Answers
The corresponding output for an input value of 3 is -1. Hence f(3) is -1
from the mapping function given, the domain values are the input values of the function while the range is the output.
To get the value of f(3), we need to check the corresponding output when the input variable is 3.
From the given one-on-one mapping, we can see that the corresponding output for an input value of 3 is -1. Hence f(3) is -1
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Related Questions
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 5 and 625, respectively.
Answers
so (a1r^4) / (a1r) = r^3 = 625/5
r^3 = 125
r = 5
so a1* 5 = 5 giving a1 = 1
explicit rule is an = 5^(n-1)
Find the coordinates of point S that lies along the directed line segment from R(-14, -1) to T(4, -13) and partitions the segment in the ratio of 1:5.
Answers
I'd like to point out, is 1:5 from R to T, since that matters, that way we know the ratio from RS is the 1 and the ratio ST is the 5.
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ R(-14,-1)\qquad T(4,-13)\qquad \qquad 1:5 \\\\\\ \cfrac{RS}{ST} = \cfrac{1}{5}\implies \cfrac{R}{T} = \cfrac{1}{5}\implies 5R=1T \implies 5(-14,-1)=1(4,-13)\\\\ -------------------------------\\\\[/tex]
[tex]\bf { S=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\ -------------------------------\\\\ S=\left(\cfrac{(5\cdot -14)+(1\cdot 4)}{1+5}\quad ,\quad \cfrac{(5\cdot -1)+(1\cdot -13)}{1+5}\right)[/tex]
Answer: The required co-ordinates of the point S are (-11, -6).
Step-by-step explanation: We are given to find the co-ordinates of the point S that lies along the directed line segment from R(-14, -1) to T(4, -13) and partitions the segment in the ratio of 1:5.
We know that
the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) in the ratio m : n is given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
According to the given information, we have
(a, b) = (-14, -1), (c, d) = (4, -13) and m : n = 1 : 5.
Therefore, the co-ordinates of the point S are given by
[tex]\left(\dfrac{1\times4+5\times(-14)}{1+5},\dfrac{1\times(-13)+5\times(-1)}{}\right)\\\\\\=\left(\dfrac{4-70}{6},\dfrac{-13-5}{6}\right)\\\\\\=\left(\dfrac{-66}{6},\dfrac{-18}{6}\right)\\\\=(-11,-3)[/tex]
Thus, the required co-ordinates of the point S are (-11, -6).
Solve this quadratic equation by completing the square.
x^2+10x=7
Answers
take 1/2 of the linear coefient and square it
10/2=5, (5)^2=25
add that to both sides
x^2+10x+25=7+25
factor perfect square trionomial
(x+5)^2=32
squaer root both sides
x+5=+/-4√2
minus 5
x=-5+/-4√2
x=-5+4√2 and -5-4√2
Which sequence of transformations creates a similar but not congruent triangle?
A. Dilation and reflection
B. Reflection and rotation
C.Reflection and translation
D.Translation and rotation
Answers
dilation will make bigger or smaller therefore it cannot be congruent
Answer:
A
Step-by-step explanation:
What is the algebraic expression for "the difference between seven times a number and three times that number"?
7 - 3x
7x - 3
7x - 3x
Answers
"difference"= -
"three times a number" = 3x so
7x-3x
Answer:
(C)7x-3x
Step-by-step explanation:
The given algebraic expression is:
"The difference between seven times a number and three times that number"
Let the number be equal to =x, then according to the statement, we have
seven times a number=7x and three times that number=3x
The difference between seven times a number and three times that number=7x-3x
which is the required algebraic expression.
Hence, option C is correct.
Graph the functions and approximate an x-value in which the quadratic function exceeds the exponential function. y = 4x y = 7x2 + 4x - 2
x = -0.5
x = 0
x = 0.5
x = 2
Answers
Answer:
Option 3th is correct
x = 0.5
Step-by-step explanation:
The given functions are:
Function 1: [tex]y = 4^x[/tex]
Function 2: [tex]y=7x^2+4x-2[/tex]
The values of function at x = -0.5, 0, 0.5 and 2 are as follow:
x values Function 1 Function 2
-0.53 0.5 -2.25
0 1 -2
0.53 2.086 2.0863
2 16 34
From the above table. It is clear that the quadratic function [tex]y=7x^2+4x-2[/tex] exceeds the exponential function [tex]y = 4^x[/tex] at x = 0.53
Therefore, the approximate x-value in which the quadratic function exceeds the exponential function at x = 0.5
Are rational numbers always, sometimes or never natural numbers?
Answers
Most rational numbers, however, are not natural. For example, 3/4, 89/88, and so on.
Answer:
SOMETIMESStep-by-step explanation:
Solve the system of equations: 2x + 9y = 0 and 3x + 5y = 17.
Answers
3x + 5y = 17 (2nd)
multiply (st) by 3 and (2nd) by 2
6x + 27y = 0 (1st)
6x + 10y = 34 (2nd)
----------------------------subtract
17y = -34
y = -2
2x + 9y = 0
2x +9(-2) = 0
2x = 18
x = 9
answer
(9, -2)
85 is 20% of what number? Enter your answer in the box.
Answers
85/0.2 = 425 ← answer
Determine whether the sequence is arithmetic or geometric. Sequence 1: –10, 20, – 40, 80, ... Sequence 2: 15, – 5, – 25, – 45, ... Which of the following statements are true regarding Sequence 1 and Sequence 2.
Answers
Answer:
Sequence 1 is arithmetic and Sequence 2 is geometric.
I need all the answers for question 2 and please explain each step to get the answer, thanks
Answers
b)
hmm where is that point A anyway? sounds like it's asking the same thing as in part a)
c)
well, where's M, the midpoint of BC, let's check.
[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) B&({{ 1}}\quad ,&{{ 4}})\quad % (c,d) C&({{ 9}}\quad ,&{{ 10}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ M=\left( \cfrac{9+1}{2}~,~\cfrac{10+4}{2} \right)\implies M=(5,7)[/tex]
now, the coordinator says that the midpoint of MC is at 6,8, let's check.
[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) M&({{ 5}}\quad ,&{{ 7}})\quad % (c,d) C&({{ 9}}\quad ,&{{ 10}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ N=\left( \cfrac{9+5}{2}~,~\cfrac{10+7}{2} \right)\implies N=\left(7~,~\frac{17}{2} \right)\implies N=\left(7~,~8\frac{1}{2} \right)[/tex]
An expression is shown below:
square root of 32 plus square root of 2
Which statement is true about the expression?
It is rational and equal to 4.
It is rational and equal to 5.
It is irrational and equal to 5 multiplied by square root of 2.
It is irrational and equal to 4 multiplied by square root of 2.
Answers
The answer is "It is irrational and equal to 5 multiplied by square root of 2."
Answer:
It is irrational and equal to [tex]5[/tex] multiplied by square root of [tex]2[/tex]
Step-by-step explanation:
we have
[tex]\sqrt{32}+\sqrt{2}[/tex]
Remember that
[tex]32=2^{5}[/tex]
substitute in the expression
[tex]\sqrt{2^{5}}+\sqrt{2}=4\sqrt{2}+\sqrt{2}=5\sqrt{2}[/tex]
therefore
It is irrational and equal to [tex]5[/tex] multiplied by square root of [tex]2[/tex]
you borrow $90 from your grandmother. you pay back $15 each week.
a. write an equation in standard for that represents the amount owed y after x weeks.
b. find the y intercept of the graph. what does this represent?
c. find the x intercept of the graph. what does this represent?
Answers
b. y = 90, The money you owe her initially, or after 0 weeks.
c. x = 6, The number of weeks until you pay her back all $90.
Answer: a) y = 90-15x
b) y = 90
c) x = 6
Step-by-step explanation:
Since we have given that
Amount borrowed from his grandmother = $90
Amount he pay back each week = $15
Let the number of weeks be 'x'.
Let total amount owed be 'y'.
So, it becomes
[tex]y=90-15x[/tex]
a) write an equation in standard for that represents the amount owed y after x weeks.
Our equation is [tex]y=90-15x[/tex]
b. find the y intercept of the graph. what does this represent?
For this , we put x = 0.
[tex]y=90-15(0)\\\\y=90[/tex]
So, the y-intercept of the graph is 90.
It represents that the graph intersect y-axis at (0,90)
c. find the x intercept of the graph. what does this represent?
For this, we put y = 0.
[tex]0=90-15x\\\\90=15x\\\\x=\dfrac{90}{15}\\\\x=6[/tex]
So, the x intercept of the graph is 6.
It represents that the graph intersect the x-axis at (6,0)
(4.05 LC)
The graph shows y as a function of x:
Graph of x against y shows 4 segments. Segment A is a horizontal line parallel to the x-axis. Segment B is a slanting straight line going up. Segment C is a horizontal line parallel to the x-axis. Segment D is a slanting straight line going down that touches the x-axis.
In which segment is the function increasing?
A
B
C
D
Answers
Answer: I think the answer is A.
Step-by-step explanation:
I think this because its the only time that It could stay the same.
A cone is a solid that has one circular base and only one face. true or false
Answers
The cone is made by rotating a right triangle for 360°
The base is a circle, formed by one of the leg. The other leg makes the only one face.
Josh has 40 minutes to complete a government exam. There are 15 multiple-choice questions worth 3 points each. There are also 5 short-answer questions worth 11 points each. It takes about 2 minutes for Josh to answer the multiple-choice questions m and about 8 minutes to complete the short-answer questions s. The system of inequalities that represents this problem is graphed below. Which ordered pair is not a vertex of the feasible region?
Answers
The feasible vertices of the system representing Josh's exam are (0,0), (12,5), and (15,1.25). The non-feasible vertices are (15,0), (0,5), and (20,0). Therefore, the ordered pair (15,0) is not a vertex of the feasible region.
1. System of Inequalities:
- Time constraint: [tex]\(2m + 8s \leq 40\)[/tex]
- Number of multiple-choice questions: [tex]\(m \leq 15\)[/tex]
- Number of short-answer questions: [tex]\(s \leq 5\)[/tex]
2. Feasible Vertices:
- (0,0), (12,5), (15,1.25)
3. Non-feasible Vertices:
- (15,0), (0,5), (20,0)
So, the ordered pair (15,0) is not a vertex of the feasible region.
What is the factorization of the polynomial below?
x²+12x+27
A. (x+3)(x+9)
B. (x+9)(2x+9)
C. (12x+1)(x+2)
D. (3x+3)(x+9)
Answers
(x + 3)(x + 9) = x^2 + 3x + 9x + 27, which simplifies to x^2 + 12x + 27
how to write 314,207 in word form
Answers
Answer: three hundred fourteen thousand, two hundred seven
explanation for the comma after thousand: I’m used to putting one there because it says 314, not just 314 so I added one. Hope I helped !
Determine the equation of the graph and select the correct answer below.
y = (x + 1)2 + 3
y = (x + 1)2 − 3
y = (x − 1)2 − 3
y = (x − 1)2 + 3
Answers
vertex form is y = (x-h)^2 + k
where h,k) is the vetex
so here we have y = (x - 1)^2 - 3
Its C
How to simplify all this numbers to make one equation?
Answers
6-x-2-4x, then you must combine like terms
(-x-4x)+(6-2)
-5x+4
Which linear inequality is represented by the graph? y ≥ 1/3x – 4 y ≤ 1/3x – 4 y ≤ 1/3x + 4 y ≥ 1/3x + 4
Answers
thats gonna be 2nd answer choice
Answer:
[tex]y\leq \frac{1}{3}x-4[/tex]
Step-by-step explanation:
we know that
The solution of the inequality is the shaded area below the solid line
The slope of the line is positive
The y-intercept of the solid line is equal to [tex]-4[/tex]
therefore
The inequality must be
[tex]y\leq \frac{1}{3}x-4[/tex]
Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work.
a. 3in, 4in, 5 in
b. 5in, 6in, 7in
c. 8in, 9in, 12in
Answers
The triangle will be:
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²
a.
a=3, b=4 and c=5
a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25
25 = 25 ⇒ right triangle.
b.
a=5, b=6 and c=7
a² + b² = 5² + 6² = 25 + 36 = 61 and c² = 7² = 49
61 > 49 ⇒ аcute triangle.
c.
a=8, b=9 and c=12
a² + b² = 8² + 9² = 64 + 81 = 145 and c² = 12² = 144
145 > 144 ⇒ аcute triangle.
From the information, A is a right angle, B is an acute triangle and C is an acute angle.
How to solve the triangleIt will be a right triangle if a² + b² = c². It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².
For the first one,
a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25
25 = 25
This is a right triangle.
For the second one,
a² + b² = 5² + 6²
= 25 + 36 = 61
c² = 7² = 49
61 > 49 = аcute triangle.
For the third one,
a² + b² = 8² + 9²
= 64 + 81 = 145
c² = 12² = 144
145 > 144 = аcute triangle.
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What percentage is the fraction 2/4 equal to?
Answers
When 2/4 is simplified, it becomes 1/2, which is equal to 0.5.
A parallelogram has vertices E(−4, 6), F(1, 3), G(3, −4), and H(−2, −1). What are the coordinates of the midpoint of each diagonal?
(−3.5, 2.5)
(−0.5, −1)
(−0.5, 1)
(0.5, −1)
Answers
Hope this helped!
A video game club charges a fixed annual membership fee of $18 and $3 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $20 the next year?
Answers
f(x)=mx+b, where m=slope and b=y-intercept so in terms of n, games rented, the cost, f(n) is:
f(n)=3n+18
Answer:
The correct answer is f(n)=3n+38
Step-by-step explanation:
Put in y=mx+b form, so y= f(n), $3 is fee per video game rented and n is the number of video games rented, b is ($18 fixed fee for this year +$20 fee for next year). So, f(n)=3n+38.
The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 392 hours and a standard deviation of 9 hours. find the first quartile, q1.
Answers
The 1st quartile q1 is also called the 25th percentile (the bottom 25% of a data set). In this case, if we choose 100 light bulbs, then the 1st quartile will be the 25 bulbs with shortest useful life.
To solve this problem, we would have to use the z statistic.
Using the standard distribution tables for z, we locate for the value of z at P
= 0.25:
z = - 0.674
Then to calculate for the 1st quartile, we use the
formula:
Q1 = x + z * s
where x is the mean, and s is the standard deviation, therefore:
Q1 = 392 + (- 0.674) (9)
Q1 = 385.934
To find the first quartile of a normal distribution, use the z-score corresponding to an area of 25%. For these lightbulbs with a mean of 392 hours and standard deviation of 9 hours, the first quartile is approximately 386 hours.
Explanation:In statistics, the quartiles of a dataset divide the data into four equal parts. The first quartile, Q1, is the value below which 25% of the data fall. To determine Q1 for the lifetime of a certain type of lightbulb, we use the properties of the normal distribution.
First, realize that 25% of data falls below Q1, and hence using the z-table, we find that z=-0.675 corresponds to an area of 0.25. We then use the formula for a z-score in a normal distribution, z = (X - μ)/σ. Solving for X we find X = z*σ + μ.
Plugging in the known values we get Q1 = -0.675*9 + 392 = 386.025 hours. So, for these lightbulbs, 25% will have failed by around 386 hours.
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Your little brother just learned how to flip and catch a coin. He believes that by catching the coin in mid-air, he can influence the probability that it will land heads up. Based on your understanding of theoretical probability, explain to your little brother why his theory of influence is false.
Answers
If a coin is fair then it has two faces , one is heads and the another is tails.
The probability getting any favorable outcomes is given by the formula :-
[tex]\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]
So the factor effecting probability is just the number of favorable outcomes and total outcomes.
If a coin is tossed then the probability of getting heads will be :-
[tex]P(H)=\dfrac{1}{2}=0.5=50\%[/tex]
To get heads always this should be 1 , which can be happen if number of favorable outcomes is equal to total outcomes.
i.e. Number of heads = Number of total outcomes, this means coin should be biased.
Catching the coin in mid-air can never be a factor for this.
Therefore, the little brother's theory is false.
Answer:
Sample Response: The probability of a coin landing heads up is 1/2, or 50%. That fact will not change if the coin is caught in midair.
Step-by-step explanation:
Based on the graph, what are all of the solutions to f(x) = x3 − 7x − 6? x = −6 x = −2, −1 x = −2, −1, 3 x = −6, −2, −1, 3
Answers
x = −2, −1, 3 are solutions of equation : f(x) = 0
because : f(-2) = f(-1) = f(3) = 0
(08.05)The box plot shows the total amount of time, in minutes, the students in a class spend traveling to school each day: A box plot is titled Daily Travel Time and labeled Time (min). The left most point on the number line is 10 and the right most point is 45. The box is labeled 16 on the left edge and 36 on the right edge. A vertical line is drawn inside the rectangle at the point 28. The whiskers are labeled as 11 and 43. What information is provided by the box plot?
Answers
The left-most point on the number line is 10.
Minimum value = 10
The right-most point is 45.
Maximum value= 45
First quartile or lower quartile = 16
Third quartile or upper quartile = 36
The median is 28.
Given thatThe box plot shows the total amount of time, in minutes, the students in a class spend traveling to school each day:
A box plot is titled Daily Travel Time and labeled Time (min).
The left-most point on the number line is 10 and the right-most point is 45.
The box is labeled 16 on the left edge and 36 on the right edge.
A vertical line is drawn inside the rectangle at point 28.
The whiskers are labeled as 11 and 43.
We have to determineWhat information is provided by the box plot?
According to the questionIn the box plot, the information is given as follows.
The left-most point on the number line is 10.Minimum value = 10
The right-most point is 45.Maximum value= 45
First quartile or lower quartile = 16Third quartile or upper quartile = 36The median is 28.To know more about Median click the given below.
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Answer the questions that aren't covered please? Thanks