Answer the questions about the following function.
f(x) = 3x²-x-2
(a) Is the point (2,8) on the graph of f?
(b) If x= -1, what is f(x)? What point is on the graph of f?
If f(x) = -2, what is x? What point(s) are on the graph of f?
(d) What is the domain of f?
(c)
(e) List the x-intercept(s), if any, of the graph of f.
(f) List the y-intercept, if there is one, of the graph of f.
Answers
Step-by-step explanation:
f(x)=3x²-x-2
a) (2,8)
f(2)=3(2²)-2-2
f(2)=3(4)-4
f(2)=12-4
f(2)=8
Hence, the point (2,8) is on the graph of f(x)
b) x=-1
f(-1)=3((-1)²)-(-1)-2
f(-1)=3(1)+1-2
f(-1)=3-1
f(-1)=2
c) x=-2
f(-2)=3((-2)²)-(-2)-2
f(-2)=3(4)+2-2
f(-2)=12+0
f(-2)=12
[tex]d)\ f(x)\in(-2\frac{1}{12} ,\infty)[/tex]
e) y=0
3x²-x-2=0
3x²-x-2=0
3x²-3x+2x-2=0
3x(x-1)+2(x-1)-0
(x-1)(3x+2)=0
x-1=0
x=1
3x+2=0
3x=-2
Divide both parts of the equation by 3:
x=-2/3
f) x=0
f(x)=3(0²)-0-2
f(x)=3(0)-2
f(x)=0-2
f(x)=-2
Related Questions
Two basketball players are trying to have the most
points per game for the season. The current leader has
2112 points in 77 games and the second place player
has 2020 in 74 games. How many points per game did
the leading team score?
Helpppppp
Answers
The leading team has scored 0.13 points per game for the season that the second place player.
What is PPG Statistics?
The average number of points a player scores in a game of a sport, over the course of a series of games, a season, or a career, is known as points per game, or PPG, and it is an important statistic. By dividing the total points by the number of games, it is calculated. Basketball and ice hockey are two sports that frequently use PPG statistics.First, consider the PPG of the current leader of the season from among the two basketball players.
The total number of points obtained by the current leader is equal to 2112.
The total number of games played by the current leader is equal to 77.
The points per game obtained by the current leader can be calculated as follows,
PPG = Total Points Obtained / Total Number of Games
[tex]\implies PPG=\frac{2112}{77}\\\implies PPG=27.42[/tex]
Now, consider the PPG of the second place player for the season.
The total number of points obtained by the second place player is equal to 2020.
The total number of games played by the second place player is equal to 74.
The points per game obtained by the second place player can be calculated as follows,
PPG = Total Points Obtained / Total Number of Games
[tex]\implies PPG=\frac{2020}{74}\\\implies PPG=27.29[/tex]
Subtracting the points per game of both players, we get
[tex]27.42-27.29=0.13[/tex]
Hence, the leading team has scored 0.13 points per game (PPG) for the season compared to the second place player.
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Which ordered pair satisfies the inequality? 6x + 5y < -15
Answers
The ordered pair of the inequality 6x + 5y < -15 are (2, 0) and (3, 2).
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Considering the provided inequality and the provided ordered pairs, we will check it by replacing one by one in the inequality; if the inequality is fulfilled, they are the solution; otherwise, they are not, so we obtain:
(2, 0):
6x + 5y > 2
6(2)+5(0)>2
12+0>2
12>0
Since the inequality holds, then the ordered pair is a solution.
(7, -8):
6x + 5y > 2
6(7)+5(-8) > 2
42-40>2
2>2
Since the inequality is not satisfied, then the ordered pair is not a solution.
(3, 2):
6x + 5y > 2
6(3)+5(2) >2
18+10>2
28>2
Since the inequality holds, then the ordered pair is a solution.
(-8, 6):
6x + 5y > 2
6(-8)+5(6) >2
-48 + 30 > 2
-18 > 2
Since the inequality is not satisfied, then the ordered pair is not a solution.
