Finding the equivalent angle of [tex]\theta[/tex], the correct statements are given as follows:
The Measure of the reference angle is 45.[tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].[tex]\tan{\theta} = 1[/tex][tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, the given angle is as follows:
[tex]\theta = \frac{5\pi}{4}[/tex]
It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:
[tex]\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}[/tex]
The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:
The Measure of the reference angle is 45.[tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].[tex]\tan{\theta} = 1[/tex][tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].More can be learned about equivalent angles at https://brainly.com/question/24787111
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Answer:
The measure of the reference angle is 45 degrees
tan(theta) = 1
Step-by-step explanation:
Lamar is taking a stunt man training course. he scored a 99 on his first test, but he only scored an 85 on his second test. what is the lowest score that lamar can make on his third and final test in order to have an overal average of 90?
Answer:
86.
Step-by-step explanation:
His total score is 99 + 85 + x where x is score on third test,
99 + 85 + x = 3 *90 (as his average must be 90, so:
184 + x = 270
x = 270 - 184
= 86.
Answer:
86
Step-by-step explanation:
Let x be the required score for Lamar's third test in order to get an average of 90 or higher.
Start with the initial equation:
[tex]\frac{99+85+x}{3}\geq 90[/tex]
Simplify the numerator in the fraction:
[tex]\frac{184+x}{3}\geq90[/tex]
Multiply both sides by 3 to cancel out division on left side of equation:
[tex]184+x\geq 270[/tex]
Subtract 184 from both sides to isolate the x variable:
[tex]x\geq86[/tex]
Leaving us with x must be greater than or equal to 86.
If f(x) = 5x, what is f¹(x)?
Answer:
C
Step-by-step explanation:
For any function x, inverse will = 1/x. so the answer is C
Answer:
C. [tex]f^{-1}(x) = \frac{1}{5} x[/tex]
Step-by-step explanation:
The question is asking to find [tex]f^{-1}(x)[/tex] of f(x)=5x, which is the same as finding the inverse of the function.
To find the inverse of a function, we first need to replace f(x) with y.
The function will therefore be:
y = 5x
Now, we solve the equation for x.
So divide both sides by 5.
y = 5x
÷5 ÷5
_________
[tex]\frac{y}{5} = x[/tex]
Now, we replace x with y and y with x.
[tex]\frac{x}{5} = y[/tex]
Finally, we replace y with [tex]f^{-1}(x)[/tex].
[tex]\frac{x}{5} = f^{-1}(x)[/tex]
We can re-write this though, to make it easier to read.
We can write [tex]f^{-1}(x)[/tex] first, and rewrite [tex]\frac{x}{5}[/tex] as [tex]\frac{1}{5}x[/tex].
[tex]f^{-1}(x) = \frac{1}{5} x[/tex]
Therefore, the answer is C.
Indicate the equation of the line meeting the given conditions. Put the equation in standard form.
Containing E(4, 3) and A(6, 1)
Answer:
x + y = 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = E (4, 3 ) and (x₂, y₂ ) = A (6, 1 )
m = [tex]\frac{1-3}{6-4}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , then
y = - x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, 3 )
3 = - 4 + c ⇒ c = 3 + 4 = 7
y = - x + 7 ← equation in slope- intercept form ( add x to both sides )
x + y = 7 ← equation in standard form
bennett was visiting five cities that lie on a coordinate grid at A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1). What is the midpoint between A and E
The midpoint between A and E is (0,1)
How to determine the midpoint between A and E?The coordinates of the cities are given as:
A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).
From the above, we have:
A = (-2,3)
E = (2,-1)
The midpoint between A and E is calculated using
Midpoint = 1/2 * (x1 + x2, y1 + y2)
Substitute the known values in the above equation
Midpoint = 1/2 * (-2 + 2, 3 - 1)
This gives
Midpoint = 1/2 * (0, 2)
Evaluate the product
Midpoint = (0, 1)
Hence, the midpoint between A and E is (0,1)
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Which of the
following satisfies
this graph?
Answer:
C
Step-by-step explanation:
y is greater or equal to 0
x is also greater or equal to 0
you can see that only one answer choice can be the answer
the line is x-y = 2
the upper side is x-y <= 2
proves that c is the answer
x-y ≤ 2
y ≥ 0
x ≥ 0 satisfies this graph. Thus option C is correct.
What is a graph?A schematic or visual presentation that organizes the depiction of data or quantities is known as a graph. The relationships connecting two or more objects are frequently represented by the spots on a graph. They are employed to arrange data in order to highlight correlations and patterns. This data is presented as a pattern on a graph.
