Topic: The Quadratic Formula
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your answer
Match each equation on the left with the number and type of its solutions on the right.
x + 3x – 4= 0
two complex (nonreal) solutions
x2 + 3x + 4 = 0
two real solutions
4x² + 1 = 4x
one real solution
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Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your
the target before Feleasing. The target will highlight or the cursor will change. Need help? Watch this vide
Answers
Answer:
Step-by-step explanation:
The quadratic formula for a equation of form
ax²+bx + c = 0 is
[tex]x= \frac{-b +- \sqrt{b^2-4ac} }{2a}[/tex]
For the first equation,
x²+3x-4=0,
we can match that up with the form
ax²+bx + c = 0
to get that
ax² = x²
divide both sides by x²
a=1
3x = bx
divide both sides by x
3 = b
-4 = c
. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.
Plugging our values into the equation, we get
[tex]x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1[/tex]
as our possible solutions
Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.
Next, we have
x²+3x+4=0
Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus
[tex]x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\[/tex]
Because √-7 is not a real number, this has no real solutions. However,
(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions
Finally, for
4x² + 1= 4x,
we can start by subtracting 4x from both sides to maintain the desired form, resulting in
4x²-4x+1=0
Then, a=4, b=-4, and c=1, making our equation
[tex]x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2[/tex]
Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution
Related Questions
Which key feature depends on the leading coefficient and the degree of the
function?
A.Axis of symmetry
B.End behavior
C.Intercepts
D.Rate of change
Answers
Answer:
B.End behavior
Step-by-step explanation:
Limit as x goes to infinity:
To find the limit as x goes to infinity of a function, we consider only the leading coefficient and the term with the highest degree of the polynomial, and this limits determines the end behavior of a function, and thus, the correct answer is given by option b.
How many paths are there from C to E?
Оeri
В
12
8
О 10
O 14
Answers
9514 1404 393
Answer:
(b) 8
Step-by-step explanation:
We assume that a path must not repeat any node. (So, loops at G are forbidden.)
There are 2 paths through B to A.
There are 2 paths through D to A, so a total of 4 ways to get from C to A.
There is one path from A to H.
There are two paths from H to F, and one path from F to E.
The total number of possible paths is (4)(1)(2)(1) = 8.
Here is a list.
CBAHFE, CDBAHFE, CBAHGFE, CDBAHGFE,
CDAHFE, CBDAHFE, CDAHGFE, CBDAHGFE
find the exact value of tan -75
Answers
ms.+sanchez+bought+3+pounds+of+turkey+to+make+sandwiches+for+her+family+.+She+uses+.25+of+a+pound+for+each+sandwich+.+How+many+sandwiches+can+she+make+?
Answers
Answer:
she can make 12 sandwiches
Step-by-step explanation:
3/.25 is the solution
A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence.
a. True
b. False
Answers
Answer:
a. True
Step-by-step explanation:
A series in the field of mathematics is defined as the operation of adding up or summation of infinitely many quantities of terms of a sequence. In other words, it is the sum of the terms of the sequence provided.
Another way of defining a 'series' is it is list of numbers with the "addition" operations between the numbers.
Thus the answer is (a). True
Write the complex number in polar form:
Answers
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Answer:
2√30 ∠-120°
Step-by-step explanation:
The modulus is ...
√((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30
The argument is ...
arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle
The polar form of the number can be written as ...
(2√30)∠-120°
_____
Additional comments
Any of a number of other formats can be used, including ...
(2√30)cis(-120°)
(2√30; -120°)
(2√30; -2π/3)
2√30·e^(i4π/3)
Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).
__
At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)
How do you know if a radical can be simplified? Explain.
Answers
Answer:
An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.
What is the domain of the relation described by the set of ordered pairs (-2,8), (-1,1) (0,0) (3,5), (4,-2)?
Answers
Step-by-step explanation:
(-2,-1,0,3,4) are the domain
(x,y)=(domain,range)
simply x components are the domain whereas y components are the range
Chris is reading a book that has nine-hundred seventy-eight pages in it. Every night
Chris reads a number of pages that can be rounded to the nearest hundred. The rst
night Chris reads one-hundred two pages. The second night Chris reads ninety-eight
pages. The third night Chris read one-hundred fty-four pages. The fourth night Chris
reads fty-six pages. The fth night Chris reads two-hundred thirty-four pages. The
sixth night Chris reads forty-eight pages. The seventh night Chris reads one-hundred
seventy pages. On what nights does Chris read a number of pages that can be rounded
to the nearest hundred? Show all your mathematical thinking.
Answers
9514 1404 393
Answer:
Every night
Step-by-step explanation:
The problem statement tells you ...
