Polynomial multiplication is the process of multiplying two polynomials together to get a new polynomial that represents the product of the two original polynomials.
What is Polynomial multiplication?It should be noted that to multiply two polynomials, you need to perform a distributive operation. You take each term of the first polynomial and multiply it by each term of the second polynomial. Then, you add all the resulting terms together to get the final polynomial.
For example, let's say you want to multiply the polynomials (x + 2) and (x - 3).
First, you multiply the x term in the first polynomial by the x term in the second polynomial:
(x) * (x) = x²
Next, you multiply the x term in the first polynomial by the -3 term in the second polynomial:
(x) * (-3) = -3x
Then, you multiply the 2 term in the first polynomial by the x term in the second polynomial:
(2) * (x) = 2x
Finally, you multiply the 2 term in the first polynomial by the -3 term in the second polynomial:
(2) * (-3) = -6
Now, you add up all the resulting terms to get the final polynomial:
x² - x - 6
Therefore, the product of (x + 2) and (x - 3) is x² - x - 6.
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John invest R500, at 12% per annum using simple interest for 4 years. How much money will John have at the end of 4 years?
Simple Interest = (Principal x Rate x Time)
where:
Principal = R500 (the amount invested)
Rate = 12% per annum = 0.12 (expressed as a decimal)
Time = 4 years
So, the simple interest earned by John over 4 years is:
Simple Interest = (500 x 0.12 x 4) = R240
To find the total amount of money John will have at the end of 4 years, we need to add the simple interest to the principal:
Total amount = Principal + Simple Interest = 500 + 240 = R740
Therefore, John will have R740 at the end of 4 years.
Answer:
The total amount he has at the end is ₹740.
Step-by-step explanation:
Simple Interest = [tex]\frac{PRT}{100}[/tex]
= [tex]\frac{500 * 12 * 4}{100}[/tex] = ₹240
Total amount he has at the end of 4 years = Principal + Interest
= ₹500 + ₹240
= ₹740
Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. Assume ≈ 4. 0 thousand dollars
An effective indicator for assessing retail store efficiency, spotting market trends, and making strategic business decisions is annual earnings per employee for profits.
The retail sales industry's annual profits per employee are shown in the data. The data's mean or median is most likely about $4,000,000, according to the assumption. You may compare the productivity of several retail stores by looking at the annual profits per employee. Businesses that generate more annual earnings per employee are typically more productive than those that do not.
The information can also be utilized to spot patterns in the retail sector, such as which businesses are operating better than others. For instance, if a business has been steadily increasing its annual profit per employee, it can be a sign that it is growing or streamlining its operations. In contrast, a business with declining annual profits per employee might be having trouble or seeing a drop in the demand for its goods.
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Jason wants to create a box with the same volume as the one shown below. He wants the length to be 4
inches. What would be the measurements of the width and height?
Answer:
Step-by-step explanation:The width would be 2 the same for the height
Type the correct answer in each box. Diagram shows an array of 5 squares (left) and 2 triangles (right), in two rows. The ratio of the number of squares to the number of triangles in simplest form is : . The number of triangles that need to be added to make the ratio of the number of squares to the number of triangles 1 : 1 is .
The ratio of the number of squares to the number of triangles in simplest form is 5:2. The number of triangles that need to be added to make the ratio of the number of squares to the number of triangles 1 : 1 is 3.
What is the ratio?
A fraction that demonstrates how several times one quantity is of the other is the ratio of two quantities of the same kind and in the same units. Ratio is represented by the symbol ":". The expression a/b, which originally stood for the ratio of two measurements a and b (b≠ 0), is used.
Given that the number of squares are 5 and the number of triangles are 2.
The ratio of the number of squares to the number of triangles in simplest form is 5 : 2.
Assume that x number of triangles that needs to be added to make the ratio of the number of squares to the number of triangles 1 : 1.
The equation is:
5:(2+x) = 1:1
5/(2+x) = 1/1
Cross multiply both sides:
5 = 2 + x
x = 5 - 2
x = 3
3 triangles need to be added to make the ratio of the number of squares to the number of triangles 1 : 1
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The angle of depression of the top of a house from the top of a column of height 95.62 m. is 45° and the angle of elevation of the top of a column from the bottom of the house is 60°. Find the height of the house.
