Answers
For A, for example, the x value of 1 has 2 y values. For C, the x value of 7 has 2 y values as well, 10 and 3.
A functions B and D are valid functions because they meet the criteria of each x value having only one corresponding y value.
Function B: You mentioned that B is a function because each x value has only one corresponding y value. In mathematical terms, a function is defined as a relation between a set of inputs (x values) and a set of outputs (y values), where each input (x) maps to exactly one output (y). So, if B satisfies this definition, it is indeed a function.
Function D: Similar to B, if D also adheres to the definition of a function, where each x value corresponds to only one y value, then it is a function as well.
Function A: You mentioned that for A, the x value of 1 has 2 y values. In mathematical terms, a function cannot have one input (x) mapping to multiple outputs (y). If this is the case for A, it does not meet the definition of a function.
Function C: You mentioned that for C, the x value of 7 has 2 y values, 10 and 3. Again, if one input (x) is associated with multiple outputs (y) in C, it does not qualify as a function.
In summary, functions B and D are valid functions because they meet the criteria of each x value having only one corresponding y value. Functions A and C do not meet this criterion and are not functions in the mathematical sense.
To know more about functions:
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Related Questions
What is the area of a rectangle with a length of 15 feet and a width of 9 feet?
Answers
Final answer:
The area of a rectangle with a length of 15 feet and a width of 9 feet is 135 square feet.
Explanation:
The area of a rectangle can be found by multiplying its length and width.
In this case, the length is 15 feet and the width is 9 feet.
To find the area, multiply 15 feet by 9 feet:
Area = 15 feet x 9 feet = 135 square feet
Therefore, the area of the rectangle is 135 square feet.
Susie is paying $558.16 every month for her $150,000 mortgage. If this is a 30 year mortgage, how much interest will she pay over the 30 years of payments?
Answers
558.16 x 12 = 6697.92 every year
6697.92 x 30 = 200937.60 total
200937.60-150000 = $50,937.60 total interest paid
What is the equation of the following line? Be sure to scroll down first to see all answer options.
Answers
Answer:
Option C. is the correct option.
Step-by-step explanation:
Equation of line is represented as y = mx + c
where m = slope of the line
c = y - intercept
Since line is passing through origin (0, 0) and a point (6, 2)
Therefore y intercept of the line will be 0.
c = 0
Slope of the line [tex]m=\frac{y-y'}{x-x'}[/tex]
[tex]m=\frac{2-0}{6-0}[/tex]
[tex]m=\frac{2}{3}[/tex]
So the equation will be
[tex]y=\frac{1}{3}x[/tex]
Therefore, option C. is the answer.
How many sides does a polygon have with an interior angle of 108?
Answers
360/72 = 5
Solve for x and y: 28x-49y=35 and 4x-7y=5
Answers
What is a variable?
a.
A variable is an unknown number or value represented by a letter
c.
A variable represents a change in value
b.
A variable always represents the total amount
d.
A variable is always represented by the letter x
Please select the best answer from the choices provided
Answers
hope this helps:))
A variable is an unknown number or value represented by a letter.
A variable is an unknown number or value represented by a lower case letter.
A shoe repairman is working with his assistant, who takes twice as long to repair a pair of shoes. Together they can fix 16 pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?
Answers
[tex]\boxed{\boxed{Answer: \tex{ }$45$ minutes}}[/tex]
Hello!
The number of pairs of shoes each man can repair is its speed times the time.
Call x the repair speed of the assistant. Then, the repair speed of the repairman is 2x, and the joint speed is 2x + x = 3x.
Also, the joint speed is 16 pairs in 8 hours = 16 pairs/ 8 hours = 2 pairs/hour.
Thus, we can equate:
[tex]3x = 2 pairs/hour, \text { or } x = (2/3) pairs / hour.$\\[/tex]
That is the speed of the assistant. Then, the speed of the repairman is:
[tex]2x = 2 (2/3) pairs/hour\\2x = (4/3) pairs/hour.[/tex]
That means that the repairman takes the inverse of 4/3 of an hour to repair one pair of shoes. That is 3/4 of an hour (to repair on pair)
3/4 of an hour is 45 minutes and this is the answer.To find out how long it takes the repairman alone to fix a pair of shoes, we solve a joint work rate problem. By setting equations based on their combined and individual work rates, we find out it takes the repairman 0.75 hours or 45 minutes to fix one pair of shoes by himself.
Explanation:To determine how long it takes the repairman to fix one pair of shoes by himself, we start by establishing the rates at which both the repairman and his assistant work.
