The linear function c(x) to represent the cost of tuition as a function of "the number of years since 1990" denoted by "x" is [tex][c(x) = 14x+94][/tex].
As per the question statement, the cost of tuition at a large Midwestern university was $94 per credit hour in 1994 while it had risen to $290 per credit hour in 2004.
We are required to determine a linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x".
To solve this question, we need to know the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as
[tex](y-y_{1} )=(\frac{y_{2} -y_{1} }{x_{2} -x_{1}})(x-x_{1})[/tex].
Here, if we consider (x = 0) at 1990, c(x) = 94.
And since the standard form of conversion of functions into coordinate points goes as [y = f(x)], i.e., the ordinate is a function of the abscissa, therefore in this case, [y = c(x) = 94].
Thus, we can consider (x₁, y₁) as (0, 94).
Similarly, at 2004, [x = (2004-1990) = 14], and c(x) = 290, i.e.,
We can consider as (x₂, y₂) as (14, 290).
Using the values of (x₁, y₁) and (x₂, y₂), in the above mentioned standard equation of line passing through two points, we get,
[tex](y-94)=\frac{290-94}{14-0} (x-0)\\or, (y-94)=\frac{196}{14}x\\or,(y-94)=14x\\or,y=14x+94[/tex].
Hence, the linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x" is [tex][c(x) = 14x+94][/tex].
Linear Function: In Mathematics, a function is an operator which when provided with a input, gives a certain output, and when a function can be depicted in form of a linear equation, it is known as a linear function.To learn more about Linear Functions, click on the link below.
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Evaluate the function
f(x) = 3x^2 + 4x + 19
Find f(-7)
Answer:
Step-by-step explanation:
3
x
2
+
4
x
+
19
−
f
(
x
)
=
0
4 rounded to the nearest place
Concert R charges an admission fee of $10.00 and $6.25 per souvenir brochure. Concert S charges an admission fee of $13.00 and $5.75 per souvenir brochure.
How many souvenir brochures must be purchased in order for the total cost at Concert R and Concert S to be the same?
6 souvenir brochure
10 souvenir brochure
12 souvenir brochure
18 souvenir brochure
The number of souvenir brochures that must be purchased in order for the total cost at Concert R and Concert S to be the same is 6 souvenir brochure
When does the number of souvenir brochures for both concerts become the same?
In order for the total cost of souvenir brochures to be the same in for both concerts, their total costs must be the same
Concert R:
let x be the number of souvenir brochures for both concerts
total cost=10.00+6.25x
Concert S:
let x be the number of souvenir brochures for both concerts
total cost=13.00+5.75x
10.00+6.25x=13.00+5.75x
6.25x-5.75x=13.00-10.00
0.50x=3.00
x=3.00/0.50
x=6
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Select the best answer for the question.
1. Identify the binomial
O A. x² - 4x + 2
O B. 2x2 + 3x -1 + y
C.x²
O D. x² - 4
Mark for review (Will be highlighted on the review page)
The only option that is a Binomial is; D. x² - 4
What is the binomial?A binomial is defined as a polynomial with two terms.
Examples of binomials are; x − 2 and x − 6 are both binomials.
A) x² - 4x + 2; This is a quadratic function with 3 terms and is therefore a trinomial and not a binomial.
B) 2x² + 3x - 1y; This is a quadratic function with 3 terms and is therefore a trinomial and not a binomial.
C) x²; This has only one term and is therefore a monomial and not a binomial.
D) x² - 4; This is a polynomial with two terms and is therefore a binomial.
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The point b is the midpoint of ac find the location of a
Answer:
A = -23
Step-by-step explanation:
If B is directly between A and C, and C is 9 points above B, then A must be 9 points below B.
-14 - 9 = -23
Flower Power shop in Davenport, FL sells 6 sunflowers for $13.50.
What would be the cost for 1 sunflower?
Answer: 2.25
Step-by-step explanation: divide 13.50 by 6 and then you get 2.25 to check you can do 2.25 times 6 and get 13.50
Kelly worked on a straight 9% commission. Her friend worked on a salary of $850 plus a 6% commission. In a particular month, they both sold $21,100 worth of merchandise.
How much did her friend earn for the same month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
Answer:
$1260
Step-by-step explanation:
Step 1: Read and analyze the problem
In this problem, you are asked to find out how much her friend earned in the same month. You are given information about their commission rates and the total amount of merchandise they sold.
Step 2: Identify the known values and the unknown value
The known values in this problem are the commission rates and the total amount of merchandise sold. The unknown value is the amount her friend earned in the same month.
Step 3: Create an equation or system of equations
You can create an equation to solve for the unknown value using the information given in the problem.
Step 4: Solve the equation or system of equations
If you solve the equation, you will find that her friend earned $1,260 in the same month.
Hope this helps! Please mark me brainliest
Answer:1260
Step-by-step explanation:
In round 1 in a game, Daniel earned 8.925 points. In round 2 he earned 11.6 points, and in round 3 he earned twice as many points as he did in round 2.