"Every night Chris reads a number of pages that can be rounded to the nearest hundred."
Then it asks you ...
"On what nights does Chris read a number of pages that can be rounded to the nearest hundred?"
If we take the problem statement at face value, the answer must be ...
"Every night."
For this exercise assume that the matrices are all nn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer.
If there is an n x n matrix D such that Ax =0, then there is also an nxn matrix C such that CAI.
a. True
b. False
Answers
Answer:
A) True
Hope this helps!
Find the perimeter of the quadrilateral in simplest form A quadrilateral has side lengths of 2 StartRoot 27 EndRoot inches, StartRoot 12 EndRoot inches, 3 StartRoot 3 EndRoot inches, 2 StartRoot 12 EndRoot inches.
Answers
Answer: c on edge
Step-by-step explanation:
just finished
Answer:
112.5 inches
Step-by-step explanation:
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=tcost, y=tsint, t=π
Answers
Step-by-step explanation:
the answer is in the image above
The longest leg is Select one:
a. 5√3
b. 10√3
c. 5
d. 20
Answers
Answer:
D:20
sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20
Step-by-step explanation:
The diameter of a circle is inches what is the area?
Answers
Answer:
Pie( r ^2)
Step-by-step explanation:
Here value of r is in inches
The stopping distance on wet pavement at 20mph is about 60feet. The stopping distance at 30mph is 120feet. What would you estimate the stopping distance is at 40mph? Construct a formula
Answers
Answer:
[tex]y = 6x - 60[/tex] --- formula
The stopping distance at 40mph is 180ft
Step-by-step explanation:
Given
[tex](x,y) = (20,60)[/tex]
[tex](x,y) = (30,120)[/tex]
Solving (a): Construct a formula
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{120 - 60}{30-20}[/tex]
[tex]m = \frac{60}{10}[/tex]
[tex]m=6[/tex]
So, the equation is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 6(x - 20) + 60[/tex]
Open bracket
[tex]y = 6x - 120 + 60[/tex]
[tex]y = 6x - 60[/tex]
Hence, the formula to use is: [tex]y = 6x - 60[/tex]
Solving (b): y, when x = 40
[tex]y = 6x - 60[/tex]
[tex]y = 6 * 40 - 60[/tex]
[tex]y = 180[/tex]
Answer quick please.
Answers
Answer
The Answer is A C D
Step-by-step explanation:
I need help with this anyone?????????
Answers
Answer:
No, because sum of co-interior angle is not equal to 180°.
You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x - 3y = 12
-x + 2y = 13
O A. Multiply the left side of equation 2 by 2. Then subtract the result from equation 1.
O B. Multiply equation 1 by 2 and equation 2 by 3. Then add the new equations.
C. Multiply equation 2 by-2. Then add the result to equation 1.
Answers
Answer:
A.
Step-by-step explanation:
The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.
If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.
If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.
When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).
So, option B is not allowed (it is not allowed to multiply only one part of the equation)
The product of a negative integer and a positive integer is?
PLEASE ANSWER A, B, C
Answers
Answer:
a. negative
b. negative
c. positive
Step-by-step explanation:
a. When a negative and positive integer are being multiplied the product will always be negative. For example, -3*2=-6.
b. Before answering this question it is helpful to realize that it is the exact same as part a. This is because the commutative property states that order does not matter in multiplication. So the answer is also negative, 2*-3=-6.
c. If two negative integers are multiplied then the product will be positive. Whenever two integers of the same sign are multiplied the product is positive. The opposite is true when they have different signs; the product will always be negative. An example of two negative integers would be -3*-2=6.
Hii guys plz help me
Answers
Answer:
B is the answer
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
you would have to multiply 2000 and the 25 and then divide
Help? Thanks!!!!!!!!!!!
Answers
Answer:
A
Step-by-step explanation:
You can't really show work for this, but it's A because the angles are opposite each other.
El largo de un terreno es el doble de la medida de su ancho, como se muestra en la imagen. Si el perímetro es de 96 hectómetros, ¿cuáles son las dimensiones del terreno?
Answers
Answer:
Step-by-step explanation:
The following configured particulars are states, in accordance by the interrogate:
Perimeter = 96 hectometers.
Assuming the figure is a square, we can assume that,
S = A side length where,
4s = 96, where all side lengths are equivalent.
If so, then s = 24
Thus, that means that w, denoted as width, must be less than or equal to 24.
In addition, likewise, l, denoted as length, must be less than or equal to 24.
Furthermore, the length is acknowledged or stated to be twice that of the width:
Length = 2w
The listed above may be equated to the following:
2w + 2L = 96
2(24) + 2L = 96
2L + 48 = 96
2L = 48
L = 24
Thus, the width of the figure is equivalent to 24. (Length divided by two).
