Answer:
There is a 1 and 6 chance (16.666...%)
Need help with this counterclockwise rotation
Answer: [tex](-2,1)[/tex]
Step-by-step explanation:
It is important to remember that a rotation is a transformation in which the shapes and sizes do not change, but the object can be turned in different directions.
By definition, the rule for 180° counterclockwise rotation is this:
[tex](x,y)[/tex]→ [tex](-x,-y)[/tex]
Therefore, we know that the image of the point [tex]P=(2,-1)[/tex] under a 180° counterclockwise rotation is:
[tex](2,-1)[/tex]→ [tex](-2,1)[/tex]
Which statements about this system of equations are true? Check all that apply. - x + 6y = 16 8x - 6y = -2 The x-variable will be eliminated when adding the system of equations. The y-variable will be eliminated when adding the system of equations. The sum of the system of equations is - x + 6yThere is only one solution to the system of equations.
Answer:
The true statements are:
The y-variable will be eliminated when adding the system of equations
There is only one solution to the system of equations is
Step-by-step explanation:
* Lets explain how to solve the problem
- We use the elimination method to solve the system of the
linear equation
- The solution is one of three cases
# Exactly one solution ⇒ the 2 lines which represented the equations
intersect each other at one point
# No solution ⇒ the 2 lines which represented the equations are
parallel to each other
# Infinite solutions ⇒ the two lines are coincide
- In the system of the linear equations of the problem we have two
linear equations -x + 6y = 16 and 8x - 6y = -2
- To solve we must to eliminate one of the two variables
∵ The y's in the two equations have the same coefficients and
different signs
∴ We add the equations to eliminate y
∴ (-x + 8x) + (6y - 6y) = 16 + -2
∴ 7x = 14 ⇒ divide both sides by 7
∴ x = 2
- Substitute the x in any one of the two equations by 2
∴ -2 + 6y = 16 ⇒ add 2 to both sides
∴ 6y = 18 ⇒ divide both sides by 6
∴ y = 3
∴ The solution of the system of the equations is (2 , 3) ⇒ only one
solution
- Lets check the statements to find the true statements
# The x-variable will be eliminated when adding the system of
equations is not true
# The y-variable will be eliminated when adding the system of
equations is true
# The sum of the system of equations is - x + 6y is not true
# There is only one solution to the system of equations is true
Statements 1 and 2 are true, while statements 3 and 4 are false.
Let's analyze each statement:
1. The x-variable will be eliminated when adding the system of equations.
- When adding the equations, the x-variables are eliminated because (x) in one equation cancels with (-8x) in the other equation. So, this statement is true.
2. The y-variable will be eliminated when adding the system of equations.
- When adding the equations, the y-variables are also eliminated because (6y) in one equation cancels with (-6y) in the other equation. So, this statement is true.
3. The sum of the system of equations is -x + 6y.
- The sum of the two equations is indeed (-x + 6y). Adding the equations directly gives ( -x + 6y = 14), not ( 16). So, this statement is false.
4. There is only one solution to the system of equations.
- Since the system of equations represents two equations with two variables, the solution can either be a unique solution, no solution, or infinitely many solutions. To determine this, we need to solve the system of equations. We can do this by eliminating one variable and solving for the other. However, from the given equations, we can't determine the nature of the solution without further analysis. So, this statement is indeterminate based solely on the provided equations.
Therefore, statements 1 and 2 are true, while statements 3 and 4 are indeterminate based on the given information.
Simplify square root of -36
a. 6i
b. -6i
c. 6
d. -6
Answer:
A. 6i
Step-by-step explanation:
Apply by the radicial rule.
[tex]\sqrt{-36}=\sqrt{-1}\sqrt{36}[/tex]
[tex]\sqrt{-1}\sqrt{36}[/tex]
Imaginary number.
[tex]\sqrt{36 i}[/tex]
Square root the numbers from left to right.
[tex]6^2=36[/tex]
[tex]\sqrt{6^2}=6[/tex]
6i is the correct answer.
I hope this helps you, and have a wonderful day.
Answer:
A
Step-by-step explanation:
PLEASE HELP ME WITH THIS MATH QUESTION
WHERE IS THE QUESTION ??
1. Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today?
A.8,000 + 24x
B.8,000 − 24x
C.8,000 + 2x
D.8,000 − 2x
2. Avi and Sergi are saving money to buy a game system. Avi has $2 more than double the amount of money Sergi has. Together, they have $40. Write an equation to determine how much money Sergi and Avi have together.
