Drag each label to the correct location. Not all labels will be used.First, drag a value to represent the missing angle in the triangle. Then, complete the trigonometry equality statements.59°90 +33 57°90-8 62° sin(e) cos(0)Bsin(280) = cos(cos(33°) = sin(cos(31°) = sin(cos(908) =90 +0
Answers
The triangle's missing angle, according to the provided assertion, is (a) 62° (b) 57° (c) 59° (d) sin0
Trigonometry is what degree of mathematics?Trigonometry is typically included in math courses for sophomores or juniors. Trigonometry is frequently included as a unit or term emphasis in other math classes in adding to being given as a separate course.
(a) sin(28°) = cos(90° - 28°) = cos(62°)
62° is right answer.
(b) cos (33°) = sin (90° – 33°) = sin (57°)
57° is correct answer.
(c) cos (31°) = sin(90° - 31°) = sin (59°)
59° is correct answer
(d) cos(90° - 0) = sin0
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Related Questions
Simplify (3x2+9x-1)+(-5x2+6x-10)
Answers
= 3x2 + 9x - 1 + -5x2 + 6x - 10
Now we can rearrange the terms so like terms are together.
= 3x2 - 5x2 + 9x + 6x - 1 - 10
Combine like terms. Just like 3 apples - 5 apples = -2 apples ....so does 3x2 - 5x2 = -2x2
= -2x2 + 15x - 11
HELP ASAP QUESTION 2!
Answers
The area of the circular section is equal to 3π square meters. (Correct choice: C)
How to find the area of a circular section
Herein we find the case of a circular section whose area must be found by the following formula:
A = (θ / 360) · π · R²
Where:
θ - Central angle, in degrees.R - Radius, in meters.A - Area, in square meters.If we know that θ = 270° and R = 2 m, then the area of the circular section is:
A = (270 / 360) · π · (2 m)²
A = (3π / 4) · (2 m)²
A = 3π m²
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write an exponential function that has a y-intercept of -4 and passes through the points (1, -1.6) and (2, -0.64)
Answers
The function can be used to model the exponential growth or decay that occurs in real-life situations that fit this particular pattern is y = 4(-0.4)ˣ + -4
An exponential function is a mathematical function that has the form
=> y = abˣ,
where a is a constant and b is the base of the exponential.
To start, we will use the first point, (1, -1.6), to write an equation that relates x and y. Let's call the constant a in our exponential function "k". Using the point (1, -1.6), we can write the equation:
=> -1.6 = k * b¹
Next, we will use the second point, (2, -0.64), to write another equation that relates x and y. Using the point (2, -0.64), we can write the equation:
=> -0.64 = k * b²
Now that we have two equations, we can solve for the two unknowns, k and b, by dividing the two equations:
=> (-0.64) / (-1.6) = k * b² / k * b¹
b = (0.64 / -1.6)¹
b = -0.4
With b determined, we can substitute it back into one of the equations and solve for k:
=> -1.6 = k * (-0.4)¹
=> k = -1.6 / (-0.4)
=> k = 4
So our exponential function that passes through the points (1, -1.6) and (2, -0.64) and has a y-intercept of -4 is:
y = 4 * (-0.4)ˣ + -4
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What is the inverse of a function?
A function for which the domain remains the same, and reciprocal values of the range are used
A function for which the values or the domain and the range are interchanged
A function for which the range remains the same, and reciprocal values of the domain are used
Answers
The requried, inverse of a function is a function for which the values or the domain and the range are interchanged. Option C is correct.
What is an inverse function?The inverse of a function is a new function that results from interchanging the input (domain) and output (range) of the original function.
Here,
if f(x) is a function, its inverse function is denoted by f⁻¹(x), and it is defined such that f⁻¹(y) = x, where y = f(x) is the original function.
For example, if f(x) = 2x + 3, the inverse function f⁻¹(x) is found by interchanging x and y, and solving for y:
x = 2y + 3
2y = x - 3
y = (x - 3)/2
Therefore, f⁻¹(x) = (x - 3)/2, and it is the inverse of the original function f(x). Note that the domain and range of the inverse function are interchanged with respect to the original function.
