the same expenditure is 25%.
This means that a housewife needs to reduce her consumption of butter by 25% in order to keep her expenditure the same.
Thus, the percentage of reduction in consumption required to keep the same expenditure is 25%.
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y=-x+8 4x+y=5
Help me pls
Answers
Answer: x = -1 and y = 9
Step-by-step explanation:
To solve this system of equations, we can use the substitution method.
First, solve the first equation for y:
y = -x + 8
Now, substitute this expression for y into the second equation and solve for x:
4x + y = 5
4x + (-x + 8) = 5 (substituting -x + 8 for y)
3x + 8 = 5
3x = -3
x = -1
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
y = -x + 8
y = -(-1) + 8
y = 9
Therefore, the solution to the system of equations is x = -1 and y = 9.
Profit is defined as total revenue minus total cost. The profit function of a company that manufactures and sells x units of a product is given by P(x)= R(x)-C(x), where
Prepresents the company's profits, R represents the company's revenue, and C represents the company's cost. If a company sells a calculator for $11, its revenue
function is R(x)=11x. The cost of each calculator manufactured is $8. In addition, it renewed its lease on the plant, so its weekly fixed costs are $1220.
(a) Determine the profit function. (b) Determine and interpret P(800)
Answers
Answer:
a.) P(x)= 3x - 1120
b.) make $1,180 profit in 1 week by selling 800 calculators
Step-by-step explanation:
a.) P(x)=R(x)-C(x)
R(x)=11x; C(x)=8x + 1220 assuming they are asking for profit in a week
P(x)= 3x - 1220
b.) P(800) = 3(800) -1220 = 1180
C(x)= 20+4000x+0.09x^2
A. Find the marginal cost function
Use it to estimate how fast the cost is increasing when x=4
Answers
The marginal cost function is $ 4000.72.
What is the marginal cost function?
The overall costs involved in producing an additional good are what is referred to as the marginal cost. Hence, it can be evaluated by changes in the costs associated with each extra unit. Marginal Cost is calculated as Total Expenditure Change / Unit Production Change.
Here, we have
Given: C(x) = 20+4000x+0.09x²
We have to find the marginal cost function.
We differentiate the given function and we get
C(x) = 20+4000x+0.09x²
C'(x) = 4000 + 2×0.09x
To determine how fast the cost is increasing when x=4.
C'(4) = 4000 + 2×0.09(4)
C'(4) = 4000.72
Hence, the marginal cost function is $ 4000.72.
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2sinx-1 = 0 (Solve with the inverse domain)
Answers
Answer:x = π/6 + 2πn , 5π/6 + 2πn, for any integer n
The volume of a cuboid is 108cm3.
The length is 4cm and the width is 9cm.
Work out the height of the cuboid.
Answers
Answer:
You can use the formula for the volume of a cuboid, which is Volume = length x width x height
You are given the volume of the cuboid as 108cm^3, the length as 4cm, and the width as 9cm. Let's substitute these values into the formula and solve for the height:
108cm^3 = 4cm x 9cm x height
To solve for height, you can divide both sides by 36 (which is equal to 4cm x 9cm) to isolate height:
108cm^3 ÷ 36 = 4cm x 9cm x height ÷ 36
3cm = height
So the height of the cuboid is 3cm.
(1/64)^(2/3)
SOLVE LAW OF INDICES
Answers
Answer:
To solve this problem, we can use the laws of indices, specifically the law that states that (a^m)^n = a^(m*n).
So, we have:
(1/64)^(2/3) = (1^(2/3))/(64^(2/3))
Since any number raised to the power of 1 is itself, we can simplify the numerator to just 1.
Now, we have:
(1/64)^(2/3) = 1/(64^(2/3))
To evaluate 64^(2/3), we can use the law of indices again, which states that a^(1/n) = nth root of a. In this case, we have:
64^(2/3) = (64^(1/3))^2 = 4^2 = 16
So, substituting this back into the original expression, we have:
(1/64)^(2/3) = 1/16
Therefore, (1/64)^(2/3) simplifies to 1/16.
