The unit vector that has the same direction as the given vector is[tex]& (3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
The given vector(v) is -3i+7j
The unit vector is found by dividing the vector by its magnitude
Unit vector of [tex]$v=\frac{v}{\|v\|}$[/tex]
A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector.The formula of unit vector in the direction of a given vector is:
Unit Vector = Vector/Vector's magnitudeWe have to find the magnitude first
So,
[tex]& \|v\|[/tex] =[tex]\sqrt{(3)^{2}+(-7)^{2} } =\sqrt{9+49} =\sqrt{58}[/tex]
[tex]& \|v\|=\sqrt{58}[/tex]
The unit vector is:
The i, j, and k are the unit vectors in the directions of the x-axis, y-axis, and z-axis respectively in a 3-dimensional plane. i.e.,
|i| = 1|j| = 1|k| = 1[tex]$$\begin{aligned}& =(1 / \sqrt{58})(3 \mathrm{i}-7 \mathrm{j}) \\& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}\end{aligned}$$[/tex]
Therefore, the unit vector is [tex]& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
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The side length of a square is 5x - 7. Find x if the perimeter is 125.
The numerical value of x in the expression 5x - 7 is 7.65.
What is the numerical value of x?A square is simply a 2-dimentional plane figure with four equal sides and four right (90°) angles.
The perimeter of the square is the sum of the length of all four sides of the square.
P = 4l
Given the data in the question
Side length of square l = 5x - 7Perimeter P = 125Value of x = ?To find the value of x, plug the given values into the above equation and simplify.
P = 4l
125 = 4( 5x - 7 )
125 = 20x - 28
125 + 28 = 20x
153 = 20x
20x = 153
x = 153/20
x = 7.65
Therefore, the value of x is 7.65.
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If the two triangles in the map below are similar, what is the distance from Arrow Road to the end of the forest (x)?
We can write the measurements as -
a = 7.8
b = 9.24
(B) = 50°
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that two triangles in the map below are similar.
We can write -
{ 1 } -
sin (A) = a/c
a = c sin(A)
a = 12 sin(40°)
a = 12 x 0.65
a = 7.8
{ 2 } -
cos (A) = b/c
b = c cos(A)
b = c cos(40°)
b = 12 x 0.77
b = 9.24
{ 3 } -
tan (B) = b/a
tan (B) = 9.24/7.8
tan (B) = 1.19
(B) = 50°
Therefore, we can write the measurements as -
a = 7.8
b = 9.24
(B) = 50°
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I need help on part b
Answer:
a) The pattern 6 has 26 sticks,b) The pattern number n has 4n + 2 sticks.--------------------------
If we put the number of sticks in a sequence we get:
6, 10, 14, ...As we see the difference of the terms is common and is 4, and the first term is 6. It is therefore an arithmetic progression with:
a = 6 and d = 4Use the nth term equation:
a(n) = a + (n - 1)dPart a)Substitute n = 6 to find the number of sticks of the 6th term:
a(6) = 6 + (6 - 1)*4 = 6 + 5*4 = 6 + 20 = 26Part b)Find the nth term:
a(n) = 6 + (n - 1)*4 = 6 + 4n - 4 = 4n + 2a board has a red space, a blue space, and a yellow space. a checker is situated on the red space. on each move the checker is transferred to one of the other two spaces. in how many ways can one make a series of 11 moves which result in the checker returning to the red space?
There are 2 ways to make a series of 11 moves.
Since the checker can move to either the blue or yellow space in each move, there are 2 possibilities for each move. We want to find the number of sequences of 11 moves that result in the checker returning to the red space, i.e., a sequence of moves that alternates between the red and one of the other two spaces.
There are 2 possible sequences of 11 moves: RBYB...BYBR and BYBY...YBRB, where R represents the red space, B represents the blue space, and Y represents the yellow space.
So, in total there are 2 ways to make a series of 11 moves which result in the checker returning to the red space.
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Lorenzo orders 3 pizzas for delivery. The total bill, including a $4.00 delivery fee, is $42.85. He uses the following equation to figure out the cost of each pizza. 3c+4.00=42.85
Lorenzo uses the following equation to figure out the cost of each pizza. 3c+4.00=42.85
The cost of each pizza is $12.95.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
Lorenzo orders 3 pizzas for delivery.
The total bill, including a $4.00 delivery fee, is $42.85.
