It is possible for an angle to have another value whose sine, cosine, or tangent is equal to the given ratio, and this value may be in a different quadrant.
A) To find the value of each inverse trigonometric ratio in degrees, we need to use a calculator or reference table to determine the angle whose sine, cosine, or tangent equals the given ratio.
The inverse sine, cosine, and tangent functions are denoted as [tex]sin^-1, cos^-1, tan^-1[/tex] respectively.
For example, if we are given sin^-1(1/2), we need to find the angle whose sine is 1/2. Using a calculator or reference table, we can determine that the angle is 30 degrees. Therefore, [tex]sin^-1(1/2) = 30degree[/tex]
Similarly, [tex]cos^-1(1/2) = 60 degrees[/tex] and [tex]tan^-1(1) = 45 degrees[/tex] .
B) To find the exact value of each inverse trigonometric ratio in radians, we need to convert the degree value to radians by multiplying by π/180. For example, if [tex]sin^-1(1/2) = 30 degrees[/tex] , we can convert to radians as follows:
[tex]sin^-1(1/2) = 30 degrees = (30\pi/180) radians = (\pi/6) radians[/tex]
Therefore,[tex]sin^-1(1/2) = \pi/6 radians[/tex]
Similarly, [tex]cos^-1(1/2) = 60 degrees = (60\pi/180) radians = (\pi/3) radians[/tex]
and [tex]tan^-1(1) = 45 degrees = (45\pi/180) radians = (\pi/4) radians.[/tex]
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�
=
5
9
(
�
−
32
)
The equation above shows how temperature
�
, measured in degrees Fahrenheit, relates to a temperature
�
, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.
What is meant by temperature?
Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.
The given equation is:
[tex]C = \frac{5}{9} (F- 32)[/tex]
where C = temperature in Celsius
F = temperature in Fahrenheit
The above equation can be rewritten as:
C = 5/9F - 160/9
Now, this is an equation of a straight line with a formula,
y = mx + c
Comparing,
m = 5/9 which is the slope of the equation.
This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.
So the option I is true.
Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.
So option II is true.
Option III is not true as is discussed above.
Therefore for the given equation of temperature, the correct option is Option D.
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Answer:
D
Step-by-step explanation:
I have nothing else to say- lol
= #14 i
PRECISION Figures A and B are similar. Figure A has a
perimeter of 72 meters and one of the side lengths is 18
meters. Figure B has a perimeter of 120 meters. Find the
missing corresponding side length.
The missing corresponding side length is
Previous
meters.
Next
The missing corresponding side length of figure B is 30 meter.
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
Two figures are said to be similar if the ratio of their corresponding sides are in the same proportion.
Figures A and B are similar. Figure A has a perimeter of 72 meters and one of the side lengths is 18 meters. Figure B has a perimeter of 120 meters. Find the missing corresponding side length.
Let x represent the missing side length. Hence:
Scale factor = figure B perimeter / figure A perimeter = 120/72
Hence:
scale factor = figure B side length / figure A side length
substituting:
120/72 = x / 18
x = 30 meter
The missing side length is 30 meter.
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HELP PLSSSSSSSSSSSSSSSSSSSSSSSSS
Answer: 165 (look at the image for the solution)
Step-by-step explanation:
Answer:
x = 655
Step-by-step explanation:
find the pressure of x and y by using radical expressions and then solving it with the theory called x ^2+ y^2 = c^2
A ladder which is 6.9 m long is placed on the ground 2.9 m from a vertical wall and then leaned over to the wall. How high up the wall can the ladder reach? Give your answer rounded to 1 DP.
Not sure but i think it's 6.3.
Pythagoras theorem
a²+b²=c²
6.9 is the hypotenuse (c)
2.9 is the base (b)
a is the altitude of the wall or the height of the wall (a)
a²+2.9²=6.9²
a= 6.3
Factor each quadratic expression. If it cannot be factored, write PRIME. Use slide division if needed. 1. 8x^2+2x-3
2. 16x^2-1
3. 36x^2+6
The factored form of 8x^2+2x-3 is (8x-3)(x+1).