Step-by-step explanation:
Answer:
Using the law of indices, we have:
(1/64)^(2/3) = (1^(2/3))/(64^(2/3))
Now we need to simplify the denominator by finding the cube root of 64:
64^(1/3) = 4
Substituting this value in the original expression, we get:
(1/64)^(2/3) = (1^(2/3))/(4^2)
Simplifying further, we have:
(1/64)^(2/3) = 1/16
Step-by-step explanation:
Can someone explain how to find cordinates from slop in graph to find angle
Answers
Answer:
Find the components of the line (x,y)
And then use Tan ^-1(y/x)= Theta or angle
I hope you understand, and I go explain further.
Step-by-step explanation: In "simple terms". Slope is rise/run. Rise is the change in y value, which will equal the length of the opposite side of the right triangle. Run is the change in x value, which is the length of the adjacent side. The trigonometric function Tangent is opposite/adjacent. Use the inverse tangent of the slope to find the angle.
The only catch is that sometimes inverse tangent will give you a negative angle. It is generally not acceptable to provide the angle in a triangle as the negative angle. If you get a negative angle, use the absolute value of the angle.
Convert 41 divided by 2 day.
to an
hour
Answers
41/2 days is equivalent tο 492 hοurs.
What is divisiοn?Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.
We knοw that there are 24 hοurs in day therefοre,
Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:
41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs
Therefοre, 41/2 days is equal tο 492 hοurs.
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Functions for -4,-6,-9,-27/2,-81/2
Answers
The function of the sequence -4,-6,-9,-27/2,-81/2 is f(n) = -4(3/2)^(n - 1)
Identifying the function of the sequence
from the question, we have the following parameters that can be used in our computation:
-4,-6,-9,-27/2,-81/2
The above sequence is a geometric sequence
This is because it has a common ratio calculated as
r = -6/-4
So, we have
r = 3/2
The sequence is then represented as
f(n) = ar^n-1
So, we have
f(n) = -4(3/2)^(n - 1)
Hence, the function is f(n) = -4(3/2)^(n - 1)
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I need helppppppppp please help me
Answers
We know interior angles in a Pentagon sum to 540 degrees.
We can add all 5 angles and expressions to sum 540.
148 + 3x + 10 + x + 112 + 90 = 540
Combine like terms
4x + 360 = 540
Subtract 360 from both sides to isolate x
4x + 360 - 360 = 540 - 360
Simplify
4x = 180
Divide both sides by 4 to solve for x
4/4 x = 180/4
x = 45
Now find angle B = 3x + 10
Substitute value of x = 45 into expression
B = 3 * 45 + 10
B = 135 + 10
B = 145
Calculate the volume of the triangular prism shown below. Give your answer in cm³. 5 cm 9 cm 11 cm 6 cm
Answers
The volume of the triangular prism is 135 cm³.
To calculate the volume of a triangular prism, we multiply the area of the triangular base by the height of the prism.
Given the dimensions provided:
Base: Length = 5 cm, Width = 9 cm
Height: 6 cm
To find the area of the triangular base, we use the formula for the area of a triangle:
Area = (1/2) * base * height
Substituting the values:
Area = (1/2) * 5 cm * 9 cm
Area = 22.5 cm²
Now, to calculate the volume of the prism, we multiply the area of the base by the height:
Volume = Area * Height
Volume = 22.5 cm² * 6 cm
Volume = 135 cm³
Consequently, the triangular prism has a 135 cm3 volume.
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DRAW THE TWO GRAPHS OF Y=+X^3 AND Y=-X^3 OF THE SAME AXEL SYSTEM
Answers
The blue curve represents y = x³ and the red curve represents y = -x³.in the attached image.
What are the quadrants?
The quadrant refers to one of the four regions in a two-dimensional coordinate system, formed by two perpendicular lines that intersect at their common origin, or point of intersection.
a graph of y = x³ and y = -x³ on the same axes:
We can see the graph of equations y = x³ and y = -x³ in the attached image.
The blue curve represents y = x³ and the red curve represents y = -x³.
They are symmetric about the origin, and the blue curve is in the first and third quadrants while the red curve is in the second and fourth quadrants.
Hence, The blue curve represents y = x³ and the red curve represents y = -x³.in the attached image.
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Use a graphing utility to graph the function and find the absolute extrema of the function on the given interval. (Round your answers to three decimal places. If an answer does not exist, enter DNE.)
