Answers
Answer:
Last one.
Step-by-step explanation:
Let's look at the fist one
x+1<-1 and x+1<1
Subtract one on both sides for both inequalities:
x<-2 and x<0
Graph it!
*********************************o x<0
*************o x<-2
________(-2)_________(0)____________
So the inequalities do have some common sets of numbers shared so there is a solution and it is any number less than -2.
Let's look at the second one
x+1<=1 and x+1>=1
Subtract one on both sides for both inequalities:
x<=0 and x>=0
Graph it!
@***************** x>=0
*********************@ x<=0
-----------------------(0)-------------------
The only number included by both graphs is 0 so it still has a solution. The solution is 0.
Let's look at the third one:
x+1<1 and x+1>1
Subtract one on both sides for both inequalities:
x<0 and x>0
Graph it!
************************O x<0
O************************* x>0
---------------------------(0)------------------------------
These inequalities have no overlap. They don't even both include zero because of the open circle (the lack of equal sign). This is the compound inequality that has no solution.
Related Questions
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
Answers
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.
7z-[(2z+y)-(-5y+3z)+9]-12z
Answers
Answer:
-4z-6y-9
Step-by-step explanation:
7z-[(2z+y)-(-5y+3z)+9]-12z
=7z-[2z+y+5y-3z+9]-12z
=7z-2z-y-5y+3z-9-12z
=7z-2z-12z+3z-y-5y-9
=-4z-6y-9
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
Answers
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.
Make n the subject of the formula t= square root of n+3/n
Answers
Step-by-step explanation:
hi I have answered ur question
To make n the subject of the formula t = square root of n+3/n, we can isolate the square root term by squaring both sides of the equation and rearranging the equation to make n the subject.
Explanation:To make n the subject of the formula t = √(n+3)/n, we can start by isolating the square root term. To do this, we square both sides of the equation:
t2 = √(n+3)/n2
Next, we can multiply both sides by n2 to get rid of the denominator:
t2n2 = n + 3
Finally, we can rearrange the equation to make n the subject:
n = (t2n2 - 3)/t2
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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
Answers
[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....
#20-12: Simplify this complex fraction. 1/4 / 2/5
Answers
Answer:
=1/40
Step-by-step explanation:
=1/8/5
=1/40
The width of a soccer field should be 60% of its length. Write and simplify an expression for the perimeter of a soccer field with a length of x feet.
Answers
Answer:
here you go
Step-by-step explanation:
W = (0.6) L
P = 2 ( L + W )
P = 2 [ L + (0.6) L ]
P = 2 ( 1.6 L )
P = (3.2) L
P = (3.2) x
The perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to
[tex]3.2x[/tex] feet.
What is the perimeter?" Perimeter is defined as the total length around the given geometrical shape."
Formula used
Perimeter of the soccer field [tex]= 2 ( L + W)[/tex]
[tex]L=[/tex] length of the soccer field
[tex]W =[/tex] width of the soccer field
According to the question,
Given,
[tex]'x'[/tex] represents the length of the soccer field
As per the given condition,
Width = [tex]60\%[/tex] of length
[tex]= \frac{60}{100} \times x\\\\= 0.6x[/tex]
Substitute the value in the formula to get the perimeter,
Perimeter of the soccer field [tex]= 2 ( x+ 0.6x)[/tex]
[tex]= 2(1.6x)\\\\= (3.2x) feet[/tex]
Hence, the perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to [tex]3.2x[/tex] feet.
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find the distance between the points (5, -3) and (0, 2).
Answers
Answer:
Distance between points (5, -3) and (0, 2) is √50 or 7.07
Step-by-step explanation:
We need to find distance between two points (5,-3) and (0,2)
The distance formula used is:
[tex]d= \sqrt {\left( { x_2-x_1 } \right)^2 + \left( {y_2-y_1} \right)^2 }[/tex]
here
x₁= 5, y₁=-3, x₂=0 and y₂=2
Putting values in the formula:
[tex]d= \sqrt {\left( {x_2-x_1} \right)^2 + \left( {y_2-y_1} \right)^2 }\\d= \sqrt {\left( {0-5} \right)^2 + \left( {2-(-3)} \right)^2 }\\d= \sqrt {\left( {-5} \right)^2 + \left( {2+3} \right)^2 }\\d= \sqrt {25+25}\\d= \sqrt {50}\\d= 7.07[/tex]
So, distance between points (5, -3) and (0, 2) is √50 or 7.07
Hope that this is helpful :)
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
Answers
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.
