For a quadratic equation, we start out seeking 2 solutions.
According to the statement
We have to find about the quadratic equation.
So, For this purpose, we know that the
Quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power
From the given information:
when we solve a quadratic equation, how many solutions should we always start out seeking.
Then
Here, we are required to search out out what number solutions to start out out seeking while solving a equation and also the condition for a quadratic graph not having zeros ( no x-intercepts).
Therefore, where X³ occurs in an equation, it's cubic and consequently has 3 solutions.
And, a quadratic can haven't any zeros ( no x intercepts) if the roots of the equation are complex numbers.
A quadratic is one which has the very best degree of its variable ( usually x) to be 2.
Consequently, after we solve a quadratic, one should start out seeking two (2) solutions.
This is so because, the quantity of solutions to begin out seeking corresponds with the very best power of the experimental variable, X.
Therefore, where X³ occurs in an equation, it's cubic and consequently has 3 solutions.
Therefore, where X¹ occurs in an equation, it's linear and consequently has 1 solution.
And, where X² occurs in an equation, it's quadratic and consequently has 2 solutions.
It is possible to possess a quadratic with no zeros (i.e no x-intercepts).
So, For a quadratic equation, we start out seeking 2 solutions.
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2(i + 3) > 4(1 - i)
[tex]2(i+3)>4(1-i)[/tex]
Distribute 2 in (i+3) and 4 in (1-i)
[tex]2i+6>4-4i[/tex]
Move -4i to another side and 6 to another side. When moving to another side, you'll have to change the sign/operator to opposite (Plus -> Minus, Multiply -> Divide)
[tex]2i+4i>4-6\\6i>-2\\[/tex]
For this part, move 6 to divide -2.
[tex]i>\frac{-2}{6} \\i>\frac{-1}{3}\\i>-\frac{1}{3}[/tex]
Whenever either a numerator or a denominator is in negative, we can pull out the negative in the middle of fraction.
Note that i is the symbol of imaginary number - as defined - i = √-1 But for this one, It's just a variable if I assume.
Thus, the answer is i > -1/3
4 - 1 1/4
A. 3 1/4
B. 3 3/4
C. 2 3/4
D. 2 1/4
Fabulous fitness charges a one time fee of $90 and an additional $25 per month wonder weights charges a one time fee of only $ 27 dollars but charges an additional $32 each month for how many months is fabulous fitness less expensive than wonder weights? Set up and solve an equality to determine your answer
Answer:
9 months
Step-by-step explanation:
Given
Fabulous fitness charges a one-time fee of $90 and an additional $25 per month
let the number of months be x
and the total charges be y
y= 25x+90---------1
Wonder weights charges a one-time fee of only $ 27 dollars but charge an additional $32 each month
let the number of months be x
and the total charges be y
y= 32x+27------------2
Required
The value of x, that is the number of months
Step two:
Equating both equations we have
25x+90=32x+27
collect like terms
25x-32x=27-90
-7x=-63
7x=63
divide both sides by 7
x= 63/7
x= 9 months
copy and paste the link in the download in a new tab
Answer:
lol ok
Step-by-step explanation:
Answer:
ok Y?
Step-by-step explanation:
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(-7, 134) (-3, 10) (5, 50)
Given:
The three points are (-7,134), (-3,10) and (5,50).
To find:
The equation of parabola using quadratic regression.
Solution:
The general equation of quadratic regression is
[tex]y=ax^2+bx+c[/tex] ...(i)
The three points are (-7,134), (-3,10) and (5,50).
Using the graphing calculator, we get a=3, b=-1 and c=-20. Putting these values in (i), we get
[tex]y=3x^2+(-1)x+(-2)[/tex]
[tex]y=3x^2-x-2[/tex]
Therefore, the equation of parabola is [tex]y=3x^2-x-2[/tex] and the missing values in the given equation are 3, -1 and -20.
A bag contains 4 red marbles and 6 blue marbles. Brandon selects one marble from the bag. Without replacing the marble he then
selects a second marble. What is the probability he selects a red marble given that he first selects a blue marble?
A)1/5
B)2/5
C3/5
D)4/15
HELP ASAP ILL GIVE BRAINLIEST
Find the solution of the system of equations.
