Answers
================================================
Explanation:
If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.
Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.
The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.
A function assigns the values. The only function that represents y as a function of x is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For any relation to represent a function in terms of x that represents the value of y, the order of y in the function should be equal to 1, therefore, the power of y should be 1, also, the y variable should be alone(Isolated) on one side of the equal sign.
A.) x = y⁴
It represents x in terms of y, therefore, No.
B.) 6x² + y = 4
It represents constant in terms of x and y, therefore, No.
C.) 6x + y² = -1
It represents constant in terms of x and y, therefore, No.
D.) [tex]y = \sqrt{1-x^2}[/tex]
The given function represents y in terms of x, therefore, it is a function that represents y as a function of x.
E.) -2xy = 1
It represents constant in terms of x and y, therefore, No.
Hence, the only function that represents y as a function of x is D.\
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Related Questions
What is the algebraic rule for a translation that moves the points right 4 units and down 3 units?
Answers
Answer: (x,y) —> (x+4, y-3)
it could also be T 4, -3 (x,y)
Step-by-step explanation:
If you move something right 4, x+4. Moving something down 3 is y-3.
the general form is always (x,y) —> (x + (whatever)), y + (whatever))
Or T whatever, whatever (x,y)
The first (whatever) is applied to x, second is for y.
hopes this helps
What is the value of this expression?
6 + 24 % 3 x 4 %2
Answers
Answer:
22
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
6 + 24 ÷ 3 x 4 ÷ 2
Step 2: Divide
6 + 8 x 4 ÷ 2
Step 3: Multiply
6 + 32 ÷ 2
Step 4: Divide
6 + 16
Step 5: Add
22
students surveyed about birthdays. How many more students were born on monday than friday?
a) 4 students
b) 1 students
c) 2 students
d) 3 students
Answers
Explanation
Take Monday’s amount and subtract Friday’s
3-1=2
explain all steps in detall. Incluide your final answer.. 9²+3•(9-5)²/4=
Answers
Answer: 93
Step-by-step explanation:
To solve this problem, we need to use the order of operations, or PEMDAS.
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
For multiply/divide and add/subtract, you don't necessarily go in that specific order. You go from left to right, depending on what comes first. For example, if division comes before multiply, you would divide first, then multiply. Same goes for add/subtract.
9²+3×(9-5)²/4 [solve parenthesis]
9²+3×(4)²/4 [solve exponent]
81+3×16/4 [solve multiply or divide, whichever comes first]
81+12 [solve add or subtract, whichever comes first]
93
Now, we know that 93 is our final answer.
If presented with the following equation, what is the next step in the equation solving sequence? x + 3x = -50 - 23+5
Answers
Answer:
Add the similar elements
[tex]x+3x=4x\\-50-23+5=-68\\\\4x=-68[/tex]
Step-by-step explanation: Further steps
Divide both sides by 4
[tex]\frac{4x}{4}=\frac{-68}{4}[/tex]
Simplify
[tex]x=-17[/tex]
Answer:
combine like
Step-by-step explanation:
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.) midpoint (1,6), endpoint (-2,1)
Answers
Answer:
(4,11)Step-by-step explanation:
Given two coordinates (x₁, y₁) and (x₂,y₂), the midpoint of the coordinates is expressed as M(X,Y) = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex] where;
[tex]X = \dfrac{x_1+x_2}{2}\ and \ Y = \dfrac{y_1+y_2}{2}[/tex]
Given the midpoint (X, Y) = (1,6) and one end point to be (-2,1), to get the unknown endpoint (x,y), we will apply the formula above. from the coordinates given X = 1, Y = 6, x₁ = -2 and y₁ = 1
[tex]Given \ X = \dfrac{x_1+x_2}{2}\\1 = \dfrac{-2+x}{2}\\cross \ multiply\\2 = -2+x\\x = 2+2\\x = 4[/tex]
Similarly to get y;
[tex]Given \ Y = \dfrac{y_1+y}{2}\\6 = \dfrac{1+y}{2}\\cross \ multiply\\2*6 = 1+y\\12 = 1+y\\y = 12-1\\y = 11[/tex]
Hence the unknown endpoint (x,y) is (4,11)
