The values of x for which A U B = ø (empty set) are x > 3 AND x < 2, but no number can satisfy both inequalities simultaneously.
Explanation:To find the values of x for which A U B = ø (empty set), we need to find the values that make both inequalities false. Let's solve each inequality separately:
Inequality 1: 3x + 4 > 13
Subtracting 4 from both sides, we get 3x > 9. Dividing both sides by 3, we have x > 3.
Inequality 2: 1/2x + 3 < 4
Subtracting 3 from both sides, we get 1/2x < 1. Multiplying both sides by 2, we have x < 2.
Therefore, the values of x that satisfy both inequalities are x > 3 AND x < 2.
However, no number can be greater than 3 and less than 2 at the same time, so the solution for A U B = ø (empty set).
Learn more about Solving inequalities here:https://brainly.com/question/26855203
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You are a math superstar and have been assigned to be a math tutor to a third grade student. Your student has a homework assignment that requires measuring angles within a parallelogram. Explain to your student how to measure the angles within the shape.
To measure angles within a parallelogram, use a protractor. Align the protractor with the vertex of the angle and read the number where the other side crosses. Repeat for each angle.
Explanation:To measure the angles within a parallelogram, you can use a protractor. A protractor is a tool that helps measure angles. Here’s how you can use it:
Place the protractor on one side of the parallelogram, aligning the center hole with the vertex of the angle you want to measure.Read the number on the protractor where the other side of the angle crosses it. This number represents the measure of the angle in degrees.Repeat this process for each angle within the parallelogram.For example, if you want to measure one of the angles in a parallelogram and the protractor shows that the two sides of the angle cross at the 60° mark on the protractor, that means the angle has a measure of 60 degrees.
How can x^2+3x+1=2x^2+2x+3 be set up as a system of equations?
Answer:
System of equations of x^2+3x+1=2x^2+2x+3 is x^2-x+2=0.
Step-by-step explanation:
We need to make system of equations of:
x^2+3x+1=2x^2+2x+3
Solving,
Adding -2x^2 on both sides
x^2+3x+1-2x^2=2x^2+2x+3-2x^2
-x^2+3x+1=2x+3
Adding -2x on both sides
-x^2+3x+1-2x=2x+3-2x
-x^2+x+1=3
Adding -3 on both sides
-x^2+x+1-3=3-3
-x^2+x-2=0
Multiplying with -1
x^2-x+2=0
System of equations of x^2+3x+1=2x^2+2x+3 is x^2-x+2=0.
Write the Explicit Rule for the arithmetic sequence:
an = a1 + (n-1)d
1, 3, 5.7. ...
[tex]a_1=1\\d=2\\a_n=1+(n-1)\cdot 2=1+2n-2=2n-1[/tex]
What is the final step in solving the inequality -2(5 - 4x)
6x – 4?
Step 1 -10 + 8x < 6x-4
Step 2: -10 <-2x - 4
Step 3: -6<-2x
Step 4
O X<-3
0 x>-3
0 x<3
© x>3
VAVA
Answer:
Answer is x>3
Step-by-step explanation:
The last step is: divide -2 to both sides and since the 2 is negative the sign flips so it would be x>3.
Hope my answer has helped you and if not i'm sorry.
PLEASE HELP!!!!!!!!!!!!!!Given that B, C, and D are the midpoints of AZYA, find the perimeter of AZYA.
A. 70.6
B. 72.6
C. 76.6
77.6
What elements are in A and B?
Answer:
Zack and bo
Step-by-step explanation:
A and B is where the circles intersect so zack and bo are the only names I see there.
The elements {Zack, Bo} are in A and B.
What is set A intersection set B?The element that is present in both set A and set B i.e. at the common area of set A and set B in Venn diagram is called set A intersection set B.
Here In Venn diagram set A is green colored which contains the element {Kalie, Noah, Zack, Bo}
Set B is orange colored which contains the element {Julia, Zack, Bo}.
The elements which are present in both A and B are the intersection of set A and set B.
These elements are available at the common joint area of set A and set B.
Here, dark color represents the area that contains the element present in A and B.
In that dark-colored region, the elements present are {Zack,Bo}.
Therefore The elements {Zack, Bo} are in A and B.