Answers
Answer:
minimum: (0.345, -1.339)maximum: (0, 1)Step-by-step explanation:
You want the absolute extremes of f(x) = -x +cos(3πx) in the interval [0, π/6].
GraphThe attached graph shows the extremes to be ...
minimum: (0.345, -1.339)maximum: (0, 1)__
Additional comment
The x-value at the minimum is (π+arcsin(1/(3π)))/(3π) ≈ 0.344612473782. The corresponding y-value is about −1.33896758676.
What is 55 increased by 10%
Answers
Answer:
60.5
Step-by-step explanation:
Answer: 60.50
Step-by-step explanation:
.
The mug is 5/8 full, the mug contains 3/4 of water find the capacity of the mug
Answers
The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).
What is capacity?It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.
In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.
Let the capacity of the mug be x.
Given,
Mug is 5/8 full and contains 3/4 of water
So, 5/8 of the mug is filled with water
Therefore,
5/8 of x = 3/4
(5/8 )x = (3/4)
x = (3/4) × (8/5)
x = (24/20)
x = 1.2
Therefore, the capacity of the mug is 1.2.
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Please help me i need it for today!
Answers
1) The area of the garden in Design A and Design B is 108 [tex]feet^{2}[/tex]and 84[tex]feet^{2}[/tex]
2)The area of the deck not including the garden in Design A and Design B is 342 [tex]feet^{2}[/tex]and 372 [tex]feet^{2}[/tex]
3)The cost of $4.20 per [tex]feet^{2}[/tex]required to install the deck in Design A and Design B is $1890 and $1764 respectively
4) The cost of $1.40 per [tex]feet^{2}[/tex]required to install the garden in Design A and Design B is $151.2 and $117.6
5)Mr. and Mrs. Harper would like to choose Design A because its most affordable than Design A.
Therefore Mr. and Mrs. Harper save money $159.6.
How to calculate the money saved by Mr. and Mrs. Harper By choosing the affordable design?1) The area of the rectangular garden in design A
Area = length * width
From the fig, length = 9 feet
width = 12 feet
Area = 12 * 9 = 108 [tex]feet^{2}[/tex]
The area of the triangular garden in Design B
From the fig, Height = 12 feet
base = 14 feet
Therefore the area of the triangle = [tex]\frac{1}{2} * base *height\\\frac{1}{2} * 14 * 12[/tex]
= 84 [tex]feet^{2}[/tex]
2) The area of the rectangular deck is in design A
Area = length * width
= 18 * 25
= 450 [tex]feet^{2}[/tex]
The area of the rectangular deck is in design B
Area = length * width
= 21 * 20
= 420 [tex]feet^{2}[/tex]
The area of the rectangular deck without a rectangular garden in design A is =
= 450 - 108 = 342 [tex]feet^{2}[/tex]
The area of the rectangular deck without a triangular garden in design B is =
= 420 - 84[tex]feet^{2}[/tex] = 372 [tex]feet^{2}[/tex]
3) The cost of $4.20 per [tex]feet^{2}[/tex]required to install the deck in Design A and Design B
Therefore the total cost required to install the deck in design A
= 450 * 4.20
= $ 1890
Therefore the total cost required to install the deck in Design B
= 420 * 4.20
= $ 1764
4) The cost of $1.40 per [tex]feet^{2}[/tex]required to install the garden in Design A and Design B
Therefore the total cost required to install the garden in design A
= 108 * 1.40
= $ 151.2
Therefore the total cost required to install the garden in Design B
= 84 * 1.40
= $ 117.6
5) Mr. and Mrs. Harper would like to choose Design A because its most affordable than Design A.
Mr. and Mrs. Harper save money if they choose design B over design A
= (1890 + 151.2) - (1764 +117.6)
= 2041.2 - 1881.6
= $159.6
Therefore Mr. and Mrs. Harper save money $159.6.
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A person places $741 in an investment account earning an annual rate of 5.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe
rt
, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 13 years.
Answers
The nearest cent, the amount of money in the account after 13 years is $2,094.18.
The formula for continuous compound interest is:
V = Pe^(rt)
where V is the value of the account after t years, P is the principal (initial amount) invested, e is the base of natural logarithms (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time period in years.
