Find the discriminant for the following guodutie function. Describe the number and Apes of roots it will have. Then find the roots. Write your answer in simplest radical form. Sketch a graph of the parabola using 5 points, including the vertex. f(x)= 1/2x^2-2x+10
Answers
Answer:
discriminant: -16, two complex conjugate rootsroots: 2±4igraph: see attachedStep-by-step explanation:
You want the discriminant, roots, and graph of the quadratic function ...
f(x) = 1/2x² -2x +10
DiscriminantThe discriminant of the quadratic function
y = ax² +bx +c
is ...
d = b² -4ac
The given function has a=1/2, b=-2, c=10, so the discriminant is ...
d = (-2)² -4(1/2)(10) = 4 -20 = -16
The discriminant of -16 means there will be two distinct complex conjugate roots.
RootsThe roots are ...
x = (-b ±√d)/(2a)
x = (-(-2) ±√(-16))/(2(1/2)) = 2 ±4i
Graph
A graph of the function is attached.
Related Questions
Match the linear equation to the correct graph.
Answers
Answer: y= 1/2x + 2
Step-by-step explanation:
The linear equation is y= mx + b
The y-intercept is located at (0,2), so b equal to 2
Let's pick two points ( 0,2) ( 2, 1)
To find the slope, we need to find the rise over run.
Rise decrease by 1, and run increase by 2, so the slope is 1/2
So the equation is y= 1/2x +2
pls help super easyy due tomm!!!
Answers
If a < b, then multiplying both sides of the inequality by -4 will reverse the direction of the inequality. The resulting inequality will be:
-4a > -4b
This is because multiplying a negative number by a negative number results in a positive number, and multiplying a positive number by a negative number results in a negative number. Therefore, the inequality must be reversed when both sides are multiplied by a negative number.
-10m3+25m2 show how you got it please
Answers
Answer is 3(4x2-3x)
Which equation represents the vertical asymptote of the graph?
x= -8
y= -8
x= 0
y= 0
Answers
Answer: x= -8
Step-by-step explanation:
A vertical asymptote is a line cut in the middle of both graphs!
It can't be x= 0 or y= 0 because it is not the middle of both graphs!
It can't be y= -8 because it is not cut in the middle.
So x=-8 is the right answer!
PLEASE HELP ASAP ITS URGENT!!!!!!!!!!!!!!!!!!
Answers
Answer:
The lie is #2
Step-by-step explanation:
Just like how dividing powers with the same bases is like subtracting exponents, multiplying them is like adding exponents.
If you substitute 4 as x in #1, you get [tex]13^2*13^4=13^6[/tex]. This is the same as saying [tex]13^2^+^4=13^6[/tex], which is true.
If you substitute 4 as x, 6 as y, and 8 as z in #2, you get [tex]m^6*m^8=m^4[/tex]. This is the same as saying [tex]m^6^+^8=m^4[/tex], which is not true.
If you substitute 6 as y in #3, you get [tex]5^6*5^6=5^1^2[/tex]. This is the same as saying [tex]5^6^+^6=5^1^2[/tex], which is true.
(1 point) 5 dice of different colors are rolled, and the number coming up on each die is recorded. how many different outcomes are possible? your answer is :
Answers
There are 7776 different outcomes possible when 5 dice of different colors are rolled.
What is probability?The ratio of favorable outcomes to the total number of outcomes of an event is said to be the probability of that event.
P(E) = n(E)/n(S)
Calculation:It is given that, there are 5 dice with different colors.
There are 6 outcomes for each die rolling. That is the number coming up on each die when it is rolled (1, 2, 3, 4, 5, 6).
So, for five dice when rolled, the number of possible outcomes is
n = 6 × 6 × 6 × 6 × 6
⇒ n = 7776
Therefore, 7776 different outcomes are possible.
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Which relation is a function?
Answers
A function is a relation where each conceivable input value results in exactly one potential output value. The phrase "the output is a function of the input" frequently used.
Explain about the function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
3 ,-3 is an input value of the function
0 is an output value of the function in this graph
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Which positive even integer, when added to the following2 consecutive odd integers, creates a sum of 40?
Answers
Answer:
Let the odd numbers be 2n + 1 and 2n + 3 where n is any positive integer. Therefore, the numbers are 19 and 21.
On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
Complete the relative frequency table, showing all necessary calculations.
Answers
Students do not likes to fly, can drive is 0.13. Therefore, the completed relative frequency table is given below.
Given that, on a recent survey, students were asked if they like to fly and if they can drive.
What is the relative frequency?Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.