Let's denote the time it takes the repairman to repair one pair of shoes by x hours.
Since the assistant takes twice as long, their time would be 2x hours for one pair.
Working together, their combined rate allows them to fix 16 pairs in 8 hours, or 2 pairs per hour.
Now, we express their combined work rate as the sum of their individual work rates.
The repairman's rate is 1/x pairs per hour, and the assistant's rate is 1/(2x) pairs per hour.
Together, this should equal their combined rate of 2 pairs per hour:
1/x + 1/(2x) = 2
Solving this equation for x, we first find a common denominator and get:
2/2x + 1/2x = 2
3/2x = 2
3 = 4x
x = 3/4
Therefore, it takes the repairman 0.75 hours, or 45 minutes, to fix one pair of shoes by himself.
Help please.........,
Answers
y-6 = -4(x+1)
y-6 = -4x-4
add 6 to each side
y=-4x+2
A is the correct answer
Which of the following would best represent a cosine function with an amplitude of 3, a period of pi/2 , and a midline at y = –4? (1 point)
f(x) = –4 cos 4x + 3f(x) = 3 cos(x – pi/2 ) – 4
f(x) = 4 cos(x – pi/2 ) + 3
f(x) = 3 cos 4x – 4
Answers
To transform the function [tex]f(x)=cos(x)[/tex] to have the midline [tex]y=-4[/tex] we need to subtract [tex]f(x)[/tex] by 4, so we have [tex]y=f(x)-4[/tex],
To transform the function [tex]f(x)=cos(x)[/tex] to have period of [tex] \frac{ \pi }{2} [/tex], we need to divide the original period [tex]2 \pi [/tex] by 4, so we have [tex]y=f(4x)[/tex]. Note that it is the [tex]4x[/tex] gives the effect of dividing the points on x-axes by 4 and the period is read on x-axes
Hence, the full transformation is given [tex]y=3f(4x)-4[/tex] which is the last option
Answer:
D) f(x) 3 cos 4x-4 (I just took it)
The screen aspect of a widescreen tv is 16.9. What are the width and height of a 32 inch tv? Round answer to the nearest tenth of an inch.
Answers
thus
[tex]\bf 32^2=w^2+\left( \cfrac{9w}{16} \right)^2\implies 32^2=w^2+\cfrac{(9w)^2}{16^2}\implies 32^2=w^2+\cfrac{9^2w^2}{16^2} \\\\\\ 32^2=\cfrac{16^2w^2+81w^2}{16^2}\implies 32^2\cdot 16^2=337w^2 \\\\\\ (32\cdot 16)^2=337w^2\implies \sqrt{(32\cdot 16)^2}=\sqrt{337w^2} \\\\\\ 32\cdot 16=w\sqrt{337}\implies \cfrac{32\cdot 16}{\sqrt{337}}=w\implies \boxed{\cfrac{512}{\sqrt{337}}=w}\\\\ -------------------------------\\\\[/tex]
and we can rationalize that to [tex]\bf \cfrac{512}{\sqrt{337}}\cdot \cfrac{\sqrt{337}}{\sqrt{337}}\implies \boxed{\cfrac{512\sqrt{337}}{337}}[/tex]
thus, its height is [tex]\bf h=\cfrac{9w}{16}\implies h=\cfrac{9}{16}\cdot \cfrac{512\sqrt{337}}{337}\implies \boxed{h=\cfrac{4608\sqrt{337}}{5392}}[/tex]
What of the above terms indicates imaginary parallel lines that circle the earth?
Answers
Between these two, the imaginary lines parallel to the equator of the Earth are the latitudes. Imagine a Cartesian plane that is revolved about either the x or y axis. You would form a sphere with x and y coordinates. The x-coordinates or the horizontal axis with respect to the equator of the Earth are the latitudes. The vertical axis are the longitudes.
Solve the inequality -2x is less than or equal to 3x + 1 is less than or equal to 10
Answers
split them
-2x < = 3x + 1 3x + 1 < = 10
-2x - 3x < = 1 3x < = 10 - 1
-5x < = 1 3x < = 9
x > = -1/5 x < = 3
solution is : -1/5 < = x < = 3 <==
in the diagram which pair of angles are corresponding angles
Answers
C
Answer:
Option C is correct .i.e., ∠3 and ∠7
Step-by-step explanation:
Corresponding angles are the angles that are at the same corner at each Point of Intersection.i.e., if first angle is at the top left corner of one intersection then the angle at the other intersection is also at the top left.