– 2 – 8y = -30
2x + 8y = 36
Answer:
x= 1.5
y= 4.125
Step-by-step explanation:
Step one:
given the two equations
[tex]-2x - 8y = -30-------1\\\\2x + 8y = 36--------2[/tex]
Step two:
let us subtract the equations
[tex]-2x - 8y = -30-------1\\\\ -(2x + 8y = 36)--------2\\\\0x-16y=-66[/tex]
[tex]-16y=-66\\\\16y=66[/tex]
divide both sides by 16
[tex]y=66/16\\\\y=4.125[/tex]
put y= 4.125 in equation 2
[tex]2x + 8(4.125)= 36\\\\2x+33=36\\\\2x=36-33\\\\2x=3\\\\x= 3/2\\\\x= 1.5[/tex]
Find the volume of the shape
Answer:
The volume of cylinder is 58.2 cm³.
Step-by-step explanation:
The formula of volume of cylinder is :
[tex]v = \pi \times {r}^{2} \times h[/tex]
So, you have to substitute the values into the expressions :
[tex]let \: r = 2.1,h = 4.2[/tex]
[tex]v = \pi \times {2.1}^{2} \times 4.2[/tex]
[tex]v = 58.2 \: {cm}^{3} \: (3sf)[/tex]
the multiplicative property of
-1 1/4
Answer:
Step-by-step explanation:
1 is the answer
Raymond can paint 5/8 of a wall in 16 minutes. How long would it take to for him to paint 1/3 of a wall
Answer: 128/15 min or 8.5 min
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trust
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HELPPPPP
Which of the following are roots of the polynomial function below?
Check all that apply.
F(x) = x^3 -3x²+2
The roots of the polynomial function f(x) = x³ - 3x² + 2 are [tex]\frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, \ and \ 1[/tex].
What are the roots of the polynomial function?Given the polynomial function in the question:
f(x) = x³ - 3x² + 2
To find the roots of the polynomial function f(x) = x³ - 3x² + 2, we need to solve for values of x that make the function equal to zero.
f(x) = x³ - 3x² + 2
x³ - 3x² + 2 = 0
Factor the equation using the rational root test:
( x - 1 )( x² - 2x - 2 ) = 0
Equate each factor zero and solve for x:
( x - 1 ) = 0
x - 1 = 0
x = 1
( x² - 2x - 2 ) = 0
x² - 2x - 2 = 0
Using the quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4(ac)} }{2a} \\\\x = \frac{-(-2)\±\sqrt{(-2)^2 - 4(1*-2)} }{2*1} \\\\x = \frac{2\±\sqrt{4 + 8} }{2} \\\\x = \frac{2\±\sqrt{12} }{2}\\\\Hence:\\\\x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}[/tex]
Therefore, the roots are [tex]x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, 1[/tex].
Options A, B and D are the correct answers.
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4) What is the equation of the line that passes through the points (3,0) and 2 points
(5,4)?
Your answer
Consider the line y=8x-9
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
compare the line y=8x-9 to y=mx+b where m is a slope and b is y-intercept
so, the line y=8x-9 has a slope m=8
by definition, the slope of a line parallel to this line will be same, m=8
by definition, the slopes of perpendicular lines are negative reciprocals to each other; so, m = -1/8
cual de las siguientes compraraciones es correcta? a)1\8>1\2 b) 1/3<1\5 c)1\12>1\100 d)1\4>1\6
Las comparaciones correctas son (c) ( 1/12 ) > ( 1/100 ) y (d) ( 1/4 ) > ( 1/6 ).
Considere las comparaciones,
Para la opción (a),
( 1/8 ) > ( 1/2 )
Ahora, encuentre el valor de cada término en forma decimal.
( 1/8 ) = 0.125 y;
( 1/2 ) = 0.5
Por lo tanto, ( 1/2 ) > ( 1/8 )
Por lo tanto, esta opción es incorrecta.
Para la opción (b),
( 1/3 ) < ( 1/5 )
Ahora, encuentre el valor de cada término en forma decimal.
( 1/3 ) = 0.333 y;
( 1/5 ) = 0.2
Por lo tanto, ( 1/3 ) > ( 1/5 )
Por lo tanto, testa opción es incorrecta.
Para la opción (c),
( 1/12 ) > ( 1/100)
Ahora, encuentre el valor de cada término en forma decimal.