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The equation of the graph
is y = pq* where p and q are
positive constants.
Find the values of p and q.
Answers
It might be easier to read as y = 3(2^x)
Not sure what pq* meant in your question but p is probably 3 and q is 2
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
Answers
Answer:
182 feet
Step-by-step explanation:
Taking the fact that 112/40 = 2.8, you would need to multiply the miles per hour by 2.8 to get the feet needed.
Why is that, well I cant really explain...its just math and it works out /:
can someone help quick? someone gave me the answer but didn’t explain. what’s the inequality? where do i graph this? please give the right answers only
Answers
An inequality that represents the height h, in inches, of a person allowed to ride rollar coaster is h ≥ 48
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Let h represent for the height of any member allowed to ride rollar coaster
From the question we know that everyone's height must be greater that 48 inches.
It means the inequalities would be
h ≥ 48 tall inches
Thus, an inequality that represents the height h is h ≥ 48
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Complete the ratio 4:16 = 1:?
Answers
Answer:
1:4
Step-by-step explanation:
4:16 = 1:?
4/4 = 1
16/4 = 4
= 1:4
A side of the triangle below has been extended to form an exterior angle of 156°. Find the value of x.
Answers
The value of x inside the triangle is 24°
How to calculate the value of x(angle)?
A straight line's total number of angles adds up to 180°. Supplementary angles are two angles whose sums equal 180 degrees. Angles are referred to as neighbouring if they have a similar vertex and side.A straight angle in mathematics is one with a degree value of 180. Because it resembles a straight line, it is called straight.Angles in a straight line are the total of all the angles that can be arranged in a straight line. Straight line angles add up to 180°.The angle of the straight line = 180°
156° + x = 180°
x = 180° - 156°
x = 24°
Hence, the value of x inside the triangle is 24°.
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PS bisects ∠QPR . Complete the proof that ∠PSR ≅ ∠PSQ .
Answers
The proof is shown in the image.
Reasons for statement
Any line that bisects an angle divides the angle into two equal parts The two lines are congruent by cpct as the triangles are congruent The angle subtended the bisector line divides equally into two angles. Also, the triangles are congruent so angle QPS = angle RPS by cpct The common line between congruent triangles is the same Triangles are congruent by side angle side rule Angles are equal by corresponding parts of the congruent triangle rule.To know more about congruent triangles,
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PLS HURRY The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one-fifteenth times x, where y represents the number of rare trading cards and x represents the number of packs of trading cards. Determine how many rare trading cards you would find if you bought 90 packs of trading cards.
6
15
1,350
one-fifteenth
Answers
If you bought 90 packs of trading cards then Rare trading cards are 6
What is probability?The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.
If the conditions are met, Y = 1/15 * X = 90 , then Y = 1/15 x 90 Y = 6.
A deck of cards has 52 cards. Therefore, 52 outcomes overall.
The number of positive results is 4 (as there are 4 kings in a deck)
Hence, there is a chance that this will happen.
P(E) = 4/52 = 1/13.
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
Answers
Using the normal distribution, it is found that a student has to score 0.675 standard deviations above the mean to be publicly recognized.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
z=x-nuo/sigmaIt measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The top 25% is at least the 100 - 25 = 75th percentile, which is X when z has a p-value of 0.75.Looking at the z-table, z = 0.675 has a p-value of 0.75.Hence, a student has to score 0.675 standard deviations above the mean to be publicly recognized.To know more about Standard deviation here
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What is the inverse of f(x)=2x+9?