The factored form of 16x^2-1 is (4x+1)(4x-1). The expression 6x^2+1 cannot be factored further,
So the factored form of 36x^2+6 is 6(6x^2+1).
Factoring is a mathematical process that involves breaking down a complex expression into simpler terms that can be multiplied together to obtain the original word. In algebra, factoring is finding the factors or the prime numbers that multiply together to give the original polynomial.
For example, the expression x^2 + 5x + 6 can be factored as (x+2)(x+3). Factoring is a useful tool in solving equations and simplifying expressions, as it allows us to manipulate the original expression in a more manageable way. In addition, factoring is used in various fields such as cryptography, signal processing, and computer science. For instance, factoring large numbers is an important problem in cryptography and is used to secure data transmission.
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By first completing the square, solve x² + 12x + 4 = 0.
Give your answers fully simplified in the form x = a +b√c, where a, b and c are integers.
Answer:
x=-2(3-2√2), -2(3+2√2)
Find the sum. Write your answer in simplest form. 3 3/4 + 1 2/4=
Answer: 5 1/4
Step-by-step explanation:
PLEASE HELP
Simplify quantity 4 x squared plus 12 x minus 16 all over quantity 2x plus 10 over quantity 6 x plus 24 over quantity x squared plus 9x plus 20 . (2 points)
Exponents, terms in parenthesis, multiplication, division, addition, and finally subtraction. You can use PEMDAS as a helpful acronym to help you remember this.
What is subtraction?One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction. Removal of items from a collection is represented by the operation of subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches. The number that the other number is deducted from is known as a minuend. Subtrahend: The amount that needs to be deducted from the minuend is known as a subtrahend. Difference: A difference is the outcome obtained by deducting a subtractor from a minimum.[tex]$\frac{4 x^2+12 x-16}{\frac{2 x+10}{\frac{6 x+24}{x^2+9 x+20}}}$[/tex]
Here we have two fractions top and bottom
[tex]$\frac{4 x^2+12 x-16}{2 x+10}$ divide by $\frac{6 x+24}{x^2+9 x+20}$[/tex]
We have division in between . we reverse the second fraction and multiply it with first fraction.
[tex]$\frac{4 x^2+12 x-16}{2 x+10} * \frac{x^2+9 x+20}{6 x+24}$[/tex]
Now we factor both numerator and denominator
[tex]$\begin{aligned} & 4 x^{\wedge} 2+12 x-16=4(x+4)(x-1) \\ & 2 x+10=2(x+5) \\ & x^{\wedge} 2+9 x+20=(x+5)(x+4) \\ & 6 x+24=6(x+4)\end{aligned}$[/tex]
Replace the factors,
[tex]$\frac{4(x+4)(x-1)}{2(x+5)} * \frac{(x+5)(x+4)}{6(x+4)}$[/tex]
We cancel out same factors at the top and bottom
So it becomes ,[tex]$\frac{(x-1)(x+4)}{3}$[/tex]
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How do you find the leading coefficients of a parabola graph?
well, if we use the vertex form of a parabola, we can pretty much see the parabolas all pretty much have a vertext at the origin, (0,0), now, let's take a look of a point they go by, Check the picture below.
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=4\\ y=4 \end{cases} \\\\\\ 4=a(4-0)^2 + 0\implies 4=16a\implies \cfrac{4}{16}=a\implies \cfrac{1}{4}=a~\hfill \boxed{y=\cfrac{1}{4}x^2}[/tex]
now let's do D
[tex]\begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=-1\\ y=-3 \end{cases} \\\\\\ -3=a(-1-0)^2+0\implies -3=a\hspace{5em}\boxed{y=-3x^2}[/tex]
The graph of the sales of a new product at a candy store, where x is time in months and y is number sold in hundreds, goes through the points (4, 2) and (6, 8). What is the rate of change.
in candies sold per month?