Answer: We can solve this problem using trigonometry and basic geometry. Let's first draw a diagram:
A (top of house)
/|
/ | h
/ |
/ |
/θ1 |
/ |
/ |
/ |
/ |
/ |
/ |
/ |
/ |
/ |
B (top of column)
| d
|
|
|
C (bottom of column)
We are given that angle theta 1 (θ1) is 45 degrees, angle theta 2 (θ2) is 60 degrees, and the height of the column BC is 95.62 meters. We want to find the height of the house AB, which we'll call "h".
First, we can use trigonometry to find the length of segment CD. Since we know angle θ2 and the length of BC, we can use the tangent function:
tan(θ2) = opposite / adjacent
tan(60°) = d / 95.62
d = 95.62 * tan(60°)
d ≈ 165.30 meters
Now we can use the fact that angles ABD and CBD are complementary to find the length of segment AD:
tan(θ1) = opposite / adjacent
tan(45°) = h / (d + 165.30)
h = (d + 165.30) * tan(45°)
h ≈ 165.30 meters
Therefore, the height of the house is approximately 165.30 meters.
Step-by-step explanation:
what does banana + potato equal?
A Bonato
B Ponana
I'll give brainliest if you get it right :)
Answer: Bonato
Step-by-step explanation:
onica deposits $400 into a savings account that pays a simple interest rate of 3.3%. Paul deposits $500 into a savings ccount that pays a simple interest rate of 2.7%. Monica says that she will earn more interest in 1 year because her interest te is higher. Is she correct? Justify your response. Monica is incorrect. Monica will earn $6.80 in 1 year while Paul will earn $8.40 in 1 year. Enter your answer in the edit fields and then click Check Answer. All parts showing (TE) ogress Clear All Check Answer
Monica is not correct. Monica will earn $13.50 in 1 year while Paul will earn $13.20 in 1 year.
Who would earn the higher interest?
Simple interest is a linear function of the amount deposited, the interest rate and the number of years.
Simple interest = amount deposited x interest rate x time
Interest earned by Monica = $400 x 0.033 x 1 = $13.20
Interest earned by Paul = $500 x 0.027 x 1 = $13.50
Difference in the interest = $13.50 - $13.20 = $0.30
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A painter mixed 56 oz of blue and yellow paint. The ratio is 3 to 11, how many ounces of blue paint did he use?
If a painter mixed 56 ounces of blue and yellow paint. The ratio is 3 to 11, 12 ounces of blue paint were utilized by the painter.
To solve the problem, we can use the ratio of blue to the total amount of paint to determine how many ounces of blue paint were used. The ratio of blue to the total paint is 3 to 11. This means that for every 3 parts of blue paint, there are 11 parts of total paint. We can use this information to set up a proportion:
3/14 = x/56
Where x represents the number of ounces of blue paint used. To solve for x, we can cross-multiply and simplify:
356 = 14x
168 = 14 × x
x = 12
Therefore, the painter used 12 ounces of blue paint.
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Help me please, I am not good at this unfortunately
Answer: Its 12 the answer.
Step-by-step explanation:
m
A: BC, AB, AC
b: AB ,BC, AC
c: AC ,AB, BC
d: AB ,AC, BC
In triangle ABC, AB + BC > AC is the correct option.
What is the triangle?Three straight sides and three angles make up the two-dimensional geometric shape known as a triangle. they can be of many types .
I think that the question is related to the triangle,
Choose the correct option for ∆ABC,
a. AB + BC > AC
b. AB + BC < AC
c. AB + AC < BC
d. AC + BC < AB
Given, ABC is a triangle.
We are aware that the length of a triangle's third side is always greater than the sum of its other two sides.
Let the two sides of ∆ABC is AB and BC and the third side is AC.
So, AB + BC > AC
Therefore, option a is true.
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What are the possible orderings of the sides of triangle ABC, given the three sides are AB, BC, and AC?
a: BC, AB, AC
b: AB ,BC, AC
c: AC ,AB, BC
d: AB ,AC, BC
When Hector found a rare coin a few years ago, it was worth $190. Since then, it has been increasing in value by the same percentage each year. One year after
Hector found the coin, it was worth $209.
If c(n) represents the value in dollars of the coin n years after Hector found it, which expression is equal to c(n)?
190 (0.01^n)
190 (0.1^n)
190 (1.01^n)
190 (1.1^n)
The required expression represents the value in dollars of the coin n years after Hector found is [tex]$c(n) = 190 \times (1.1)^n$[/tex].