From Given Figure,
Following are pairs of corresponding angles,
∠1 and ∠5
∠2 and ∠6
∠4 and ∠8
∠3 and ∠7
Therefore, Option C is correct .i.e., ∠3 and ∠7
Find S8 for the geometric series 3 + -6 + 12 + -24 +…
Answers
Sum = a₁(1-rⁿ)/(1-r), where a₁ is the 1st term, r=common ratio and n=number of terms:
the 1st term a₁ =3
common ratio r = - 2 (since -6/3 = - 2, and 12/-6 = - 2, etc.)
Sum = 3[(1- (-2)⁸]/(1-2) = 3(1- 256)/(1/2)
Sum = -1530
the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].
To find the sum [tex]\( S_8 \)[/tex] of the geometric series [tex]\( 3 - 6 + 12 - 24 + \ldots \)[/tex], we need to determine the common ratio [tex](\( r \))[/tex] and the first term [tex](\( a \)).[/tex]
The general form of a geometric series is [tex]\( a + ar + ar^2 + \ldots + ar^{n-1} \)[/tex], where:
- [tex]\( a \)[/tex] is the first term,
- [tex]\( r \)[/tex] is the common ratio,
- [tex]\( n \)[/tex] is the number of terms.
In our series:
- [tex]\( a = 3 \)[/tex] (the first term),
- To find the common ratio [tex](\( r \))[/tex], we can divide any term by its preceding term:
- [tex]\( \frac{-6}{3} = -2 \)[/tex]
- [tex]\( \frac{12}{-6} = -2 \)[/tex]
- [tex]\( \frac{-24}{12} = -2 \)[/tex]
So, [tex]\( r = -2 \)[/tex].
Now, [tex]\( S_n \)[/tex], the sum of the first [tex]\( n \)[/tex] terms of a geometric series, is given by the formula:
[tex]\[ S_n = \frac{a(1 - r^n)}{1 - r} \][/tex]
Substituting the values of [tex]\( a \), \( r \)[/tex], and [tex]\( n = 8 \)[/tex], we get:
[tex]\[ S_8 = \frac{3(1 - (-2)^8)}{1 - (-2)} \][/tex]
[tex]\[ S_8 = \frac{3(1 - 256)}{1 + 2} \][/tex]
[tex]\[ S_8 = \frac{3(-255)}{3} \][/tex]
[tex]\[ S_8 = -255 \][/tex]
So, the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].
Decide if the situation involvesâ permutations, combinations, or neither. explain your reasoning.
Answers
Combinations are when the order doesn't matter, like if you had 3 numbers behind your back and you had to guess the 3 not in order
It needs neither when you don't need to find the amount of choices you have (or something similar) for something
He number of years of education of self-employed individuals in the united states has a population mean of 13.6 years and a population standard deviation of 3.0 years. if we survey a random sample of 100 self-employed people to determine the average number of years of education for the sample, what is the standard deviation of the sampling distribution of (the sample mean)
Answers
We can solve this problem by using the formula:
s = σ / sqrt(n)
where,
s = standard deviation of the sample
σ = standard deviation of the population = 3 years
n = number of samples = 100
Substituting:
s = 3 years / sqrt (100)
s = 0.3 years (ANSWER)
find the magnitude of 6+2i
Answers
Final answer:
The magnitude of 6 + 2i is 2√10.
Explanation:
To find the magnitude of the complex number 6 + 2i, we can use the Pythagorean theorem. The magnitude, or absolute value, of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 6 and the imaginary part is 2. So the magnitude is:
|6 + 2i| = √(6^2 + 2^2) = √(36 + 4) = √40 = 2√10
Therefore, the magnitude of 6 + 2i is 2√10.
Grace is standing 14 feet from a lighthouse and Kelly is standing 12 feet from Grace. The angle that Grace looks up to see the top of the lighthouse is 45°. The angle that Kelly looks up to see the top of the lighthouse is y°. Find the height, h, of the lighthouse. Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse. To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations
Answers
Case A. Kelly is 26 feet from the lighthouse.
The arcTangent of 14/26 is a 28.3 degree angle.
Case B. But if Kelly stood closer to the lighthouse, i.e. 2 feet away, then her angle is arcTangent of 14/2 = 81.9 degrees
what type of number can be written as a fraction where p and q are intergers and q is not equal to zero
Answers
Irrational numbers are the opposite.
Hope this helps!