Learn more about the intersection of set
here: https://brainly.com/question/2166579
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SUBJECT: Algebra
LESSON: Multiplying Polynomials
(x^3 + 2x − 3)(x^4 − 3x^2 + x)
Answer:
Step-by-step explanation:
(x^3 + 2x − 3)(x^4 − 3x^2 + x)
Multiply each value of 2nd bracket with 1st bracket:
=x^4(x^3 + 2x − 3) - 3x^2(x^3 + 2x − 3) +x(x^3 + 2x − 3)
=x^7+2x^5-3x^4-3x^5-6x^3+9x^2+x^4+2x^2-3x
Now combine the terms with same power:
=x^7-x^5-2x^4-6x^3+11x^2-3x
You can also take the common from the expression:
x(x^6-x^4-2x^3-6x^2+11x-3)....
The product of (x^3 + 2x − 3)(x^4 − 3x^2 + x) is x(x^6-x^4-2x^3-6x^2+11x-3)....
If the figure below is rotated 90degrees clockwise about the origin, what is the new location? the options are:
A’ (0, 8), B’ (6, 0), C’ (0, -8), D’ (0, -6)A’ (-8, 0), B’ (0, 6), C’ (8, 0), D’ (0, -6)A’ (0, 8), B’ (6, 0), C’ (0, -8), D’ (-6, 0)A’ (0, -8), B’ (6, 0), C’ (0, 8), D’ (-6, 0)
Answer:
A'(0, -8), B'(6, 0), C'(0, 8), D'(-6, 0)
Step-by-step explanation:
Whenever you are doing a 90° clockwise rotation ABOUT THE ORIGIN, it is in the form of [y, -x], meaning you take the y and make it your x, then take your original x and put its OPPOSITE.
90° counterclockwise rotation → [-y, x]
90° clockwise rotation → [y, -x]
I hope this helps, and as always, I am joyous to assist anyone at any time.
The slope of MN is −3. Which segments are parallel to MN ? Select each correct answer.
A= RS, where R is at (1, 3) and S is at (4, 2)
B= PQ, where P is at (5, 6) and Q is at (8, 7)
C= TU, where T is at (8, 1) and U is at (5, 10)
D= WX, where W is at (2, 6) and X is at (4, 0)
Report by TurtleAnderson
Answer:
Option C and D is correct
Step-by-step explanation:
We need to find the slopes of the given segments.
The lines are parallel if there slopes are equal.
A) = RS, where R is at (1, 3) and S is at (4, 2)
[tex]Slope\,\,of\,\,RS =\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\Slope\,\,of\,\,RS=\frac{2-3}{4-1}\\Slope\,\,of\,\,RS=\frac{-1}{3}[/tex]
Option A is incorrect because Slope of MN = -3 while slope of RS = -1/3
B)= PQ, where P is at (5, 6) and Q is at (8, 7)
[tex]Slope\,\,of\,\,PQ =\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,PQ=\frac{7-6}{8-5}\\Slope\,\,of\,\,PQ=\frac{1}{3}[/tex]
Option B is incorrect because Slope of MN = -3 while slope of PQ = 1/3
C)= TU, where T is at (8, 1) and U is at (5, 10)
[tex]Slope\,\,of\,\,TU=\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,TU\,\,=\frac{10-1}{5-8}\\Slope\,\,of\,\,TU\,\,=\frac{9}{-3} \\Slope\,\,of\,\,TU=-3[/tex]
Option C is correct because Slope of MN = -3 while slope of TU = -3
D)= WX, where W is at (2, 6) and X is at (4, 0)
[tex]Slope\,\,of\,\,WX\, =\frac{y_{2}-y_{1}}{x_{2}-xx_{1}} \\Slope\,\,of\,\,WX\,=\frac{0-6}{4-2}\\Slope\,\,of\,\,WX\,=\frac{-6}{2} \\Slope\,\,of\,\,WX\,=-3[/tex]
Option D is correct because Slope of MN = -3 while slope of WX = -3
Segments TU and WX have the slope -3, which is the same as line MN's slope, making them parallel to segment MN.
The question asks which line segments are parallel to a line MN with a slope of
-3. To determine if two segments are parallel, they must have the same slope. The slope of a line through two points (x1, y1) and (x2, y2) is calculated with the formula
m = (y2 - y1) / (x2 - x1).