When y is bigger than 0 and x is also.
The equation is 2x-y.
x-y ≤ 2 on the upper side of the graph is represented in this same way.
x-y ≤ 2; y ≥ 0 and x ≥ 0 will be the correct represented points in the graph. Therefore, option C is the correct option.
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If a girl lifts a load of 60N to a height of 3m, find work.
Let the mass of the object exists at 60 N and the height exists at 3m then work
exists in 1764.
What is work?
The work done by a force exists determined to be the product of a component of the force in the direction of the displacement and the magnitude of this displacement.
Work can be estimated by multiplying Force and Distance in the direction of force as follows.
W = F × d. Unit.
Given data:
m = mass of the object = 60 N
h = height = 3 m
Work = Fh = mgh
g = gravity = 9.8 m/s²
work = Fh = mgh
[tex]= 60*3*9.8[/tex]
= 1764
Therefore, the work exists in 1764.
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please help I don't understand
Answer:
Each number is increasing by [tex]\frac{1}{4}[/tex]. The next number would be 1 [tex]\frac{1}{4}[/tex] or [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
I am not sure what the question is. I am wondering if they are asking how is the list growing or what would be the next number.
Each number is increasing by 1/4
[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] To change [tex]\frac{1}{2}[/tex] to [tex]\frac{2}{4}[/tex] you multiple the top and the bottom of [tex]\frac{1}{2}[/tex] by2 to get [tex]\frac{2}{4}[/tex]
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{4}[/tex] or 1
If tan A 3/4 find the value of: sin2A
Answer:
24/25
Step-by-step explanation:
use tan^-1 to find the angle
tan^-1(3/4)=36.86989765°
A =36.86989765°
2A= 2×36.86989765
=73.73979529°
sin2A>>>>sin(73.73979529°)
=24/25 or 0.96
Answer:
sin2A = [tex]\frac{24}{25}[/tex]
Step-by-step explanation:
using the identity
sin2A = 2sinAcosA
given
tan2A = [tex]\frac{3}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
then this is a 3- 4- 5 right triangle with
hypotenuse = 5, opposite = 3 , adjacent = 4 , then
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex] and cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]
Then
sin2A = 2 × [tex]\frac{3}{5}[/tex] × [tex]\frac{4}{5}[/tex] = [tex]\frac{2(3)(4)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]
Part III: Is x+1 a factor of the polynomial 12x+5x+3x²-5? Explain your answer. (2 points)
Answer:
no
Step-by-step explanation:
So you can express a polynomial in factored form as such: [tex]a(x)*b(x)*c(x)...[/tex] where a(x), b(x), and c(x), each represent a polynomial which are each factors of the equation. It's important to note that each factor is being multiplied by each other, meaning if any of the factors output 0, the entire thing is 0, no matter the value of the other factors, since 0 * some value = 0. For this reason, if we plug in the value that makes (x+1) 0, into the polynomial, and the polynomials value is 0, that means it is a factor.
x + 1 = 0
x = -1
The value that makes the factor 0, is -1. This means that if it is a factor of the polynomial, then plugging in -1 as x into the polynomial should make the value 0.
Original Equation:
[tex]12x+5x+3x^2-5[/tex]
Plug in -1 as x
[tex]12(-1)+5(-1)+3(-1)^2-5[/tex]
Multiply values
[tex]-12-5+3(1)-5[/tex]
Simplify:
[tex]-17+3-5\\-14-5\\-19[/tex]
Since the value of the polynomial is not 0, this means x+1 is not a factor
You can also solve this use the Remainder Theorem and Factor Theorem which essentially uses the same logic
Remainder Theorem:
If a polynomial P(x) is divided by x-a, the remainder is P(a)
Using the remainder theorem, if x-a is indeed a factor, then that means the remainder should be 0, just as 11 is a factor of 77, and 77/11 has a remainder of 0. This is what the factor theorem essentially states
Factor Theorem:
The expression "x-a" is a factor of P(x) if and only if P(a) = 0
How many different integers are there such that the square of the square of the integer is a two-digit integer
The number of different integers there are for the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.
How many integers satisfy the given condition?According to the task content, the square of the square of such integers must be a two-digit number, that is, less than or equal to 99.
The numbers in discuss, x must satisfy;
x⁴ < 99.
The numbers in this regard are therefore, -2, -3, 2, 3.
Ultimately, the integers which satisfy the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.