A 200
B 300
C 400
D 600
The rate of change in candies sold per month can be found by finding the slope of the line that goes through the two points (4, 2) and (6, 8). The slope of a line can be found by using the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the values from the two points, we have:
slope = (8 - 2) / (6 - 4) = 6 / 2 = 3
So the rate of change in candies sold per month is 3. This means that the number of candies sold is increasing by 300 (3 * 100) per month. Therefore, the answer is B) 300.
Avery has a loyalty card good for a discount at her local pharmacy. The item she wants to buy is priced at $6, before discount and tax. After the discount, and before tax, the price is $5.04. Find the percent discount.
Answer:
16% is the answer.
Answer:
16%
Step-by-step explanation:
$6 divided by $5.04 = 0.84
0.84 x 100 = 84%
100 - 84 = 16
6 - 5.04 = 0.96
0.96 divided by 6 = 0.16
0.16 x 100 = 16
B =
Round your answer to the nearest hundredth.
B
?
CT
5
4
A
C
3
Answer:answer
Step-by-step explanation:because
Solve for x questions in picture
Answer:
x = 1
Step-by-step explanation:
2(4x + 5) - 3 = 5x(2+1)
Distribute.
8x + 10 - 3 = 10x + 5x
Subtract 8x from both sides.
10 - 3 = 10x + 5x -8x
Solve
7 = 15x - 8x
7 = 7x
1 = x
A family wants to rent a car to go on vacation. Company A charges $35.50 and 9¢ per mile. Company B charges $75.50 and 14¢ per mile. How much more does Company B charge for x miles than Company A?
(Write a simplifed expression. Use integers or decimals for any numbers in your expression.)
No need for explainations, please provide the answer. I have a C in Math and I want to increase my grade! Thank you!
How To Solve:
Write the expression to represent how much Company B charges to rent a car, then do the same for Company A. Next, subtract the expression which represents how much Company A charges to rent a car from the express which represents how much Company B charges to rent a car. Subtract the two expressions by subtracting each term of the second expression. They simplify by combining like terms.
Answer:
75.50 + 14x - (35.50 + 9x) = 40 + 5x
Step-by-step explanation:
Find the lengths of the diagonals of rectangle WXYZ.
WY = 24x-8
XZ = -18x+13
The length of each diagonal is ___ units.
In rectangle WXYZ, the length of each diagonal are 40.97 units and 39.98 units.
To find the lengths of the diagonals of rectangle WXYZ, we can use the Pythagorean theorem.
The diagonal WX is the hypotenuse of right triangle WXY, so we have:
WX^2 = WY^2 + XY^2
Similarly, the diagonal YZ is the hypotenuse of right triangle XYZ, so we have:
YZ^2 = XY^2 + XZ^2
Substituting the given values for WY and XZ, and x = 2, we get:
WY = 24(2) - 8 = 40
XZ = -18(2) + 13 = -23
Plugging these values into the equations above and simplifying, we get:
WX^2 = 40^2 + XY^2
YZ^2 = XY^2 + (-23)^2
Since XY is a common side of both triangles, we can solve for it by setting the two expressions for XY^2 equal to each other:
40^2 + XY^2 = XY^2 + (-23)^2
Simplifying, we get:
40^2 + 23^2 = 2XY^2
XY^2 = (40^2 + 23^2) / 2 = 1039
Substituting this value for XY^2 in the equations for WX^2 and YZ^2, we get:
WX^2 = 40^2 + 1039 = 1679
YZ^2 = 1039 + (-23)^2 = 1598
Taking the square roots, we get:
WX = sqrt(1679) ≈ 40.97
YZ = sqrt(1598) ≈ 39.98
Therefore, the length of each diagonal of Rectangle are approximately 40.97 units and 39.98 units.
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_____The given question is incomplete, the complete question is given below:
Find the lengths of the diagonals of rectangle WXYZ.
WY = 24x-8
XZ = -18x+13
x= 2
The length of each diagonal is ___ units.