NarStor, a computer disk drive manufacturer, claims that the median time until failure for their hard drives is more than 14,400 hours. You work for a consumer group that has decided to examine this claim. Technicians ran 16 NarStor hard drives continuously for almost three years. Recently the last drive failed. The times to failure (in hours) are given in the following table. Give the test statistic.330 620 1870 2410 4620 6396 7822 81028309 12882 14419 16092 18384 20916 23812 25814
Answers
Answer:
The test statistics is [tex]t = -1.727[/tex]
Step-by-step explanation:
From the question we are told that
The data given is
330 620 1870 2410 4620 6396 7822 81028309 12882 14419 16092 18384 20916 23812 25814
The population mean is [tex]\mu = 14400[/tex]
The sample size is n = 16
The null hypothesis is [tex]\mu \le 14400[/tex]
The alternative hypothesis is [tex]H_a : \mu > 14400[/tex]
The sample mean is mathematically evaluated as
[tex]\= x = \frac{\sum x_i}{n}[/tex]
So
[tex]\= x = \frac{330+ 620+ 1870 +2410+ 4620+ 6396+ 7822+ 8102+8309+ 12882+ 14419+ 16092+ 18384 +20916+ 23812+ 25814 }{16}[/tex]
=> [tex]\= x = 10799.9[/tex]
The standard deviation is mathematically represented as
[tex]\sigma =\sqrt{\frac{ \sum (x_i - \=x)^2}{n}} [/tex]
So
[tex]\sigma =\sqrt{\frac{(330- 10799.9)^2 + (620- 10799.9)^2+ (1870- 10799.9)^2 +(2410- 10799.9)^2 + (4620- 10799.9)^2 +(6396- 10799.9)^2 +(7822- 10799.9)^2 }{16}} \ ..[/tex]
[tex]..\sqrt{ \frac{(8102 - 10799.9)^2 +(8309 - 10799.9)^2 + (12882 - 10799.9)^2 + (14419 - 10799.9)^2 + (16092 - 10799.9)^2 + (18384 - 10799.9)^2 +(20916 - 10799.9)^2 }{16}} \ ...[/tex]
[tex]\ ... \sqrt{\frac{(23812 - 10799.9)^2 +(25814 - 10799.9)^2 }{16}}[/tex]
=> [tex]\sigma = 8340[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{10799.9- 14400}{ \frac{8340}{\sqrt{16} } }[/tex]
[tex]t = -1.727[/tex]
From the z-table the p-value is
[tex]p-value = P(Z > t) = P(Z > -1.727) = 0.95792[/tex]
From the values obtained we see that
[tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis
Which implies that the claim of the NarStor is wrong
If KL = x + 4, LM = 2, and KM = 5x − 3, what is KL?
Answers
2x- 6 is 5x + 3
your answwr
Which statement is true about the two lines whose equations are given below?
y =
= 3x + 2
y = -4x + 9
A.
The lines are parallel.
B.
The lines are perpendicular.
The lines intersect but are not perpendicular.
C.
D.
The lines coincide.
Answers
Answer:
C. The lines intersect but are not perpendicular.
Step-by-step explanation:
The slopes (x-coefficients) of these lines are 3 and -4. They are different, but their product is not -1. Lines with different slopes are distinct lines that will intersect. If the product of their slopes is -1, they are perpendicular.
The lines intersect but are not perpendicular.
Jeson formed two-digit numbers using the following rules. (i) The digit in the tens place is an EVEN number. (ii) The two-digit number is divisible by 5. How many numbers did Jeson form? a) 5 b) 8 c )16 d) 18
Answers
Answer:
b) 8.
Step-by-step explanation:
The tens digit must be 2, 4, 6 or 8.
The units digit must be 0 or 5 ( as the 2 digit number must be divisible by 5).
So they are:
20, 25, 40, 45, 60, 65 , 80 and 85.
Answer:The tens digit must be 2, 4, 6 or 8.
The units digit must be 0 or 5 ( as the 2 digit number must be divisible by 5).
So they are:
20, 25, 40, 45, 60, 65 , 80 and 85.
Step-by-step explanation:
A square calendar has sides that are 7 inches long. What is the calendar's area?
Answers
Answer:
49
Step-by-step explanation:
7x7=49
Answer:
49
Step-by-step explanation:
7x7=49
If 3 out of 24 students made an "A" what percent of students
made an "A"?
Answers
what is 9 as a percent of 90
Answers
Answer:
8.1
Step-by-step explanation:
the answer the problem is 8.1
Answer:
10%
Step-by-step explanation:
convert fraction (ratio) 9/90 Answer : 10%
Before the election, you want to determine the number of possible president/vice-president combinations for the sorority you belong to. if both positions are chosen from nine people, how many combinations are possible
Answers
Answer:
The possible number of combination to select two positions from 9 people is 72.