How to find the function of time?Let's call the percentage increase in value each year "r". We know that after one year, the coin was worth $209, which is 209/190 = 1.1 times what it was worth when Hector found it. So we can set up an equation:
[tex]$190 \times (1 + r)^1 = 209$[/tex]
Simplifying this equation,
[tex]$1 + r = \sqrt[1]{\frac{209}{190}}$[/tex]
1 + r = 1.1
r = 0.1
So the percentage increase in value each year is 10%. To find the value of the coin "n" years after Hector found it, we can use the formula:
[tex]$c(n) = 190 \times (1 + r)^n$[/tex]
Substituting the value we found for "r", we get:
[tex]$c(n) = 190 \times (1.1)^n$[/tex]
So the expression for the value of the coin "n" years after Hector found it is:
[tex]$c(n) = 190 \times (1.1)^n$[/tex]
Thus, required expression represents the value in dollars of the coin n years after Hector found is [tex]$c(n) = 190 \times (1.1)^n$[/tex].
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Find The Domain of each expression 5/√5-x
Write an explicit formula for � � a n , the � th n th term of the sequence 36 , 32 , 28
If the sequence is 36 , 32 , 28, then the explicit formula for term aₙ , the nth term is 40 - 4n.
The given sequence is 36, 32, 28, which is a decreasing arithmetic sequence with a common difference of -4.
To find the nth term of an arithmetic sequence, we can use the formula:
aₙ = a₁ + (n - 1)d
where a₁ is the first term, d is the common difference, and n is the term we want to find.
In this case, a₁ = 36, d = -4, and we want to find the nth term.
So, the formula for the nth term of the sequence is:
aₙ = 36 + (n - 1)(-4)
Simplifying this expression:
aₙ = 36 - 4n + 4
aₙ = 40 - 4n
Therefore, the explicit formula for the nth term of the given sequence is aₙ = 40 - 4n.
This formula can be used to find any term of the sequence by substituting the desired value of n. For example, to find the 6th term, we would plug in n = 6:
a₆ = 40 - 4(6) = 16
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Rowan is taking his siblings to get ice cream. they can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. if w = 4 in, x =6 in, y = 6 in, z = 2 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? use 3.14 for π, and round your answer to the nearest tenth.
The cup will hold more ice cream than cone since volume of cup is 169.6 cubic inches which is greater than volume of 25.1 cubic inches.
The volume of a cone is given by the formula:
V= 1/3.π[tex]r^{2}[/tex]h
where r is the radius of the circular base and h is the height.
The volume of a cylinder is given by the formula:
V= π[tex]r^{2}[/tex]h
where r is the radius of the circular base and h is the height.
Assuming that the height of both the cone and the cup is the same, we can compare their volumes by comparing their radii.
For the cone, the radius r is equal to half the diameter of the circular base, which is equal to w/2 = 2 in.
The height of the cone is equal to y, which is 6 in.
V= 1/3.π[tex]r^{2}[/tex]h= 1/3.π[tex]2^{2}[/tex]6
For the cup, the radius r is equal to x/2 = 3
The height of the cup is equal to y, which is also 6 in.
Using these values, we can calculate the volume of the cup as:
[tex]V_cup[/tex]= π[tex]r^{2}[/tex]h=π[tex]3^{2}[/tex]6
Therefore, the cup will hold more ice cream than the cone.
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Help with pre calc question
[tex]\tan^2(\theta )+3\tan(\theta )=0\implies \tan(\theta )[\tan(\theta )+3]=0 \\\\[-0.35em] ~\dotfill\\\\ \tan(\theta )=0\implies \theta =\tan^{-1}(0)\implies \theta = \begin{cases} 90^o\\ 270^o \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \tan(\theta )+3\implies \tan(\theta )=-3\implies \theta =\tan^{-1}(-3)\implies \theta \approx \begin{cases} \stackrel{ II~Quadrant }{108.43^o}\\ \stackrel{ IV~Quadrant }{288.43^o} \end{cases}[/tex]
Write an exponential function in the form y= ab* that does through points (0,20) and (2,180)
The exponential function of the line that goes through points (0, 20) and (2, 180) is y = 20 × 3ˣ.
What is the exponential function of a line that goes through the points (0,20) and (2,180)?To find the exponential function of a line that goes through two points, we need to use the general form of the exponential function:
y = a × bˣ
where a is the initial value, b is the base, and x is the independent variable (usually time).