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The function f(x) = 2x 1 represents the altitude of a plane, where x is the time in minutes. the function g(x) = x2 − 10 represents the time in minutes, where x is the height in thousands of feet of the plane. what is the value of f[g(10)]? 271 181 90 21
To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then [tex]$g(x) =x^2-10[/tex] exists g(10) = 90.
The value of g(10), we have to substitute in every x of f(x), the
[tex]f(x) = 2x + 1[/tex] exists f(90) = 181
Therefore, the value of f[g(10)] exists 181.
How to estimate the value of f[g(10)]?
To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then
[tex]$g(x) =x^2-10[/tex]
substitute the value of x = 10
[tex]$g(10) = (10)^2-10[/tex]
simplifying the equation, we get
g(10) = 100 - 10
g(10) = 90
We have the value of g(10), we have to substitute in every x of f(x), then
f(x) = 2x + 1
substitute the value of x = 90
f(90) = 2(90) + 1
simplifying the equation, we get
f(90) = 180 + 1
f(90) = 181
The value of f[g(10)] exists 181.
Therefore, the correct answer is option b) 181.
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Can someone help me with this? I cannot figure it out
Answer:
Step-by-step explanation:
To graph by hand I would first convert both equations into y=mx+b.
We start with:
[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]
Solve for y for 2x-2y=4
[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]
Solve for y for x+2y=8
[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]
Giving the new but equal system of equations:
[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]
From this point on you can graph the two functions to find where the two lines intersect, thats your solution.
I've gone ahead and graphed it on desmos for you
[tex]\frac{12}{20}[/tex] = ______% = ______ hundredths
The percentage form of given fraction is 60% and the hundredths form is 0.60
According to the statement
we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.
So, For this purpose,
The given fraction is 12/20.
Then the definition of the percentage is that
The Percentage, a relative value indicating hundredth parts of any quantity.
so, the percentage of given fraction is :
Percentage fraction = 12/20 * 100
After solving it, The percentage fraction will become:
Percentage fraction = 60%
and Now convert into the hundredths form then
In the hundredths form it will become
from 60% to 0.60.
So, The percentage form of given fraction is 60% and the hundredths form is 0.60
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what is 3x+4=8 please answer quick
Hello,
[tex]3x + 4 = 8[/tex]
[tex]3x + 4 - 4 = 8 - 4[/tex]
[tex]3x = 4[/tex]
[tex] \frac{3x}{3 } = \frac{4}{3} [/tex]
[tex]x = \frac{4}{3} [/tex]
What is the point-slope form of a line with slope 4/5 that contains the point (-2,1)?
Answer: [tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]
Step-by-step explanation:
Given the requirement for function
Point-slope form : y - y₁ = m (x - x₁)
m = slope(x₁, y₁) = Any points on the lineGiven information
m = 4/5
Point = (x₁, y₁) = (-2, 1)
Substitute values into the function form
y - y₁ = m (x - x₁)
y - (1) = (4/5) (x - (-2))
Simplify the function
[tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find the total surface area of the square pyramid in the figure.
each base side is 8 yds, vertex to centr of base is 3 yds, vertex to center of one side of base is 5 yds. 9Cannot send picture, only link)
The total surface area of the square pyramid (SA) = 144 yd².
What is a Square Pyramid?A square pyramid is a solid shape that has a square base and four rectangular lateral faces.
How to Find the Total Surface Area of a Square Pyramid?The total surface area of a square pyramid is the sum of the area of its square base and four rectangular lateral faces. To find the total surface area, the following formula is used:
Total surface area of a square pyramid (SA) = A + 1/2(Pl), where:
Area of base = APerimeter of base = PSlant height of pyramid = lGiven the following:
Area of base (A) = 8² = 64 yd²
Perimeter of base (P) = 4(8) = 32 yds
Slant height of pyramid (l) = 5 yds
Plug in the values
Total surface area of a square pyramid (SA) = 64 + 1/2(32)(5)
Total surface area of a square pyramid (SA) = 64 + 80
Total surface area of a square pyramid (SA) = 144 yd².
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Draw an area model to represent 4x^2+12x+9 = (2x+3)^2. Label the length and width of the whole square and label each individual small square and rectangle.
See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2
What are area models?Area models are shapes used to model or illustrate products, multiplications, divisions and quotients
How to draw the area model?The equation is given as:
4x^2+12x+9 = (2x+3)^2
Express (2x+3)^2 as the product of (2x+3) and (2x+3)
4x^2+12x+9 = (2x+3) * (2x+3)
The above means that the area model is a square.