How can x^2+3x+1=2x^2+2x+3 be set up as a system of equations?
Answers
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.
The average (arithmetic mean) of k scores
is 20. The average of 10 of these scores
is 15. Find the average of the remaining
scores in terms of k.
(A) 20k +150/10
(B) 20k -150/10
(C) 150-20k/10
(D) 150 - 20k/k-10
(E) 20k -150/k-10
Answers
Answer:
(E) (20k - 150)/(k - 10)
Step-by-step explanation:
Sum of all scores = average × number of scores = 20 × k = 20k
Sum of 10 scores = 15 × 10 =150
Sum of remaining scores = 20k - 150
Number of remaining scores = k -10
Average of remaining scores = sum of remaining/no. remaining
= (20 k -150)/(k-10)
hey, need some help with this
Answers
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:
:)
What is the measure of PQR
Answers
Since it tells you the measurements of two arcs that are opposite of one another you just add them together and divide it by two since the arcs correspond with the angle you’re looking for 86 is your answer
Answer:
C. 86°
Step-by-step explanation:
I just did it on A p 3 x
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
Answers
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.
Please show to answer this
Answers
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].
Find the exact value of sec30º.
Answers
Answer:
2 /√3 or 2√3 / 3.
Step-by-step explanation:
Referring to the 30-60-90 triangle: hypotenuse = 2 , smaller leg = 1 and longer leg = √3 and the shorter side is opposite the 30 degree angle.
So cos 30 = √3/2
Sec 30 = 1 / cos 30
= 2 /√3
or 2√3 / 3.
The exact value of sec(30º) using trigonometric identity for secant is 2.
To find the exact value of sec(30º), use the trigonometric identity for secant:
sec(θ) = 1/cos(θ)
Using the special right triangle with angles 30º, 60º, and 90º, it is known that the side lengths are in the ratio 1:√3:2.
The cosine is defined as the adjacent side divided by the hypotenuse.
For a 30º angle, the adjacent side = 1 and the hypotenuse = 2.
So, cos(30º) = 1/2
Substituting this into the formula for secant:
sec(30º) = 1/cos(30º)
= 1/(1/2)
= 2
Therefore, the exact value of sec(30º) is 2.
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Sheila is looking at some information for the obstacle course she is interested in completing. The x-coordinate is the number of the obstacle, while the y-coordinate is the average time to complete the obstacle, measured in minutes. (1, 8.25), (2, 9.075), (3, 9.9825), (4, 10.98075) Help Sheila use an explicit formula to find the average time she will need for the 8th obstacle.
A. f(8) = 8.25(1.1)^8; f(8) = 17.685
B. f(8) = 8.25(1.1)^7; f(8) = 16.077
C. f(8) = 1.1(8.25)^7; f(8) = 2861345
D. f(8) = 1.1(8.25)^8; f(8) = 23606102
Answers
Answer:
f(8) = 8.25(1.1)^7 ; f(8) = 16.077 ⇒ answer B
Step-by-step explanation:
* Lets explain how to solve the problem
∵ The x-coordinate is the number of the obstacle
∵ The y-coordinate is the average time to complete the obstacle
∵ The order pairs of function are (1 , 8.25) , (2 , 9.075) , (3 , 9.9825) ,
(4 , 10.98075)
- From these order pairs
# The time to finish the 1st obstacle is 8.25 minutes
# The time to finish the 2nd obstacle is 9.075 minutes
# The time to finish the 3rd obstacle is 9.9825 minutes
# The time to finish the 4th obstacle is 10.98075 minutes
∵ 2nd ÷ 1st = 9.075/8.25 = 1.1
∵ 3rd ÷ 2nd = 9.9825/9.075 = 1.1
∵ 4th ÷ 3rd = 10.98075/9.9825 = 1.1
∴ There is a constant ratio 1.1 between each 2 consecutive terms
∴ The order pairs formed a geometric series
- Any term in the geometric series Un = a r^(n - 1) , where a is the 1st
term in the series , r is the constant ratio and n is the position of the
term in the series
∵ a = 8.25 ⇒ the time of the first obstacle
∵ r = 1.1
- Sheila wants to find the average time she will need for the 8th
obstacle
∴ n = 8
∵ The explicit formula is f(x) = a r^(n - 1)
∴ f(8) = 8.25 (1.1)^(8 - 1)
∴ f(8) = 8.25(1.1)^7
∴ f(8) = 16.076916 ≅ 16.077
* f(8) = 8.25(1.1)^7 ; f(8) = 16.077
Answer:
Option) BEE is the correct answer!