We can use the two points given to find the values of a and b.
Let's start with the point (0, 20):
y = a × bˣ
Plug in x = 0 and y = 20
20 = a × b⁰
20 = a × 1
a = 20
Next, let's use the point (2, 180):
y = a × bˣ
Plug in x = 2 and y = 180
180 = 20 × b²
b² = 180/20
b² = 9
b = 3
Now, plug these values into y = a × bˣ
Therefore, the exponential function y = 20 × 3ˣ
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A high school in a small town always has its homecoming day and parade on the first Saturday in October. From historical records, it has been determined that the probability of rain during the parade is 0.16. Amina will attend the high school for the next four years and plans to play in the marching band in the parade.(a) What is the probability that it will not rain on the homecoming parade in Amina's first year?(b) What is the probability that it will not rain on any of the homecoming parades during Amina's four years at the school? (Round your answer to three decimal places.)(c) What is the probability that it will rain on Amina's parade at least once during her four years of attendance? (Round your answer to three decimal places.)
a) The probability that it will not rain on the homecoming parade in Amina's first year is 0.84. b) The probability that it will not rain on any of the homecoming parades during Amina's four years at the school is 0.49. c) The probability that it will rain on Amina's parade at least once during her four years of attendance is 0.51.
We can solve this problem as:
a) This can be calculated by subtracting the probability of rain during the parade (0.16) from 1.
So, the probability is,
1 - 0.16 = 0.84.
b) This can be calculated by taking the probability of no rain (0.84) and multiplying it by itself four times.
So, the probability is,
0.84^4 = 0.49.
c) This can be calculated by subtracting the probability of no rain (0.49) from 1.
So, the probability is,
1 - 0.49 = 0.51.
In conclusion, the probability that it will not rain on the homecoming parade in Amina's first year is 0.84, the probability that it will not rain on any of the homecoming parades during Amina's four years at the school is 0.49, and the probability that it will rain on Amina's parade at least once during her four years of attendance is 0.51.
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For all positive values of x, which of the following
√√x1⁰ (√√x³) ?
expressions is equivalent to
10
PLEASE SHOW WORK
The expression [tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}[/tex] is equivalent to 10 for [tex]x = 10^{(8/15)}[/tex].
What are exponents?In mathematics, an expοnent (alsο called pοwer οr index) is a shοrthand nοtatiοn used tο represent the repeated multiplicatiοn οf a number by itself.
We can simplify the given expressiοn using the prοperties οf expοnents and rοοts.
First, we can simplify the expression inside the first square root as:
√√x1⁰ = [tex]\rm \sqrt{(x^{10})^{(1/4)} }= (x^{10})^{(1/8)} = x^{(10/8)} = x^{(5/4)}[/tex]
Next, we can simplify the expression inside the second square root as:
[tex]\sqrt{(\sqrt{x\³})} = \sqrt{(x^3)^{(1/4) }}= (x^3)^{(1/8)} = x^{(3/8)[/tex]
Therefore, the entire expression becomes:
[tex]\sqrt{(\sqrt{x1\⁰)}} (\sqrt{(\sqrt{x\³})} = x^{(5/4)} * x^{(3/8) }= x^{(15/8)}[/tex]
Now, we need to find the value of x that makes this expression equal to 10.
[tex]x^{(15/8) }= 10[/tex]
Taking the eighth power of both sides:
[tex]x^{15} = 10^8[/tex]
Taking the 15th root of both sides:
[tex]x = (10^8)^{(1/15)}[/tex]
[tex]x = 10^{(8/15)}[/tex]
the equivalent expression is:
[tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}= x^{(5/4) }* x^{(3/8)} = x^{(15/8)} = (10^{(8/15)})^{(15/8)} = 10[/tex]
Therefore, the expression [tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}[/tex] is equivalent to 10 for [tex]x = 10^{(8/15)}[/tex].
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Which point is a solution to the equation 2x-7y=7?
The point which is a solution to the equation 2x - 7y = 7 as required to be determined is; (0, -1).
Which point represents a solution to the given equation?As evident from the task content; the point which is a solution to the given equation is to be determined.
For a given equation; the y-intercept represents a solution to the equation.
On this note, if x = 0; therefore, we have that;
2 (0) - 7y = 7
y = 7 / -7
y = -1.
Ultimately, the point which is a solution to the equation is; (0, -1).