A.x + 2x + 2 = 40
B.2x + 2 = 40
C.x + 2x − 2 = 40
D.2x − 2 = 40
Isabella solved the following equation:
4x − 2x + 8 = 6(x + 4)
Step Work Justification
1 4x − 2x + 8 = 6x + 24 Distributive Property
2 2x + 8 = 6x + 24 Combine like terms
3 −4x + 8 = 24 Addition Property of Equality
4 −4x = 16 Subtraction Property of Equality
5 x = −4 Division Property of Equality
Which step has an incorrect justification?
A.Step 1
B.Step 2
C.Step 3
D.Step 4
Answer:
1. C. 8000 - 24x; 2 A. x + 2x + 2 = 40; 3. C. Step 3
Step-by-step explanation
1. Desmond
[tex]\begin{array}{rcl}\text{Value of car two years ago} & = & 8000\\\\\text{Less depreciation = 24 mo} \times\dfrac{x}{\text{1 mo}} & = & -24 x\\\\\text{Current value} & = & \mathbf{8000 - 24x}\\\end{array}[/tex]
2. Avi and Sergi
[tex]\begin{array}{rcl}\text{Sergi's money} & = & x\\\text{Double Sergi's money} & = & 2x\\\text{Avi's money} & = & 2x + 2\\\text{Avi's money + Sergi's money} & = & x + 2x + 2\\\text{Avi's money + Sergi's money} & = & 40\\x + 2x + 2 & = & 40\\\end{array}[/tex]
3. Isabella
[tex]\begin{array}{crl} \textbf{Step} & \textbf{Work} & \textbf{Justification} \\ & 4x - 2x + 8 = 6(x + 4) & \\ 1 & 4x - 2x + 8 = 6x + 24 & \text{Distributive Property} \\ 2 & 2x + 8 = 6x + 24 & \text{Combine like terms} \\ 3 & -4x + 8 = 24 & \textbf{Subtraction Property of Equality}\\ 4 & -4x = 16 & \text{Subtraction Property of Equality} \\ 5 & x = -4 & \text{Division Property of Equality} \\ \end{array}[/tex]
Step 3 has the incorrect justification. Isabella subtracted 6x from each side, so she should have used the Subtraction Property of Equality
Stuck on this question. May I please have some help?
Answer:
So a point is (-3,-5) and the vertex is (-4,-3)
Step-by-step explanation:
This is in vertex form. Vertex form is y=a(x-h)^2+k where (h,k) is the vertex.
The vertex here is (-4,-3)... now just use a value of x to plug in (any value besides -4)
I will choice -3. This gives -2(-3+4)^2-3
f(-3)=-2(1)^2-3
f(-3)=-2-3
f(-3)=-5
So a point is (-3,-5) and the vertex is (-4,-3)
Answer:(-4,-3)
Step-by-step explanation:
parent function: f(x)=x
transformation: y=f(x+1)
Write the equation of the transformed function
Describe the effect the given transformation will have on the parent function (in words)
Answer:
a) y = x+1
b) The transformation shifts the graph 1 unit to the left
Step-by-step explanation:
a) Put (x+1) where (x) is in the function definition:
y = f(x+1)
y = x+1
__
b) This transformation has the effect of shifting the graph one unit to the left. Any point (x, f(x)) on the original curve, will now be (x-1, f(x)), shifted one unit to the left.
How would you plot the graph of x²-2x-4 ?
Please include an explanation. Thanks in advance :)
Step-by-step explanation:
This equation is written in standard form, y = ax² + bx + c.
a = 1 , b = -2 , c = -4
First, the x² tells you that this is going to be a parabola. Since the a is positive, the parabola will be facing up (with the ends pointing up).
Next, you find the axis of symmetry, or vertex, which is where the middle of the parabola is. The formula for this is [tex]\frac{-b}{2a}[/tex].
[tex]\frac{-(-2)}{2(1)}[/tex] Simplify
[tex]\frac{2}{2}[/tex] Simplify
1
So, the middle of your parabola will be at x = 1.
Now, find the x-intercept. Since the x-intercept of a graph is where y = 0, just plug 0 into the equation for y.
y = x² - 2x - 4 Plug in 0
0 = x² - 2x - 4 Factoring won't work, so use the Quadratic Formula.