Step-by-step explanation:
How do you graph
f(x)=7sec(2x)
Answers
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.
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?
Answers
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 ....
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)
Answers
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.
Men and women (ages 22–40) were surveyed to choose a favorite free-time activity: playing sports, dancing, or watching movies/TV. The survey showed the following frequencies: Men—playing sports: 11; dancing: 3; watching movies/TV: 6 Women—playing sports: 5; dancing: 16; watching movies/TV: 9 Which of the following is a correct two-way frequency table for the data?
Answers
can you please add the answers to choose from? I'd like to help
Answer:
B. The second graph displayed.
Step-by-step explanation:
Recieved an 100% on my test with this question!!
Hope I could help! (´⊙◞⊱◟⊙｀)
Suppose that g(x) = f(x) - 3. Which statement best compares the graph of
g(x) with the graph of Rx)?
Answers
Answer:
The graph of g(x) is a translation of f(x) 3 units down.
Step-by-step explanation:
The given function is
[tex]g(x) = f(x) - 3[/tex]
The parent function now is f(x).
The -3 tells us that there is a vertical translation of the parent function 3 units down.
Therefore the graph of g(x) is obtained by translating the graph of f(x) down by 3 units.
which of the following correctly describes the end behavior of the polynomial function f(x)=-x^3+x^2-4x+2
Answers
Answer:
The left end goes up and the right end goes down.
Step-by-step explanation:
Lets solve the function first and then find out the end behavior of the polynomial:
The given function is f(x)=-x^3+x^2-4x+2
First step is: Identify the degree of the polynomial. For this we have to find out the variable with the largest exponent.
The variable with the largest exponent in the given function is -x³
The degree of the polynomial is the largest exponent on the variable.
3 is the degree of the polynomial.
Since the degree is Odd, the ends of the function will point in the opposite direction.
Now find out the leading coefficient of the polynomial which is -1.
Since the leading coefficient is negative the graph falls to the right.
To find the behavior we have to use the degree of the polynomial as well as the sign of leading coefficient.
If it is ODD and NEGATIVE then the the left end goes up and the right end goes down.
Therefore the end behavior of the given function will be described as "the the left end goes up and the right end goes down"....
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
Answers
Add everything together to get 38.8 and multiply by 2
Question 1 of 10
2 Points
If F(x) = x- 5 and G(x) = x?, what is G(F(x))?
O A. x2(x-5)
O B. x2 + x-5
O C. (X - 5)2
O D. x2.5
SUBMIT
Answers
Answer:[tex]\large\boxed{C.\ (x-5)^2}[/tex]Step-by-step explanation:
[tex]f(x)=x-5,\ g(x)=x^2\\\\g\bigg(f(x)\bigg)-\text{put}\ x-5\ \text{expression instead of}\ x\ \text{in}\ g(x):\\\\g\bigg(f(x)\bigg)=(x-5)^2[/tex]
What are the center and radius of the circle defined by the equation x^2+y^2-6x+4y+4=0
Answers
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
what is the first term of the sequence below? ___1, 5,25,125
Answers
Answer:
The first term of the sequence is 1/5
Step-by-step explanation:
The first term is 1/5.
The reason is that there is a common ratio between each term. In this case multiplying the previous term in the sequence by 5 would give the next term.
So in this case 1/5 is the first term.
If we multiply 1/5 by 5, it will give the next term which is 1.
1/5*5=1
Thus the first term in the sequence = 1/5....
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?
Answers
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....
Which of the following data sets has the mean, median, and mode as the same number?
A. 10,10,12,12,13,13
B. 2,3,4,4,5,7
C. 4,7,11,11,16,17
D. 1,2,3,3,5,6
Answers
Answer:
C. 4, 7, 11, 11, 16, 17
Step-by-step explanation:
The mean is the average of the numbers'
The median is the middle number
The mode is the number that occurs most often.
Let's look at each data set I turn.
A. 10, 10, 12, 12, 13, 13
Mean = 11. 7; Median: = 12; Modes: 10, 12, 13
All three measures are different.
B. 2, 3, 4, 4, 5, 7
Mean = 4.2; median = 4; mode = 4
Median and mode are the same, but the mean is different.
C. 4, 7, 11, 11, 16, 17
Mean = 11; median = 11; mode = 11
All three measures are the same.
D. 1, 2, 3, 3, 5, 6
Mean = 3.3; median = 3; mode = 3
Median and mode are the same, but the mean is different.
simplify 3 divided by 5-6i
Answers
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]