Thus, the length of the figure is equivalent to 24 (twice the width).
*I hope this helps.
Initial value question help
Answers
Answer:
Initial amount of fish: 530
Population increase or decrease: decrease
Decrease rate: 92%
Step-by-step explanation:
P(t) = Size/population of fish after t years
t = numbers of years
Good luck! :D
Evaluate f (5)
f(5) =
Answers
Answer:
100
Step-by-step explanation:
f(5) means find the output value when x=5
When x =5 f(x) = 100
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
100Explanation:-
we have to find the value of f(5)
But in the questions attachment it tells that
f(5)=100
Which of the following relations represents a function?
Question 4 options:
{(–1, –1), (0, 0), (2, 2), (5, 5)}
{(0, 3), (0, –3), (–3, 0), (3, 0)}
{(–2, 4), (–1, 0), (–2, 0), (2, 6)}
None of these
Answers
Answer:
The first option
Step-by-step explanation:
A function is where one input only has one output, in the other options we can see inputs having different outputs, 0,3 and 0-3 in the second and in the third -2,4 and -2,0.
What is the area of a triangle with a base of 9 units and a height of 7 units? O A. 15.75 sq. units O B. 126 sq. units O c. 63 sq. units O D. 31.5 sq. units SUBMIT வன் PREVIOUS
Answers
Answer:
D. 31.5 sq. units
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
A = 1/2 ( 9)(7)
A = 63/2
A = 31.5 units^2
Step-by-step explanation:
For this, we'll use a formula for the area of a triangle.
Area (A) = ( Base (B) * Height (H) ) / 2
[tex]A = (B * H )/2[/tex]
Plug in given values.[tex]A = (9*7)/2[/tex]
Multiply within parentheses.[tex]A = (63)/2[/tex]
Divide by 2.[tex]A = 31.5[/tex]
Answer:
D. 31.5 sq. units
Use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. Then compare this with the actual change in cost.
Function x-Value
C=0.025x^2 + 3x + 4 x=10
dC= ___________
ΔC= __________
Answers
Answer:
dC=3.5
DC is between 3.475 and 3.525
Step-by-step explanation:
So let dx=1 since the change there is a change in 1 unit.
Find dC/dx by differentiating the expression named C.
dC/dx=0.05x+3
So dC=(0.05x+3) dx
Plug in x=10 and dx=1:
dC=(0.05×10+3)(1)
dC=(0.5+3)
dC=3.5
Let D be the change in cost-the triangle thing.
Since dx=1 we only want the change in unit to be within 1 in difference.
So this means we want it to be from x=9 to x=1] ot from x=10 to x=11.
Let's do from x=9 to x=10 first:
DC=C(10)-C(9)
DC=[0.025×10^2+3×10+4]-[0.025×9^2+3×9+4]
DC=[2.5+30+4]-[0.025×81+27+4]
DC=[36.5]-[2.025+31]
DC=[36.5]-[33.025]
DC=3.475
Now let's do from x=10 to x=11
DC=[0.025×11^2+3×11+4]-[0.025×10^2+3×10+4]
DC=[0.025×121+33+4]-[36.5]
DC=[3.025+37]-[36.5]
DC=[40.025]-[36.5]
DC=3.525
So DC, the change in cost where the change in unit is 1, is between 3.475 and 3.525.
If a student (represented by initials) was chosen at random, find P(HHU C).
Answers
Answer:
[tex]P(HH\ u\ C) = \frac{13}{16}[/tex]
Step-by-step explanation:
Given
The Venn diagram
Required
[tex]P(HH\ u\ C)[/tex]
This is calculated as:
[tex]P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}[/tex]
Where:
[tex]n(U) = 16[/tex] --- count of students
[tex]n(HH\ u\ C) =13[/tex]
So, we have:
[tex]P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}[/tex]
[tex]P(HH\ u\ C) = \frac{13}{16}[/tex]
Which table repsents a linear function?
Answers
Answer:
Option 3
Step-by-step explanation:
Exclude option 1: a linear function will not have a repeated y coordinate
Exclude option 2: the y coordinate is - 3, - 4, - 5, gradually increasing. Thus the line is a curve, not linear function
Option 3: - 8 is the change in every y coordinate. The line is linear because the slope is constant
Exclude option 4: the difference of y coordinate is becoming greater and greater, thus the line is a curve. Not an linear function.
Brainliest please~
Round 61,565 to the
nearest hundred.
Answers
Answer:
61600
Step-by-step explanation:
the 3rd digit is the hundreds. because the digit in the 10s is greater 5, we round it up
Answer:
61,600 is your answer please