From the table
Likes to fly
Row totals = Can drive + Cannot drive
0.32+Cannot drive =0.70
Cannot drive =0.38
Can drive:
Column totals=Likes to fly + Do not likes to fly
0.32 + Do not likes to fly=0.45
Do not likes to fly=0.13
Cannot drive:
Column totals=Likes to fly + Do not likes to fly
0.38 + Do not likes to fly=0.55
Do not likes to fly=0.55-0.38
= 0.17
Row totals = 0.13 + 0.17
= 30
Students do not likes to fly, can drive is 0.13. Therefore, the completed relative frequency table is given below.
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Which of the following is a set of all real numbers x, such that x + 1 > x + 8?
A. The set containing zero
B. The set containing all real numbers
C. The set containing all positive numbers
D. The set containing all negative numbers
E. The empty set
Answers
Answer:
EE.
Step-by-step explanation:
x+1>x+8. 1+8. ∅
Name two sets of alternate interior angles.
Answers
Answer:
∠ a & ∠ d
∠ b & ∠
Answer:
∠ A and ∠ D
∠ B and ∠ E
Step-by-step explanation:
Determine the number of solutions for the equation below.
-7x + 7 + 12x = 5x + 7
A. infinite solutions
B. Two solutions
C. One solution
D. no solution
Answers
Answer:
ANS:- No solution
Step-by-step explanation:
-7x + 7 + 12x = 5x + 7
5x + 7 = 5x + 7
0 = 0
PLEASE HELP!!!!! 20 POINTS!!! The Shultz family went apple picking. Jeshua picked 16 red apples, ½ as many yellow apples as red apples and 28 green apples. How many apples dir he pick in all?
Answers
Answer:
He picked a total of 52
Step-by-step explanation:
You would add 16 (red apples), then divide 1/2 from the 16 red apples, +28 green apples which would equal 52.
Jim began a 255-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 7 hours. If Jim walks at a rate of
3 miles per hour and rides at 39 miles per hour, find the amount of time he spent on the bicycle.
Answers
The amount of time Jim spent on the bicycle is 6.5 hours.
What is distance?The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.
Given:
Total distance, d = 255 miles,
Total time, t = 7 hours,
The speed of walking, s = 3 miles / hour,
The speed of riding bicycle, S = 39 miles/hour,
Calculate the time spent on the bicycle as shown below,
Total time = Time on bicycle + Time walking
7 = Distance on bicycle/speed + Distance of walking / speed
7 = b / 39 + w / 3
Here w is the distance by walking and b is the distance covered by bicycle,
b + w = 255 (As given)
Solve both equations,
w = 1.5 miles and b = 255 - 1.5 = 253.5 miles
Calculate the time spent on a bicycle as shown below,
The time spent on the bicycle = b / 39
The time spent on the bicycle = 253.5 / 39 = 6.5 hours
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Factorise 64(x²-9x+18)=4x²
Answers
Step-by-step explanation:
Here, not sure if it got the answer you were looking.
What is the remainder when the product 1998 × 1999 × 2000 is divided by 7?
Answers
Answer:
As a fraction: 7988004000/7
As a decimal: 1141143428.571429
Step-by-step explanation:
Multiply (1998)(1999)=3994002
Multiply (3994002)(2000)=7988004000
As a fraction it will be 7988004000/7
Turn it into a decimal!
Just divide 7988004000 by 7 or 7988004000/7
This should be: 1141143428.571429
how do i do 10 and 12
Answers
In the given Isosceles trapezoid, the value of x and y is 12 and 5 respectively.
What is Isosceles trapezoid?An isosceles trapezoid, or isosceles trapezium in British English, is a convex quadrilateral in Euclidean geometry that has a line of symmetry cutting through one pair of opposite sides.
It is an uncommon instance of a trapezoid.
Alternately, it can be described as a trapezoid with equal amounts of both the base angles and the legs.
Note that the second requirement, or the fact that it lacks a line of symmetry, prevents a non-rectangular parallelogram from being an isosceles trapezoid.
Two opposite sides (the bases) of each isosceles trapezoid are parallel, while the remaining two sides (the legs) are each the same length (properties shared with the parallelogram).
So, solve for x and y:
For x:
4x - 27 = x + 9
3x = 36
x = 36/3
x = 12
For y:
3y + 19 = 11y - 21
8y = 19 + 21
8y = 40
y = 40/8
y = 5
Therefore, in the given Isosceles trapezoid, the value of x and y is 12 and 5 respectively.
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Need a two column proof for this problem, can't use any parallelogram or quadrilateral theorems, only triangle related and equidistance, altitude, median, and perpendicular bisector related theorems. Thank you!
Answers
Therefore , We have proved AE ≅ CF in the given quadrilateral .
What is congruence ?Two figures or objects are said to be congruent in geometry if they are the same size and shape, or if one is the mirror image of the other.