So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9
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If the length of the minor axis of an ellipse is 6 units and the length of the major axis is 10 units, how far from the center are the foci located? a. 4 units b. 2 units c. units d. units e. 5 units
The distance from the center to where the foci are located exists 8 units.
How to determine the distance from the center?The formula associated with the focus of an ellipse exists given as;
c² = a² − b²
Where c exists the distance from the focus to the center.
a exists the distance from the center to a vertex,
the major axis exists 10 units.
b exists the distance from the center to a co-vertex, the minor axis exists 6 units
c² = a² − b²
c² = 10² - 6²
c² = 100 - 36
c² = 64
[tex]c = \sqrt{64}[/tex]
c = 8
Therefore, the distance from the center to where the foci are located exists 8 units.
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A satellite orbits the earth at a height of 343 kilometers. if the satellite makes 8 revolutions around the earth, how many kilometers does it travel? (earth's diameter is 6371 kilometers.) use 3.14 as the approximate value of pi.
The satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
How many kilometers does the satellite make 8 revolutions around the earth?
The orbital velocity of the satellite exists independent of its mass. The radius of the orbit exists as the only variable. If the satellite orbits near the planet at such a low height, its orbital speed must be extremely fast. If the orbital speed exists less than the required value, the satellite will be drawn to the earth's surface by gravity.
The satellite rotates around the earth to form a circle,
diameter of circle = Diameter of earth + 2(Height)
d = 6714 + 2(343)
d = 6714+ 686
d = 7057
Perimeter = πd
Perimeter = 3.14 (7057)
Perimeter = 22158.98
Total Revolution exists 8
Therefore, 8πd = 8(22158.98)
= 177272 kilometers.
Therefore, the satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
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There are 12 marbles in a box. 8 are purple, and 4 are green. What is the probability of picking a purple marble and then a green marble, without replacing the first marble?
Answer: 8/33
Step-by-step explanation:
So the probability of picking a purple marble is 8/12, after that there are 11 marbles left in the box
Now the probability of picking a green marble without placing the first marble back is 4/11
So the probability of doing both is 8/12 x 4/11 = 8/33
Diego measured the length of a pencil to be 22 cm. the actual length of the pencil is 23 cm. which of these is closest to the percent error for diego’s measurement?
An error exists in the distinction between the exact length of an object and its measured length.
The closest to the percent error for Diego's measurement exists at 4.3%.
What is an error?An error exists in the distinction between the exact length of an object and its measured length.
Error = Actual length - Measured length
= 23cm - 22cm
= 1 cm
Percent error = Error/ Actual length × 100
= 1 /23 × 10
= 4.35%
Therefore, the closest to the percent error for Diego's measurement exists at 4.3%.
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Sea World's dining card offers a choice of a three main entrees, a choice from five sides and a choice from four desserts. How many different meals can be selected?
PLEASE HELP IMMEDIATELY
Use the function f(x) to answer the questions:
f(x) = 5x2 + 2x − 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
For the given function f(x) = 5x² + 2x - 3,
Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).
Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).
Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.
How to calculate x-intercepts of a function?The x-intercepts of a function or equation are obtained at y = 0.
Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.
How to calculate the coordinates of the vertex of a function?To calculate the x coordinate of vertex(h, k), use the formula mentioned below:
h = -b/2a
When the function is in the form of ax² + bx + c.
Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.
Thus, the required coordinates of the vertex are obtained as (h, k).
Calculation:It is given that,
f(x) = 5x² + 2x - 3
Part A: Finding the x-intercepts:
Substituting y = 0 i.e., f(x) = 0;
⇒ 5x² + 2x - 3 = 0
On simplifying/factorizing,
⇒ 5x² + 5x - 3x - 3 = 0
⇒ 5x(x + 1) - 3(x +1) = 0
⇒ (5x - 3)(x + 1) =0
∴ x = 3/5 or x = -1
Thus, the x-intercepts are (3/5, 0) and (-1, 0).
Part B: Finding the vertex of the given function:
We have h = -b/2a
From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3
So, h = -2/2(5) = -1/5 = -0.2
Then, on substituting h = x = -0.2 in the function we get
k = 5(-0.2)² + 2(-0.2) - 3
k = -3.2
Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).
Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.
Part C: Steps to graph f(X):
Step 1: Plot the x-intercepts in the coordinate plane
Step 2: Plot the vertex of the function
Step 3: draw a curve line passing through them, opening towards up.
Thus, the graph of the given function is plotted as shown below.