He uses the following equation to figure out the cost of each pizza. 3c+4.00=42.85
3c = 42.85 - 4
3c = 38.85
c = 12.95
Therefore, the cost of each pizza is $12.95.
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PLEASE HELP, I NEED THE ACTUAL ANSWER ASAP!
Amelia drinks half a gallon of milk each week. She also drinks six 6-oz cans of apple juice, 1 gal of water, and 52 oz of orange juice. How many ounces of liquids does Amelia average in 1 day?
The average amount of fluid consumed is 35.7 oz of fluid each day.
What is the amount of the liquid that she takes each day?We have to note that in this case of the question, we have the following information;
Amelia drinks half a gallon of milk each weekAmelia drinks ix 6-oz cans of apple juiceAmelia drinks 1 gal of waterAmelia drinks 52 oz of orange juiceWhen we convert the galloons to oz, we can see that the amounts of the milk and the water are actually 64 oz and 128 oz respectively.
Total fluid consumed in the week = 64 oz + 6 0z + 128 oz + 52 oz
= 250 oz
The average amount of fluid that is consumed per day is; 250 oz/7
= 35.7 oz of fluid each day.
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Caroline has a discount card that gives her 4% off the purchase of each pizza. If p is the cost of a regular pizza, how much does Caroline pay for her pizza?
Please Solve 7x-3y=-5?
Step-by-step explanation:
there should be two question like this
researchers wanted to see which species of lizard (a, b, or c) is most likely to survive a bacterial infection. so they infected a total of 38 lizards and recorded how many survived after 48 hours. of the 15 species b lizards, 40% survived. for those that were species c, one more survived than died. and of the 24 lizards that died, one-third of them were species a. a. create a contingency table to display this data. (3pt) b. what proportion of the lizards in this study were either species b or c? (1pt) c. what is the probability that a species b lizard in this study did not survive? (1pt) d. are survival and being species c independent events for these lizards? justify your answer. (3pt)
a. The contingency table for the given data is attached file below.
b. The proportion of lizards that were either species A or B is 0.605.
c. The probability that a species C lizard in this study did not survive is 0.4667.
a.
The contingency table for the given data is attached file below.
b.
The proportion of lizards that were either species A or B can be calculated as:
P(A or B) = (15+8)/(15+8+6+9+4)
P(A or B) = 23/38
P(A or B) = 0.605
c.
The probability that a species C lizard in this study did not survive can be calculated as:
P(Not survive| C) = 7/15
= 0.4667
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Suppose 60% of the graduating class in a certain high school goes to collage if 240 students from this graduating class are going to collage how many student's are in this class
Total number of students in the graduating class when 60% of the students are going to college is equal to 400 students.
Percent of students of the graduating class going for college is equal to 60%
let 'y' represent the total number of students in the graduating class.
Number of students of the graduating class going to the college are 240.
60% of y = 240
⇒ ( 60 / 100 ) × y = 240
⇒ y = 240 × ( 100 / 60 )
⇒ y = 400 students.
Therefore, when 240 students of the graduating class going for a college then total number of students in the graduating class is equal to 400 students.
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1. The expression that represents the mass of an atom is:
a) p+ + n
b) e- + n
c) p+ + e-
d) p+ + e. + n
It is the a) p+ + n
Step by step explanation:[tex] \large\boxed{ \bold{A=p^{+}+n}}[/tex]
Protons are used since they do not change, otherwise with electrons, of which some elements can give or receive them.
When all team members agree on the level of performance that is acceptable, they have a _____. Clear goal leader shared standard team structure
When all team members agree on the level of performance that is acceptable, they have a shared standard.
Teamwork is a collective approach in order to achieve a common goal for the growth of the organization. Each member of the team must be agreed on the methods and sources to be implemented in achieving the goal.
In order to achieve the goal, each individual has to work on his area but with the team to achieve the goal of the company. Each individual works together and share their efforts collectively so that the goal can be achieved.
Shared standard refers to the point of acceptance by each individual on a particular point and must agreed on the merging of the work collectively.
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Lauren and her sister are buying their mom a
watch for her birthday. The price of the watch is
$50, but Lauren has a 25% off coupon on
watches and her sister has a $5 store credit.
Which one should they use first to get the best
discount? Explain why.
The sisters should use the store credit first because if the store credit is used first and then the discount the cost is lower.
Which option should the sisters use first?Consumers always want to pay the least price possible for a good or service. The option the sisters would choose is the cheaper option.
Cost of the watch if the coupon is used first = price of the watch x (1 - coupon)
= $50 x (1 - 25%/100)
= $50 x (1 - 0.25)
= $37.50
Cost of watch after the store credit = $37.50 - $5 = $32.50
Cost of the watch if the store credit is used = cost of the watch - store credit
$50 - $5 = $45
Cost of the watch after the coupon = (1 - 25/100) x $45
(1 - 0.25) x $45
0.75 x $45 = $33.75
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0.18 rounded to the nearest tenth
Answer:
0.2
Step-by-step explanation:
8 is bigger than 5 so we will make 8 zero and will will add 1 to the next number
Answer:
0.2
Step-by-step explanation:
Hope this helps
~~Wdfads~~
Consider the following number pattern: -7; 0; 9; 20; ... Show that the general term of this quadratic number pattern is given by T₁ = n² +4n-12. 2.1
Hence the general term of the given quadratic number pattern is given by Tn = n²+4n-12 is verified.
The number pattern = -7,0,9,20
What is the formula for quadratic equation?Let the general term of the given quadratic number pattern is given by
Tn = an²+bn + c
When T = -7; n = 1
⇒ -7 = a(1)² +b (1) +6
⇒ a + b + c=-7 -----------1
At n=2, T₂ = 0
⇒ 0 = a(2)²+b(2)+c
4a+2b+c=0 ---------------2
At n=3, T = 9
⇒ 9 = a(3)²+b(3) +c
⇒ 9a+3b+c= 9 ---------3
Subtracting 3 from 2
⇒-5a-b = -9 --------4
Subtracting 2 from 1
-3a-b = -7 -----------5
Subtracting 5 from 4
2a = 2
⇒ a=1
Using eq 5, we get
-3(1) - b = -7
-b = -7 + 3
b = 4
From eq 1, a + b + c=-7 we get the value of c,
1 + 4 + c = -7
c = -7 -5
c = -12
substitute the values of a, b, and c in Tn = an²+bn + c
Tn = n² + 4n - 12
Hence the general term of the given quadratic number pattern is given by Tn = n²+4n-12.
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01. De 200 melones, 80 resultaron en mal estado.
¿Qué porcentaje de los 200 están buenos para la venta?
200 melons are good in 60% of the cases.
Qué es bueno para la buena venta?Create a favourable first impression. Offers customers problems-solutions and a positive experience. Make good use of the newest technologies. clear language for business transactions. Maintain open communication.
The Most Important Characteristic for Sales. No matter what kind of sale it is, or what industry it is in, the most crucial factor that influences someone's decision to buy is always the price. And making oneself increasingly valuable is the key to selling and selling oneself.
200 equates to 100%.
Are good = 200 - 80 = 120
200me = 100%
120me = 100%/200me x = 120000%/200me x = 60%
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Calculator
Lilyana runs a cake decorating business, for which 10% of her orders come over the telephone. Let C be the
number of cake orders Lilyana receives in a month until she first gets an order over the telephone. Assume the
method of placing each cake order is independent.
Find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
You may round your answer to the nearest hundredth.
PC <5) =
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If Lilyana runs a cake decorating business for which 10% of her orders come over telephone , then probability that it takes fewer than 5 orders for Lilyana to get her first telephone is 0.3439 .
The geometric distribution is used to calculate the required probability ,
In this case, the success is a telephone order, and
the failure is an order placed in some other way.
Let probability of success is ⇒ p , and
let the number of orders needed to get the first telephone order be = x . Then, X follows a geometric distribution with parameter p, so we have:
Probability of P(X = k) is = (1-p)^(k-1) × p ;
where k is the number of orders needed.
the probability of success (p) is = 10% = 0.1
we have to find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
that means : P(X<5) = P(X=1) + P(X=2) + P(X=3) + P(X=4)
Substituting the values of p = 0.1 ,
we get ;
= (1-0.1)⁰ × 0.1 + (1-0.1)¹ × 0.1 + (1-0.1)² × 0.1 + (1-0.1)³ × 0.1
Simplifying further ,
we get ;
= 0.1 + 0.09 + 0.081 + 0.0729
Adding all the terms ,
we have ;
= 0.3439
Therefore , the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month is 0.3439.