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex] Plug in[tex]$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-4)}}{2(1)}$[/tex] Simplify
[tex]$x=\frac{2\pm\sqrt{4+16}}{2}$[/tex] Simplify
[tex]$x=\frac{2\pm\sqrt{20}}{2}$[/tex] The square root of 20 is about 4.47.
[tex]$x=\frac{2+4.47}{2}$[/tex] and [tex]$x=\frac{2-4.47}{2}$[/tex] Simplify
x = 3.235 and -1.235
These are your x-intercepts, where your parabola crosses the x-axis.
Now, just put all of this information together on a graph!
Which expressions are monomials? – 4 + 6 b + 2b + 2 (x – 2x)2 (rs)/(t) 36x2yz3 ax x(1)/(3)
Answer: A C and E
Step-by-step explanation:
-4+6 (x-2x)^2 36x^2yz-3
(A) (C) (E)
There's a screenshot of the answers below
Let Events A & B be described as follows: P(A) = watching a movie P(B) = going out to dinner The probability that a person will watch a movie is 62% and the probability of going out to dinner is 46%. The probability of watching a movie and going out to dinner is 28.52% Are watching a movie and going out to dinner independent events? No, because the P(A) + P(B) ≠ P(A and B). Yes, because the P(A) + P(B) is greater than 100%. No, because the P(A)P(B) ≠ P(A and B). Yes, because the P(A)P(B) = P(A and B).
Answer:
Yes, because the P(A) · P(B) = P(A and B) ⇒ last answer
Step-by-step explanation:
* Lets study the meaning independent and dependent probability
- Two events are independent if the result of the second event is not
affected by the result of the first event
- If A and B are independent events, the probability of both events
is the product of the probabilities of the both events
- P (A and B) = P(A) · P(B)
* Lets solve the question
∵ P(A) = watching a movie
∵ P(B) = going out to dinner
∵ The probability that a person will watch a movie is 62%
∴ P(A) = 62% = 62/100 = 0.62
∵ The probability of going out to dinner is 46%
∴ P(B) = 46% = 46/100 = 0.46
∵ The probability of watching a movie and going out to dinner
is 28.52%
∵ P(A and B) = 28.52% = 28.52/100 = 0.2852
- Lets find the product of P(A) and P(B)
∵ P(A) = 0.62
∵ P(B) = 0.46
∵ P(A and B) = 0.2852
∴ P(A) · P(B) = 0.62 × 0.46 = 0.2852
∴ P (A and B) = P(A) · P(B)
∴ Watching a movie and going out to dinner are independent events
because the P(A) · P(B) = P(A and B)
what is the exact value of cos 45degrees as found on the unit circle
Answer:
sqrt of 2/2
Step-by-step explanation:
Answer:
The exact value of cos 45° is: [tex]\frac{\sqrt{2} }{2}[/tex].
Step-by-step explanation:
The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 2. cross sections of the solid perpendicular to the base are squares. what is the volume, in cubic units, of the solid?
The volume of the solid is 8/3 cubic units.
Explanation:Visualization:
Imagine a right triangle with one leg on the x-axis and the other on the y-axis. The hypotenuse of the triangle intersects the line x + y = 2 at a point (x, y). The solid is formed by stacking square cross-sections perpendicular to the base triangle, with each square having a side length equal to the distance between the line x + y = 2 and the triangle's hypotenuse at that point.
Volume Calculation:
Let x be the distance from the origin to the point where the hypotenuse intersects the line x + y = 2. Then, the length of the side of each square cross-section is (2 - x). The area of each cross-section is therefore (2 - x)^2.
As we move from the origin to the vertex of the triangle where the hypotenuse intersects the line, the distance x increases from 0 to 2. Thus, the volume of the solid can be calculated by integrating the area of the cross-sections over the range of x:
Volume = ∫(2 - x)^2 dx from x = 0 to x = 2
Integration:
Solving the integral using the power rule, we get:
Volume = [4/3 * x^3 - 2x^2 + x] from x = 0 to x = 2
Evaluating the expression at the limits of integration:
Volume = (32/3 - 8 + 2) - (0 - 0 + 0) = 32/3 - 6 = 8/3 cubic units
Therefore, the volume of the solid is 8/3 cubic units.
NEED HELP WITH A MATH QUESTION
Answer:
Step-by-step explanation:
Add all the students: 4+6+2+2+3+4+6+3 = 30
Add all the male students = 14
divide : 14/30=0.466666
multiply by 100
0.466*100=4.66
round
Answer = 5
WILL GIVE BRAINLIEST\
please help!
evaluate the following when a=2 b=-3 c=4
5a-b^2+2c(a-b)
Answer:
41
Step-by-step explanation:
plug in each number with the corresponding variable so
5*2-(-3)^2+2*4(2-(-3))
the use pemdas and you get 41
((PLEASE ANSWER WITH A B C or D))
What is m NMO?
A. 90°
B. 30°
C. 45°
D. 60°
Answer:
D. 60°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relationship of interest is ...
Sin = Opposite/Hypotenuse
sin(M) = ON/OM = 4(√3)/8 = (√3)/2
M = sin⁻¹((√3)/2) = 60°
I need help with (half way done
which probability symbols do I use for each one 'P(R)="
7.Drawing a yellow marble, given that a red marble was drawn on the first draw and not replaced?
The probability of drawing a blue marble will be 1/3.
How to calculate probability?Blue marbles = 3
Red marbles = 2
Yellow marbles = 4
Total marbles = 3 + 2 + 4 = 9
The probability of drawing a blue marble will be:
= 3/9
= 1/3
The probability of drawing a marble that isn't red will be:
= 3/9 + 4/9
= 7/9
The probability of drawing a red and yellow marbles will be:
= 2/9 + 4/9
= 2/3
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The function f(x) = ?(x + 5)(x + 1) is shown.What is the range of the function? all real numbers less than or equal to 4 all real numbers less than or equal to ?3 all real numbers greater than or equal to 4 all real numbers greater than or equal to ?3
It is best to graph the function when searching for the range.
For the function f(x) = (x + 5)(x + 1), the range is ALL REAL NUMBERS when y is greater than or equal to -4.
Get it?
Which of the following is the statement of the triangle inequality theorem?A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle.B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.C. The longest side of a triangle is opposite the largest angle.D. The largest angle of a triangle is between the two longest sides.
Answer:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side ⇒ answer B
Step-by-step explanation:
* Lets explain the triangle inequality theorem
- The triangle Inequality Theorem is the sum of the lengths of any two
sides of a triangle is greater than the length of the third side.
- That means when we add the lengths of the shortest two sides,
the answer will be greater than the length of the longest side.
- Examples:
# Is the set of {4 , 5 , 9} could form a triangle
- Add 4 , and 5 because they are the shortest sides
∵ 4 + 5 = 9
∵ The third side is 9
∵ In any triangle the sum of the lengths of any two sides of a triangle
must be greater than the length of the third side
∴ The set {4 , 5 , 9} couldn't form a triangle
# Is the set of {4 , 5 , 8} could form a triangle
- Add 4 , and 5 because they are the shortest sides
∵ 4 + 5 = 9
∵ The third side is 8
∵ In any triangle the sum of the lengths of any two sides of a triangle
must be greater than the length of the third side
∴ The set {4 , 5 , 8} could form a triangle
# Is the set of {3 , 5 , 9} could form a triangle
- Add 3 , and 5 because they are the shortest sides
∵ 3 + 5 = 8
∵ The third side is 9
∵ In any triangle the sum of the lengths of any two sides of a triangle
must be greater than the length of the third side
∴ The set {3 , 5 , 9} couldn't form a triangle
* Lets solve the problem
∵ The triangle inequality theorem is the sum of the lengths of any two
sides of a triangle is greater than the length of the third side
- It talks about the relation between the lengths of the sides
∴ The right answer is B. The sum of the lengths of any two sides of
a triangle is greater than the length of the third side
Answer:
B
Step-by-step explanation:
A cannot be correct as it is measuring angles, and the theorem is not abt the angles.
B is correct because the theorem is abt triangle sides.
C is incorrect because that is just ridiculous.
D is incorrect because is not always true and the theorem once again, is not abt angles.
PLEASE HELP ASAP I WILL MARK BRAINLIEST!! ABCD is rotated counterclockwise about the origin. By how many degrees was ABCD rotated?
Answer:
270 degrees
Step-by-step explanation:
180 would be diagonal from original, 360 would be where the original is and 90 would be in the second quadrant so therefore its 270
Answer:
B) 270°
Step-by-step explanation:
it was correct for me
What is Steven’s slugging average if his stats are- Show steps. 25 singles 10 doubles 3 triples 10 homeruns 140 at-bats
a. 25 + 10 + 3 + 10 = 48/140 = .3428
b. 25(.1) + 10(.2) + 3(.3) + 10(.4) = 9.40/140 = .06714
c. 25(1) + 10(2) + 3(3) + 10(4) = 94/140 = .671
d. 25 + 10(2) + 3(3) + 10(3) = 84/140 = .600
The answer is:
The correct answer is c.