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find p if (p, 2p+1) is solution of 11x-2y=5
Answers
Answer:
p = 1
Step-by-step explanation:
since (p, 2p + 1) is a solution then it makes the equation true.
substitute x = p and y = 2p + 1 into the equation and solve for p
11p - 2(2p + 1) = 5 ← distribute parenthesis and simplify left side
11p - 4p - 2 = 5
7p - 2 = 5 ( add 2 to both sides )
7p = 7 ( divide both sides by 7 )
p = 1
Please help me out! Just put these in order from the picture below.
Answers
Answer:
1) {2,0,-2}
2) {1,-3,1}
3) {1,3,5}
4) {0,1,2}
Why is [tex]0,3^{-1}[/tex] = [tex]\frac{10}{3}[/tex] ?
Answers
By the inverse of a number, 0.3⁻¹ = 10/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 0.3⁻¹ = 10/3
Now, We can simplify as;
⇒ 0.3⁻¹
⇒ (3/10)⁻¹
⇒ 10/3
Thus, By the inverse of a number, 0.3⁻¹ = 10/3
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brian is splitting 4 quarts of ice cream with members of the team. If the ice cream is split evenly, how many cups will each person get
Answers
Each person will get 1 [tex]\frac{7}{9}[/tex] cups of ice cream.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that, Brian is splitting 4 quarts of ice cream with members of the team.
Assume the number of members of the team = 9
We have to find how many cups each member gets.
First we have to convert the measurement quarts to cups.
1 quart = 2 pints
1 pint = 2 cups
1 quart = 2 × 2 cups = 4 cups
We have 4 quarts of ice cream.
4 quarts = 4 × 4 = 16 cups
Number of cups each member gets = 16/9 cups = 1 [tex]\frac{7}{9}[/tex] cups
Hence there will be 1 [tex]\frac{7}{9}[/tex] cups for each member.
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Zachary purchased a computer for $1,300 on a payment plan. Two months after he purchased the computer, his balance was $1,090. Seven months after he purchased the computer, his balance was $565. What is an equation that models the balance y after x months?
The equation ______ models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)
Answers
Answer:
[tex]y=-105x+1300[/tex]
Step-by-step explanation:
Define the variables:
Let x be the number of months after Zachary purchased a computer.Let y be the balance of the payment plan (in dollars).Given information:
Purchase price of the computer = $1,300Balance = $1,090 after 2 months.Balance = $565 after 7 months.Therefore:
x = 0, y = 1300x = 2, y = 1090x = 7, y = 565[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Determine if the equation is linear by calculating the slope between each pair of (x, y) points:
[tex]\implies \text{Slope}\;(m)=\dfrac{565-1090}{7-2}=-105[/tex]
[tex]\implies \text{Slope}\;(m)=\dfrac{1090-1300}{2-0}=-105[/tex]
As the slope is the same, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The initial purchase price of the computer was $1,300. So when x = 0, y = 1300. Therefore, the y-intercept is 1300.
We have already calculated the slope as -105.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:
[tex]y=-105x+1300[/tex]
Mike buys 3 oranges and 1 lemon at the
farmers market. What fraction of his
purchase were oranges?
Answers
Mike buys 3 oranges and 1 lemon at the
farmers market. What fraction of his
purchase were oranges?
answer :
3/4
Answer: 3/4
Step-by-step explanation:
there are a total of four purchases and three of them were purchases we can represent this with the fraction 3/4
Prove that the value of the expression (3/5x^2-0.4cy-1.5y+1)-(y^2-2/5xy+0.6x^2) does not depend on x
Answers
Therefore, we have proved that the value of the expression
(3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.
Expression: What is it?In mathematics, addition, multiplication, and division are necessary. They result in the following when combined: An equation, some data, and a mathematical function Values, parameters, and mathematical operations like additions, subtractions, multiplications, and divisions can all be found in a declaration of fact. Different phrases and words can be compared and evaluated.
Here,
To prove that the value of the expression doesn't depend on x, we need to show that the x-term disappears when we simplify the expression.
