Answers
The table of solutions for this quadratic equation (y = -2x²) include the following:
x y_
-2 -8
-1 -2
0 -0
1 -2
2 -8
A graph of the solution of the given quadratic equation has been plotted in the image attached below.
How to determine the solutions?In Mathematics, the graph of any quadratic equation or function always forms a parabola, which simply means a u-shaped curve. In order to determine the correct solutions to the given quadratic equation, we would have to substitute the x-values contained in the table into the quadratic equation.
At point x = -2, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(-2)²
y = -2 × 4
y = -8
At point x = -1, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(-1)²
y = -2 × 1
y = -2
At point x = 0, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(0)²
y = -2 × 0
y = 0
At point x = 1, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(1)²
y = -2 × 1
y = -2
At point x = 2, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(2)²
y = -2 × 4
y = -8
In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.
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Related Questions
in the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a
Answers
If all other values remain constant, an increase in sample size will result in a broader confidence interval when constructing one.
The definition of the MoE, or margin of error, is
MoE = sigma ÷ sqrt(n)
The population standard deviation is represented by sigma. If you don't know sigma, utilize s to get a rough idea of it. The sample standard deviation is denoted by the variable s.
The MoE increases along with the sigma. The width or narrowness of the confidence interval is directly determined by the MoE. A smaller MoE indicates greater confidence with less error, whereas a larger MoE indicates greater net casting but increased error.
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Solve for x.
4(2x-17)=4x+(-5)
Answers
Step-by-step explanation:
4(2x-17) = 4x+(-5)
Open the bracket
8x - 68 = 4x - 5
Collect like terms
8x - 4x = -5 + 68
2x = 63
x = 63/2
x = 31.5
8x-68=4x-5
Move variables to one side.
4x=73
Divide.
x=18.25 or 73
—
4
3 (2− k) = −3k + 2
I need this for class
Answers
The value of k for the expression, 3 (2− k) = −3k + 2, does not exist.
According to the question,
We have the following expression:
3 (2− k) = −3k + 2
Now, we will multiply 3 into the bracket:
6-3k = -3k+2
Now, moving -3k from the left hand side to the right hand side will result in the change of the sign from minus to plus:
6-3k+3k = 2
Now, 3k will get subtracted from 3k. So, we do not have any variable left for this equation.
Hence, the value of k for the expression, 3 (2− k) = −3k + 2, does not exist.
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the data set has 80 observations and has mean 30 and standard deviation 5. approximately how many observations lie between 20 and 40?
Answers
A minimum of 71 observations must fall inside the interval (20, 40).
Define Chebyshev's theorem.It is true that Chebyshev's Theorem holds true for all conceivable data sets. The minimal percentage of measurements that must fall within one, two, or more standard deviations of the mean is described. The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.
Given,
The data set has 80 observations and has mean 30 and standard deviation 5.
Chebyshev's theorem states that for each data set, the proportion (or percentage) of values that lie within k standard deviations of the mean (that is, the interval (x -ks , x +ks) is at least 1-1/k² . where k > 1.
x = 30
s = 5
Three standard deviations are added to and subtracted from the mean to get the interval (10, 40).
(30 - 3.5, 30 + 3.5) = (10, 40)
According to Chebyshev's Theorem, this interval contains at least 1 -1/3² = 8/9 of the data. Given that 8/9 of 80 is 71.11, the interval must include at least 71.11 observations. However, one cannot make a fractional observation, so we draw the conclusion that the interval must contain at least 71 observations.
A minimum of 71 observations must fall inside the interval (20, 40).
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given a normal distribution with a mean of 50 and standard deviation of 5, what percent of the values are between 40 and 60? enter answer as a percent with no decimals.
Answers
For the given normal distribution, 95% of the values lie between 40 and 60.
Let the said distribution be X
Here it is given that X follows a normal distribution and it has a mean of 50 and a standard deviation of 5.
Therefore we can write X~ N(50, 25)
Now we need to find P(40< X< 60)
= P(40< X< 60) = P(X < 60) - P(X<40)
To find this we need to convert it into the form of a standard normal and then look up the p-values from the Z-table.
To do this we need to use the formula
P(X < x) = Φ[(x - μ) / σ]
where,
μ is the mean
σ is the standard deviation
Therefore we get
P(X < 60) - P(X<40) = Φ[(60 - 50) / 5] - Φ[(40 - 50) / 5]
= Φ[2] - Φ[-2]
Φ(-x) = 1 - Φ(x)
Therefore,
Φ[2] - Φ[-2]
= 2Φ(2) - 1
We get the p-value
2 X .97725 - 1
= 1.9545 - 1
= 0.9545
= 95% (approx)
Hence 95% of the values are between 40 to 60.