Here,
Statement
1)AB≅CD , AB║CD ,BF⊥AC and
DE⊥AC
2)ABCD is a parallelogram
3) AD≅BE , AD║BE
4)ΔDAE≅ ΔBCF
5)ΔDAE≅ ΔBCF are right Δ's
6) ΔDEA≅ ΔBFC
7) ΔADE≅ ΔCBF
8)AE ≅ CF
Reasoning
1)Given
2)if a quadrilateral has 1 pair of opposite side both side ≅, ║, then it is a parallelogram
3)In a parallelogram opposite side are ≅, ║
4)Alternate interior angles Δ's are congruent.
5)⊥ segments forms right Δ's.
6)right Δ's. are ≅.
7)AAS congruency theorem
8)Cpetc
Therefore , We have proved AE ≅ CF in the given quadrilateral .
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A new club sent out 250 coupons to boost sales for next year's memberships. They provided 4 times as many to potential members than to existing members. How many coupons did they send to existing members?
A.
4
B.
50
C.
5
D.
54
Answers
Answer:
B. 50
Step-by-step explanation:
Let x be the number of coupons sent to existing members.
The number of coupons sent to potential members is 4 times the number of coupons sent to existing members, or 4x.
The total number of coupons sent is the sum of the number of coupons sent to existing members and the number of coupons sent to potential members, or x + 4x = 5x.
The club sent out 250 coupons, so 5x = 250.
Dividing both sides of the equation by 5, you get x = 250 / 5 = 50.
Therefore, the club sent 50 coupons to existing members.
Juliet needs to rewrite 3 (x + 2) = 6 y in slope-intercept form so she can easily graph it. Which step would be correct to start the process?
She could combine the x and 2 to get 3 (2 x) = 6 y.
She could divide both sides by 3 to get x + 2 = 2 y.
She could distribute the 3 to get 3 x + 2 = 6 y.
She could subtract the 6y to get Negative 6 y = 3 (x + 2).
Answers
The first step to start the is dividing both sides by 3, so the correct option is the second one.
The linear equation in slope-intercept form is:
y = (1/2)*x + 1
How to write the line in the slope-intercept form?To do that, we need o isolate the variable y in one of the sides of the linear equation:
3*(x + 2) = 6y
We can divide both sides by 3 to get:
x + 2 = (6/3)*y
x + 2 = 2y
Now, we can divide both sides by 2, so we will get:
(x + 2)/2 = y
y = (x + 2)/2
y = (1/2)*x + 1
The equation in the slope-intercept form is:
y = (1/2)*x + 1
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Describe the graph of the system of inequalities:
Answers
The x = 5-y line passes through (0,5) and (5,0).
The y = 2x -4 line passes through (0,4) and (2,0).
What is a linear equation?
The graphs of all first-degree equations in two variables will be straight lines. This fact will be used here even though it will be much later in mathematics before you can prove this statement. Such first-degree equations are called linear equations.
Here, we have
Given inequalities
x - y < 5
y ≥ 2x - 4
We have to describe the graph of the system of inequalities.
For, x < 5+y
x = 5-y
We put y = 0, we get
x = 5
We put x =0, and we get
y = 5
Hence, the x = 5-y line passes through (0,5) and (5,0).
For, y ≥ 2x - 4
y = 2x -4
We put x = 0, and we get
y = 4
We put y = 0, we get
x = 2
Hence, the y = 2x -4 line passes through (0,4) and (2,0).
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Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded quarterly until
April 1 of the flllowing year.
Answers
Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded is $58.83
What is compounded?
to combine into a single unit; combine: to mix medications to create a new medication. to create something by putting pieces, things, etc. together; construct: to combine elements of various previous plans to create a new one.The interest on a loan or deposit calculated based on the initial principal, and the collective interest from previous periods is called compound interest. It is basically 'interest earned on money that was previously earned as interest'.
Given that, principal=$3620, rate of interest=6.5% and time period=9 months.
Here, principal compounded quarterly
Thus, Amount
[tex]\$ 3,620 \times 6.5 \% \times \frac{1}{4}=\$ 58.83[/tex]
The first period interest is product of the principal, the annual interest rate and the interest period (expressed in years).
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Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded is $58.83
What is compounded?
To combine into a single unit; combine: to mix medications to create a new medication. to create something by putting pieces, things, etc. together; construct: to combine elements of various previous plans to create a new one.The interest on a loan or deposit calculated based on the initial principal, and the collective interest from previous periods is called compound interest. It is basically 'interest earned on money that was previously earned as interest'.
Given that, principal=$3620, rate of interest=6.5% and time period=9 months.