Starting with:
(3/5x² - 0.4cy - 1.5y + 1) - (y² - 2/5xy + 0.6x²)
Distributing the negative sign in the second set of parentheses:
3/5x² - 0.4cy - 1.5y + 1 - y² + 2/5xy - 0.6x²
Rearranging the terms by collecting like terms, we get:
(3/5 - 0.6)x² + (2/5y - 0.4c)y - y²- 1.5y + 1
Simplifying further, we get:
(-0.1)x² + (0.4y - 0.4c)y - (y² + 1.5y - 1)
Notice that there is no x-term in the final expression, which means that the value of the expression doesn't depend on x.
Therefore, we have proved that the value of the expression (3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.
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Lourdes can buy 3-packs of paper for $10.50, or she can buy 4-packs of paper for $13.50. She wants to buy 12 packs of paper. How much more will she spend if she buys only 3-packs of paper
Answers
Lourdes will spend an amount of $1.50 more if she buys only 3-packs of paper.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
If Lourdes buys only 3-packs of paper, she will need to buy 12 / 3 = 4 sets of paper.
At $10.50 per set, this will cost her 4 x $10.50 = $42.
If Lourdes buys only 4-packs of paper, she will need to buy 12 / 4 = 3 sets of paper.
At $13.50 per set, this will cost her 3 x $13.50 = $40.50.
So, Lourdes will spend $42 - $40.50 = $1.50 more if she buys only 3-packs of paper.
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A business development manager discusses international steel production and economic development at a conference. He passes out this graphic and asks for comments. Which comment about the data is most accurate? Japan’s production has increased and shows no signs of decreasing. China’s steel production is increasing while its major competitors’ production is declining. By 2009, China’s tons of steel produced per US million ($) GDP was 50, about 10 tons less than Japan’s all-time high. At 50 tons of steel produced per US million ($) GDP, China has the highest steel production of all producers shown as of 2009.
Answers
The most accurate comment about the graph data is: "China's steel production is increasing while its major competitors' production is declining."
A graph is what?Academics are using graphs to logically chart or graphically depict events or quantities. A graph point is a common way to depict how different things interact. The non-linear storage structure known as a graph is made up of nodes, also referred to as vertices, and lines. Glue ought to be used to connect the edges, also known as nodes , respectively. (4.5).
Here,
The most accurate comment about the data is: "China's steel production is increasing while its major competitors' production is declining."
This is because the graph shows that China's steel production has been steadily increasing since the early 2000s, while the steel production of other major producers such as Japan, the United States, and Germany has been declining or stagnant. This trend is particularly evident after the global financial crisis of 2008-2009.
While it is true that Japan's steel production has increased and shows no signs of decreasing, this comment does not address the overall trend of declining steel production among major producers.
The other two comments are not accurate. The statement "By 2009, China’s tons of steel produced per US million ($) GDP was 50, about 10 tons less than Japan’s all-time high" is not supported by the graph, as there is no information about tons of steel produced per US million ($) GDP on the graph.
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Determine the domain for the interval of decrease.
d
Distance (km)
60
50
40
30
20
10
8 9 10 11 12 1 2 3 4
am
noon
p.m.
Time of the day
A2≤x≤5
B8≤x≤ 10
3≤x≤5
Answers
Answer:
The domain for the interval of decrease is 3 ≤ x ≤ 5
Determine when the function is positive, negative, increasing, or decreasing: y = -9ˣ
Answers
Solve the formula for the indicated variable.
Z=m+mwg for m
m=
(Simplify your answer.)
Answers
The value for variable m in equation Z = m + mwg is m = Z - mwg.
What are variables?
The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.
The equation is given as -
Z = m + mwg
To get the value for variable m, subtract mwg from Z and take it to left-hand side.
Z - mwg = m
Reverse the equation and get it in right form -
The equation obtained is -
m = Z - mwg
Therefore, the value is m = Z - mwg .
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You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $85.00, two for $83.00 each, and in general the group rate per room is found by taking $2 off the base of $85 for each extra room rented.
(c) Find a formula for a function R = R(n) that gives the total revenue from renting rooms to a convention host.
(d) Use functional notation to show the total revenue from renting a block of 9 rooms to a group. Calculate the value.