Answer:
23.2 points
Step-by-step explanation:
If the question is how many points did he earn in round 3, this is the answer.
Hope this helps, have a great day :)
Find the 96th term of the arithmetic
sequence -3, -14, -25,
The 96th term of this arithmetic sequence is -1059.
In an Arithmetic Progression (AP), the nth term is given by the formula-
a9 = a + (n-1)d
where a = first term of the AP
d = common difference
Here, we are given an AP-
-3, -14, -25
Here a = -3
and d = -14 + 3 = -11
Let the 96th term of the AP be a96
Therefore, according to the formula for finding the nth term of an AP, we get-
a96 = a + (96-1)d
a9 = a + 95d
Substituting the values of a and d given in the question-
a96 = -3 + 96(-11)
a96 = -3 - 1056
a96 = -1059
Thus, the 96th term of the arithmetic sequence is -1059.
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if x is directly proportional to y³ and x = 32 when y = 8,
i) find an equation connecting x & y
ii) find the values of x when y = 6
iii) find the value of y when x = 108
Quick pls!!
Answer:
i) x = ky³
ii) 13.5
iii) 12
Enter the missing values in the area model to find 6(2w+5)
7+8-2x3=25 how to make this statement true
- - - - - - - - - - - - - - - - - - - - - - - -
Work below. Enjoy!
- - - - - - - - - - - - - - - - - - - - - - - -
Break up the statement first, and then find the answer.
(7 + 8) - (2 x 3) = 25
15 - 6 = 25
Since it isn't true, try playing around with different functions. I'll spare time and write down my work:
(7 x 8) - (2 x 3) / 2 = 25
56 - 6 /2 = 25
50 / 2 = 25
- - - - - - - - - - - - - - - - - - - - - - - -
Good luck! :)
~pinetreee
Someone help with this fast!
Alex wrote checks on Tuesday for $35 and $45. He also made a
deposit in his checking account of $180. Find the overall change in
the amount in his checking account.
Step 1: Analyze Information
Step 2: Formulate a Plan
Step 3: Solve
Step 4: Justify and Evaluate
1
Write answer for step 2 here.
*||«
r notes
Answer: here is ur answer
He would have $100 in his bank account from the information provided
Step-by-step explanation:i really hope this helps please lmk if i am wrong have a good day/night (:
For any two integers a and b, (a - b) squared = a squared - b squared.
^^^^
Determine if the conjecture is true or false.
If False give a counterexample.
a = 1, b = 2 is a counterexample, and with that, we conclude that the conjecture is false.
Is the conjecture true or false?Here we have the conjecture:
"For any two integers a and b, (a - b)^2 = (a^2 - b^2)"
Notice that if we find a single pair of integers a and b such that the equality in the conjecture is false, then we have found a counterexample and that is enough to conclude that the conjecture is false.
If we define=
a = 1
b = 2
Replacing that in the equation of the conjecture we get:
(1 - 2)^2 = (1^2 - 2^2)
(-1)^2 = 1 - 4
1 = -3
This is false, then a = 1, b = 2 is a counterexample, and with that we conclude that the conjecture is false.
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changes color every 12 seconds Strand 2: changes color every 13 seconds
Both strands just changed color. After how many seconds will the strands change color at the same time again?
The strands will change color at the same time again after
seconds.
After 156 seconds the strands will change color at the same time again.
As strand 1 changes color every 12 seconds and Strand 2 .changes color every 13 seconds. we are provided that both strands just changed color and we need to find that After how many seconds will the strands change color at the same time again
To know After how many seconds will the strands change color at the same time again we need to find the least common multiple (LCM) of 12 second and thirteen seconds
The factors of 12 = 2*2*3
The factors of 13 = 1 *13
LCM =2 * 2* 3*13 = 156
Hence, After 156 seconds the strands will change color at the same time again
Correct question is Strand 1 changes color every 12 seconds Strand 2: changes color every 13 seconds . Both strands just changed color. After how many seconds will the strands change color at the same time again?
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What is the product of 4.5 ⋅ 10^5 and 1.6 ⋅ 10^2?
Answer: 450000, 160
Step-by-step explanation:
4.5 ⋅ 10^5 =
4.5*100000=
4*100000+0.5*100000=
400000+50000=450000
1.6 ⋅ 10^2=
1.6*100=
1*100+0.6*100=
100+60=160
There are 11 reams of paper in a case. How many total reams of paper are in 23 cases?
Answer: 253 reams of paper
Hope this helps!
Simplify the expression
(2*2.3) + (3.14) (4) -5
The value of the given expression after simplification is 12.16
Expression:
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is called an expression or an algebraic expression.
Simplification:
The act of substituting a complex mathematical expression with a simpler counterpart is known as simplification (usually shorter).
Simplifying the given expression i.e.(2)(2.3) + (3.14)(4) - 5
⇒(2)(2.3) + (3.14)(4) - 5
⇒4.6 + 12.56 - 5
⇒17.16 - 5
⇒12.16
⇒(2)(2.3) + (3.14)(4) - 5 = 12.16
Therefore,The value of the given expression after simplification is 12.16
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(24÷4 x 3)+5(2)
I need a little bit of help
Answer: 28
Step-by-step explanation: I am just like that
Explain how to find the constant of proportionality for the ratio of robins to cardinals.
Not really sure how this works!! Thank you for all help
The constant of proportionality is 3 for the ratio of robins to cardinals.
We have a table:
Cardinals Robins
5 15
6 18
9 27
10 30
We need to find the constant of proportionality.
The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
We know that:
Robins ∝ Cardinals
Robins = K × Cardinals
K = the constant of proportionality
15 = k (5)
k = 3
So, we get the constant of proportionality as 3.
Therefore, the constant of proportionality is 3 for the ratio of robins to cardinals.
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Your question was incomplete. Please refer the content below:
Explain how to find the constant of proportionality for the ratio of robins to cardinals.
A 2-column table with 4 rows. Column1 is labeled Cardinals with entries 5, 6, 9, 10. Column 2 is labeled Robins with entries 15, 18, 27, 30.
Write the quadratic equation whose roots are -5 and 3, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
Answer: (x-3)(x-5) = x2 - 8x + 15
The roots will be unchanged by multiplication by 3: 3x2 - 24x + 45
Step-by-step explanation:
Answer:
y = 3x² + 6x - 45
Step-by-step explanation:
given roots x = a and x = b then the factors are (x - a) and (x - b)
then the quadratic is the product of its factors
y = a(x - a)(x - b) ← a is a multiplier
here x = - 5 and x = 3 with a = 3 , then factors are
(x - (- 5)) and (x - 3) , that is (x + 5) and (x - 3) , then
y = 3(x - 3)(x + 5) ← expand factors using FOIL
y = 3(x² + 2x - 15) ← distribute parenthesis by 3
y = 3x² + 6x - 45
What is the answer of , if n+2=7 then n= what
Answer: I
think n is 5
Step-by-step explanation:
What the answer to (-9.5)(-2)
Answer:
19
Step-by-step explanation:
Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. (If the quantity diverges, enter DIVERGES.)
an = n^3 − 1/n^3 + 1.
lim an =
n→∞
How many significant figures does 163 have?
Answer:
3
Step-by-step explanation:
The Significant Figures are 1_6_3
Hope it helps! :)
Translate 12y + 3 into an english expression
Answer: No hablo english
Step-by-step explanation: Hola como estas
Answer if you know your right, bur dont answer just for the points
Answer:
2/11 = 0.18
22% = 0.22
1.42 = 1.42
That leaves the answers down to B and C.
B has a lesser hundredths place than 0.18.C is greater than 0.18 in the tenths place, making it bigger.Thus, the answer is C, 22%.
Answer:
C
Step-by-step explanation:
2/11 = 0.18181
22% = 0.22
1.42
which of the following indicates the division property of equality when solving -12x = 48
From division it is possible to find x= -4.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:
a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex] .
b= the constant term that represents the y-intercept.
For the given example: a=7 and b=2.
For solving linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.
Therefore for -12x=48, you should follow the steps below
-12x=48
x=48/ (-12)
x= -4
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The table to the right shows the volume discounts offered by a company, where x is the volume of a purchase in dollars. Assume that the volume discounts in the table apply to the entire purchase. That is, if the volume x satisfies $300≤x<$1,000, the entire purchase is discounted 4%. Answer a) and b) below.
$300≤x<$1,000
$1,000≤x<$3,000
$3,000≤x<$5,000
$5,000≤x
4%
5%
6%
10%
Volume Discount
(Excluding tax)
Volume($x)
Discount Amount
Question content area bottom
Part 1
a) If x is the volume of a purchase before the discount is applied, write a piecewise definition for the discounted price D(x) of this purchase.
D(x)= x if 0≤x<300 enter your response here if 300≤x<1,000 0.95x if 1,000≤x<3,000 enter your response here if 3,000≤x<5,000 0.90x 5,000≤x
The piecewise function for the discounted price of the purchase is given by:
D(x) = 0.96x, 300≤x<1,000.D(x) = 0.95x, 1,000≤x<3,000.D(x) = 0.94x, 3,000≤x<5,000.D(x) = 0.9x, 5,000≤x.What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For $300≤x<$1,000, the discount is of 4%, hence the discounted price is 96% of the original price, that is:
D(x) = 0.96x, 300≤x<1,000
For $1,000≤x<$3,000, the discount is of 5%, hence the discounted price is 95% of the original price, that is:
D(x) = 0.95x, 1,000≤x<3,000.
For $3,000≤x<$5,000, the discount is of 6%, hence the discounted price is 94% of the original price, that is:
D(x) = 0.94x, 3,000≤x<5,000.
For $5,000≤x, the discount is of 10%, hence the discounted price is 90% of the original price, that is:
D(x) = 0.9x, 5,000≤x.
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