. Jessica went to the grocery store and purchased a box of cereal for $3.75, milk for $1.50, and bread for $2.25. She paid with a $20.00 bill. How much change did Jessica receive?
Answers
$1.50 - milk
$2.25 - bread
—————————
$7.50
$20.00
- 7.50
—————
$ 12.50
She received $12.50 back
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answers
Step-by-step explanation:
z=y+16
y=y
:.z+y=5x where z=y+16
2y+16=5x
x=(2y+16)/5
.:z+y+x=180
y+16+y+(2y+16)/5=180
12y+80+16=900
y=67
z=16+67=83
x=30
The Megasoft company gives each of its employees the title of programmer (P) or project manager (M). In any given year 70% of programmers remain in that position 20% are pro- moted to project manager and 10% are fired (state X). 95% of project managers remain in that position while 5% are fired. How long on the average does a programmer work before they are fired?
Answers
Answer:
it will take a programmer about 16.67 times to work before they are fired
Step-by-step explanation:
From the information given;
The transistion matrix for this study can be computed as:
P M X
P 0.7 0.2 0.1
M 0 0.95 0.05
X 0 0 1
where;
The probability that the programmer remains a programmer = [tex](P *P)[/tex]
The probability that the programmer turns out to be a manager = [tex](P*M)[/tex]
The probability that the programmer is being fired = [tex](P*X)[/tex]
Thus, the required number of years prior to the moment being fired for an employee y(P), for programmer and y(M) for manager is represented by ;
[tex]y(P)=1+0.7y(P)+0.2y(M)[/tex]
[tex]y(M)=1+ 0.95y(M).[/tex]
[tex]0.05y(M)=1[/tex]
y(M) = [tex]\dfrac{1}{0.05}[/tex]
y(M) =20
y(P)=1+0.7y(P)+0.2y(M)
y(P) - 0.7y(P) = 1 + 0.2y(M)
0.3y(P) = 1 + 0.2(20)=1+4
0.3y(P) = 1 + 4
0.3y(P) = 5
[tex]y(P)=\dfrac{5}{0.3}[/tex]
[tex]y(P)=16.67[/tex]
Therefore, it will take a programmer about 16.67 times to work before they are fired
Josiah subtracts 337 from 600 and writes the following
600 minus 300 is 300. Then I can subtract 40 more and get 260. But I should have only subtracted 37
more, so I'll add 3 back to my difference to get 263
Which montal math strategy did Josiah use?
Answers
Answer:
Associative property is the math strategy Josiah used
What is the image point of
(−5,−3) after a translation right 4 units and down 1 unit?
Answers
Answer:
(-1,-4)
Step-by-step explanation:
(-5,-3) if we're moving four units right on the x axis, it would be a bigger number near the center. Think of it as adding -5 and 4, which would get you -1 for x (-1,x)
Now to get y, we would basically do the same thing except if it's going down, it would be a negative. We would add both -1 and -3 together to get -4, hence the answer, (-1,-4)
I suggest drawing a graph and doing it yourself, it'll really help you.
Alan can do 2/3 part of his work and sam can do 3/4 part of her work .Who can do more work
Answers
Answer:
Sam can do more work.
Step-by-step explanation:
2/3 equals out to just over half of his work done. 0.66666667.
3/4 equals out to almost all of her work done. 0.75.
*hope this helps*
Answer:
Sam can do more work:)
Step-by-step explanation:
Simplify the expression.
(2x^2y)^3
Answers
Answer:
=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6=
4
x
4
y
6
Explanation:
(
2
1
x
2
y
3
)
2
Here
2
needs to be multiplied with each term within the bracket:
=
2
1
.
2
x
2
.
2
.
y
3
.
2
=
2
2
.
x
4
.
y
6
=
4
x
4
y
6
Step-by-step explanation:
Find the function rule
X Y
0 -5
10 15
20 35
y=___
Answers
Answer:
y=2x-5
Step-by-step explanation:
y is double x minus 5
An image point after 180 rotation is Z'( 3,7) what are the coordinates of the pre-image point
Answers
Answer:
(-3 , -7)
Step-by-step explanation:
Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.15%. They have 500 grams of substance B which decays at a rate of 0.37%. They are trying to determine how many years it will be before the substances have an equal mass.