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what was the major flaw in the stanford prison experiment? question 9 options: a) the respondents wanted to leave, but zimbardo would not let them. b) the students were not randomly assigned. c) the study went on too long. d) zimbardo did not use a control group.
Answers
Zimbardo did not use a control group. Experiments are performed to reach meaningful conclusions using the appropriate research method. The correct answer is (A).
Experiments whether they are done in natural settings or in a controlled environment need to follow certain ethics. But the Stanford Prison Experiment is an exception. In this experiment, Philip Zimbardo, the Stanford psychologist, took paid participants and asked them to be “guards” in a mock prison at Stanford University.
As soon as the experiment began, the “guards” began mistreating the “prisoners,” in order to provoke evil circumstantially. The conclusion of the study suggested innocent people, thrown into a situation where they have power over others, will begin to misuse that power. And people who are put into a situation where they are powerless will be driven to submission.
The Stanford Prison Experiment has proved to be a Fraud. Philip Zimbardo, the Stanford psychologist who did the experiment, and interviews of the participants, offers convincing evidence that the guards in the experiment were trained to be cruel. This proves that the experiment’s most memorable moment of a prisoner screaming out of rage and proclaiming, “I’m burning up inside!” was the result of the prisoner's acting skills. Many of them think of this study as more of a dramatic demonstration with no real outcomes. The Zimbardo prison experiment is a classic study that has been recently reevaluated and exposed as a fraud.
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9) Willie took a trip to Oman. Upon leaving he decided to convert all of his Rials back into dollars. How many dollars did he receive if he exchanged 12 Rials at the rate of 1 Rial to $3?
10) A rectangle is 2 in wide and 1 in tall. If it is enlarged to a width of 14 in then how tall will it be?
Answers
number 9 is 36 12x3 is 36
2(x + 3) = x-4
What is the answer?
Answers
distribution ( 2 . x, 2 . 3)
2x + 6 = x - 4
-x
x + 6 = - 4
- 6
x = - 10
Answer : x = -10
Answer:
x=-10
Step-by-step explanation:
2(x+3) = 2x+6
2x+6=x-4
2x+6-6=x-4-6
2x=x-10
2x-x=x-10-x
x=-10
14 The equation u = 0. 99c shows the value of the U. S. Dollar compared to
the Canadian dollar on one particular day, where c = the value of the
Canadian dollar and u = the value of the U. S. Dollar. The table shows
the value of the U. S. Dollar compared to the Australian dollar on the
same day. Was the U. S. Dollar closer in value to the Canadian dollar or
the Australian dollar that day?
N
t
sed the
the unit
Australian Dollar
1
2
3
4
compare
U. S. Dollar
0. 95
1. 90
2. 85
3. 80
Show your work.
Answers
On that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.
Define the term comparison of numbers?In arithmetic, comparing numbers is described as the process or method of determining whether one number is smaller, bigger, or equal to some other number based on their values.The equation u = 0. 99c depicts the value of the US dollar in relation to the Canadian dollar on a specific day.
c = the Canadian dollar's valueu denotes the value of the US dollar.From the equation,
For Australian dollar; (from table)
u = 0.95 c -->
a = 1/0.95 u
a = 20/19 u
(20/19u - u)/ u = 1/19 ....1
For Canadian dollar:
u = 0. 99c
c = 1/0.99 u --> c = 100/99 u
Thus,
(100 u / 99 - u)/ u = 1/99 .....2
From 1 and 2]
1/19 > 1/99
Thus, on that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.
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which graph represents a by traveling at a constant rate of 12 mph
Answers
There is no graph in your question
the mean selling price of senior condominium in green valley over a year was $215,000. the population standard deviation was $25,000. a random sample of 100 new unit sales was obtained. a. what is the probability that the sample mean selling price was more than $210,000?
Answers
The probability that the sample mean selling price was more than $210,000 is 0.9772.
The given values are:
The mean selling price(μ) = $215000
Standard deviation(σ) = $25000
The random sample (n) = 100
We have to find the probability that the sample mean selling price was more than $210000.
z-score with z-bar= 210000
z = (x-bar - μ) / (σ/ √n)
= ( 210000 - 215000) / (25000/ √100)
= -5000/ 2500
=-2
Using z-tables, the probability is:
Probability = P[z> -2]
= 1 - 0.0228
= 0.9772
Therefore the probability is 0.9772.
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Solve the following proportion for u. 7/u=3/11 Round to the nearest tenth.
Answers
The solution for u in the expression given as 7/u = 3/11 is u = 25.7
How to determine the solution to the variable u in the expression?From the question, the algebraic expression is given as
7/u = 3/11
There is no constant to add to or subtract from the expression
So, the equation remains the same
7/u = 3/11
Multiply both sides of the equation by u
This gives
u * 7/u = 3/11 * u
Evaluate the products
So, we have the following equation
7 = 3/11u
Multiply both sides of the equation by 11/3
This gives
11/3 * 7 = 3/11u * 11/3
Evaluate the products in the above expression
77/3 = u
So, we have
25.6667 = u
Approximate
25.7 = u
Rewrite as
u = 25.7
Hence, the solution is u = 25.7
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Graph the parabola
y=3x^2-x-2
Answers
A parabola is a bowl-shaped figure. Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].
Since the additional point is [tex](3,22)[/tex]
What is a parabola?
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface: a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. : something that is bowl-shaped.
Here the given quadratic equation is
[tex]y=3x^{2}-x-2[/tex]
The standard form of the quadratic equation is
[tex]y=ax^{2}+bx+c[/tex]
where [tex]a=3,b=-1,c=-2[/tex]
The axis of symmetry is the x-axis of the vertex
[tex]x=\frac{-b}{2a}\\x=\frac{1}{2(3)}\\x=\frac{1}{6}[/tex]
The y-value of the vertex is determined by substituting [tex]\frac{1}{6}[/tex] for [tex]x[/tex] into the equation and solving it for [tex]y[/tex].
[tex]y=3(\frac{1}{6})^{2}-\frac{1}{6}-2\\y=3(\frac{1}{36})-\frac{1}{6}-2\\y=\frac{3-6-72}{36}\\y=\frac{3-78}{36}\\y=\frac{-75}{36}[/tex]
Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
Since [tex]a < 0[/tex] the vertex is the maximum point and the parabola opens downward.
X-intercept values of [tex]x[/tex] when [tex]y=0[/tex]
Substituting [tex]0[/tex] for [tex]y[/tex] and solving for [tex]x[/tex] using the quadratic formula
[tex]0=3x^{2}-x-2\\x=\frac{-b+-\sqrt{b^{2}}-{4ac}}{2a}\\x=\frac{1+-\sqrt{1}-{4(3)(-2)}}{2(3)}\\\\x=\frac{1+-\sqrt({1}+{24})}{6}\\\\\\x=\frac{1+-\sqrt(25)}{6}\\\\\\\\x=\frac{1+-5}{6}\\\\\\x=\frac{1+5}{6} , x=\frac{1-5}{6}\\\x=\frac{1+5}{6},x=\frac{1-5}{6}\\\\\x=1,x=\frac{-2}{3}[/tex]
Y-intercept values of [tex]y[/tex] when [tex]x=0[/tex]
Substituting [tex]0[/tex] for [tex]x[/tex] and solving for [tex]y[/tex] using the quadratic formula
[tex]y=3(0)^{6}-0-2\\y=-2[/tex]
Y-intercept [tex](0,1)[/tex]
Now substitute [tex]3[/tex] for [tex]x[/tex] and solve for [tex]y[/tex]
[tex]y=3(3)^{2}-3-2\\y=3(9)-5\\y=27-5\\y=22[/tex]
So the point is [tex](3,22)[/tex].
Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].
Since the additional point is [tex](3,22)[/tex]
The parabola is of the form
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PLEASE ANSWER THE QUESTIONS BELOW.. A PICTURE WILL BE PROVIDED ABOVE^^^^^
1: RADIUS FOR NEW TANK?
2. EXISTING VOLUME?
3.SPHERE VOLUME?
4. TOTAL VOLUME?
5. NEW TANK VOLUME?
6. TRIAL OF VALUES FOR R?
Answers
1) Radius of the standard tank = 3 feet
2) Existing volume for the tank is 126[tex]\pi[/tex] cubic feet.
3) Sphere volume for the tank is 36[tex]\pi[/tex] cubic feet.
4)Total volume of the tank is 36[tex]\pi[/tex] + 126[tex]\pi[/tex] = 162[tex]\pi[/tex] cubic feet
5) New volume for the tank is 252[tex]\pi[/tex] cubic feet.
6)Trails of values for r is 4 feet.
What do you mean by Volume?
A three-dimensional object's volume, expressed in cubic units (such as inches, quarts, or centimeters): cubic volume. the volume that a material takes up in a given space.
What is radius?
A line segment connecting the circumference or boundary surface of a circle or sphere to its center.
Given that;
Volume of the standard tank [tex]= \pi r^2h + \frac{4}{3} \pir^3[/tex]
[tex]= \pi 3^2h + \frac{4}{3} \pi3^3\\= 90\pi +36\pi\\= 126\pi \ cubic \ feet[/tex]
Volume of new tank = 2 x Volume of standard tank
= 2 x 126π
= 252π
But according to formula, volume of new tank will be;
[tex]V = \pi r^2h + \frac{4}{3}\pir^3[/tex]
where r = radius of new tank
[tex]\pi r^2 \times 10 + \frac{4}{3} \pi r^3 = 252 \pi\\30r^2 +4 r^3 = 756\\2r^3 + 15r^2-378 = 0\\r = 4.04591\\r \approx 4 feet[/tex]
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Evaluate x³ if x = 6
Show work pls
Answers
Answer:
216
Step-by-step explanation:
x^3
6^3
6x6x6
36x6
216
Hopes this helps pleas mark brainliest
Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter, what is the total amount she earned?
Answers
The total amount of the money earned by Paige will be $1591.92.
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.
Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.
The total amount of earnings will be,
TA = ( 50 x 30 ) + ( 0.02 x 4596)
TA = 1500 + 91.92
TA = $1591.92
Therefore, the total amount of the money earned by Paige will be $1591.92.
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a group of people were given a spelling test. the table shows their marks. work out the range of the marks. how many students are in the group. work out the mean mark of the group.
Answers
Answer: a) = 4
b) = 30
Step-by-step explanation:
a) They are asking for the range of the marks so you do 10-6 as 10 is the highest mark and 6 is the lowest
b) You find this out by adding the frequency up 10+4+7+4+5 = 30
In triangle ABC, the measure of angle C is 6 times the measure of angle B. 2 times angle A is 20 more than 3 time angle B. Find the measure of each angle in degrees.
Answers
Answer:
∠
A
=
x
=
32
∘
∠
B
=
3
x
=
3
⋅
32
=
96
∘
∠
C
=
x
+
20
=
32
+
20
=
52
∘
Step-by-step explanation: Every triangle adds up to 180.
Which of the following is NOT a SOLUTION to the inequality shown? *
y> 2x - 3
A. (4,3)
B. (-1,5)
C. (-2,-5)
Answers
The equation D show the multiplication property of inequality if n+4 =11
What is inequality?
inequality, In mathematics if a statement of an order relationship—greater or greater than or equal to, less than, or less than or equal between two number or algebraic expressions.
An inequality show the relationship between two values in an algebraic equations that are not equal.
Sol-
If n+4 =11
Then by applying the product rule -
(n+4)×2 =11×2
So the correct option is D.
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At a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three. If there are 100 in the party, is the data consistent?
Answers
Answer:
no because 60+48+36 is 144
Step-by-step explanation:
please mark brainliest
The total number of people is 144. The data is not consistent.
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.
Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.
The total number of the people in the party,
60+48+36 is 144
But it is given in the question that there are 100 in the party.
Therefore, the total number of people is 144. The data is not consistent.
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find the value of the expression when a=2 and b=7
Answers
The value of the expression when a=2 and b=7 is 41.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information, the expression given is 3a + 5b and we want to find the value of the expression when a=2 and b=7.
This will be illustrated thus:
= 3a + 5b
= 3(2) + 5(7)
= 6 + 35
= 41
The value is 41.
The complete question is given below.
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Complete question
The expression given is 3a + 5b. Find the value of the expression when a=2 and b=7
Solve for x:
[tex]\sqrt{x-3} =\sqrt{x} +3[/tex]
A. -2
B. 2
C. no solution
D. 4
Answers
Answer: The answer is C: No solution
Step-by-step explanation:
By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]
You then cancel out the equal terms, in this case x, to reach the equation:
[tex]-3=6\sqrt{x} +9[/tex]
This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.
What number should go in the empty boxes to complete the calculation for finding the product of
Answers
To do the multiplication, we multiply 0.63 by each of the digits & decimal places of 0.24 (and align the products that we get) then add them together.
0.63 x 4 = 2.52, therefore the first missing spot is a 2.
0.63 x 2 = 1.26, therefore the second missing spot is a 2 (the 0 is so that the decimal point can be aligned for the result.)