[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]
Why?To calculate the slugging average or slugging percentage, we need to divide the number of total bases by the total times at bat.
[tex]SluggingAverage=\frac{TotalBases}{TimesAtBat}[/tex]
We know that:
A single means 1 base.
A double means 2 bases.
A triple means 3 bases.
A homerun means 4 bases.
So, we know that:
[tex]Singles=25=25bases\\Doubles=2*10=20bases\\Triples=3*3=9bases\\Homeruns=10*40=40bases\\TimesAtBat=140[/tex]
Then, substituting and calculating we have:
[tex]SluggingAverage=\frac{25bases+20bases+9bases+40bases}{140}[/tex]
[tex]SluggingAverage=\frac{94bases}{140times}=0.671[/tex]
Hence, the correct answer is c.
[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]
Have a nice day!
Heather has 45.71 in her savings account.She brought six packs of markers to donate for school. Write an expression for how much money she has in her bank account after the donation
Answer:
45.71 - 6x
Step-by-step explanation:
If Heather bought markers to donate, the amount she donates is subtracted from her balance of 45.71. We know she bought 6 packs of markers, but we do not know how much each pack cost. We will make this our unknown "x". The expression for packs of markers costing "x" is 6x. Because she buys them from her account, which takes aways from her balance, the expression that represents this donation is:
45.71 - 6x
(Notice that the question asks for the EXPRESSION after she buys the markers, not the EQUATION. The difference between an expression and an equation is the lack of an equals sign in the expression.)
Answer:
M= 45.71 - 6x
Step-by-step explanation:
M represents money and x is how much each pack of markers cost. 45.71, which is the original amount, minus 6x will give the correct amount.
Three different divers kept track of the number of treasure boxes they've found this year. Diver Dives Treasure boxes found Scuba Sam 11 33 Wet Suit Willy 18 81 Deep Diving Dan 26 104 Which diver found the most treasures per dive?
Answer:
Wet Suit Willy
Step-by-step explanation:
To find boxes per dive, divide boxes by dives:
Sam: 33/11 = 3 . . . boxes per dive
Willy: 81/18 = 4.5 . . . boxes per dive
Dan: 104/26 = 4 . . . boxes per dive
Wet Suit Willy found the most treasure boxes per dive: 4.5.
HELP WITH ANGLE THEOREMS! Brainliest! Find the values of c and d.
Give reasons for each value you find.
Please EXPLAIN each theorem please!
Thank you!
Answer:
c = 25, d = 65
Step-by-step explanation:
∠d + 90 = 155 ( vertical angles )
Subtract 90 from both sides
d = 65
The angle above 155 = 180 - 155 ( straight angle ) = 25
Hence c = 25 ( corresponding angles )
Answer:
<d = 65 degrees.
<c = 25 degrees.
Step-by-step explanation:
<d + 90 = 155 since vertically opposite <'s are equal. Therefore <d = 155-90
= 65 degrees.
The angle adjacent to <d is 180-155= 25 degrees since <'s on a line = 180 degrees.
Therefore <c= 25 degrees since corresponding <'s on parallel lines are equal.
Is trapezoid ABDC the result of a dilation of trapezoid MNPQ by a scale factor of ? Why or why not? Yes, because AB and CD are each the lengths MN and QP. Yes, because sides AB and CD are parallel to sides MN and QP. No, because AB is the length MN but CD is the length QP. No, because sides AB and CD have different slopes from sides MN and QP.
No, because AB is 2/5 the length MN but CD is 1/3 the length QP.
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
Given:
As, Comparing the corresponding sides, the length of AB is 4.
The length of MN is 10. This makes their ratio 4/10 = 2/5.
and, the CD length is 2.
QP has a length of 6. Consequently, their ratio is 2/6 = 1/3.
Therefore, because the side ratios differ, the figure is not proportionate and is not a dilation.
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Trapezoid ABCD is not the result of the dilation of trapezoid MNPQ by a scale factor of 2/5 because AB is 2/5 the length MN but CD is 1/3 the length QP.
What is Scale Factor?Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.
Given a trapezoid ABCD and another trapezoid MNPQ.