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please help if you can
The domain of function f is (-∞, 10) U (10, ∞) or {x|x ≠ 10}.
The range of function f is (-∞, -3) U (-3, ∞) or {y|y ≠ 3}.
The inverse of this function is f⁻¹ = (10x - 4)/(3 + x).
The domain of function f⁻¹ is (-∞, -3) U (-3, ∞) or {x|x ≠ 3}.
The range of function f⁻¹ is (-∞, 10) U (10, ∞) or {y|y ≠ 10}.
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = y = (3x + 4)/(10 - x)
x = (3y + 4)/(10 - y)
10x - yx = 3y + 4
3y + yx = 10x - 4
y(3 + x) = 10x - 4
f⁻¹ = (10x - 4)/(3 + x)
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Explain how the amount of a down payment affects your monthly mortgage payments.
Nick found his dream home that has a purchase price of $192,000. Nick earns $3,325 a month and wants to spend no more than 30% of his income on his mortgage payment. He has saved up $35,000 for a down payment. Nick is considering the following loan option: 20% down, 30 year at a fixed rate of 6. 25%. What modification can be made to this loan to make it a viable option, given Nick’s situation?
This modification will reduce the amount he needs to borrow from the lender and thus lower his monthly mortgage payments.
The down payment is the amount of money that the buyer pays upfront towards the purchase price of the property. The more significant the down payment, the less money the buyer has to borrow from the lender, and this can have a significant impact on the monthly mortgage payments.
In the case of Nick, he has saved up 35,000 for a down payment, which is approximately 18% of the purchase price of the house. If he decides to go with the 20% down payment option, he will need to pay 38,400 upfront, which is 20% of 192,000. The remaining 153,600 will be the amount he borrows from the lender.
Now, let's assume that Nick has taken a 30-year fixed-rate mortgage at 6.25% interest. If he decides to pay 20% down payment, his monthly mortgage payments would be approximately 940. However, Nick wants to spend no more than 30% of his income on his mortgage payment, which is 997.50 per month (30% of 3,325). Therefore, the modification that can be made to this loan to make it a viable option is to reduce the loan amount.
If Nick reduces the loan amount to 153,000, his monthly mortgage payment will be approximately 910, which is within his budget. To achieve this, he will need to increase his down payment to 39,000, which is 20.3% of the purchase price. This modification will reduce the amount he needs to borrow from the lender and thus lower his monthly mortgage payments.
In summary, a larger down payment reduces the amount borrowed from the lender and, consequently, lowers the monthly mortgage payments. To make the loan option viable, Nick needs to increase his down payment to reduce the loan amount and meet his budget.
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due in 5 minutes 12-3y< 27
Answer:
y > -5
Step-by-step explanation:
Kiel determines the zeros of the function f (a) to be -2, -5, and 7. Write a possible function to represent Kiel's function?
This function has zeros at x = -2, x = -5, and x = 7, since when any of these values are plugged into the function, the corresponding factor becomes zero, making the entire expression zero.
What is an expression?An expression is a combination of numbers, variables, and operators that represents a mathematical quantity or relationship. It can consist of a single number or variable, or it can be a more complex combination of terms.Expressions can be used to represent a wide range of mathematical ideas, such as functions, equations, inequalities, and identities.
In the given question,
A possible function that has zeros at -2, -5, and 7 is:
f(x) = a(x+2)(x+5)(x-7)
where a is a constant that determines the scale of the function.
Expanding the expression, we get:
f(x) = a(x³ + 5x² - 14x - 70)
This function has zeros at x = -2, x = -5, and x = 7, since when any of these values are plugged into the function, the corresponding factor becomes zero, making the entire expression zero.
Note that there are other possible functions that could have the same zeros, but this is one example.
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Select All ordered pairs that satisfy the function y= 5x + 5
A. (-3,-25)
B. (8,-10)
C. (8,45)
D. (-2,-5)
Answer:
Step-by-step explanation:u better not be him cause im him
In a right triangle, cos
(
8
x
)
∘
(8x)
∘
= sin
(
2
x
−
10
)
∘
(2x−10)
∘
. Find the larger of the triangle’s two acute angles.
Answer:
80°
Step-by-step explanation:
You want the larger of two acute angles in a right triangle if their relationship is cos(8x°) = sin(2x-10°).
Complementary anglesThe cosine of an acute angle is equal to the sine of its complement. The given relation between the angles means ...
