Use the Quadratic Formula to solve for x and then determine whether your solution is real or
complex.
y = x2 - 4x + 9
**Remember y = 0**
O Real
o Complex
Answers
Answer:
[tex] {x}^{2} - 4x + 9 = 0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-( - 4)\pm\sqrt{( - 4)^2-4(1)(9)}}{2(1)} \\x=\frac{ 4\pm\sqrt{ 16-36}}{2} \\ x=\frac{ 4\pm\sqrt{ - 20}}{2} \\ x=\frac{ 4\pm2i\sqrt{ 5}}{2} \\ x = 2\pm \: i\sqrt{ 5} \\ D = {b^2-4ac} \\D = { 16-36} \\ = - 20 < 0 \rightarrow \: x \in \: \mathbb{C} \: \\ x \: is \: complex [/tex]
Related Questions
help me again please 7⅕ ÷ ⅗ =
Answers
Answer:
7 3/5 is the correct answer
If I want to buy a pair of shoes that cost 86.71 and 17% sales tax is added approximately how much are the shoes?
Answers
Answer:
$101.45
Step-by-step explanation:
change 17% to .17 then multiply it by 86.71=14.74 then add that to 86.71 and you get your answer $101.45
The school need to make $750 in order to cover all of their expenses.They estimate 200 students will come to the dance.If they made $150 from a fundraising bake sale what they need to charge per ticket to cover their cost?--
Answers
9514 1404 393
Answer:
$3
Step-by-step explanation:
The cost that hasn't been covered by bake sale proceeds is ...
$750 -150 = $600
If that cost is divided among 200 students, the amount each student needs to pay is ...
$600/(200 students) = $3/student
They need to charge $3 per ticket.
7. In a quiz bee, Marlon scored 132 points during the first round. This score was thrice as much as his score during the second round. What score did he get in two rounds?
Answers
Answer:
II + III = 176
II = 44
III = 132
Step-by-step explanation:
Third round: 132
Second round: 3x=132
x=44 (second round)
2rounds: 132+44=176
Last year, the Galaxy Fair Amusement Park installed a family roller coaster they named The Twist. This coaster was designed to accommodate riders from age 4 to adult and features a tall climb hill and several banking turns. Overall, the park has been disappointed in the reception of The Twist, and very few families are riding the coaster this season. After some research, they discovered that park guests think the climb hill is too tall and fast for younger riders. Galaxy Fair Amusement Park has asked a roller coaster design firm to help them redesign The Twist during the coming off season. The quadratic function that represents the current climb hill is () = −0.102 + 3.6 − 2.4 and the quadratic function that represents the proposed redesign of the climb hill is () = −0.032 + 1.62 − 6.87. In these functions, the value of x represents the time, in seconds, since the roller coaster train cars have left the station, and the output variable is the height of the roller coaster track, in feet, above the ground. 1. Rewrite both () and () from standard form into vertex form. Explain your process. HINT: Each function has a common factor. Start by dividing it out. 2. State the vertex of each function. What does each vertex represent in context of The Twist? 3. Compare the a-value of () to the a-value of the parent quadratic function. What effect does this value have on a parabola? 4. Sketch both of the functions () and () on a single xy-plane. Describe the steps you took to create your sketch. 5. Use the vertex forms of () and () and the sketch you created in question 4 to describe the track changes that occur when the function that represents the climb hill is altered from () to (). Do you think these changes will help younger riders better enjoy The Twist? Explain.
Answers
Answer:
can you add a picture or summerize this
Step-by-step explanation:
PLEASE HURRY HELP!
Find the product (3a4 + 4)2
Answers
Answer:
(3a4 + 4)2
= (12a+4)2
= 24a+8
)
2.
4
3
0.4
15 )
3
0.875
4
1
0
0.5
2
16 )
0.625
5) 3
6)
7)
음
7
1
2
0.6
) 를
17)
0.4
34 23
w/ color on alo.
4
8)
0.717
6
18 )
0.825
4
9)
0.65
5
19 )
0.592
10) ▣
)
0.667
3
20) 그
)
2
3
0.692
Need Kona talaga para bukas please
Answers
Answer:8
Step-by-step explanation:
A farmer sold did he sell? of his sheep. His original flock was 300 sheep. How many sheep did he sell?
Answers
all of his sheep
Hope that helps :)
The perimeter of a rectangle is equal to 54 units. The length of the rectangle is 2k units, and the width of the rectangle is k units
Which expression represents the perimeter, and what is the width of the rectangle?