Simplify 1 over quantity x minus 3 plus 4 over x all over 4 over x minus 1 over quantity x minus 3
Answers
(1/(x-3)+4/x)/(x-1)/(x-3), giving us the common denominator of x(x-3). We then take each individual fraction in the complex fraction, making it so that each one has the denominator x(x-3). 1/(x-3) becomes x/x(x-3), 4/x becomes 4(x-3)/x(x-3), and (x-1)/(x-3) becomes x(x-1)/x(x-3).
Now, our fraction is (x/x(x-3)+ 4(x-3)/x(x-3))/x(x-1)/x(x-3), or simply ((x+4(x-3)/x(x-3))/x(x-1)/x(x-3)). If we multiply the numerator and denominator by x(x-3), we get the fraction (x+4(x+3))/(x(x-1)).
Distributing the 4, we get (x+4x+12)/(x(x-1)), or (3x+12)/(x(x-1)). (I don't know if you want the denominator factored or not, but if you want it expanded then it's (3x+12)/(x^2-x).)
I hope this was easy enough to follow! I haven't written anything like this before so I'm sorry if it wasn't very good.
Given expression: [tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}[/tex].
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x-3:\quad x\left(x-3\right)[/tex]
[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}[/tex]
[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{4\left(x-3\right)}{x\left(x-3\right)}-\frac{x}{x\left(x-3\right)}[/tex]
[tex]=\frac{4\left(x-3\right)-x}{x\left(x-3\right)}[/tex]
[tex]=\frac{3x-12}{x\left(x-3\right)}[/tex]
[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{x}{x\left(x-3\right)}+\frac{4\left(x-3\right)}{x\left(x-3\right)}[/tex]
[tex]=\frac{x+4\left(x-3\right)}{x\left(x-3\right)}[/tex]
[tex]=\frac{5x-12}{x\left(x-3\right)}[/tex]
[tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}=\frac{\frac{5x-12}{x\left(x-3\right)}}{\frac{3x-12}{x\left(x-3\right)}}[/tex]
[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]
[tex]=\frac{\left(5x-12\right)x\left(x-3\right)}{x\left(x-3\right)\left(3x-12\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]
[tex]=\frac{\left(5x-12\right)\left(x-3\right)}{\left(x-3\right)\left(3x-12\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x-3[/tex]
[tex]=\frac{5x-12}{3x-12} \ \ \ : Final Answer.[/tex]
You will be charged 12.5% interest on a loan of $678. how much interest will you pay on the loan?
Answers
0.125(678) = 84.75 <==
It is given in the question that
You will be charged 12.5% interest on a loan of $678.
So to find the interest, we have to find 12.5% of 678. And 12.5% = 0.125
So we have to find the value of 0.125 of 678.
[tex]0.125*678 = 84.75[/tex]
Therefore the interest that you will have to pay on loan is $84.75 .
Given a polynomial f(x), if (x + 7) is a factor, what else must be true?
f(0)=7
f(0)=-7
f(7)=0
f(-7)=0
Answers
Because that makes the (x+7) factor equal zero and any other factor multiplied by zero also results in zero.
Answer:
f(-7)=0 that is option 4th is correct.
Step-by-step explanation:
If we have given any polynomial then its factor means that value is giving zero of that polynomial
And opposite sign of factor is the zero of the polynomial
For example:
x+a is factor of any polynomial f(x) then f(-a)=0
Similarly, If x+7 is a factor of any polynomial then f(-7)=0
Hence, option 4th is correct.
Find all solutions in the interval [0, 2π). 7 tan3x - 21 tan x = 0
Answers
7(tan x)^3-21tanx=0
this can be written as:
7(tan x)^3=21tanx
dividing through by 7 we get:
(tan x)^3=tan x
dividing through by tan x we get:
(tanx)^1=1
hence;
tan x=+\-1
when tan x=1
x=45
when tan x=-1
x=-45
Given that our answer should be at the interval [0,2π] the answer:
45=45/180=1/4π
What is the r value of the following geometric sequence?
64, 48, 36. 27
2/3
3/4
5/8
3/8
Answers
Find the possible value or values of n in the quadratic equation 2n2 – 7n + 6 = 0
Answers
2n^2-4n-3n+6=0
2n(n-2)-3(n-2)=0
(2n-3)(n-2)=0
n=3/2, n=2
Answer:
[tex]n=\frac{3}{2},\,\,n=2[/tex].