A circular flower garden surrounds a sculpture on a square base as shown.
What is an expression for the area of the flower garden?
well, let's first off get the whole area of the circular garden, and then from it subtract the area of the squarish sculpture, thus what's leftover is simply the shaded area, or just the garden minus the sculpture.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{whole~circle}{\pi (6x)^2}~~ - ~~\stackrel{square}{(4x)(6x)}}\implies 36\pi x^2-24x^2\implies {\Large \begin{array}{llll} 12x^2(3\pi -2) \end{array}}[/tex]
Graph the inequality below on the number line. a<3
The number line for a < 3 is as shown in the figure below and we use an open circle on 3 and all the numbers to the left of 3 in the number line will be the values of a.
What is a number line?
A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. The endpoints of this line go on forever.
We can see the values that inequality represents by placing them on a number line. On a number line, inequalities are represented by drawing a straight line and designating the endpoints with either an open or closed circle. An empty circle indicates that the value is not included. A closed circle indicates that the value is included.
Given the inequality a < 3.
This means that the value of a is less than three and does not include three.
Therefore we use an open circle on 3 and all the numbers to the left of 3 in the number line will be the values of a.
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Pls help me do this its kinda hard for me sense im not in a higher grade
A 6 ft. 2 in. tall man is standing next to a tree that is 20 ft. tall and casts a 14 ft. shadow. How long is the shadow of the man? Do not include units. (Answer in inches)
Answer: 168 in.
Step-by-step explanation:
Feet to inches:
14ft = 168 in.
or
12 x 14 = 168.
Answer: 4 ft 3.8 inches
Step-by-step explanation:
First I converted the measurements to inches to make it easier-
Man - 74in
Tree - 240in
Tree shadow - 168in
240/168 = 74/x
x=51.8
a two-way anova experiment has: factor a with 3 levels factor b with 7 levels 100 replications if we fit the interaction model, how many degrees of freedom for error are there?
The degrees of freedom for error in a two-way ANOVA experiment with 3 levels for factor a, 7 levels for factor b, and 100 replications is 2071.
The degrees of freedom (df) for error in a two-way ANOVA experiment depend on the sample size (n) and the number of parameters estimated in the model.
In a two-way ANOVA experiment, we are interested in modeling the response variable as a function of two factors, a and b, and their interaction. The model can be written as follows:
Yij = μ + αi + βj + (αβ)ij + εij
In general, the df for error can be calculated as follows:
df error = n - k
where k is the number of parameters estimated in the model.
In our case, we have 3 levels for factor a, 7 levels for factor b, and 100 replications. Therefore, the total sample size is n = 3 x 7 x 100 = 2100.
To estimate the parameters in the model, we need to calculate the following:
The overall mean μ
The effect of factor a, αi, for i = 1, 2, 3
The effect of factor b, βj, for j = 1, 2, ..., 7
The interaction effect between factors a and b, (αβ)ij, for i = 1, 2, 3 and j = 1, 2, ..., 7
Therefore, the total number of parameters estimated in the model is
=> k = 1 + 3 + 7 + 3 x 7 = 29.
Finally, we can calculate the df for error as:
df error = n - k = 2100 - 29 = 2071.
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look at the inequality below
-6>13+5x
which of these values of x makes the inequality true
a.-3.9
b.-1.2
c.-7/15
d.3/13
everything should be in the picture
Answer:
1.666... or 1 2/3
Step-by-step explanation:
The table needs to change number of Bags to Clementines.
And we know that they are only sold in pairs of 3 so we divide 5 by 3 to find the unit price
question 14
pls help me asap i am being timed
Answer:
164 degree is the answer
Answer:
Step-by-step explanation:
Chord PM and PN are equal
arc PM = arc PN
164=5x+4
x=32
arc PN = 5x+4 = 5(32)+4=164
In ΔOPQ, the measure of ∠Q=90°, OQ = 45, QP = 28, and PO = 53. What is the value of the cosine of ∠O to the nearest hundredth?