Let's find the slopes for each segment:
For segment RS, slope m = (2 - 3) / (4 - 1) = -1 / 3. This is not equal to -3, so RS is not parallel to MN.For segment PQ, slope m = (7 - 6) / (8 - 5) = 1 / 3. This is not equal to -3, so PQ is not parallel to MN.For segment TU, slope m = (10 - 1) / (5 - 8) = 9 / -3 = -3. This slope is equal to -3, so TU is parallel to MN.For segment WX, slope m = (0 - 6) / (4 - 2) = -6 / 2 = -3. This slope is equal to -3, so WX is parallel to MN.Therefore, the segments parallel to MN are TU and WX.
Please show to answer this
Answer:
[tex](q \circ r)(7)=22[/tex]
[tex](r \circ q)(7)=8[/tex]
Step-by-step explanation:
1st problem:
[tex](q \circ r)(7)=q(r(7))[/tex]
r(7) means to replace x in [tex]\sqrt{x+9}[/tex] with 7.
[tex]r(7)=\sqrt{7+9}=\sqrt{16}=4[/tex]
[tex](q \circ r)(7)=q(r(7))=q(4)[/tex]
q(4) means replace x in [tex]x^2+6[/tex] with 4.
[tex]q(4)=4^2+6=16+6=22[/tex].
Therefore,
[tex](q \circ r)(7)=q(r(7))=q(4)=22[/tex]
2nd problem:
[tex](r \circ q)(7)=r(q(7))[/tex]
q(7) means replace x in [tex]x^2+6[/tex] with 7.
[tex]q(7)=7^2+6=49+6=55[/tex].
So now we have:
[tex](r \circ q)(7)=r(q(7))=r(55)[/tex].
r(55) means to replace x in [tex]\sqrt{x+9}[/tex] with 55.
[tex]r(55)=\sqrt{55+9}=\sqrt{64}=8[/tex]
Therefore,
[tex](r \circ q)(7)=r(q(7))=r(55)=8[/tex].
Choose the expression that represents a cubic expression.
a. 19x^4 + 18x^3 - 16x^2 - 12x + 1
b. 10x^3 - 6x^2 - 9x + 12
c. -9x^2 - 3x + 4
d. 4x + 3
Answer:
b. 10x^3 - 6x^2 - 9x + 12
Step-by-step explanation:
A cubic expression has the highest power of the variable to the third power
x^3
b. 10x^3 - 6x^2 - 9x + 12
is the only expression that has the highest power as x^3
a has x^4 and c and d do not have an x^3 term
Final answer:
The expression that represents a cubic expression is (b) [tex]10x^3 - 6x^2 - 9x + 12[/tex], as it is the only option where the highest power of x is three.
Explanation:
The expression that represents a cubic expression is option (b) [tex]10x^3 - 6x^2 - 9x + 12[/tex]. A cubic expression is one in which the highest degree of any term is three, which means the variable (most commonly x) is raised to the third power. Looking at the options provided:
(a) [tex]19x^4 + 18x^3 - 16x^2 - 12x + 1[/tex] is not a cubic expression because it contains a term with x to the fourth power.
(b) [tex]10x^3 - 6x^2 - 9x + 12[/tex] is a cubic expression because the highest power of x is three.
(c)[tex]-9x^2 - 3x + 4[/tex] is not a cubic expression; it's a quadratic expression since the highest power of x is two.
(d) 4x + 3 is also not a cubic expression; it's linear as the highest power of x is one.
Find the value of x in the picture please
Answer:
The value of x is 4
Step-by-step explanation:
we know taht
The intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal.
so
In this problem
[tex](12)(x)=(8)(x+2)[/tex]
solve for x
[tex]12x=8x+16[/tex]
[tex]12x-8x=16[/tex]
[tex]4x=16[/tex]
[tex]x=4[/tex]
Factor the given expression.
x2 + 16
+ 64
O A. (x+4)2
B. (x + 16)(x + 4)
c. (x+3)(x - 8)
OD. (x+8)2
Answer:
D. (x+8)^2
Step-by-step explanation:
x^2 + 16x + 64
We are factoring a quadratic trinomial in which the first term is x^2.
We need to find two numbers whose product is 64 and whose sum is 8.