Step-by-step explanation:
The equation you have is a quadratic equation because the polynomial [tex]2n^{2}-7n+6[/tex] has degree 2. One of the methods available to solve kind of equations is to factorize the polynomial on the left hand side. To factorize you can do the following:
(1) [tex]2n^2-7n+6[/tex]. The given polinomial
(2) [tex]\frac{2\times(2n^2-7n+6)}{2}=\frac{(2n)^{2}-7(2n)+12}{2}[/tex]. Multiply and divide by 2, because it is the coeficient of [tex]n^{2}[/tex]
(3) [tex]\frac{(2n)^{2}-7(2n)+12}{2}=\frac{(2n-\_\_)(2n-\_\_)}{2}[/tex]. Separate the polynomial in two factors, each one with [tex]2n[/tex] as a first term. The sign in the first factor is equal to the sign in the second term of the polynomial, that is to say, [tex]-7n[/tex]. The sign in the second factor is the sign of the second term multiplied by the sign of the third term, that is to say [tex](-)\times(+)=(-)[/tex] . In the blanks you should select two numbers whose sum is 7 and whose product is 12. Those numbers must be 3 and 4.
(4)The polynomial factorized is [tex]\frac{(2n-4)(2n-3)}{2}[/tex]
(5)Use the common factor in the numerator to cancel the number 2 in the denominator to obtain [tex](n-2)(2n-3)[/tex]
Then the given equation can be written as:
[tex]{(2n-3)(n-2)=0[/tex]
The product of two expression equals zero if and only if one of the expression is zero. From here we have that
[tex]2n-3=0[/tex] or [tex]n-2=0[/tex]
From the first equality we obtain that [tex]n=\frac{3}{2}[/tex]. From the second equality we obtain that [tex]n=2[/tex].
what are the coordinates of a point on the unit circle if the angle formed by the positive x- axis and the radius is 45°??
Answers
sin(angle( = y-coordinate / radius = y-coordinate / 1 = y-coordinate = y
cos(angle) = x-coordinate / radius = x-coordinate / 1 = x
Then:
y = sin(angle) = sin(45°) = √2 / 2
x = cos (angle) = cos (45°) = √2 / 2
=> Answer: (√2 / 2 , √2 / 2), which is the option A)
The state of wyoming has roughly the shape of a rectangle that is 3.6 x 102 miles long and 2.8 x 102 miles high. what is the approximate area of wyoming? hint: the area of a rectangle is product of its length and width.
Answers
Assuming a regularly shaped rectangle, the formula for the area is given as:
A = L * W
where L and W are the length and width respectively
A = 3.6 x 10^2 miles * 2.8 x 10^2 miles
A = 100,800 square miles
or
A = 10.08 x 10^2 miles
Answer: The area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Step-by-step explanation:
The shape of wyoming is rectangular with length , [tex]L=3.6\times 10^{2}\, miles[/tex]
and height , [tex]H=2.8\times 10^{2}\, miles[/tex]
Area of rectangle , [tex]A=L\times W[/tex]
=> [tex]A=(3.6\times 10^{2})\times (2.8\times 10^{2})\, miles^{2}[/tex]
=>[tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Thus the area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
A family has two cars. the first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. during one particular week, the two cars went a combined total of 675 miles, for a total gas consumption of 40 gallons. how many gallons were consumed by each of the two cars that week?
Answers
car 1 = x
car 2 = y
x+y =40 gallons
x=40-y
15x +20y = 675
15(40-y) +20y = 675
600-15y +20y =675
600+5y = 675
5y=75
y=75/5 = 15 gallons
x=40-15 =25 gallons
Car 1 used 25 gallons
Car 2 used 15 gallons
If the lengths of two of the possible sides of a right triangle measure 4 root 15 and 7 root 6 what is the smallest possible length of the third side
Answers
using Pythagorean theorem:
c^2=a^2+b^2
c^2=(4sqrt15)^2+(7sqrt16)^2
c^2=4^2*15+7^2*16
c^2=240+784
c^2=1024
hence;
c=sqrt1024
c=32
Th possible third side is 32
Help me please!!!!!!
Answers
V1 = volume of the smaller cube (with 1/3 cm sides)
V2 = volume of the box shown
The first volume is
V1 = (1/3)*(1/3)*(1/3)
V1 = 1/27
The second volume is
V2 = (5/3)*(4/3)*(2)
V2 = 40/9
Now divide the two volumes
(V2)/(V1) = (40/9)/(1/27) = (40/9)*(27/1) = 120
Therefore you can fit 120 of the smaller cubes in the larger box shown.