Answers
Answer:Find the Inverse f (x)=-2x+9Find the Inverse f (x)=-2x+9 f (x) = −2x + 9 f (x) = - 2 x + 9 Write f (x) = −2x+ 9 f (x) = - 2 x + 9 as an equation. y = −2x+9 y = - 2 x + 9 f (x) = −2x + 9 f (x) = - 2 x + 9 Write f (x) = −2x+ 9 f (x) = - 2 x + 9 as an equation. y = −2x+9 y = - 2 x + 9
Step-by-step explanation:
Chandrani had a Rs 100 note she bought a geometry box for ₹ 37 . 75. Find the amount left with her
Answers
Answer:
The amount left with her si 62.25
Prove that the roots of the equation mx² + (m − 2)x − (m + 1) = 0 are real for all values of m
Answers
Answer:
Below
Step-by-step explanation:
For REAL numbers, the discriminant of the Quadratic Formula has to be a positive value (or zero)
b^2 - 4ac >= 0 where a = m b = m-2 c = -m-1
(m-2)^2 - 4(m)(-m-1) >=0
5m^2 +4 >= 0
5 m^2 +4 <===== will always be >= 0 for any value of 'm'
so all roots will be real
Cameron is deciding between two landscaping companies for his place of business.
Company A charges $25 per hour and a $300 equipment fee. Company B charges $55
per hour and a $150 equipment fee. Let A represent the amount Company A would
charge for t hours of landscaping, and let B represent the amount Company B would
charge for t hours of landscaping. Write an equation for each situation, in terms of t,
and determine the interval of hours, t, for which Company A is cheaper than
Company B.
Answers
Answer:
A = 25t + 300
B = 55t + 150
Less than 5 hours, company B would be cheaper. At 5 hours the cost is equal. After 5 hours, company A would be cheaper.
Step-by-step explanation:
Company B would be cheaper for lower hours.
The the two equation equal to each other and solve for to find out when the costs will be equal.
25t + 300 = 55t + 150 Subtract 25t from both sides
300 = 30t + 150 Subtract 150 from both sides
150 = 30t Divide both sides by 30
5 = t
At 5 hours the cost are the same, after 5 hours company A would be cheaper.
Question 60
Find the probabilities below using a standard 52 card deck.
Answers
By using the concept of probability, it can be calculated that-
1) P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]
5) P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur.
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
1) Number of ace card = 4
Number of '5' card = 4
P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]
= [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)
Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]
P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) Number of black coloured even numbered card = 10
Number of even numbered card = 20
Number of card of black colour = 26
P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]
= [tex]\frac{36}{52}[/tex]
5) Number of face cards of diamond = 3
P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
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If u(x) = -2x² +3 and V(x) =
X
what is the range of (u.v)(x)?
Answers
The range of u(x) = {-15, -5,1,3,1, -5, -15} and range of v(x)= {-3,-2, -1,0,1,2,3} for the domain of x = { -3,-2,-1,0,1,2,3}
What is domain and range?The domain of a function is defined by the set of the values of independent variables and the ranges are the set of values of dependent variables.
The domains act as an input of function where ranges act as an output.
How to find domain and range?We select domain randomly as domain are the set of independent variables. But how will be the ranges must depend on the function given us.
we are given 2 function u(x) = -2x²+3 and v(x)
for the 1st function the set of domain and ranges are different, but the domain and ranges have the same values for the 2nd function.
we select domain x= {-3, -2, -1, 0, 1, 2, 3}
the ranges for u(x) ={ -15, -5, 1, 3, 1, -5 , -15}
because, u(-3) = -2(-3)²+3 = -15
u(-2) = -2(-2)²+3 =-5
u(0) = 3
similarly, for the same set of x value, v(-3) = -3
v(-2) = -2
v(0) =0
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A random sample of size 36 is taken from a population with mean µ = 15 and standard deviation σ = 8. What is the probability that the sample mean is greater than 16?
Answers
Answer:
Below
Step-by-step explanation:
Deleted
12. The number of liters of fuel used on a trip
varies directly with the number of miles traveled. If
a 120 mile trip requires 12.5 liters of fuel, how
many liters are required for a 504 mile trip?
