Answers
Given in the picture that [tex]D=b^{2} -4ac[/tex]. and the value of Quadratic equation is [tex]b=\sqrt{65}[/tex].
(a) Express b in terms of a, c and D.
[tex]b=\sqrt{D-4ac}[/tex]
(b) Find the values of b when a=2, c=-2 and D=81.
[tex]b=\sqrt{65}[/tex]
By seeing the question we can say that the [tex]b^{2} -4ac[/tex] is in the quadratic formula.
We know the general Quadratic Equation is [tex]ax^{2}+bx+c=0[/tex].
The solution to find the root of the Quadratic Equation is Quadratic Formula: [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex].
The whole solution is depend on [tex]b^{2} -4ac[/tex]. The team is called discriminant.
(a) Given that,
[tex]D=b^{2} -4ac[/tex]
[tex]b^{2}=D +4ac\\[/tex]
Taking square root on both sides.
[tex]\sqrt{b^{2} } =\sqrt{D+4ac}\\ b=\sqrt{D+4ac}\\[/tex]
Therefore, [tex]b=\sqrt{D-4ac}[/tex]
(b) Given that,
a=2,c=-2 and D=81
[tex]b=\sqrt{D+4ac}\\[/tex]
[tex]b=\sqrt{81+4(2)(-2)}\\[/tex]
[tex]b=\sqrt{81-16}[/tex]
[tex]b=\sqrt{65}[/tex]
Therefore, [tex]b=\sqrt{65}[/tex]
A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is a[tex]x^2[/tex] + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant factor. The first requirement for an equation to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When expressing a quadratic equation in standard form, the [tex]x^2[/tex]term comes first, then the x term, and finally the constant term.
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Related Questions
please just answer I want an even 2,000 point's
but here's the question
Whats the best animal?
(Hint say Platypus)
Answers
Answer:
perry da platypus
Step-by-step explanation:
Australia's short beaked platypus
Step-by-step explanation:
sorry if am wrong
-4x + 15 + -49
please show work
Answers
Answer:
12
Step-by-step explanation:
that is my answer and I don't need your
19
Type A batteries and type B batteries were tested.
The cumulative frequency diagram shows information about the battery life of type A.
19 (a)
80
70
60
50
Cumulative
frequency 40
30
20
10
of
0
Type A
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800
Battery life (hours)
Estimate the interquartile range for type A.
Answer
hours
[2 marks]
Answers
300 Hours will be the Interquartile range for the batteries of type A
In the given data there is a total number of 11 terms for Hours. We have to calculate the median value of Hours by using the formula :
=> Median = [tex]\frac{n+1}{2}[/tex], and we know that Q2 = Median so Q2 can be calculated by Q2 = [tex]\frac{n+1}{2}[/tex] => Q2 = 6 => 6th term Will be the Median.
Median = Q2 = 1300 Hours.
Now we have to Calculate Lower Quartile Q1 & Upper Quartile Q3. Since We have our Median 1300 Hours. So, the lower quartile will be :
Q1 = 1100 Hours
and, the Upper Quartile will be Q3 = 1400 Hours.
We have our Upper and Lower Quartiles. We can Calculate Interquartile Range be using the formula Q3 - Q1
=> IQR = Q3 - Q1
Putting values of Q3 and Q1, We get :
=> IQR = 1400 - 1100 => IQR = 300 Hours
Hence, the Interquartile Range IQR is 300 Hours.
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Does the figure above appear to have rotational symmetry? Is yes select the angles of rotation less than 360
Answers
Answer:
the answer should be 180
Math Sets. Answer 1-9 Below.
Answers
Answer:
1. { 1 , 3, 4, 6, 7, 0, 5, 2 }
2. { 6 ,7 ,0 }
3. { 9 ,2 ,4 ,3 ,0 ,7 ,6 }
4. { 1 ,8 ,5 ,9 ,11 }
5. { 1 ,8 ,6 ,7 ,3 ,4 ,11 }
6.
7 . { 0 }
8. { 0 }
9. { 6 ,7 ,0 ,2 }
Step-by-step explanation:
for the 6th one I'm not sure about that , that's why i didn't write the answer for it
please make my answer as brainelist
Dwayne wants to redecorate his bedroom and decides to purchase new furniture. The following graph could be used to represent the value of the new bedroom furniture, f(x), after x years.
a graph of an exponential function which decreases through the points 0 comma 1100 and 2 comma 704
Which of the following statements is/are true based on the graph and the context of the problem?