( 1/12 ) = 0.0833 y;
( 1/100 ) = 0.01
Por lo tanto, ( 1/12 ) > ( 1/100 )
Por lo tanto, esta opción es incorrecta.
Para la opción (d),
( 1/4 ) > ( 1/6 )
Ahora, encuentre el valor de cada término en forma decimal.
( 1/4 ) = 0.25 y;
( 1/6 ) = 0.1666
Por lo tanto, ( 1/4 ) > ( 1/6 )
Por lo tanto, esta opción es correcta.
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What is the value of the absolute value expression |−152| + |5| − |−24|?
179
133
−125
−173
The value of absolute value expression is equal to 133. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The absolute value or modulus of a real number x abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.
The absolute value of the function will be calculated as,
E = |−152| + |5| − |−24|
E = 152 + 5 - 24
E = 133
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1 The distance on the number line from a to 7 is 0.5. Which of the following could be the value of a ? A) 7.5 B) -3.5 C 0.5 D 6.5
Answer:
6.5
Step-by-step explanation:
Answer:
6.5
Step-by-step explanation:
These diagrams show the same third-degree polynomial, P(x) = 2x3 + 5x2 + x + 10, divided by a linear factor and by a quadratic factor.
The third degree - polynomial can be factored into a linear factor of x+2 and a quadratic factor of 2x²+x+5.
A third degree polynomial is a collection of algebraic expressions such that the highest degree of the variable is 3 and there are no fractional degrees and exponential variable.
To factor a polynomial we will use the factor theorem to find the linear factor. Then by dividing the polynomial by the linear factor we will calculate the quadratic factor.
Given polynomial P(x) = 2x³ + 5x² + 7x + 10
Now by using the trial and error method factor theorem we see that
g(x) = (x+2) is a factor of P(x) .
Now let us find the quadratic factor as:
P(x) ÷ g(x) = ( 2x³ + 5x² + 7x + 10) ÷ (x+2) = 2x²+x+5
Hence the third degree - polynomial can be factored into a linear factor of x+2 and a quadratic factor of 2x²+x+5.
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Disclaimer: The correct polynomial is P(x) = 2x³ + 5x² + 7x + 10 .
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WRITE THE NEXT 2 TERMS OF EACH SEQUENCE
1) 2, 6, 18, 54, __, __
2) 2, - 4, 8, - 16, __, __
3) 1, 3, 5, 7, __, __
4) 1, 2/3, 4/6, 8/9, ___, ___
Answer:
1) 2,6,18,54,162,468 (multiply by 3 each time)
2) 2, -4, 8, -16, 32, -64 (i'm not sure what this is but i'm pretty confident i'm right lol)
3) 1,3,5,7,9,11 (add 2 each time)
4) 1, 2/3 , 4/6 , 8/9 , _ _ (i'm sorry i tried my hardest but i don't know this one)
Step-by-step explanation:
hope this helped! so sorry about 4...
A special 8-sided die is marked with the numbers 1 to 8. It is rolled 15 times with the results shown in the table. Results 3 4 5 2 7 1 3 7 2 6 2 1 7 3 6 The experimental probability of rolling an odd number is %, which is % more than the theoretical probability.
Let us consider,
A special [tex]8-[/tex]sided die is marked with the numbers [tex]1[/tex] to [tex]8[/tex].
The odd numbers on the die are [tex]1,3,5,7.[/tex]
The even numbers are [tex]2,4,6.[/tex]
For the experimental sequence of [tex]15[/tex] rolls.
There are [tex]9[/tex] odd number out of 15, which is [tex](3,5,7,1)[/tex].
So the experimental probability is,
[tex]\frac{9}{15} =\frac{3}{5} \\\\=0.60\\[/tex]
[tex]\implies0.60=60[/tex] %
The theoretical probability given that there are odd numbers [tex](1,3,5,7)[/tex] out of [tex]8[/tex] on the dice should be [tex]50[/tex] % because [tex]\frac{1}{2}[/tex] of the numbers are prime.
Thus,
The theoretical probability is [tex]50[/tex] % .
Then,
[tex]60[/tex]%[tex]-50[/tex]%[tex]=10[/tex]%
Hence, the experimental probability of rolling an odd number is [tex]60[/tex]%, which is [tex]10[/tex] % more than the theoretical probability [tex]50[/tex]%.