Answers
The formula for a function R = R(n) is R(n) = n(85 - 2n) and the total revenue for 9 room is $603
How to determine the formula for a function R = R(n)From the question, we have the following parameters that can be used in our computation:
Base fee = $85.00
Rate = $2 off
Using the above as a guide, we have the following:
R(n) = n(85 - 2n)
Where n is the number of rooms
The value of block of 9 roomsThis means that
n = 9
So, the notation is
R(9)
The value is
R(9) = 9 *(85 - 2 * 9)\
R(9) = 603
Hence, the value is $603
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suppose 5x^{2} +5x+xy=4 and y(4)=-24. Find y^'(4) by implicit differentiation.
Your answer:
Answers
if 5x² +5x+xy=4 then the value of y'(4) is -21/4
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given expression is 5x² +5x+xy=4
Five times of x square plus five times of x plus x times of y equal to four.
Differentiate with respect to x.
10x+5+y(x)+xy'(x)
if x=4
10(4)+5+y(4)+4y'(4)=0
40+5-24+4y'(4)=0
21+4y'(4)=0
4y'(4)=-21
Divide both sides by 4
y'(4)=-21/4
Hence, if 5x² +5x+xy=4 then the value of y'(4) is -21/4
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Andrew wins 4 fencing bouts for every 3 that he loses. If he had 35 bouts during the last year, how many bouts did he win?
Answers
The number of bouts that Andrew won during the last would be = 20 bouts.
How to calculate the number of bouts won?The number of fencing bouts that Andrew won = 4
The number of bouts he losses every 4 wins = 3 bouts
The total number of bouts he is having this year = 35 bouts.
The number of bouts he won amongst the number that he lost would be calculated as;
= 4+3 = 7
= 4/7 × 35/1
= 4× 5 = 20 bouts.
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Find the principal value of Arctan (-1.44) to the nearest minute.
Answers
Answer: To find the principal value of arctan(-1.44) to the nearest minute, we first need to find the value of arctan(-1.44) in radians.
We can use the arctan function in a mathematical software or calculator to find the result. The value of arctan(-1.44) in radians is approximately -0.8623.
Next, we convert the result from radians to minutes, by multiplying the radians by 180/π and then multiplying the result by 60.
-0.8623 * 180/π * 60 = -50.47 minutes
So the principal value of arctan(-1.44) to the nearest minute is approximately -50 minutes.
Step-by-step explanation:
Caleb has 12 grams of tea. He bought 5/4 of that amount for his mom. How many grams did Cameron get his mom?
Answers
He bought 12*(5/4) = 12*1.25 = 15 grams of rice.
Answer: Caleb bought 15 grams for his mom
Step-by-step explanation:
5/4 is equal to 1.25, so Caleb bought 1.25 x 12 grams.
1.25 x 12 = 15 grams.
find the dilated coordinates with the scale factor of 1/5
Answers
The dilated coordinates:
D(-7, 0) → D' (-7/5, 0)
E(-7, -5) → E' (-7/5, -1)
F(-2, -5) → F' (-2/5, -1)
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
Given:
Coordinates: D(-7, 0), E(-7, -5), F(-2, -5).
The shape is dilated by the scale factor of 1/5.
The dilation rule:
D(-7, 0) → D' (-7/5, 0)
E(-7, -5) → E' (-7/5, -1)
F(-2, -5) → F' (-2/5, -1)
Hence, the dilated coordinates are given above.
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The complete question:
Find the dilated coordinates with the scale factor of 1/5,
D(-7, 0), E(-7, -5), F(-2, -5).
HELP FAST WILL GIVE 60 POINTS For THE RIGHT ANSWER
Answers
A repeating decimal like 0.2222222.... is a rational number and can be written as the fraction 2/9.
A stopping decimal like 0.22 is a rational number and can be written as the fraction 22/100.
A non-stopping and non-repeating decimal like 0.1234567891011... or 0.121121112... is an irrational number that can be written as the fraction 1514013912/5000000
The square root of a perfect square is a rational number and also a whole number.
The square root of a prime number is an irrational number.
What are rational and irrational numbers?
The definition of a rational number is one that may be stated as a fraction or as a portion of a whole number. For example -7, 2/3, 3.75 Numbers that cannot be stated as a fraction or ratio of two integers are referred to be irrational numbers. There is no limit to how one might convey them. For example √2, √3, e
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Mark and his three friends ate dinner out last night. Their bill totaled $52.35, the tax was 8.5% and they left their server an 18% tip. If they split the bill evenly, how much did each person pay? Round to the nearest cent.