The function is positive on its entire domain.
The domain is x ≥ 0 to represent the number of years after the bedroom furniture was purchased.
The x-intercept (0, 1100) represents the initial cost of the bedroom furniture.
I only
I and II only
I and III only
I, II, and III
Answers
The correct statements regarding the function are:
I and II only.
What are the correct statements regarding the function?The functions models the value of the furniture after x years, showing exponential decrease. We have that:
Time is never negative, hence the domain is x ≥ 0, representing the number of years since the furniture was purchases.The value of a product will never be negative, and a exponential function that is not shifted never touches 0, hence the function is positive on the entire domain.(0,1100) is the y-intercept, not the x-intercept, and represents the initial cost of the bedroom furniture.Hence statements I and II are correct.
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Answer:
l and lll only
Step-by-step explanation:
just did it
Find the point-slope equation for
the line that passes through the
points (-2, -20) and (9, 79). Use
the first point in your equation.
y - [?] = [](x-[])
Answers
The point slope equation for the line that passes through the points (-2, -20) and (9, 79) is 9 x - y - 2 = 0.
We are given the points as:
(- 2 , - 20) and ( 9 , 79)
We will first find the slope:
Slope = m = y₂ - y₁ / x₂ - x₁
m = 79 + 20 / 9 + 2
m = 99 / 11
m = 9
Now, we have to find the point-slope equation for the line that passes through the points (- 2, - 20) and (9, 79).
The point slope equation is:
y - [y₁] = [m](x-[x₁])
Substituting the values, we get that:
y + 20 = 9 ( x + 2 )
y + 20 = 9 x + 18
9 x - y + 18 - 20 = 0
9 x - y - 2 = 0
Therefore, the point slope equation for the line that passes through the points (-2, -20) and (9, 79) is 9 x - y - 2 = 0.
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The ratio of the measures of three sides of a triangle is 2: 5: 4 , and its perimeter is 165 units. Find the measure of each side of the triangle.
Answers
Answer:
30 units, 75 units and 60 units respectively
Step-by-step explanation:
Solve the following quadratic equation for all values of x in simplest form.
(x + 2)^2 – 46 = 24
Answers
Answer:
x = - 2 ± [tex]\sqrt{70}[/tex]
Step-by-step explanation:
(x + 2)² - 46 = 24 ( add 46 to both sides )
(x + 2)² = 70 ( take square root of both sides )
x + 2 = ± [tex]\sqrt{70}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{70}[/tex]
then solutions are
x = - 2 - [tex]\sqrt{70}[/tex] , x = - 2 + [tex]\sqrt{70}[/tex]
ASAP. Please help me.
Answers
please help i do not understand
Answers
Answer: a. 17
b. an=-2.5n+24.5
Step-by-step explanation:
Term number: 3, 4, 5
Terms: 17, 14.5, 12
Term 3 is 17, term 4 is 14.5, and term 5 is 12.
a. The corresponding value to term 3 is 17.
b. Slope formula: m=(y2-y1)/(x2-x1) where x=term number and y=term.
m=(17-14.5)/(3-4)
m=2.5/(-1)
m=-2.5
y=mx+b ==> Linear equation with slope
12=-2.5(5)+b ==> substitute a term number and it's corresponding term
12=-12.5+b
b=12+12.5
b=24.5
y=-2.5x+24.5
an=-2.5n+24.5 ==> convert linear equation back to an form.
An inlet pipe on a swimming can be used to fill the pool in 10 hours. the drain pipe can be used to empty the pool in 30 hours. if the pool is 1/5 filled and then the inlet pipe and drain pipe are open, how long from that time will it take to fill a pool?
Answers
12 hours will it take to fill the given pool .
we can solve this problem using unitary method ,
10 hours is required to fill the full pool
1 hour is required to fill 1/10th of the pool
30 hours is required to empty the pool
1 hour is required to empty 1/30th of the pool
If two pipes are open then in 1 hour ( 1/10 - 1/30 = 2/30 = 1/15 ) pool will be filled .
The pool is 1/5th filled already as it is mentioned .