Answer: Box 1: 2 Box 2: 2
Step-by-step explanation:
So, for box one it would be 2 because 3 x 4 = 12, put the 2 on the bottom and the 1 on the 6, then 6 x 4 + 1 = 25, then put the 5 on the bottom and the 2 on the top, then 4 x 0 + 2 = 2, so the answer would be 2.
For box 2, 252 + 1?60 = 0.1512, so we have to find the missing number. So, 2 + 0 = 2, so put the two on the bottom, then 5 + 6 = 11, so put the 1 on the bottom and the other 1 on the 2 from the first box, so 2 + 1 = 3, plus 2 more would equal 5, so the second box would be 2.
Hope this helps!
Alana meauring hi dining room table to make a tablecloth the table i zero. 45 m longer than it i wide if it i 1. 06 m wide how long i it?
Answers
The length of the table is 1.51 meters.
Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.
Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.
L = 1.06 + 0.45
L = 1.51
Hence, the length of the table is 1.51 meters.
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on a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes. what is the probability of a waiting time in excess of 25 minutes between successive speeders?
Answers
There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.
Define probability.Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes. Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how likely it is that a coin will land heads up after being tossed into the air.
Given,
On a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.
Either the wait is over 25 minutes or it is less than 25 minutes. Decimal 1 represents the total of these events' probabilities. So,
P( X ≤ 25) + P(X > 25) = 1
For P(X > 25):
1 -P(X ≤ 25)
1 - e ⁻⁰⁶⁶⁶⁽²⁵⁾
0.1892
There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.
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simplify each expression x = 2x + 48
(please its for today
Answers
x-2x=48
-x=48
x= -48
Please brainliest
Find the slope (rate of change) of a line that passes through (-2,-3) and (1, 1).
Answers
We have coordinates (-2, -3) and (1, 1)
To find: Slope of a line that passes through these two coordinates
Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)
We will use the formula of Slope :
m = y₂ - y₁ / x₂ - x₁
Where 'm' stands for slope
m = 1 - (-3) / 1 - (-2)
m = 1 + 3 / 1 + 2
m = 4 / 3
The slope of the line is 4/3
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Flying against the wind, an airplane travels 7680 kilometers in 8 hours. Flying with the wind, the same plane travels 12,420 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answers
The rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.
What is speed?The distance covered in a unit of time is known as speed.
Given that, the airplane travels 7680 km in 8 hours flying against the wind, and 12420 km in 9 hours.
Therefore, the rate of the airplane against the wind is:
7680/8
= 960 km / hr
The rate of the airplane with the wind is:
12420/9
=1380 km / hr
Let the rate of the airplane in still air be a and the rate of the wind be w.
The net rate while flying against the air is:
a - w = 960 (1)
The net rate while flying with the wind is:
a + w = 1380 (2)
Add equations (1) and (2):
2a = 2340
a = 1170 km/hr
Substitute a = 1170 into equation (1):
1170 - w = 960
1170 - 960 = w
210 = w
Hence, the rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.
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2
Select the correct answer.
Which interval describes where the graph of the function is positive?
-8
O
O
O
B.
A. -∞ <<∞
C.
A
D.
N
-∞ < x < -1
-8∞ < < -2
-2 < < -1
Ň
-6
-8
-N
6 8
Answers
Option B is the correct answer, the interval in which the graph of the function is positive is -∞ < x < -1.
What do mean by interval?
In mathematics, a (real) interval is a collection of real numbers that includes all real numbers that fall inside any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The set of all real numbers, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton are additional examples of intervals.
As we can see in the graph provided in the question, the graph of function reach the positive side of the y-axis at x = -1, it means one of the two end point of the interval is going to be -1. And, the graph is constantly and slowing increasing it's value as increase in the x-axis therefore, the other endpoint of the interval cab be considered as negative infinity.
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solve this equation using the most direct method:
3x(x+6)=-10
Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using (+-) symbol
Answers
The solution set for the given quadratic equation is (-0.62, -5.38).
The given equation is 3x(x+6)=-10.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 3x(x+6)=-10
⇒ 3x²+18x=-10
⇒ 3x²+18x+10=0
By comparing 3x²+18x+10=0 with ax²+bx+c=0, we get
a=3, b=18 and c=10
Using quadratic formula x = [-b ± √(b² - 4ac)]/2a
= [-18 ± √(18² - 4×3×10)]/2×3
= [-18 ± √(324 - 120)]/6
= [-18 ± √(204)]/6
= [-18 ± √(204)]/6
= [-18 ± 14.28]/6
= [-18 + 14.28]/6 and [-18 - 14.28]/6
= -0.62 and -5.38
Hence, the solution set for the given quadratic equation is (-0.62, -5.38).
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