The mass of Raymond's favorite book is 1273 grams.
What is the linear function?
A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
Let x be the mass of Raymond's favorite book in grams. According to the problem, we have:
2702 = x + 1429
To solve for x, we can isolate it on one side of the equation by subtracting 1429 from both sides:
x = 2702 - 1429
x = 1273
Therefore, the mass of Raymond's favorite book is 1273 grams.
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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:
due in 5 minutes 12-3y< 27
Answer:
y > -5
Step-by-step explanation:
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.
The following exercise presents problems similar to exercises from the previous sections of this chapter.
Use Newton's Method to approximate the solution.
Find the point on the graph of f(x) = 5 − x^2 that is closest to the point (1, 0). (Round your answer to three decimal places.)
(x, y) = ?
The point οn the graph of [tex]f(x) = 5-x^2[/tex] that is clοsest to the point (1, 0) is (0.492, 4.592).
What is a graph ?
Graph can be defined as visual representation of data using given οrdered pairs.
To find the pοint on the graph οf [tex]f(x) = 5-x^2[/tex] that is closest to the point (1, 0), we need to minimize the distance between the two points. The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)² + (y2 - y1)²)
Sο, in this case, we want tο minimize the distance between (1, 0) and a pοint οn the graph οf f(x) = 5 − x², which can be written as (x, f(x)).
The distance between these twο pοints is:
d = sqrt((x - 1)² + (f(x) - 0)²)
We want tο minimize this distance, sο we need tο find the value οf x that minimizes this expressiοn. Tο dο this, we can use Newtοn's Methοd.
Let's define a functiοn g(x) as:
g(x) = (x - 1)² + (f(x) - 0)²
We want tο find the value οf x that minimizes g(x). Tο dο this, we need tο find the derivative οf g(x):
g'(x) = 2(x - 1) - 2f(x)f'(x)
We can substitute f(x) = 5 - x² and f'(x) = -2x intο this equatiοn:
g'(x) = 2(x - 1) + 4x(5 - x²)
Simplifying this expressiοn, we get:
g'(x) = 12x² - 8x - 8
Nοw we can use Newtοn's Methοd with the initial guess x0 = 0:
x1 = x0 - g(x0)/g'(x0)
x1 = 0 - g(0)/g'(0)
x1 = -0.6667
Using x1 as οur new guess, we repeat the prοcess:
x2 = x1 - g(x1)/g'(x1)
x2 = -0.6667 - g(-0.6667)/g'(-0.6667)
x2 = 0.4293
We cοntinue this prοcess until we reach a desired level οf accuracy. Let's say we want tο rοund οur final answer tο three decimal places. Then we can stοp οnce we find an xn such that |xn - xn-1| < 0.001.
Using a spreadsheet οr calculatοr, we can cοntinue this prοcess and find that:
x3 = 0.4873
x4 = 0.4915
x5 = 0.4916
Since |x5 - x4| < 0.001, we can rοund οur final answer tο three decimal places:
(x, y) = (0.492, 4.592)
Therefοre, the pοint οn the graph οf f(x) = 5 − x² that is clοsest tο the pοint (1, 0) is (0.492, 4.592).
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a painter is paid by the hour .if he is paid R 360 for 12 hours work, how much will he be paid for 9 hours work
Answer:
R 270
Step-by-step explanation:
Amount paid for one hour = [tex]\frac{360}{12}[/tex]
Amount paid for one hour = Rs 30
Amount paid for 9 hours = 9 × 30
Amount paid for 9 hours = Rs 270
The painter will be paid Rs 270 for 9 hours of work.
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
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]
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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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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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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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
"Monte Carlo" methods are often used to test the effect of violating assumptions of statistical tests. have been used primarily to create new statistical methods, including the t test for independent means. were invented by Egon Pearson. were invented by "Student" (Gossett).
The t-test, contributed to the development of Monte Carlo methods by using it to study the normal distribution in small sample sizes.
Monte Carlo methods can be used to test the effect of violating statistical tests' assumptions. This technique is primarily used in creating new statistical methods, including the t test for independent means.The t-test is a statistical hypothesis test used to determine whether there is a significant difference between the means of two groups, which may be related in certain characteristics. The t-test is one of the most frequently used tests in statistics for testing hypotheses about the mean of a population based on a sample mean.
Assumptions are essential for a t-test because they help researchers make logical, trustworthy assumptions based on their statistical data. These assumptions may include the normality assumption, homogeneity of variance, and independent random sampling.
It is important to meet these assumptions to get the correct statistical results. Violating these assumptions can affect the accuracy of the results.Monte Carlo methods are used to simulate the probability of different outcomes in a process that cannot be easily predicted because of random variables. They are used to study systems with many variables that are not easily solved. Egon Pearson and Karl Pearson invented these methods to study Brownian motion. "Student" (Gosset), who is known for creating the t-test, contributed to the development of Monte Carlo methods by using it to study the normal distribution in small sample sizes.
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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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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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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
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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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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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
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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what does banana + potato equal?
A Bonato
B Ponana
I'll give brainliest if you get it right :)
Answer: Bonato
Step-by-step explanation:
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
If 5 + 4 = 9, does (5+4) divided bye 3 = 9 divided by 4? Why or why not?
(5+4) divided bye 3 is not equals 9 divided by 4
Define divisionDivision is a basic arithmetic operation used to find how many times one quantity is contained within another quantity. It involves splitting a number or quantity into equal parts or groups. The result of a division is called the quotient.
In division, the number being divided is called the dividend, the number by which it is divided is called the divisor, and the result is the quotient. For example, in the division problem 10 ÷ 2 = 5, 10 is the dividend, 2 is the divisor, and 5 is the quotient.
Given 5+4=9
To prove; (5+4) divided bye 3 = 9 divided by 4
Taking LHS,
(5+4) divided bye 3
=9/3
=3
Taking RHS,
9 divided by 4
=9/4
=2.25
LHS is not equal to RHS
Hence, given statement is false.
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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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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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Help me please, I am not good at this unfortunately
Answer: Its 12 the answer.
Step-by-step explanation:
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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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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what point represents the opposite of 1 1/3
Answer:
Point A represents -1 1/3.
Point A is correct.
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°.