So , remaining is ( 1 - 1/5 = 4/5 )
If 1/15th is filled in 1 hour , then 4/5th will be filled in ( 15 × 4/5 ) hours = 12 hours
So, it will take 12 hors to fill the pool .
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Emily buys 14 balloons. 3 are red, 4 are white, and the rest are blue. what is the ratio of blue balloons to the total number of balloons a. 1/2 b. 2 to 1 c. 11:14
Answers
The ratio of blue balloons to the total number of balloons a. 1/2.
To find the ratio of blue balloons to the total number of balloons, firstly we need to find the number of blue balloons. Performing addition and subtraction for the same as follows -
Total number of balloons = Number of blue balloons + number of red balloons + number of white balloons
Number of blue balloons = 14 - (3 + 4)
Number of blue balloons = 14 - 7
Number of blue balloons = 7
Ratio = Number of blue balloons to the total number of balloons
Ratio = 7:14
Performing division of both digits by 7
Ratio = 1:2
Hence the ratio of blue balloons to the total number of balloons a. 1/2.
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6х-10 = -8 + 3x
What's the answer I can't figure it out
Answers
Answer:
So,x=2/3
Step-by-step explanation:
6x-10=-8+3x
6x-3x=-8+10
3x=2
x=2/3
Hope its helpful for you
Answer:
[tex]6x - 10 = - 8 + 3x \\ 6x - 3x = - 8 + 10 \\ 3x = 2 \\ \boxed{x = \frac{2}{3}}[/tex]
help with this math questions
Answers
Answer: the answer is A because A for apple!
Step-by-step explanation:
john thinks of a number,he adds 3 to a number and multiplies the number by 4 and then gets an answer of 10.find the number john was thinking of?
Answers
The number john was thinking of is -0.5
As in the given problem let john thinks of a number x.
He adds 3 to a number i.e x+3
Then he multiplies the number by 4 i.e. 4*(x+3)
The answer he gets is 10.
Thus we an write
4*(x+3)=10
or x+3=5/2
or x=(5/2)-3
=-0.5
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Passing through (3,3) and parallel to the line whose equation is 2x+y-2=0; slope intercept form.
Answers
Answer:
Step-by-step explanation:
y = -2x +2
y - 3 = -2(x -3)
y - 3 = -2x + 6
y = -2x + 9
The temperature in Juno, Alaska was 5 degrees at 7am. The temperature dropped 15 degrees every hour for 3 hours. What was the temperature at 10am?
Answers
Work Shown:
7 AM, temp = 5
8 AM, temp = -10
9 AM, temp = -25
10 AM, temp = -40
Shortcut: 5 - 3*15 = 5 - 45 = -40
I recommend drawing a vertical number line to see what's going on.
Side note: -40 degrees Celsius = -40 degrees Fahrenheit
Categorical data? must be numeric. cannot be numeric. may be either numeric or nonnumeric. must be nonnumeric.
Answers
Categorical data can be either numeric or nonnumeric.
What are Categorical Data?Categorical data can be described as a type of data that can be divided into group and given labels or numerical value for the sake of identification.
Some examples of numerical data are age group, race, sex, educational level, among others.
For example, we can give numerical values like 1 for male, and 2 for female when categorizing people based on sex.
Therefore, categorical data can be either numeric or nonnumeric.
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please help
A triangle with vertices at (-6, 5), (-5, 1), and (-8, 2) is reflected over the y-axis What are the coordinates of the vertices of the reflected image? Enter the correct answers in the boxes. Show Hints Preimage coordinates Image coordinates (-6,5) (-5,1) (-8,2) 03
Answers
Answers:
(6, 5)
(5, 1)
(8, 2)
==================================================
Explanation:
The rule we use is [tex](\text{x}, \text{y}) \to (-\text{x}, \text{y})[/tex] when reflecting over the vertical y axis.
The x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same. So a point like (-6, 5) reflects over to (6, 5). The x coordinate -6 flipped to +6 or simply 6. The y coordinate stayed at 5.