Answers
The equation to use is 2(2k) + 2(k) = 54
The expression to represents the perimeter is,
54 = 2 (2k + k)
And, The width of the rectangle is, 9 units.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The perimeter of a rectangle is equal to 54 units.
And, The length of the rectangle is 2k units, and the width of the rectangle is k units.
Now, We know that;
Perimeter of rectangle = 2 (Length + Width)
Substitute the given values, we get;
Perimeter of rectangle = 2 (Length + Width)
54 = 2 (2k + k)
54 = 2 × 3k
54 = 6k
54/6 = k
k = 9
Hence, The width of the rectangle is, 9 units.
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The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per
year since.
Find the population at the beginning of 1994. Round to the nearest person.
Answers
Answer:
37356
Step-by-step explanation:
MATH Topic - Coordinate system and Linear graphs Q.1) Complete the following tables and plot the points on the graph paper to represent the equations given below 1 2 3 X y=x+1 y=-3x (x, y) (x, y)
Answers
Step-by-step explanation:
Given Question
Complete the following tables and plot the points on the graph paper yo represents the equations given below :-
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = x + 1 & \sf & \sf & \sf \\ \\ \sf (x,y)& \sf & \sf & \sf \\ \end{array}} \\ \end{gathered} \\ [/tex]
and
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = - 3x & \sf & \sf & \sf \\ \\ \sf (x,y)& \sf & \sf & \sf \\ \end{array}} \\ \end{gathered} \\ [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
[tex]\rm \longmapsto\:y = x + 1[/tex]
On substituting x = 1, we get
[tex]\rm \longmapsto\:y = 1 + 1[/tex]
[tex]\rm \longmapsto\:y = 2[/tex]
On substituting x = 2, we get
[tex]\rm \longmapsto\:y = 2 + 1[/tex]
[tex]\rm \longmapsto\:y = 3[/tex]
On substituting x = 3, we get
[tex]\rm \longmapsto\:y = 3 + 1[/tex]
[tex]\rm \longmapsto\:y = 4[/tex]
Hence,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = x + 1 & \sf 2 & \sf 3 & \sf 4\\ \\ \sf (x,y)& \sf (1,2) & \sf (2,3) & \sf (3,4)\\ \end{array}} \\ \end{gathered}[/tex]
Now, draw a graph using the points (1 , 2), (2 , 3) & (3 , 4)
---------------------------------------------
Given equation is
[tex]\rm \longmapsto\:y = - 3x[/tex]
On substituting x = 1, we get
[tex]\rm \longmapsto\:y = - 3 \times 1[/tex]
[tex]\rm \longmapsto\:y = - 3[/tex]
On substituting x = 2, we get
[tex]\rm \longmapsto\:y = - 3 \times 2[/tex]
[tex]\rm \longmapsto\:y = - 6[/tex]
On substituting x = 3, we get
[tex]\rm \longmapsto\:y = - 3 \times 3[/tex]
[tex]\rm \longmapsto\:y = - 9[/tex]
Hence,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = - 3x & \sf - 3 & \sf - 6 & \sf - 9\\ \\ \sf (x,y)& \sf (1, - 3) & \sf (2, - 6) & \sf (3, - 9)\\ \end{array}} \\ \end{gathered}[/tex]
Now, draw a graph using the points (1 , - 3), (2 , - 6) & (3 , - 9)
******Please help me help please help me ******
Answers
9514 1404 393
Answer:
y = 8
Step-by-step explanation:
If the variation is direct, any multiplier of the x-value will also multiply the y-value.
old value × -1 = new value
x: 4 × -1 = -4
y: -8 × -1 = 8
The new value of y is 8.
Who ever answers first will be marked brainliest
Answers
Answer:
The answer is x≥9.
Step-by-step explanation:
Answer:
x≥9
Step-by-step explanation:
this is the answer all you have to do is solve it
Which is the largest of the following numbers? 0.1, 0.02, 0.003, 0.0004, 0.00005
Answers
answer is the option 0.1
Answer:
0.1
Step-by-step explanation:
By looking at numbers after the decimal point, the largest number comes the soonest. Looking at our options here, 0.1 would be the largest since it is the closest to 1, whereas 0.00005 is the smallest because it is very far from 1.
In the diagram, lines BC and DE are parallel.
What is the measure of Zx?
Answers
Thats all
Make me the bairnlieat
wHaT iS tHe AnWsEr?????????????
2,000 +300000000000000000000000000000000000
Answers
Answer:
3.0 E35
Step-by-step explanation:
Thanks.