8 * 8 = 64
8 + 8 = 16
The numbers are 8 and 8.
x^2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)^2
Check: If (x + 8)^2 is indeed the correct factorization of x^2 + 16x + 64, then if you multiply out (x + 8)^2, you must get x^2 + 16x + 64.
(x + 8)^2 =
= (x + 8)(x + 8)
= x^2 + 8x + 64
= x^2 + 16x + 64
We get the correct product, so our factorization is correct.
If f(x) = 2x - 6 and g(x) = 3x + 9, find (f - g)(x).
O A. (f- g)(x) = x+15
O B. (f- g)(x) = -x+3
OC. (f- g)(x) = -x - 15
O D. (f- g)(x) = 5x + 3
[tex](f-g)(x)=2x-6-(3x+9)=2x-6-3x-9=-x-15[/tex]
Answer:
The correct option is C.
Step-by-step explanation:
The correct option is C.
We have given:
f(x) = 2x - 6 and g(x) = 3x + 9
Now we have to find (f-g)(x)
(f-g)(x) = f(x)- g(x)
Now subtract g(x) from f(x)
(2x - 6) - (3x + 9)
Open the parenthesis. When we open the parenthesis the signs of second bracket will become negative because there is a negative sign outside the bracket.
(f-g)(x)= 2x-6-3x-9
Now solve the like terms:
(f-g)(x)= -x-15
Thus the correct option is C....
Alex and Rachel agreed to form a partnership. The partnership agreement requires that Alex
invest $3000 more than two- third of what Rachel is to invest. If the partnerships’ capital is to be
$55,000, how much should Alex invest?
Answer:
Alex investment = $ 23,800
Step-by-step explanation:
The statement is Alex and Rachel are forming partnership. According to the agreement Alex invest $3000 more than Rachel's two-third investment and the total capital is $55,000.Find out Alex investment.
Let x be the investment of Rachel. Lets make an equation to find the value of x.
x+2/3x +$3000=$55,000
Combine the like terms:
x+2/3x = 55,000 - 3000
x+2/3x = $52000
Now take the L.C.M of L.H.S
3x+2x/3 = $52000
Now Add the values of x.
5x/3 = $52000
Multiply both the terms by 3.
5x/3 *3 = 3* $52000
5x= 156000
Now divide both the sides by 5.
5x/5 = 156000/5
x= 31200
Now calculate Alex investment. According to the statement Alex invest $3000 more than 2/3 of Rachel.
We have found the Rachel investment which is $31200. Therefore we can write 2/3 of Rachel investment as 2/3(31200).
=2/3(31200)+$3000
=2*10400+3000
=20,800+3000
=$23,800
Rachel investment = $31200
Alex investment = $ 23,800
If you want to check whether the investments are correctly determined or not. You can add both the investments and the result will be the partnership's capital amount.
$31200+$ 23,800 = $55,000 ....
What are the center and radius of the circle defined by the equation x^2+y^2-6x+4y+4=0
Answer:
Option B
center (3,2)
radius 3
Step-by-step explanation:
Given:
x^2+y^2-6x+4y+4=0
x^2+y^2-6x+4y=-4
Now completing square of x^2-6x by introducing +9 on both sides:
x^2-6x+9+y^2+4y=-4+9
(x-3)^2+y^2+4y=5
Now completing square of y^2+4y by introducing +4 on both sides:
(x-3)^2+y^2+4y+4=5+4
(x-3)^2 + (y-2)^2= 9
Now comparing with the circle equation:
(x-h)^2 + (y-k)^2= r^2
where
r= radius of circle
h= x-offset from origin
k= y-offset from origin
In given case
r=3
h=3
k=2
Hence, option B is correct with radius =3 and center =(3,2)!
Answer:
Center (3,-2); radius 3
How do you graph
f(x)=7sec(2x)
Answer:
We know that sec(x) = 1/cos(x). Therefore:
7sec(2x) = 7/cos(2x).
The function won't be define at the points where the denomitator equals zero, which is when x=(2n+1)π/2.
Using a graphing calculator, we get that the graph of the function is the one attached.
simplify 3 divided by 5-6i
Answer:
[tex]\frac{15}{61}+\frac{18}{61}i[/tex]
Step-by-step explanation:
[tex]\frac{3}{5-6i}[/tex]
To simplify or to write in the form a+bi, you will need multiply the top and bottom by the bottom's conjugate like so:
[tex]\frac{3}{5-6i} \cdot \frac{5+6i}{5+6i}[/tex]
Keep in mind when multiplying conjugates you only have to multiply first and last.