In this case, P = $741, r = 0.058 (since the annual interest rate is 5.8%), and t = 13. Substituting these values into the formula, we get:
V = 741e^(0.058*13)
Using a calculator, we can evaluate e^(0.058*13) to be approximately 2.8302. Then, we can multiply this value by 741 to get:
V = 741*2.8302
V ≈ $2,094.18
Therefore, to the nearest cent, the amount of money in the account after 13 years is $2,094.18.
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3/2 (as a fraction) by the power of 4
Answers
Answer:
5.0625
Step-by-step explanation:because it is 1.5 as a decimel and that to the power of 4 is 5.0625
Answer:
1.97
Step-by-step explanation:
(3/2)^4
3^4 / 2^4
81/16
Decompose and find the area of the composite figure
Answers
The composite figure has a total area of 102 square units (80 + 16 + 6 square units). Consequently, the composite figure has a 102 square unit area.
How can you calculate a composite figure's entire surface area?Composite things that are three dimensional (3D) are constructed from two or more separate pieces. Finding each item's outside surface area and adding the surface areas together will yield the surface area of a 3D composite object. Another way to divide it is into a top and a bottom.
We may divide the composite figure into smaller forms and sum up their areas to determine the area of the overall figure. Here is one method for breaking down the figure:
A rectangle and two triangles make up the figure.
The rectangle has an area of 80 square units since it is 10 units long and 8 units wide.
The two triangles have right triangles with four and six unit-long legs, respectively. The equation (base * height) / 2 may be used to calculate each triangle's area.
The area of the triangle on the left is (4 * 8) / 2 or 16 square units since its base is 4 units and its height is 8 units (the length of the rectangle).
The area of the triangle on the right is (6 * 2) / 2 or 6 square units because its base is 6 units and its height is 2 units (the distance between the bottom of the triangle and the bottom of the rectangle).
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Please help me find the arc!!!
Answers
The length of the arc that is drawn in a circle of radius 14 cm and angle of arc 135° is approximately 32.67 cm.
What is an arc?An arc is a portion of a curve that is part of a circle. It is defined as a continuous portion of the circumference of a circle. In other words, an arc is a segment of a circle's circumference.
To find the length of an arc of circle, you can use the formula:
arc length = (angle of arc / 360) x (2 x π x radius)
Where π (pi) is a mathematical constant approximately equal to 3.14.
In this problem, the radius of the circle is given as 14 cm and the angle of the arc is 135°. So, By substituting these values in the formula, we get:
arc length = (135/360) x (2 x π x 14)
arc length = (3/8) x (2 x 3.14 x 14)
arc length = (3/8) x (87.92)
arc length = 32.67 cm (rounded to two decimal places)
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Answer this now please
Answers
The answer is 8.6+(-6.1). This is because addition and subtraction are inverse operations.
What is subtraction?Subtraction that involves taking one number away from another. It is the inverse of addition and is represented by the minus sign (-).
This means that when you add two numbers and then subtract the same amount, the result is the same as just adding the two numbers.
Similarly, when you subtract two numbers and then add the same amount, the result is the same as just subtracting the two numbers.
Therefore, 6.1+8.6 is equivalent to 8.6+(-6.1).
Using mathematical notation, we can represent this expression as 6.1+8.6 = 8.6+(-6.1).
To add and subtract the numbers, we can use the traditional column method.
First, we write out 6.1+8.6 as 6.1 - (-8.6). Then, we add the numbers in each column, starting with the ones column:
Ones column: 1+6=7
Tens column: 8-8=0
And our answer is 7,0. We can also write this as 8.6+(-6.1) to show that the two expressions are equivalent.
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For the given cost function
C(x)=12100+800x + x² find:
a) The cost at the production level 1200
b) The average cost at the production level 1200
c) The marginal cost at the production level 1200
d) The production level that will minimize the average cost
e) The minimal average cost
Answers
a) The cost at production level 1200 is not given in the text, b) The average cost at production level 1200 is 2101.75, c) The marginal cost at production level 1200 is 3200, d) The production level that minimizes the average cost is not meaningful as it is outside the domain of production levels, e) The minimal average cost is not meaningful as it cannot be negative.
What is an expression?An expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, division, and exponentiation) that represent some combination of numbers or other mathematical objects. Expressions can be simple, such as a single number or variable, or complex, such as a series of terms connected by operators. Expressions can be evaluated, simplified, and manipulated using algebraic techniques to solve problems and analyze mathematical relationships.