Use this idea to reflect the other points.
christina has $22 more than 3 times as much money as melissas has. together they have $122. How much money does each girl have
Answers
Then amount Christina has is "3n+22"
EQUATION:
Melissas + Christina's = $122
n + 3n+22 = 122
4n=100
n=$25 (amount Melissa has)
3n+22= 75+22= #97 (amount Christina has)
Ellason wants to solve the following system using the elimination method:
5x + 2y = 30
x + y = 8
What number should the equation x + y = 8 be multiplied by to eliminate y? (4 points)
Answers
Help with problems 8 10 and 11
Answers
8) The equation of the line in slope-intercept form is y = 5 · x - 8. (Correct choice: A)
10) The slope of the line is equal to 0. (Correct choice: A)
11) The equation for a graph that is a vertical line is 3 · x - 2 = 0. (Correct choice: C)
How to analyze and interpret linear equations and their features
Herein we must analyze and understand linear equations and their features. 8) The first exercise consists in looking for a linear equation in slope-intercept form with a slope of 5 and y-intercept of - 8, linear equations in slope-intercept form are defined by the following expression:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableIf we know that m = 5 and b = - 8, then the equation of the line in slope-intercept form is y = 5 · x - 8. (Correct choice: A)
10) The slope can be determined by the secant line formula:
m = (3 - 3) / [5 - (-4)]
m = 0
The slope of the line is equal to 0. (Correct choice: A)
11) Vertical lines on a Cartesian plane are of the form x = a or x - a = 0. Then, the equation for a graph that is a vertical line is 3 · x - 2 = 0. (Correct choice: C)
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HELP ASAP I'M TIMED!!!! Which expression is equivalent to (x y) z?
O (x + y) + z
O 2 z (x y)
O x (y z)
O x (y + z)
Answers
Answer:
I believe its O x(yz)
Step-by-step explanation:
eugfweuifwefuwefuwed
Answers
Answer:
1/8 = 0.12500
Step-by-step explanation:
23 divided by 26 = 2(3 - 6) = 2(-3) = 1/23
123+ 1223e = 1200 e -5
Answers
Answer: I worked the equation out and it came as false
Step-by-step explanation:
14.7 kilograms is how many pounds?
Answers
The given kilograms in pounds is 32.407952541177 pounds.
Given that there are 14.7 kilograms.
The SI unit of mass is the kilogram (kg). It is equal to the mass of the international prototype of the kilogram and One kg is approximately equal to 2.20462262184878 pounds.
One pound, the international peso, is legally defined as exactly 0. 5359237 kilograms.
To calculate the kilogram value with its corresponding value in pounds, simply multiply the quantity in kilograms by 2.20462262184878.
Pounds = kilograms × 2.20462262184878
Now, substitute kilograms=14 kilograms, we get
Pounds = 14.7× 2.20462262184878
Pounds=32.407952541177
Hence, in 14.7 kilograms there are 32.407952541177 pounds.
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How to express ABC in terms of x?
Answers
Check out the attached photo
Answer:
∠ ABC = 180 - 2x
Step-by-step explanation:
AB and BC are congruent , so the triangle is isosceles with base angles congruent , that is
∠ A = ∠ C = x
the sum of the 3 angles in the triangle = 180° , then
∠ ABC + x + x = 180
∠ ABC + 2x = 180 ( subtract 2x from both sides )
∠ ABC = 180 - 2x
The price of a train ticket consists of an initial fee of \$5$5dollar sign, 5 plus a fee of \$2.75$2.75dollar sign, 2, point, 75 per stop. julia has \$21$21dollar sign, 21 and would like to travel 505050 kilometers. she wants to know the largest number of stops she can afford to buy on a ticket. let sss represent the number of stops that julia buys. 1) which inequality describes this scenario?
Answers
An inequality that represents given scenario is 5 + 2.75x ≤ 21
For given question,
The $21 means that there is a limit to the number of stops she can take using the train.
From given information, we have the following parameters:
Initial Fee = $5
Rate per stop = $2.75
Amount = $21
The inequality that represents the scenario is calculated using:
Initial Fee + Rate × Number of stops ≤ Amount
We use ≤ because the total charges must not exceed the amount.
Let the number of stops be x.
The above formula becomes
5 + 2.75x ≤ 21
Therefore, an inequality that represents given scenario is 5 + 2.75x ≤ 21
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With explanation! Need it asap
Second Question: Name the polygon.
Answers
Answer:
Decagon or 10
Step-by-step explanation:
Well to find the angle of B, you would have to do 180=2(18) which is 36 + x
x=180-36 x is 144 this is a decagon with ten sides due to the equation: 180(n-2)=144n where the answer is n=10
Can I have brainliest?