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Answer:
60%, 10%
Step-by-step explanation:
Plato/Edmentum
What is the rate of change or slope?
Question 1 options:
m= 1/2
m=-2/1
m=-1/2 or m=-2/4
m=-2/1 or m=-4/2
Answer:
m=-1/2 or m=-2/4
Step-by-step explanation:
The rate of change or slope of the given line is [tex]m=-\frac{1}{2} or m=-\frac{2}{4}[/tex]
Given :
The graph of a line . To find out the slope or rate of change , we pick two points on the line.
Two points are (-8,2) and (4,-4)
Lets apply slope formula
[tex]Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
(-8,2) is (x1,y1)
(4,-4) is (x2,y2)
Substitute all the values inside the formula
[tex]Slope = \frac{y_2-y_1}{x_2-x_1}\\slope =\frac{-4-2}{4+8} =\frac{-6}{12} =-\frac{-2}{4} =-\frac{1}{2}[/tex]
The rate of change or slope of the given line is [tex]m=-\frac{1}{2} or m=-\frac{2}{4}[/tex]
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Which statement is true about the two lines whose equations are given below?
A. The lines are parallel.
B. The lines are perpendicular.
C. The lines intersect but are not perpendicular.
D. The lines coincide.
Answer: C. The lines intersect but are not perpendicular.
Step-by-step explanation:
The correct option is C, the lines intersect but are not perpendicular.
How to determine the equation of the line?To determine which statement is true about the two lines whose equations are given below:
y = 3x + 2
y = -4x + 9
We can compare the slopes of the two lines. The slopes of these lines are 3 and -4 respectively.
Two lines are parallel if and only if their slopes are equal. Since the slopes of these lines are not equal, we can eliminate options A.
Two lines are perpendicular if and only if the product of their slopes is -1. The product of the slopes of these lines is -12, which is not equal to -1. Hence, we can eliminate options B.
Since the lines are neither parallel nor perpendicular, they intersect. To determine whether they intersect perpendicularly, we can compute the angle between them using the slopes.
The angle between two lines is given by the formula:
[tex]tan \theta = \dfrac{(m_2 - m_1)}{ (1 + m_1m+_2)}[/tex]
where m₁ and m₂ are the slopes of the two lines.
Substituting the slopes of the given lines, we get:
[tex]tan \theta = \dfrac{|(-4 - 3)} { (1 + (3 \times -4))|} \\[/tex]
tanθ = 7 / 11
Therefore, the correct option is C: the lines intersect but are not perpendicular.
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The missing equation of lines are:
y = 3x + 2
y = -4x + 9
Emma can run 2 3/4 miles in 3/4 hour what is her average speed in miles per hour
Answer:The answer is 1/6
Step-by-step explanation:1/8 miles in 3/4 minutes
then, that means in 1 minute ( 1 min = 3/4 * 4/3) Emma will ride a distance of (1/8)*(4/3)= (1*4)/(8*3)= 1/6.
The answer is 1/6 (in 1 min she will ride 1/6 miles).
r = -5 + 19. r = ?
Please help me with this
Answer:
r = 14
Step-by-step explanation:
r = -5 + 19
Simplify the right side by subtracting 5 from 19
r = 14
20-34+ 8/2 =? PLS HELP ME I GIVE ALL MY POINTS.
Answer:
-10
Step-by-step explanation:
20-34=-14, 8/2 is just 4, so add 4 to -14 which = -10
i need help simplifying this problem
please help me............
Answer:
38.24
Step-by-step explanation:
You need to do 45.3-7.06 and you get x
help fast 15 points Which value of n makes this equation true? 57 – 1 9 5. A. n = -16 n = -2 n = 16
Answer:A) -16
Step-by-step explanation:
HELP PLSS I NEED THE ANSWERS ASAP PLSSS :((
Answer:
132 km :)))))))))))))))
Step-by-step explanation:
The Hint said to find the two things in comparison
they are:
99km----------→9litXkm----------→12litcross multiply the two equations
=99km*12lit=9lit*Xkm
=1188lit/km=9Xlit
note;
liters will annul liters
hence,
X=1188km/9
X = 132km
is the final answer
If EF = x + 3, FG = 3x, and EG = 7, what is FG?
Answer:
FG = 3
Step-by-step explanation:
let me know if you are still confused!
Find the slope of the line.