That is the product of (a+b) and (a-b) is (a+b)(a-b)=a^2-b^2.
(a+b) and (a-b) are conjugates
Let's multiply now:
[tex]\frac{3}{5-6i} \cdot \frac{5+6i}{5+6i}=\frac{3(5+6i)}{25-36i^2}[/tex]
i^2=-1
[tex]\frac{15+18i}{25-36(-1)}[/tex]
[tex]\frac{15+18i}{25+36}[/tex]
[tex]\frac{15+18i}{61}[/tex]
[tex]\frac{15}{61}+\frac{18}{61}i[/tex]
For this case we must simplify the following expression:
[tex]\frac {3} {5-6i}[/tex]
We multiply by:
[tex]\frac {5 + 6i} {5 + 6i}\\\frac {3} {5-6i} * \frac {5 + 6i} {5 + 6i} =\\\frac {3 (5 + 6i)} {(5-6i) (5 + 6i)} =\\\frac {3 (5 + 6i)} {5 * 5 + 5 * 6i-6i * 5- (6i) ^ 2} =\\\frac {3 (5 + 6i)} {25-36i ^ 2} =\\\frac {3 (5 + 6i)} {25-36 (-1)} =\\\frac {3 (5 + 6i)} {25 + 36} =\\\frac {3 (5 + 6i)} {61} =\\\frac {15 + 18i} {61}[/tex]
Answer:
[tex]\frac {15 + 18i} {61}[/tex]
4^-x x=-3
i need to stretch this to 20 words and im struggling to come up with things.
So,
[tex]4^{-x}[/tex]
When [tex]x=-3[/tex]
Becomes,
[tex]4^{-(-3)}=4^3=\boxed{64}[/tex]
Hope this helps.
r3t40
hey, need some help with this
Step-by-step explanation:
simplify the equation
5-x(2)-3x(4x-7)/(5-x)(3x)
=10-2x-12x²+21x/15x-3x²
=-12x²-23x+10/15x-3x³
the answer is B
yes, Robot is correct but Irum is not
Answer:
simplify the equation first
5-x(2)-3x(4x-7)/(5-x)(3x)
=10-2x-12x²+21x/15x-3x²
=-12x²-23x+10/15x-3x³
the answer is B
Step-by-step explanation:
:)
I’m giving all the points I have, plz help and get it right? Someone please help me
Answer:
The area (probability) is: 0.6864.
Step-by-step explanation:
According to the statement, we are in front of a normal distribution with the following parameters:
µ (mean) = 0
σ (Standard deviation) = 1.
Then we need to find the area of the shaded region, which is the area between the points -1.21 < z < 0.84.
And the area (probability) is: 0.6864.
Answer:
A. 0.6864
Step-by-step explanation:
The area of the shaded region between the two z-scores indicated in the diagram is 0.6864.
mean = 0
Standard deviation = 1
Kinley bought 3 notebooks that cost the same and a poster that cost $6. She spent $20.40 in all. What was the cost of each notebook?
Answer:
the cost of each notebook is $4.8
Step-by-step explanation:
Cost of each notebook= ?
Cost of a poster = $6
Total amount she spent = $20.40
If we subtract the cost of poster from total amount we get the cost of 3 notebooks.
$20.40-$6
=$ 14.4
It means the cost of 3 notebooks = $14.4
To find the cost of each notebook divide the cost of 3 notebooks by the number of books.
=14.4/3
=$4.8
Thus the cost of each notebook is $4.8....
the inverse of f(x)=4x+5
To find the inverse of a function switch the place of y (aka f(x) ) with x. Then solve for y.
Original equation:
y = 4x + 5
Switched:
x = 4y + 5
Solve for y by isolating it:
x - 5 = 4y + 5 - 5
x - 5 = 4y
(x - 5)/4 = 4y/4
[tex]\frac{1}{4}x-\frac{5}{4} = y[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Please answer this correctly
Answer:
Step-by-step explanation:
When you divide by 100, the decimal moves 2 places to the left.