According to the given information:a) The cost at the production level 1200 is[tex]C(1200) = 12100 + 800(1200) + (1200)^2 = 2522100.[/tex]
b) The average cost at the production level 1200 is [C(1200)]/1200 = 2101.75.
c) The marginal cost at the production level 1200 is the derivative of C(x) with respect to x evaluated at x = 1200. Thus, MC(1200) = 800 + 2(1200) = 3200.
d) The production level that will minimize the average cost is given by the formula x = -b/(2a) where a and b are the coefficients of [tex]x^2[/tex] and x, respectively. Thus, x = -800/(2(1)) = -400. This value is not meaningful, as it is not in the domain of production levels.
e) The minimal average cost is the average cost at the vertex of the parabola given by C(x). The x-coordinate of the vertex is x = -b/(2a) = -800/(2(1)) = -400, and the y-coordinate is C[tex](-b/(2a)) = C(-400) = 12100 + 800(-400) + (-400)^2 = 168900[/tex]. Therefore, the minimal average cost is 168900/(-400) = -422.25. This is not a meaningful answer, as average cost cannot be negative.
Therefore,a) The cost at production level 1200 is not given in the text, b) The average cost at production level 1200 is 2101.75, c) The marginal cost at production level 1200 is 3200, d) The production level that minimizes the average cost is not meaningful as it is outside the domain of production levels, e) The minimal average cost is not meaningful as it cannot be negative.
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When Sally was 10 years old, she was 140 cm tall. Two years later, her height had increased by 10%. Find Sally's height when she was 12 years old.
Answers
Answer: 154cm
Step-by-step explanation:
10% of 140 is 14
add that 10% to get 154
31 points
2a) Why wouldn’t a 2x2 area model (2 rows, 2 columns) with 4 smaller areas work to multiply
(x + 3)(2x
4 − 3x
3 − 2x
2 − 4x − 1) ? In your explanation, include a description of how to determine the correct rows
and columns for the area model [be sure to refer to and include the correct number of ‘terms’ and correct dimensions]
2b) Show what the area model SHOULD look like with the
correct lengths and widths labeled. DO NOT MULTIPLY!
2c) Draw an area model to find the ‘total area’ of a rectangle if the length is (x + 8) and the width is (x − 5). Write
your final ‘total area’ as a polynomial in Standard Form.
Final Area:
Answers
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.
b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.
c) The final total area is 2x² - 10x - 15.
What is an area model?An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.
b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.
2x⁴ − 3x³ − 2x² − 4x − 1
+---------------------------------------
x | 2x⁵ -3x⁴ -2x³ -4x² -x
|
3 | 6x⁴ -9x³ -6x² -12x -3
+---------------------------------------
c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.
x + 8 x - 5
+--------------------
x | x² + 8x x² - 5x
|
-5 | -5x + -40 -5x + 25
+--------------------
The final total area can be found by adding up the areas of the smaller rectangles:
Total area = x² + 8x + x² - 5x - 5x - 40 + 25
= 2x² - 10x - 15
= 2x² - 10x - 15.
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1383400691
Find the experimental probability that 3 of 4
children in a family are boys.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
HTHH HTTH TTTT THTT HTHT
HHTT HHHT THHT HTTH TTHH
HTTT HTHT TTHH THTH HTHH
TTHT HTTT HTHT HHHT HHHH
Experimental Probability
Answers
HTHH, HTTH, TTHH, THTH, HTHH, and HTHH
Therefore, the experimental probability of getting 3 boys out of 4 children in a family is
6/20 or 0.3 or 30%.
(100 points)
A bakery is making cupcakes using a cylindrical mold. The cupcake mold has a diameter of 3.5 centimeters and is 7 centimeters tall. Which of the following shows a correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top? Use 3.14 for π.
V = (3.14)(3.5)2(7)
V = (3.14)(7)2(3.5)
V = (3.14)(7)2(1.75)
V = (3.14)(1.75)2(7)
Answers
Answer:
for making cupcakes we need to determine its volume first
that would be πr²h for a cylinder
hence your answer is
V = (3.14)(1.75)^2(7)
V = (3.14)(1.75)^2(7)