(8x) +(2x -10) = 90 . . . . . the angles are complementary
10x = 100 . . . . . . . . . . . add 10
x = 10 . . . . . . . . . . . . . divide by 10
The two angles are 8·10° = 80° and (2·10 -10)° = 10°.
The larger of the two acute angles is 80°.
Jamal had 13 feet of decorative tape to where between 5 Freinds and himself how much tape does each person get
each person would have 2 feet and two inches of tape
Fill in the gaps below:
A. Triangle A is rotated _____ about (-1,0) to give Triangle A'.
Triangle A' is then reflected in the line ______ to give Triangle A''
b. what type of single transformation maps triangle A onto Triangle A''?
Answer:
90° CCWy = 0 (x-axis)reflection in the line x+y=-1Step-by-step explanation:
You want to know the parts of the composition of transformations that will map triangle A to A', then to A''. You also want to know what single transformation accomplishes the same thing.
A. Rotation, ReflectionThe long side of triangle A points "south". In triangle A', it points "east". To transform a segment pointing south to one pointing east requires a rotation of +90°, or 90° CCW.
The long side of triangle A' lies along the line y=1. In triangle A'', it lies on the line y=-1. The line of reflection is halfway between these values, at ...
y = (1 +(-1))/2 = 0/2 = 0
The line of reflection is y=0, the x-axis.
B. Single transformationWe know the transformation involves a reflection. The line of reflection can be found by finding the midpoints of the original and final vertices of the triangle.
The midpoint of the largest acute angle's vertex is ...
((2, -3) +(2, -3))/2 = (2, -3)
The midpoint of the right angle vertex is ...
((0, -3) +(2, -1))/2 = (1, -2)
The line through these two points is ...
x +y = -1
The transformation of A to A'' is a reflection in the line x+y=-1.
Use decomposition to find the area of the figure. 10yd 13yd 8yd
Answer:
Step-by-step explanation: It would help if you added the picture but its all good.
2) Costumes have been designed for the school play. Each boy's costume requires 5 yards of fabric, 4 yards of ribbon, and 3 packets of sequins. Each girl's costume requires 6 yards of fabric, 5 yards of ribbon, and 2 packets of sequins. Fabric costs $4 per yard, ribbon costs $2 per yard, and sequins cost $. 50 per packet. Use matrix multiplication to find the total cost of the materials for each costume.
Cost of materials for each boy's costume = 5 * 4 * 4 + 5 * 3 * $.50 = 80 + 7.5 = $87.50 Cost of materials for each girl's costume = 6 * 5 * 4 + 6 * 2 * $2 = 120 + 24 = $144
Let A = [5; 6], B = [4; 5], C = [3; 2], D = [4; 2], E = [$.50; $2].
Cost of materials for each costume = A * B * D + A * C * E
Cost of materials for each costume = [5; 6] * [4; 5] * [4; 2] + [5; 6] * [3; 2] * [$.50; $2]
Cost of materials for each costume = [80; 120] + [15; 24]
Cost of materials for each costume = [95; 144]
Total cost of materials for each costume = $239
Cost of materials for each boy's costume = 5 * 4 * 4 + 5 * 3 * $.50 = 80 + 7.5 = $87.50
Cost of materials for each girl's costume = 6 * 5 * 4 + 6 * 2 * $2 = 120 + 24 = $144
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a - use addition or subtraction to simplify.
b- find all sollutions of the simplified equation.
sin( 3 theta ) cos ( theta ) - cos ( 3 theta ) sin ( theta )
a.sin(3θ)cos(θ) - cos(3θ)sin(θ) = sin(4θ) - sin(2θ) = sin(4θ - 2θ) = sin(2θ)
b.2θ = 0, π, 2π, 3π,...
To solve this equation, first use addition or subtraction to simplify. In this case, it is best to add the two terms together and use the trigonometric identity sin(A)cos(B) + cos(A)sin(B) = sin(A+B). Applying this, we can rewrite the equation as:
sin(3θ)cos(θ) - cos(3θ)sin(θ) = sin(4θ) - sin(2θ) = sin(4θ - 2θ) = sin(2θ)
Now, to find all solutions of the simplified equation, use the fact that sin(2θ) = 0 when 2θ = 0, π, 2π, 3π,... Using this, the solutions of the equation are:
2θ = 0, π, 2π, 3π,...
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