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Find the area of the shape
3.14 for pi
[tex]a = \frac{\pi.r {}^{2} }{4} = \frac{3.14 \times 10 {}^{2} }{4} = \frac{3.14 \times 100}{4} [/tex]
[tex]a = 78.5[/tex]
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 241(1.03) t. the variable t represents the number of years since 2000. what is the projected annual percent of growth, and what should the company be worth in 2012?
Answer:
343.608 million to nearest thousand.
Step-by-step explanation:
Projected annual percent of growth = 3% ( from the values 1.03 in the equation)
Worth is 2012 ( 12 years after 2000) is:
241(1.03)^12
= 343.608 million
Solve each of the following systems of equation.
(b.) 3x + y = 1
6x^2 - y^2 - 2y - 3 = 0
(a) The solution to the given system of equations is x = 1, y = 2, z = -3
(b) The solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)
Solving system of equationsFrom the question, we are to solve the given system of equations
The given system of equation is
x + y + z = 0 ----------- (1)
2x + z = -1 ----------- (2)
x - y - z = 2 ----------- (3)
Add equations (1) and (3)
x + y + z = 0 ----------- (1)
x - y - z = 2 ----------- (3)
__________
2x = 2
x = 2/2
x = 1
Substitute the value of x into equation (2) to find z
2x + z = -1
2(1) + z = -1
2 + z = -1
z = -1 -2
z = -3
Substitute the values of x and z into equation (1) to determine the value of y
x + y + z = 0
1 + y + -3 = 0
1 + y - 3 = 0
y = 3 -1
y = 2
Hence, the solution to the given system of equations is x = 1, y = 2, z = -3
b.
The given system of equations is
3x + y = 1 --------- (1)
6x² - y² - 2y -3 = 0 --------- (2)
From equation (1)
3x + y = 1
y = 1 - 3x -------- (3)
Substitute into equation (2)
6x² - y² - 2y -3 = 0
6x² - (1 -3x)² -2(1 -3x) -3 = 0
6x² - (1 -3x)(1 -3x) -2 + 6x -3 = 0
6x² - (1 -3x -3x +9x²) -2 +6x -3 = 0
6x² - (1 -6x + 9x²) +6x -5 = 0
6x² -1 +6x -9x² +6x -5 = 0
-3x² +12x -6 = 0
3x² -12x +6 = 0
x² -4x + 2 = 0
Solve the quadratic equation by the formula method,
x = [-b±√(b²-4ac)]/2a
a = 1, b = -4 and c = 2
Thus,
x = [-(-4)±√((-4)²-4(1)(2))]/2(1)
x = [4±√(16-8)]/2
x = (4±√8)/2
x = (4+√8)/2 OR (4 - √8)/2
x = 3.4142 OR x = 0.5858
Substitute the values of x into equation (3)
y = 1 - 3x
When x = 3.4142
y = 1 - 3(3.4142)
y = -9.2426
When x = 0.5858
y = 1 - 3(0.5858)
y = -0.7574
Hence, the solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)
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1. How much does the glass for region 1 cost?
2. How much does the glass for region 2 cost?
3. What is the total cost for the glass for the sectors in circle B?
4. What is the total cost of the glass for your window?
5. You only have $100 to spend on glass supplies. Do you have enough money to buy your glass?
Answer:
1) 0.10
2) 0.15
3) 0.100
4) No
An interior designer is sketching a rough outline of a
corner room of an office building, as shown above.
If the area of the triangular-shaped room is 1,728
square feet, what is the value of sin(x)?
The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
The area of triangle A = 1728 square feet
The base length of the triangle b = 72 feet
Let h be the height of the triangle
Area = (1/2)b×h
1728 = (1/2)72×h
h = 48 feet
Half of the 72 is 72/2 = 36
As we know,
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Applying trigonometric ratio:
tan(x) = 48/36
tan(x) = 1.333
x = 53.13 degrees
Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.
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What can you say about the characteristics of a linear funct i on that has a slope of 0? write a careful explanation of your answer. you may provide a mathematical example if you wish to help you illustrate your points, but you must also use sentenc es as a part of a written description.
The characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b
How to determine the characteristics of a linear function that has a slope of 0?A linear equation is given as:
y = mx + b
Where m represents the slope of the linear equation.
When the value of is 0
i.e. m = 0, the equation becomes
y = 0 *x + b
Evaluate
y= b
The above equation is a horizontal line that passes through the y-axis at y= b
Hence, the characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b
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Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Answer:
9/41
Step-by-step explanation:
Cosine represents adjacent / hypotenuse.
When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).
9/41 is already simplified.