847.8
When you have moved the decimal 3 places to the left, you have divided by 1000
To reverse the effects of 847.8 by dividing by 10000 you need to multiply by 10000
847.8 * 10000 = 8478000 Try this on your calculator to confirm it.
Same with the last one. To get 847.8 when you have divided by 1 million, you movie the decimal in the answer 6 places.
847.8 * 1000000 = 847800000
#20-12: Simplify this complex fraction. 1/4 / 2/5
Answer:
=1/40
Step-by-step explanation:
=1/8/5
=1/40
Oatmeal is packaged in a right circular cylindrical container that has a
radius of 7 centimeters and a height of 16 centimeters.
What is the surface area of this container in terms of pi?
[tex]\bf \textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} h=height\\ r=radius\\ \cline{1-1} h=16\\ r=7 \end{cases}\implies SA=2\pi (7)(16+7) \\\\\\ SA=14\pi (23)\implies SA=322\pi[/tex]
The surface area of the right circular cylindrical container that has a radius of 7 cm and a height of 16 cm in terms of π is 322π. This is obtained by using the formula for surface area of cylinder.
What is the surface area ?
Surface area of cylinder is, S = 2πrh+2πr², where S is the surface area, r is the radius and h is the height of the cylinder.
Given that r =7 cm, h =16 cm,
S = 2πrh+2πr²
= 2π(7)(16)+2π(7)²
= 224π+98π
= 322π
Hence the surface area of the right circular cylindrical container that has a radius of 7 cm and a height of 16 cm in terms of π is 322π.
Learn more about surface area of cylinder here:
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use a graphing calculator to solve the equation 3tan1/3theta=8 in the interval 0 to 2pi round your answers to the nearest hundredth
A. 1.21,4.35
B. 3.64
C. 1.21, 2.26, 3.31, 4.35, 5.40
D. .404, 1452.5, 3.55, 4.59, 5.64
Answer:
B. 3.64 to the nearest hundredth.
Step-by-step explanation:
3tan1/3theta=8
tan1/3theta = 8/3
1/3 theta = 1.212 radians, 1.212 + π radians.
theta = 1.212 * 3 = 3.636 radians, 3(1.212 + π) radians.
The second value is greater than 2π radians.
The correct answer is C. 1.21, 2.26, 3.31, 4.35, 5.40.
To solve the equation [tex]\( 3 \tan \frac{1}{3}\theta = 8 \)[/tex] in the interval[tex]\( 0 \) to \( 2\pi \)[/tex], we first isolate [tex]\( \tan \frac{1}{3}\theta \):[/tex]
[tex]\[ \tan \frac{1}{3}\theta = \frac{8}{3} \][/tex]
Next, we take the inverse tangent (arctan) of both sides to solve for
[tex]\[ \frac{1}{3}\theta = \arctan\left(\frac{8}{3}\right) \][/tex]
Now, we multiply both sides by 3 to solve for [tex]\( \theta \)[/tex]:
[tex]\[ \theta = 3 \cdot \arctan\left(\frac{8}{3}\right) \][/tex]
Using a graphing calculator, we find the values of [tex]\( \theta \)[/tex] that satisfy the equation within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \)[/tex]. The calculator will give us the principal value and we need to consider all solutions within the given interval, taking into account the periodicity of the tangent function.
The principal value for [tex]\( \arctan\left(\frac{8}{3}\right) \)[/tex] is approximately[tex]\( 1.21 \)[/tex] radians. Since the tangent function has a period of[tex]\( \pi \)[/tex], we add multiples of[tex]\( \pi \)[/tex] to find other solutions within the interval [tex]\( 0 \)[/tex] to [tex]\( 2\pi \).[/tex]
[tex]\[ \theta \approx 1.21 + k\pi \][/tex]
where [tex]\( k \)[/tex] is an integer such that[tex]\( \theta \)[/tex] remains within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \).[/tex]
For[tex]\( k = 0 \):[/tex]
[tex]\[ \theta \approx 1.21 \][/tex]
For [tex]\( k = 1 \):[/tex]
[tex]\[ \theta \approx 1.21 + \pi \approx 4.35 \][/tex]
For[tex]\( k = 2 \):[/tex]
[tex]\[ \theta \approx 1.21 + 2\pi \approx 7.49 \][/tex]
However, this value is outside our interval, so we do not include it.