-1/3(4+z)=-5/6 I need answer ASAP
Answers
Answer:
-2/3
Step-by-step explanation:
:)
Answer:
z = - 1.5Step-by-step explanation:
Given equation:
-1/3(4 + z) = -5/6Multiply both sides by - 3 and simplify;
(-3)(-1/3(4 + z)) = (-3) (-5/6) 4 + z = 5/24 + z = 2.5z = 2.5 - 4z = - 1.5solve pls brainliest
Answers
(a) 305 (?)
(b) Fields, monroe
(c) Treevale
anyone have the answer?
Answers
Answer:
50.3 (rounded) I think? Could be wrong, however, it's what I got
Circle each input value. Underline each output value. 1. {(1, 1), (2, 3), (3,5)} 2. {(6,2), (5, 3), (4,8)}
Answers
Answer:
The first numbers in the sets are input and the second numbers are outputs.
1. {(1, 1), (2, 3), (3,5)}
Input = 1, 2, 3Output = 1, 3, 52. {(6,2), (5, 3), (4,8)}
Input = 6, 5, 4Output = 2, 3, 8The perimeter of a rectangular garden is 332 m.
If the length of the garden is 93 m, what is its width?
Answers
Answer:
73
Step-by-step explanation:
332÷2= 166
166 - 93 = 73
Which of the following functions has an inverse that is NOT a function?
A) f(x) = (1/2)x - 1/2
B) f(x) = (x - 1)^3 + 2
C) f(x) = 2^x
D) f(x) = x(x - 1)
Answers
Step-by-step explanation:
Content
Functions and their inverses
We begin with a simple example.
Example
Let f(x)=2x and g(x)=x2.
Apply the function g to the number 3, and then apply f to the result:
g(3)=32andf(32)=3.
A similar thing happens if we first apply f and then apply g:
f(3)=6andg(6)=3.
It is clear that this will happen with any starting number. This is expressed as
f(g(x))g(f(x))=x,for all x=x,for all x.
The function f reverses the effect of g, and the function g reverses the effect of f. We say that f and g are inverses of each other.
As another example, we have
(x−−√3)3=xandx3−−√3=x,
for all real x. So the functions f(x)=x3 and g(x)=x−−√3 are inverses of each other.
If x≥0, then (x−−√)2=x and x2−−√=x. If x<0, then x−−√ is not defined. So the functions f(x)=x2 and g(x)=x−−√ are inverses of each other, but we need to be careful about domains. We will look at this more carefully later in this section.
Basics
In an earlier section of this module, we defined the composite of two functions h and g by (g∘h)(x)=g(h(x)).
Definitions
The zero function 0–:R→R is defined by 0–(x)=0, for all x.
The identity function id:R→R is defined by id(x)=x, for all x.
Example
Consider a function f:R→R.
Prove that
0–∘f=0–
f∘id=f
id∘f=f.
Show that f∘0– does not necessarily equal 0–.
Solution
We have (0–∘f)(x)=0–(f(x))=0, for all x, and so 0–∘f=0–.
We have (f∘id)(x)=f(id(x))=f(x), for all x, and so f∘id=f.
We have (id∘f)(x)=id(f(x))=f(x), for all x, and so id∘f=f.
Consider the function given by f(x)=2, for all x. Then f∘0–(x)=f(0–(x))=f(0)=2, and so f∘0–≠0–.
Definition
Let f be a function with both domain and range all real numbers. Then the function g is the inverse of f if
f(g(x))g(f(x))=x,for all x,and=x,for all x.
That is, f∘g=id and g∘f=id.
Notes.
Clearly, if g is the inverse of f, then f is the inverse of g.
We denote the inverse of f by f−1. We read f−1 as 'f inverse'. Note that f inverse has nothing to do with the function 1f.
Example
Let f(x)=x+2 and let g(x)=x−2. Show that f and g are inverses of each other.
Solution
We have
f(g(x))=f(x−2)=x−2+2=x,for all x(f∘g=id)
and
g(f(x))=g(x+2)=x+2−2=x,for all x(g∘f=id).
Hence, the functions f and g are inverses of each other.
Exercise 5
Find the inverse of
f(x)=x+7
f(x)=4x+5.
Example
Let f(x)=ax+b with a≠0. Find the inverse of f.
Solution
We have x=f(x)−ba, for all x. So let g(x)=x−ba. Then
f(g(x))g(f(x))=f(x−ba)=a(x−ba)+b=x=g(ax+b)=(ax+b)−ba=x,
for all x. Hence, g is the inverse of f.
Exercise 6
Show that f(x)=x5 and g(x)=x15 are inverses of each other.
Find the inverse of f(x)=x3+2.