Answers
Answer:
$56.84
Step-by-step explanation:
52.35 + 8.5% + 18% ÷ 4 = $56.84475
Let a and b be a pair of vectors, and let θ be the angle between them. Show that ||a ×b||= ||a||||b||sin θ|.
You are not allowed to use the cross product formula directly!
Answers
Let's consider two vectors a and b in three-dimensional space and let O be the angle between them. Let's define a unit vector n perpendicular to both a and b and pointing in the direction determined by the right-hand rule.
By definition, the magnitude of the cross product a × b is given by ||a × b|| = ||a|| ||b|| sin(O). We can demonstrate this by using the definition of the dot product and the Pythagorean theorem:
a × b = ||a|| ||b|| n sin(O)
a . (a × b) = ||a|| ||b|| (a . n) sin(O) = 0
||a × b||^2 = ||a||^2 ||b||^2 sin^2(O)
Therefore, we can conclude that ||a × b|| = ||a|| ||b|| sin(O).
please help me with this problem
Answers
The images of the functions are listed below:
Case 1: f(x) = √(- x) (Correct choice: A)
Case 2: f(x) = √(x - 4) (Correct choice: D)
Case 3: f(x) = √x - 3 (Correct choice: A)
Case 4: f(x) = √(x - 4) - 4 (Correct choice: A)
How to use rigid transformations on functions
In this problem we find four cases of functions that must be transformed by rigid transformations. Rigid transformations are transformations applied on functions such that its features are not altered. We should apply, if possible, the following rigid transformations:
Reflection across the y-axis
f(x) → f(- x)
Translation to the right
f(x) → f(x - k), where k > 0
Translation downward
f(x) → f(x) - k, where k > 0
Now we proceed to determine the image of each function:
Case 1
f(x) = √x
Reflection across the y-axis
f(x) = √(- x)
Case 2
Translation 4 units right
f(x) = √(x - 4)
Case 3
Translation 3 units down
f(x) = √x - 3
Case 4
Translation 4 units right and 4 units down
f(x) = √(x - 4) - 4
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how to get the volume of a rectangular pyramid
Answers
Answer:
length x width x height divided by 3
What would 73,412 be rounded to the nearest thousand
Answers
A salesperson earned a commission of
$806.59
last week on gross sales of
$5880
. If returns and allowances were 11.5% of gross sales, what is his rate of commission based on net sales?
Answers
Using percentages we know that the rate of commission of the salesperson based on the net sales is 15.5%.
What are percentages?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and sometimes "pc" is also used, the percent symbol, "%," is frequently used to indicate it.
A % is a number without boundaries and without a standard measurement.
So, calculate as follows:
5880/100 * 11.5 = 676.2
Now,
5880 - 676.2 = 5,203.8
Now, calculate the percentage as follows:
806.59/5,203.8 * 100
15.5%
Therefore, using percentages we know that the rate of commission of the salesperson based on the net sales is 15.5%.
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Kelly can run 1/2 mile in 3 minutes. How far does
Kelly run in 1 minute if he runs at the same pace the
entire time?
Answers
Kelly can run 1/2 mile in 3 minutes. 1/6 mile Kelly run in 1 minute if he runs at the same pace the entire time.
What makes anything a mile?The word "mile" is derived from the Latin "mille passus," which means "one thousand paces." The English Parliament established the Mile at eight furlongs (one furlong is 660 feet) in 1592. A mile is a unit of measurement that is standardised as exactly 1609.344 metres by the International agreement in 1959. A mile is exactly equivalent to 5280 feet, or 1760 yards.
Kelly can run 1/2 mile in 3 minutes so the ratio is 1/2 mile per 3 minutes
= [tex]\frac{\frac{1}{2} }{3}[/tex]
For transforming 3 to 1 we need to divide by 3 because we have to keep the ratio value, we have to divide also the numerator by 3 :
= [tex]\frac{\frac{1}{2} }{3} \times \frac{\frac{1}{3} }{\frac{1}{3}}[/tex]
[tex]= \frac{\frac{1}{2} \times \frac{1}{3} }{3 \times \frac{1}{3} }[/tex]
= 1/6 / 1
= 1/6
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