Answers
Answer:
In the blue area, people live closely because of its 1.Indutrialised area 2. The land is costly. 3.urbanisation In lighter color areas its farther because 1.Village 2.Farming area 3.Less popular rural area
Step-by-step explanation:
In the blue area, people live closely because of its 1.Indutrialised area 2. The land is costly. 3.urbanisation In lighter color areas its farther because 1.Village 2.Farming area 3.Less popular rural area
the difference of a number and 6 is the same as 5 times the sum of the number and 2
Answers
Answer:
n - 6 = 5 * ( n + 2 ) ; n = -4
Step-by-step explanation:
For this problem, we will use the words to create an equation. The left hand side of the equation will be the difference of a number and 6 and the right hand side of the equation will be 5 times the sum of the number and 2. Hence, we can build the equation:
n - 6 = 5 * ( n + 2 )
If we wanted, we can solve the equation for the number, n.
n - 6 = 5 * ( n + 2 )
n - 6 = 5 * n + 5 * 2
n - 6 = 5n + 10
-16 = 4n
-4 = n
Thus, we have found the missing number to be negative four.
Cheers.
what is five added to twice a number
Answers
2x+5
Step-by-step explanation:
let the number be x
According to the question
2x+5
hope it whould help
PLEASE HELP ME I WILL MARK AS BRAINLIEST
A map has a scale of
5 in. = 10 mi. If you measured the distance between two cities to
be 17 in. on the map, how many miles would it actually be?
If necessary, round your answer to the nearest tenth.
Answers
X=34 miles
Solve for x: −2(x + 3) = −2x − 6
Answers
Answer:
All real numbers
Step-by-step explanation:
Solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).
What is equation?
" Equation is defined as when two algebraic expression which are related with the sign of equality."
According to the question,
Given,
-2(x + 3) = -2x - 6
Open the brackets of the equation we get,
-2(x) + (-2)(3) = -2x - 6
⇒ -2x - 6 = -2x - 6
Add 6 on both the sides of the equation we get,
-2x = -2x
Divide by -2 of the equation both sides
x = x _____(1)
Add (-x) both the sides we get,
0 = 0 _____(2)
From (1) and (2) we conclude ,
Solution is true for all the real values of x.
Hence, solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).
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Each ounce of Food I contains 3 g of carbohydrate and 2 g of protein, and each ounce of Food II contains 5 g of carbohydrate and 3 g of protein. Suppose x ounces of Food I are mixed with y ounces of Food II. The foods are combined to produce a blend that contains exactly 73 g of carbohydrate and 46 g of protein.
a. Explain why there are 3x + 5y g of carbohydrate in the blend and why we must have 3x + 5y = 73. Find a similar equation for protein. Sketch the graphs of both equations.
b. Where do the two graphs in part (a) intersect? Interpret the significance of this point of intersection
Answers
Answer:
The answer is below
Step-by-step explanation:
a) Food I contains 3 g of carbohydrate and food II 5 g of carbohydrate. x is the number of ounce of food I while y is the number of ounce of food II.
Therefore, the amount of carbohydrate in food 1 is 3x while that of food II is 5y. Since the blend contains exactly 73 g of carbohydrate, the total number of carbohydrate in both food I and food II is 73 g. Hence:
3x + 5y = 73 (1)
Food I contains 2 g of protein and food II 3 g of carbohydrate. Therefore, the amount of protein in food 1 is 2x while that of food II is 3y. Since the blend contains exactly 46 g of protein, the total number of protein in both food I and food II is 46 g. Hence:
2x + 3y = 46 (2)
Using geogebra to Sketch the graphs of both equations.
b) The point of intersection is gotten from the graph, this gives x = 11, y = 8.
The point of intersection shows the amount of food I and food II that give the required amount of protein and carbohydrate.
11 ounce of food I and 8 ounce of food II would produce the required amount of protein and carbohydrate
In the diagram,
AB =BC,AC = CD, and AD
12. Find the
lengths of all segments in the diagram. Suppose you
choose one of the segments at random. What is the
probability that the measure of the segment is greater
than 3? Explain your reasoning.
Answers
Answer:
Probability that the measure of a segment is greater than 3 = 0.6
Step-by-step explanation:
From the given attachment,
AB ≅ BC, AC ≅ CD and AD = 12
Therefore, AC ≅ CD = [tex]\frac{1}{2}(\text{AD})[/tex]
= 6 units
Since AC ≅ CD
AB + BC ≅ CD
2(AB) = 6
AB = 3 units
Now we have measurements of the segments as,
AB = BC = 3 units
AC = CD = 6 units
AD = 12 units
Total number of segments = 5
Length of segments more than 3 = 3
Probability to pick a segment measuring greater than 3,
= [tex]\frac{\text{Total number of segments measuring greater than 3}}{Total number of segments}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6