Here, principal compounded quarterly
Thus, Amount
$3,620x6.5%x1/4=$58.83
The first period interest is product of the principal, the annual interest rate and the interest period (expressed in years).
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2
Write an equation in slope-intercept form that models the situation. In order to go bowling,
you must pay a one-time fee of $10 for rental shoes, and then pay $3 per game. Let y
represent the total cost of bowling after playing x games. * (5 Points)
y=-3x+10
y=3x+10
y=10x-3
y=10x+3
y=-10x+3
Answers
The slope intercept form of the given situation is y=3x+10.
What is slope-intercept form?y = mx + b is the slope-intercept form, where m is the slope and b is the y-intercept.
What is the slope of a line?The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches.
Let x= $3 per game
and we have to add $10 for rental shoes. So slope form will ne
y= 3x+10.
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PLS HELP ME!!!!!! I ONLY HAVE 5 MINS!!!! 50 PTS
Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens. Let m represent the number of games that require 2 tokens; n represent the number of games that require 3 tokens; and p represent the number of games that require 4 tokens.
Janie plays the 3-token game four times. Write two equivalent expressions to represent the number of tokens that Janie will need to play each of the three games at least one time.
Answers
do your work buddy and dont cheat
Step-by-step explanation:
dont cheat and actually study
~Describe each transformation in words.
11.) _____________________.
Answers
The required transformation of the given figure is given as 4 units right and 2 units down.
Given that,
To determine the trasformation of the given figure.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
here,
As shown in the figure,
The figure is translated as of the former figure to 4 units in the positive x direction and 2 units towards the negative y direction.
Thus, the required transformation of the given figure is given as 4 units right and 2 units down.
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can you solve please
Answers
Answer:
113
Step-by-step explanation:
30° + 37° + angle c = 180° (Sum of all angles of a triangle is 180°)
or, 67° + angle c = 180°
or, angle c = 180° - 67°
or, angle c = 113°
Use compatible numbers to estimate the correct quotient.
Answers
The estimate of the quotient expression using compatible numbers is 100
How to estimate the number of quotient?From the question, we have the following parameters that can be used in our computation:
7 | 497
This quotient expression from the question can be expressed as
497 ÷ 7
From the question, we are to make use of compatible numbers
This means that we have the following approximation
497 = 500
7 = 5
Next, we estimate the quotient using approximated values
So, we have
497 ÷ 7 = 500 ÷ 5
Evaluate the quotient
497 ÷ 7 = 100
Hence, the estimate is 100
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PLEASE HELP
Explain how you can identify the opposite and adjacent sides of a right triangle and explain how these can change in any given triangle. Use a diagram to support your explanation.
Answers
In a right angled triangle, the opposite and adjacent sides are the sides proportional to the two acute angles of the triangle.
How to identify the opposite and adjacent sides?In every triangle, the sum of angles is 180⁰. In a right angled triangle, one of the angles is = 90⁰.
The side facing the right angle is called the hypothenuse side.
The sum of the other two angles is 90⁰. That each of the angles is acute angle.
The sides proportional to the acute angles are the opposite and adjacent.
If an angle is given in one of the angle, the side proportional to the given angle is called the opposite while the other one is called the adjacent.
if the angle is changed to the other angle, the side proportional to the given angle becomes the opposite while the other is the adjacent.
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please help:
show that two quadrilaterals are congruent
Answers
The ratio of all the corresponding sides and corresponding angles is one. Then the quadrilateral is congruent with each other.
What is a quadrilateral?The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.
The quadrilaterals are LMNP and LKJQ shown.
In quadrilaterals LMNP and LKJQ,
LK = LM = LQ = LP (Given)
JK = JQ = NM = NP (Given)
∠KJQ = ∠MNP (Given)
∠KLQ = ∠MLP (Given)
∠JKL = ∠NML (Given)
∠JQL = ∠NPL (Given)
The ratio of all the corresponding sides and corresponding angles is one. Then the quadrilateral is congruent with each other.
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What is the best approximation for the relative minimum of the polynomial
function graphed below?
OA. (1.5,-1.8)
B. (0,-3)
C. (-3,0)
OD. (-1.5,-1.8)
G
Answers
(0,-3) is the best approximation for the relative minimum of the polynomial function graphed below.
What is x and y-axis?A two-dimensional number line, like two perpendicular axes, can be used as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. The origin is the point at which all lines in a coordinate system intersect.
The coordinates that are shown on the x and y axes give rise to their respective names. The vertical y-axis is aligned with the horizontal x-axis. They are referred to as axes because they are perpendicular to one another.
From the graph it is shown that,
In the x axis the value is between 0 and 1 , and the y-axis is in between 0 to -3 then the answer is: (0,-3)
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The complete question is as follows: