Hailey is going to use a computer at a Internet cafe. The cafe charges $1.50 for every minute using a computer on top of an initial charge of $4. Make a table of values and then write an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the Internet cafe.
Answer:
The equation is C(t) = 1.50t + 4.00 and the data table is below.
Step-by-step explanation:
We are given that a cafe charges $1.50 for every minute that someone uses the internet. The cafe also charges an initial $4 fee to use the internet.
We need to find a function, in terms of t, that will find these values.
We can treat this as a linear equation. If we initially pay $4, this is acquired before we pay the fee every minute. Therefore, this would be our y-intercept at x = 0. Our first coordinate is (0, 4).
Secondly, if we are charged every minute, this would be a recurring payment and therefore we would spend $1.50 after each minute elapses. This gives us our slope: 1.50 or [tex]\frac{3}{2}[/tex].
Therefore, we can set up our function.
C is the total cost and t is the time, in minutes, that internet is used at the cafe. Our equation can be set up as [tex]C(t) = 1.50t + 4.00[/tex].
Now, we can create a table of values for t = 0 to t = 5 to determine what C(t) is at each of these prime intervals.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} a & 0 \\ \cline{1-2} b & 1 \\ \cline{1-2} c & 2 \\ \cline{1-2} d & 3 \\ \cline{1-2} e & 4 \\ \cline{1-2} f & 5 \\ \cline{1-2} \end{array}[/tex]
This is what our table looks like, but we need to fill the C column. Therefore, we can use substitution of our t-values into the equation and solve for C.
[tex]\bullet \ \text{For t = 0,}[/tex]
[tex]C(0) = 1.50(0) + 4\\\\C(0) = 0 + 4\\\\C(0) = 4.00[/tex]
[tex]\bullet \ \text{For t = 1,}[/tex]
[tex]C(1) = 1.50(1) +4\\\\C(1) = 1.50 + 4\\\\C(1) = 5.50[/tex]
[tex]\bullet \ \text{For t = 2,}[/tex]
[tex]C(2) = 1.50(2) + 4\\\\C(2) = 3.00 + 4\\\\C(2) = 7.00[/tex]
[tex]\bullet \ \text{For t = 3,}[/tex]
[tex]C(3) = 1.50(3) + 4\\\\C(3) = 4.50 + 4\\\\C(3) = 8.50[/tex]
[tex]\bullet \ \text{For t = 4,}[/tex]
[tex]C(4) = 1.50(4) + 4\\\\C(4) = 6.00 + 4\\\\C(4) = 10.00[/tex]
[tex]\bullet \ \text{For t = 5,}[/tex]
[tex]C(5) = 1.50(5) + 4\\\\C(5) = 7.50 + 4\\\\C(5) = 11.50[/tex]
Now, we can insert these values into our table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} 4.00 & 0 \\ \cline{1-2} 5.50 & 1 \\ \cline{1-2} 7.00 & 2 \\ \cline{1-2} 8.50 & 3 \\ \cline{1-2} 10.00 & 4 \\ \cline{1-2} 11.50 & 5 \\ \cline{1-2} \end{array}[/tex]
Therefore, our equation is C(t) = 1.50t + 4.00 and our data table is above.
expand and simply 3(2x+5) - 2(x-4)
Answer:
4x+7
Step-by-step explanation:
6x+15 - 2x-8
Combine like terms
6x-2x=4x
15-8 = 7
4x+7
Please help it would help a lot
Answer:
1/2
Step-by-step explanation:
Answer:
y÷x 1÷2=1/2 This is the answer.
1. An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answer:
3 and 12
Step-by-step explanation:
3*5=15 and 15-3=12. The product of 3 and 12 is 36.
The integers are 3 and 12.
What is Algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
let the one integer be x.
Another integer = 5x - 3
According to question,
x *(5x-3 ) =36
5x ² -3 x =36
5x² -3 x - 36 = 0
5x² -15 x +12 x - 36 =0
5x( x-3) + 12 ( x -3) =0
(5x +12)( x- 3)=0
x= -12/5 or 3
So, the integers are 3 and 12.
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2
Viviana is ordering carpet
for 16 square rooms in a
hotel. Each room will need
100 square feet of
carpet. What is the
length of 1 room?
Answer:
Length of a room is 10ft
Step-by-step explanation:
Given
[tex]Rooms = 16[/tex]
[tex]Carpet\ Area = 100ft^2[/tex]
Required
Determine the length of each room
Here, we'll assume that the carpet will cover each room completely.