Answers
Answer:
Step-by-step explanation:
If the difference follows the Normal model, what's the probability that the small bowl contains more cereal than the large one?
Answers
The probability that the small bowl contains more cereal than the large one is 0.0228.
Given :
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
we know that,
z = x - μ / σ
here
x = 0
μ = 1
σ = 0.5
= 0 - 1 / 0.5
= -1/0.5
= -1 / 05 / 10
= -1 * 10 / 5
= -10 / 5
= -2
if z = -2 then p value = 0.0228
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Full question :
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
If the difference follows the Normal model, what's the probability that the small bowl contains more cereal than the large one?
Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
Answers
The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².
What is Area :The space around a shape's perimeter or boundary is known as its area. To determine the areas of various forms, many mathematical formulae are available.
Area of circle = πr², where r is the radius of the circle. Area of rectangle = lb, where l = length and b = breadth.Here we have
composed of a rectangle and two semicircles.
Dimensions of the rectangle are,
Length = 14 and breadth = 4
=>Area of the rectangle = 14 × 4 = 56 units²
If we join the two semicircles,
we will have one circle with a diameter of 4 units
=> As we know Radius of the circle = Diameter/2
=> Radius of circle = 4/2 = 2 units
=> Area of the circle = 2πr
= [tex]2 \times\frac{22}{7} \times 2[/tex] = 12.56 unit²
Area of the figure = Area of rectangle + Area of the circle
= 56 units² + 12.56 unit²
= 68.56 unit²
Therefore,
The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².
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Data regarding fuel efficiency of an 18-wheel truck were collected. The graph shows the correlation between the average speed above 40 miles per hour (in miles per hour) and the money spent on gas (n dollars): Estimate the average rate of change from x = 5 to x = 9.
Answers
The average rate of change of the function at the interval x = 5 to x = 9 is 1.25
How to determine the average rate of changeThe interval is given as
x = 5 to x = 9
From the question (see attachment), we have the following parameters that can be used in our computation:
x = 5 and y = 15
x = 9 and y = 20
This means that
f(5) = 15 and f(9) = 20
The average rate of change is then calculated as
Average rate of change = [f(9) - f(5)]/[9 - 5]
Substitute the known values in the above equation, so, we have the following representation
Average rate of change = [20 - 15]/[9 - 5]
Evaluate
Average rate of change = 1.25
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8) Tom climbs 25 feet into the pear tree and pulls a pear from the tree. He throws it with an upward
velocity of 30 feet/second. How long will the pear be in the air if his Dad sees him and catches it at 6 feet above the ground?
Answers
The distance the pear will be in the air if his Dad sees him and catches if at 6 feet above the ground is 19/30 meters.
How to calculate distance?The term distance can be defined as a numerical qualitative measurement of how far apart points are from each other.
Distance is defined by the formula
d=v*t
The given parameters are:
v=30
s=6
height=25
Applying these parameters into the formula
d=30*t
d=30t
If the Dad stands 6 feet above the ground, we have
[tex]\frac{25-6}{30}[/tex]
=[tex]\frac{19}{30}[/tex]
Therefore the pear will be 19/30 feet in the air if the Dad sees him and catches it at 6 feet above the ground.
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A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?
Answers
The required value of the production at which the company attained the same profit is 4 thousand skin care items.
Given that,
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t³ + 8t² + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million.
Here,
Plotting the graph of the polynomial equation,
P(t) = –2t³ + 8t² + 2t,
From the graph at x = 4,
The polynomial gives the same value as it gave at x = 1,
Thus, the required value of the production at which the company attained the same profit is 4 thousand skin care items.
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the first term of an arithmetic sequence is -27. the common difference of the sequence is 6. What is the sum of the first 50 terms
Answers
Answer: 6000
Step-by-step explanation:
The formula for the first [tex]n[/tex] terms of an arithmetic sequence with first term [tex]a[/tex] and common difference [tex]d[/tex] is [tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex].