From the figure,
length of AB = 2 + 2 = 4
Length of MN = 5 + 5 = 10
Scale factor = 4/10 = 2/5
Now,
Length of CD = 1 + 1 = 2
Length of QP = 3 + 3 = 6
Scale factor = 2/6 = 1/3
That is, the scale factor differs.
Hence the correct option is C.
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Sam is 5 years old. His older brother Tom, is three times as old as Sam. When Sam is 20, how old will Tom be?
Answer:
60
Step-by-step explanation:
Sam is 5, Tom is 3 times as old, 5 times three is 15, so tom is 15, 20 is 4 times 5, so you take 15, and multiply it by 4, and that's your answer
Find the distance between the points (3, 8) and (-1, 9).
Square root 15
Square root 15
Square root 17
Answer:
√17
Step-by-step explanation:
The distance formula is ...
d = √((x2 -x1)² +(y2 -y1)²)
Filling in the point values, we have ...
d = √((-1-3)² +(9-8)²) = √(16 +1)
d = √17
The vertices of a triangle are labeled clockwise A(–5, 3), B(6, 1), and C(–2, –3). How could you show that the figure is a right triangle?
Explanation:
When the points are plotted on a graph, it is easy to see that the slope of AC is -2 and the slope of BC is 1/2. These slope values have a product of -1, so the corresponding line segments are perpendicular to each other.
___
If you have studied vectors, you can find the dot product of AC with BC:
AC = (-5, 3) -(-2, -3) = (-3, 6)
BC = (6, 1) -(-2, -3) = (8, 4)
The dot product is ...
(-3, 6)·(8, 4) = (-3)(8) + (6)(4) = -24+24 = 0
When the dot product of vectors is zero, they are perpendicular.
PLEASE HELP!! WILL MARK BRAINLY!!
For what values of the domain {-3, -1, 0, 2, 4} does f(x) = g(x)?
f(x) = 2x + 5
g(x) = x^2 - 3
Answer:
{4}
Step-by-step explanation:
It is helpful to let a calculator or spreadsheet perform the function evaluations for you. The two functions have the same value only for x=4 in the domain.
f(4) = 13 = g(4)
_____
The functions also have the same value for x=-2, but that is not in the domain given.
Please Help! I need to get this right
Answer:
sin(x) = -2(√6)/5csc(x) = -5/(2√6)tan(x) = 2√6cot(x) = 1/(2√6)Step-by-step explanation:
In the third quadrant, sine and its inverse, cosecant, are negative. In that quadrant, tangent and its inverse, cotangent, are positive. The sine function always has a magnitude less than or equal to 1, while the cosecant function always has a magnitude at least 1.
The negative numbers on your list can be assigned to sin(x) and csc(x) based on their magnitudes. 2√6 = √24 < 5, so 2(√6)/5 < 1. The number with this magnitude is the sine; its inverse is the cosecant.
sin(x) = -2(√6)/5csc(x) = -5/(2√6)The tangent is the ratio of sine to cosine, so is ...
tan(x) = ((-2√6)/5)/(-1/5) = 2√6
and the cotangent is the inverse of that:
tan(x) = 2√6cot(x) = 1/(2√6)Of course, the secant is the inverse of the cosine, so would be -5. That is not one of the number choices, so sec(x) can be ignored.
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. 2x+y+z=-3 3x-5y+3z=-4 5x-y+2z=-2
Answer:
(x, y, z) = (1, -1, -4)
Step-by-step explanation:
A suitable graphing or scientific calculator can find the reduced row-echelon form for you. There are on-line calculators that will do that, too.
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In general, if you want to do this by hand, you want to use row operations on the augmented matrix to make the diagonal elements 1 and the off-diagonal elements 0 as shown in the attached result.
If a[i,j] represents the element at row i, column j, you do that by dividing row i by a[i, i] (to make a[i, i] = 1), then subtracting the product of row i and a[k,i] from row k. (for all rows k ≠ i) For this 3-row matrix, repeat these steps for i = 1 to 3.
In the general case of an n by n+1 augmented matrix, you will be doing n^2 row operations, each one involving evaluation of n+1 expressions. The work rapidly grows with matrix size, so readily justifies use of a calculator.
As with many "elimination" problems, appropriate choice of sequence can reduce the work. The above algorithm always produces the reduced row-echelon form, but may result in messy arithmetic along the way.
Answer: A
Step-by-step explanation: edge 2021