We do not yet have a general enough concept of inverses, since x2 and x−−√ do not fit into this framework, nor do ex and logex. We will give a definition that covers these functions later in this section.
The horizontal-line test
Consider the function f(x)=x2, which has domain the reals and range A={x:x≥0}. Does f have an inverse?
The following graph shows that it does not. We have f(−2)=f(2)=4, and so f−1(4) would have to take two values, −2 and 2! Hence, f does not have an inverse.
Graph of y = x squared and the line y = 4 on the one set of axes.
This idea can be formulated as a test.
Horizontal-line test
Let f be a function. If there is a horizontal line y=c that meets the graph y=f(x) at more than one point, then f does not have an inverse.
Notes. Remember that the vertical-line test determines whether a relation is a function.
Example
Consider the function
f(x)=x3−x=(x+1)x(x−1).
Its graph is shown in the following diagram.
Graph of y = x cubed minus x.
Does f have an inverse?
Solution
The line y=0 meets the graph at three points. By the horizontal-line test, the function f does not have an inverse.
The function whose inverse does not exist is f(x) = x(x - 1)
The correct option is (D) f(x) = x(x - 1)
What is inverse of a function?An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
First, f(x)= [tex]\frac{1}{2} x -\frac{1}{2}[/tex]
let y= [tex]\frac{1}{2} x -\frac{1}{2}[/tex]
On solving for x we get a unique value
Then replace x and y.
It shows that the function have a unique value, which satisfies the condition of inverse.
Now, f(x) =[tex](x - 1)^3 + 2[/tex]
Again, solving for y we can get a cube root function which is a inverse of cube.
Hence, the inverse of [tex](x - 1)^3 + 2[/tex] exists.
Next, f(x) =[tex]2^x[/tex]
Solving for above we get logarithmic value. Log function are inverse of exponential function.
Hence, the inverse of [tex]2^x[/tex] exists.
Last, f(x)= x(x-1)
Solving for above create a square value.
The inverse of square never exist because having square root gives two value one is positive and other is negative.
Hence, the inverse of x(x-1) not exists.
Hence the function whose inverse does not exist is x(x-1).
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if 8 ^ x=2 sqrt 2 find the value of x.
Answers
Answer:
[tex]{ \rm{ {8}^{x} = \sqrt{2} }} \\ \\ { \rm{ {2}^{3x} = {2}^{ \frac{1}{2} } }} \\ \\ { \rm{3x = \frac{1}{2} }} \\ \\ { \rm{x = \frac{1}{6} }}[/tex]
How many 0.25 are there in 10.5?
Answers
the answer is 42
Answer:
42
Step-by-step explanation:
to find how many 0.25 there are in 10.5 we have to divide 10.5 by 0.25
10.5÷0.25
=42
Hope this helped you- have a good day bro cya)
Please help out with this question
Answers
Step-by-step explanation:
5⁴+5³-6(5)²-5(5)-15
= 560
Find the slope and y intercept of the line 3x+2y=-6
Answers
Answer:
Step-by-step explanation:
Slope - -3/2
y-intercept- (0,-3)
Do the fractions 6/7 and 16/25convert to repeating or terminating decumals numbers
Answers
Answer:
terminating decimals
Step-by-step explanation:
they don't seem to repeat numbers
Answer:
repeating
Step-by-step explanation:
6÷7= 1.111111111111
PLEASE HELP ITS MATH THANK YOUUUU
Answers
7.3/2 = 18.25/?
Cross multiply
18.25*2 = 7.3*?
36.5 = 7.3*?
Divide both sides by 7.3
36.5/7.3 = ? (Because 7.3/7.3 is 1 you’re just left with ?)
36.5/7.3 = 5
So 5 hours
How much work is done lifting a 100 Newton book onto a shelf that is 2 meters high on Earth?
Answers
We want to find the work done by lifting a book a given distance.
The answer is 200 N*m
We know that the book weighs 100 Newtons and that we lift it a distance of 2 meters.
Remember that the work needed to lift an object of mass M to a height H is:
W = M*g*H
where g is the gravitational acceleration.
Knowing that:
weight = M*g
We can replace the things we know to get the work:
W = 100N*2m = 200 N*m
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Greatest common factor of 30 and 75
Answers
Step-by-step explanation:
The prime numbers 5 and 3 are both factors that are common to 30 and 75. The product of these factors is 3×5 = 15. Thus, the “Greatest Common Factor” of 30 and 75 is 15.
Answer:
the Greatest common factor of 30 and 75 is 15
Step-by-step explanation:
The product of these factors is 3×5 = 15. Thus, the “Greatest Common Factor” of 30 and 75 is 15.