In this question, [tex]a=-27, d=6, n=50[/tex].
So, [tex]S_{50}=\frac{50}{2}[2(-27)+(50-1)(6)]=6000[/tex].
is a parallel to b? Explain using angels and measurements. Angel measrment should be part of your explanation.
Answers
Answer:
Not parallel.
Step-by-step explanation:
Given:
m∠9 = 110°m∠8 = 70°Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Angles 9 and 10 form a linear pair:
⇒ m∠9 + m∠10 = 180°
⇒ 110° + m∠10 = 180°
⇒ m∠10 = 70°
Angles 7 and 8 form a linear pair:
⇒ m∠7 + m∠8 = 180°
⇒ m∠7 + 70° = 180°
⇒ m∠7 = 110°
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
As line p is parallel to line q, and according to the vertical angles theorem and the corresponding angles postulate:
m∠1 = m∠6 = m∠9 = m∠14 = 110°m∠2 = m∠5 = m∠10 = m∠13 = 70°m∠3 = m∠8 = m∠11 = m∠16 = 70°m∠4 = m∠7 = m∠12 = m∠15 = 110°If line a was parallel to line b, then according to the corresponding angles postulate:
m∠1 = m∠3 = m∠6 = m∠8m∠2 = m∠4 = m∠5 = m∠7As m∠1 ≠ m∠8 and m∠2 ≠ m∠7 then lines a and b are not parallel.
Solve the equation for v.
0.5v + 0.03 > 2.83
v > 1.3
v < 1.3
v > 5.6
v < 5.6
Answers
Answer:
[tex] \huge{ \boxed{v > 5.6}}[/tex]
Step-by-step explanation:
[tex]0.5v + 0.03 >2.8[/tex]
In order to solve this inequality, first subtract 0.03 from both sides of the inequality to isolate 0.5v
[tex]0.5v + 0.03 - 0.03 > 2.83 - 0.03 \\ 0.5v > 2.8[/tex]
Next divide both sides by 0.5
[tex] \frac{0.5v}{0.5} > \frac{2.8}{0.5} \\ v > 5.6[/tex]
We have the final answer as
[tex] \bold{v > 5.6}[/tex]
A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value you win (or lose) per game.
Answers
The correct answer is option B which is -1.67 is the expected value.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
You have a higher probability of losing money than gaining it due to the distribution of probability.
There are more chances to lose than win.
As a result, you are expected to lose money.
Only -1.67 is the only negative option, which means that we don't even need to do real math since there's already only one choice.
Hence, the correct answer is option B which is -1.67 is the answer.
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Answer:
You will Gain 5 points.
Step-by-step explanation:
Got it right on the test!
Express with an exponent.
125 =
A
5/3
с 3/5
B 5/5
Answers
Answer:A
Step-by-step explanation: 5 to the power of 3 is 5x5x5 which is 25x5 which then equals 125
A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N). A support cable running to the ground is inclined 71° from the horizontal.
Find the tension in the support cable. Give answer to the nearest whole number.
Answers
The tension in the support cable is 2731 N
How to find the tension in the support cable?Given that:
A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N) and a support cable running to the ground is inclined 71° from the horizontal.
This can sketch as shown in the attached image. Considering the image:
T is the tension in the support cable
Using trigonometric ratio:
cos 71° = 889/T (adjacent/hypotenuse)
T = 889/cos 71°
T = 2731 N
Therefore, the tension in the support cable is 2731 N
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Angle ABC is taken by a dilation with centerpoint, P and scale factor of four to angle A’B’C’ the measure of angle, BCA is 75° what is the measure of angle B’C’A’
Answers
Answer:
75°
Step-by-step explanation:
You want to know the measure of the image angle B'C'A' after angle A'B'C' is dilated by a factor of 4 about point P. Angle BCA is 75°.
DilationDilation does not affect angle measures, so angle B'C'A' has the same measure as angle BCA, 75°.
m∠B'C'A' = 75°