For[tex]\( k = 3 \):[/tex]
[tex]\[ \theta \approx 1.21 + 3\pi \approx 10.63 \[/tex]]
This value is also outside our interval, so we do not include it.
Since the tangent function is periodic with a period of [tex]\( \pi \),[/tex] we also need to consider the solutions in the second half of the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \),[/tex] which are obtained by subtracting the principal value from[tex]\( 2\pi \):[/tex]
[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]
[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]
For [tex]\( k = 0 \)[/tex]:
[tex]\[ \theta \approx 2\pi - 1.21 \approx 5.40 \][/tex]
For [tex]\( k = 1 \)[/tex]:
[tex]\[ \theta \approx 2\pi - 1.21 + \pi \approx 8.54 \][/tex]
This value is outside our interval, so we do not include it.
Therefore, the solutions within the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \)[/tex], rounded to the nearest hundredth, are: [tex]\[ \boxed{1.21, 2.26, 3.31, 4.35, 5.40} \][/tex]
Note that [tex]\( 2.26 \)[/tex] and [tex]\( 3.31 \)[/tex] are obtained by adding [tex]\( \pi \) to \( 1.21 \)[/tex] and [tex]\( 2.26 \)[/tex]respectively, which are the first two solutions in the first half of the interval. These values are within the interval [tex]\( 0 \) to \( 2\pi \)[/tex] and are also solutions to the original equation.
What is the equation of a line that contains the point (2, 1) and is perpendicular to the line y= 3x - 4
Answer:
see explanation
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 )
y = 3x - 4 ← is in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex], hence
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation of the line
To find c substitute (2, 1 ) into the partial equation
1 = - [tex]\frac{2}{3}[/tex] + c ⇒ c = [tex]\frac{5}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line
Mr. Gomez owns a carpet cleaning bus
different jobs his company was hired to do. For
carpet cleaning business. Problems 1-4 show four
pany was hired to do. For each situation:
Let a represent the initial charge (1
the house.
present the initial charge in dollars) for coming to
Let b represent the number of hours the job takes.
Let c represent the charge (in dollars) for each hour the
job takes.
Let d represent the total cost in dollars) of the job.
1. Determine the total cost of a job.
a. If a = 60, b = 4, and c = 50, write an equation for calculating the total
Answer:
a) The equation of the total cost is d = a + bc
The equation for calculating the total is d = 60 + 4(50)
b) The total cost for the job is $260
Step-by-step explanation:
* Lets explain how to solve the problem
- Mr. Gomez owns a carpet cleaning business
- The situation of the job;
# a represents the initial charge (in dollar) for coming to the house
# b represents the number of hours the job takes
# c represents the charge (in dollars) for each hour the job takes
# d represents the total cost (in dollars) of the job
* Lets make the equation of the total cost
∵ The initial amount of the job is a dollars
∵ The number of hours the job takes is b
∵ The charge per hour is c dollars
∵ The total cost of the job is d
- The total cost is the sum of the initial amount and the product of
the number of hours the job takes and the charge per hour
∵ The total cost = initial amount + the number of hours × charge
per hour
∴ d = a + b × c
∴ d = a + bc
a)
* The equation of the total cost is d = a + bc
∵ a = $60 , b = 4 hours , c = $50
∴ d = 60 + 4(50)
* The equation for calculating the total is d = 60 + 4(50)
b)
∵ d = 60 + 4(50)
∴ d = 60 + 200
∴ d = 260
* The total cost for the job is $260
Which best describes the graph of the cubic function f(x) = x^3 +x^2 +x +1?
A. x increases, y increases along the entire graph.
B. As x increases, y increases, decreases, and then increases again.
C. As x increases, y decreases, increases and then decreases again.
D. As x increases, y decrease along the entire graph.
Answer:
A.
Step-by-step explanation:
Now since the degree is odd (3 in this case) and the leading coefficient is positive (1), then the end behavior is going to be:
for left-end behavior, it is down
for right-end behavior, it is up
We are going to definitely have some increasing action going on because it goes from down to up reading from left to right.
Let's graph it in our ti-84's or whatever you have.
This is a very rough graph but you can see it is just increasing on the entire domain. This means reading the graph from left to right, there is only rise.
I can give you an answer with calculus in it if you prefer.