The value of the trigonometric relation cos ∠O = 0.849
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔPQR
Now , the measure of ∠PQR = 90° and it is a right triangle
The measure of the hypotenuse PO = 53
The measure of adjacent side OQ = 45
The measure of opposite side QP = 28
Now , from the trigonometric relations ,
cos θ = adjacent / hypotenuse
cos θ = OQ / PO
Substituting the values in the equation , we get
cos θ = 45 / 53
cos θ = 0.849
Therefore , the value of cos ∠O is 0.849
Hence , the trigonometric relation cos θ = 0.849
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Let f(x) = 3x + 5 and g(x) = 4x - 1. Find (f + g)(x), then evaluate when x = 2.
The resulting sum function if x is equivalent to 2 is 18
Solving composite functionsComposite functions are known as function of a function
Given the following functions
f(x) = 3x + 5 and;
g(x) = 4x - 1.
(f+g)(x) = f(x) + g(x)
(f+g)(x) = 3x + 5 + 4x - 1
(f+g)(x) = 7x + 4
Substitute x = 2 into the result
(f+g)(2) = 7(2) + 4
(f+g)(2) = 18
Hence the value of the sum of the function when x = 2 is 18
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I know that a number in scientific notation is written as the _______ of two factors.
power of ten
Step-by-step explanation:
A line has a slope of -2/3 and passes through the point (6, -10). What is the equation of the line?
Answer:
= 3y-2x+18=0
Step-by-step explanation:
Gradient (m) = -2/3
The equation of the line is given by the formula
[tex] = \frac{y - y1}{x - x1} = m[/tex]
Point = (6,-10)
y1 = -10
x= 6.
note// y and x were not given .
=
[tex] = \frac{y - ( - 10)}{x -6} = \frac{ - 2}{3} \\ = \frac{y + 10}{x - 6} = \frac{ - 2}{3} \\ = 3(y + 10) = - 2(x - 6) \\ = 3y + 30 = - 2x + 12 \\ = 3y = - 2x + 12 - 30 \\ = 3y = 2x - 18 \\ = 3y - 2x + 18 = 0[/tex]
therefore the equation of the line = 3y-2x+18=0
The table shows the number of condo sales per month for a new building. Select all
the equations that could represent the number of sales,
Month
1
2
3
4
Sold
12
9
6
3
A. y 12-3(x-1)
B. y+6=-3(x+3)
C. y 12 = 3(x - 1)
Answer:
Option 1 and 5 will be your answer :)
Step-by-step explanation:
Let the equation representing number of sold is,
y - y' = m(x - x')
Where m = number of condo sold per month
(x', y') is a point from the given table,
Slope of line passing through two points and =
Slope of the passing through (1, 8) and (0, 11) will be,
m = = -3
Therefore, equation of the line passing through (3, 2) and slope (-3),
y - 2 = (-3)(x - 3)
y - 2 = -3(x - 3)
Similarly, equation of the line passing through (0, 1) and slope (-3),
y - 11 = -3(x - 0)
Therefore, Option (1) and (5) will be the answer.
Name two things that you would like to have in a ratio of 5:1. Explain your reasoning
Answer:
A ratio of 5 parts water to 1 part fertilizer for watering plants. This ratio ensures that the plants receive the proper amount of nutrients without being over-fertilized, which can harm their growth.
A ratio of 5 parts rest to 1 part exercise for a healthy lifestyle. This ratio helps to maintain a healthy balance between rest and physical activity, allowing for proper recovery and growth. It also ensures that a person does not over-exercise and become exhausted, which can lead to injury or burnout.
Find the total surface area of the prism. 8.6. 7. 14.5.
The total surface area of the given prism would be = 504
How to calculate the surface area of a prism?The formula that can be used to calculate the total surface area of a square prism = 2a² + 4a L
where a = 7
L = 14.5
Area = 2(7²) + 4 ( 7× 14.5)
= 2×49 + 4( 101.5)
= 98 + 406
= 504
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