The given question is incomplete , the complete question is
Lilyana runs a cake decorating business, for which 10% of her orders come over the telephone. Let C be the number of cake orders Lilyana receives in a month until she first gets an order over the telephone. Assume the method of placing each cake order is independent.
Find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
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Which ordered pair is a solution of the equation? 6 x + 3 y = 15 6x+3y=15
Choose 1 answer:
(Choice A)
A
Only
(
3
,
−
2
)
(3,−2)left parenthesis, 3, comma, minus, 2, right parenthesis
(Choice B)
B
Only
(
2
,
2
)
(2,2)left parenthesis, 2, comma, 2, right parenthesis
(Choice C)
C
Both
(
3
,
−
2
)
(3,−2)left parenthesis, 3, comma, minus, 2, right parenthesis and
(
2
,
2
)
(2,2)left parenthesis, 2, comma, 2, right parenthesis
(Choice D)
D
Neither
Neither of the ordered pairs is a solution of the equation 6x + 3y = 15.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given linear equation is 6x + 3y = 15
Substitute each of the point given in the options.
A : (3, -2)
6x + 3y = (6 × 3) + (3 × -2) = 18 - 6 = 12 ≠ 15
B : (2, 2)
6x + 3y = (6 × 2) + (3 × 2) = 12 + 6 = 18 ≠ 15
Neither (3, -2) nor (2, 2) are the solutions of the equation.
Hence neither is the solution of the given linear equation.
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The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b. Which table of values matches the equation and includes only viable solutions?
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries negative 2, 0, 2, 4. The second column is labeled cost (c) with entries negative 7, 0, 7, 14.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 0.5, 1, 1.5. The second column is labeled cost (c) with entries 0, 1.75, 3.5, 5.25.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 3, 6, 9. The second column is labeled cost (c) with entries 0, 10.5, 21, 31.5.
The table which matches the equation and includes only viable solutions is the third table.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
Given that equation is,
c = 3.5b
Here b is the number of loaves of bread and c is the total cost of the bread.
All the table values matches the equation when we substitute the value of b and c in the equation.
But number of loaves of bread cannot be fractions or negative numbers.
So the most viable solution is the third table consisting of values of b as 0, 3, 6, 9 and corresponding value of c as 0, 10.5, 21, 31.5.
Hence the 2-column table with the first column labeled loaves (b) with entries 0, 3, 6, 9 and the second column labeled cost (c) with entries 0, 10.5, 21, 31.5 is the correct one.
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Answer:
The third one
Step-by-step explanation:
is 1+4(3x-10)-12x equivalent to - 39? explain
Answer:
1+4(3x-10)-12x is equivalent to -39 .The order of operations applies here, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).Working from the inside out:4(3x-10) = 43x - 410 = 12x - 40Then we have1 + (12x - 40) - 12x = 1 - 12x + 40 = -12x + 41So the equation 1+4(3x-10)-12x = -12x + 41 = - 39By following the order of operations, we can see that the two expressions are equivalent.
Step-by-step explanation:
1+4(3x-10)-12x is equivalent to -39 .The order of operations applies here, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).Working from the inside out:4(3x-10) = 43x - 410 = 12x - 40Then we have1 + (12x - 40) - 12x = 1 - 12x + 40 = -12x + 41So the equation 1+4(3x-10)-12x = -12x + 41 = - 39By following the order of operations, we can see that the two expressions are equivalent.
The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s) to f(x)=g(x)? Explain your answer(s). (4 points)
x –3 –2 –1 0 1 2
f(x) 0.4 4.5 7 11.3 15 16.2
g(x) 4 8 10 11.3 15 17
The solutions to the system of equations f(x) = g(x) are given as follows:
x = 0 and x = 1.
The reason for these solutions is that f(x) and g(x) have the same numeric value at x = 0 and at x = 1.
How to interpret the solution of a system of equations?A system of equations is composed by multiple equations.
The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.
The x-values for which the numeric values of f(x) and g(x) are the same are given as follows:
x = 0 and x = 1.
Which are the solutions to the system of equations.
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write the equations described below.
a subtraction equation with one variable that has a solution of 2/3.
Answer: o
Step-by-step explanation:
preciso de ajuda por que eu não sei matemática
Answer:
¡Hola, soy Za'Riah! Con gusto te ayudaré con este problema. (ver explicación)
Step-by-step explanation:
Resolvamos tu problema usando la división larga.
(See image)
Perry used the formula V (t) = 24,450(1-0. 13)
to find the value of his car t years after he purchased it.
What does 0. 13 represent?
A the price of the new car
B the time of year the car was purchased
the value of the car after t years
a 13% decrease in value each year
The expression 0.13 represents a 13% decrease in value each year. Thus, Option D is the correct option.
Perry used the formula V (t) = 24,450(1-0.13)^t to find the value of his car t years after he purchased it.
The expression given above represents an expression of exponential decrease which is given by the formula -
y = a(1 - r)^t
Where,
y = Value after time t
a = Initial value
r = Rate of decrease
t = Time
Comparing both expressions we get,
r = 0.13
This is the rate of decrease in the value of the car.
Converting to Percentage = 0.13 × 100
= 13% decrease.
Hence, the expression 0.13 represents a 13% decrease in value each year. Thus, Option D is the correct option.
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50 POINTS (and its easy im just kinda dmb)
find the number of possible outcomes
1. A softball player bats six times in a game. Each at-bat results in an out, getting on base or hitting a homerun.
2. A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each s andwich can be ordered with white bread or multi-grain bread. Customers can add any combination of the six available toppings h
The number of outcomes for each case is given as follows:
1. 729 outcomes.
2. 36 outcomes.
How to obtain the number of outcomes?The number of outcomes for each case is obtained using the Fundamental Counting Theorem, with the multiplication of the number of outcomes for each trial.
For item 1, we have six trials, each with three possible outcomes, hence the total number of outcomes is given as follows:
3^6 = 729.
For item 2, the outcomes are given as follows:
3 types of sandwich.2 types of bread.Six toppings.Hence the number of outcomes is given as follows:
3 x 2 x 6 = 36 outcomes.
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How do you find the value of x and y?
Check the picture below.
[tex]5x+70=24x-25\implies 70=19x-25\implies 95=19x \\\\\\ \cfrac{95}{19}=x\implies \boxed{5=x} \\\\[-0.35em] ~\dotfill\\\\ 4y+2=x+y\implies 4y+2=5+y\implies 3y+2=5 \\\\\\ 3y=3\implies y=\cfrac{3}{3}\implies \boxed{y=1} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{5(5)+70}{\measuredangle R=95^o}\hspace{5em}\stackrel{24(5)-25}{\measuredangle C=95^o}\hspace{5em}\stackrel{4(1)+2}{QR=6}\hspace{5em}\stackrel{5+1}{BC=6}[/tex]
What is 223,692 divided by 42 using the standard algorithm and showing work?
The value of 223,692 divided by 42 using the standard algorithm and showing work is 5326.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
The value of 223,692 divided by 42 using the standard algorithm and showing work is given below:
Dividing the two values by 2, a common factor
223,692 / 42
= 111,846 / 21
Dividing the two values by 3, a common factor
111,846 / 21
= 37282 / 7
Dividing the two values by 7, a common factor
37282 / 7
= 5326 / 1
Hence, the value of the division is 5326.
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explain how the sequence 10.6, 11.8, and 13 is a function even though there are multiple rules that can represent it.
The correct option is Option C.
C.) The sequence is a function because each rule produces one output for each input.
Meaning of a sequence:
A grouping of any objects or a collection of numbers in a particular order that follows some rule is known as a sequence.
The difference between all the following terms in the sequence 10..6.11.8.13 is 12.
As a result, the series is an example of a linear function.
As a linear function, the sequence will always provide an output that complies with the rule.
As a result, the sequence is a function because each rule yields a single output for each input; hence, option C is the right response.
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The following question may be like this:
Explain how the sequence 10.6, 11.8, and 13 is a function even though there are multiple rules that can represent it.
A)The sequence is a function because the domain is unrestricted.
B)The sequence is a function because more than one rule can represent it.
C)The sequence is a function because each rule produces one output for each input.
D)The sequence is a function because each rule produces multiple outputs for each input.
Someone please help! I’ll give Brainliest!!
Answer:
BAD
Step-by-step explanation:
i think its triangle BAD sorry if its not would make the most sense i think
What is the solution for this inequality?
Answer:
r > -3
Step-by-step explanation:
dwbi jus know that's the answer lil one