If so:
[tex]Carpet\ Area = Length * Length[/tex]
[tex]100ft^2 = Length * Length[/tex]
[tex]100ft^2 = Length^2[/tex]
Take square root of both sides
[tex]\sqrt{100ft^2} = \sqrt{Length^2}[/tex]
[tex]\sqrt{100ft^2} = Length[/tex]
Take positive square root
[tex]10ft = Length[/tex]
[tex]Length = 10ft[/tex]
Hence, the length of a room is 10ft
For f(x) =1/x^2-3
find:
(a) f(3) (3 points)
(b) f(2+h) (3 points)
Answer:
[tex]f(3) = \frac{-26}{9}[/tex]
[tex]f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{x^2} - 3[/tex]
Required
Find f(3) and f(2 + h)
Solving f(3)
Substitute 3 for x in [tex]f(x) = \frac{1}{x^2} - 3[/tex]
[tex]f(3) = \frac{1}{3^2} - 3[/tex]
[tex]f(3) = \frac{1}{9} - 3[/tex]
Take LCM
[tex]f(3) = \frac{1 - 27}{9}[/tex]
[tex]f(3) = \frac{-26}{9}[/tex]
Solving f(2 + h)
Substitute 2 + h for x in [tex]f(x) = \frac{1}{x^2} - 3[/tex]
[tex]f(2 + h) = \frac{1}{(2 + h)^2} - 3[/tex]
[tex]f(2 + h) = \frac{1}{(2 + h)(2 + h)} - 3[/tex]
[tex]f(2 + h) = \frac{1}{4 + 2h + 2h + h^2} - 3[/tex]
[tex]f(2 + h) = \frac{1}{4 + 4h + h^2} - 3[/tex]
Take LCM
[tex]f(2 + h) = \frac{1- 3(4 + 4h + h^2)}{4 + 4h + h^2}[/tex]
[tex]f(2 + h) = \frac{1- 12 - 12h - 12^2}{4 + 4h + h^2}[/tex]
[tex]f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}[/tex]
1. What is the Potential Energy of a 6 kg object that is 10 m above the
ground?
3 The lyy Hill Sunshine Club collected 524 cans for a canned food drive. The cans were then split up equally into 8 boxes. (a) Part A How many cans were in each box? Part B How many cans were left over after the boxes were filled? (b) А 65.5 cans < NEXT
Answer:
sorry I wish I could it help you but if you have any other question let me know
There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?
Answer:
Small=36
Large=13
Step-by-step explanation:
As given there are 49 dogs signed up
36 are small so the equation is
36+x=49
x=49-36
x=13
So 13 large dogs and 36 small dogs
Find the values of x and y that satisfy the equation.
- 12x + yi = 60 - 13i
What is the value of x in the equation 2(6x+4)-6+2x = 3(4x+3)+1? 0 1 & 03 O 4 06
Answer: its 4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable. im prob to late but i need points
The value of x in the equation is 4.
What is an algebraic expression?An Algebraic expression shows the expression of variables with numbers. The purpose of an algebraic expression is to determine the unknown variable represented by an unknown letter.
From the given information:
2(6x + 4) - 6 + 2x = 3(4x + 3) + 1
Open brackets
12x + 8 - 6 + 2x = 12x + 9 + 1
Collect like terms
12x + 2x - 12x = -8 + 6+9 + 1
14x - 12x = -8 + 16
2x = 8
x = 8/2
x = 4
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can someone please help, don't use this for points pls :/
(I'll give brainly)
Answer:
x = 3
AB = 18
Step-by-step explanation:
Based on the midsegment theorem:
[tex] MN = \frac{1}{2}(AB) [/tex]
MN = 9
AB = x + 15
Plug in the values and solve for x
[tex] 9 = \frac{1}{2}(x + 15) [/tex]
Multiply both sides by 2
[tex] 9 \times 2 = \frac{1}{2}(x + 15) \times 2 [/tex]
[tex] 18 = x + 15 [/tex]
Subtract 15 from each side
[tex] 18 - 15 = x + 15 - 15 [/tex]
[tex] 3 = x [/tex]
x = 3
AB = x + 15
Plug in the value of x
AB = 3 + 15
AB = 18
304,056 trying to represent the value of this number using expanded notation we give the answer but is giving us an error so we want to find out our error
Answer:
(3 * 100,000) + (0 * 10,000) + (4 * 1000) + (0 * 100) + (5 * 10) + (6 * 1)
Step-by-step explanation:
We want to represent the value of this number using expanded notation
Mathematically, that will be;
(3 * 100,000) + (0 * 10,000) + (4 * 1000) + (0 * 100) + (5 * 10) + (6 * 1)
= 300,000 + 0 + 4000 + 0 + 50 + 6
= 304,057
Help Me!! Please. Its important
Answer:
answer to 3 is
Step-by-step explanation:
1 hour = 0.7
2 hours = 1.4
3 hours = 2.1
4 hours = 2.8
5 hours = 3.5
6 hours = 4.2
7 hours = 4.9
8 hours= 5.6
9 hours= 6.3
10 hours= 7.0
11 hours = 7.7
12 hours =8.4
Express the following to percentage into fractions.
Answer:
65.2/100
Step-by-step explanation:
1/5 = 0,2
then:
65 1/5 = 65 + 0.2 = 65.2
65.2/100
Step-by-step explanation:
[tex]65 \div 1 \frac{5 \times 100 = 32500}{?} [/tex]
it comes to 325
Attachment look at it
A hotel has 22 clean towels and 78 dirty towels. What is the ratio of the number of clean towels to the total number of towels?
Answer:
22:78
Step-by-step explanation:
lol
Of the 100 oil paintings at the museum, 28 were portraits. What percentage of the oil paintings on display were portraits?
Answer:
28/100 * 100
the answer is 28 %
Evaluate this expression.
112.212 - (- 3.25)
Answer:
115.462
Step-by-step explanation:
Answer: 115.462
Step-by-step explanation:
To start, the first thing we can observe is two negative signs, which we know turns into a positive sign.
Therefore, we now have:
112.212 + 3.25
115.462
Hope this helps!
Choose the solutions to the quadratic equation
x2 - 8x - 9 = 0.
-21
ex? - 8x = 9 to
-1
9
29
DONE
When Carla looked out at the school parking lot, she noticed that for every 2 vans, there were 5 trucks. If there
were 84 total vehicles in the parking lot, how many of them were trucks?
Answer:
60 trucks
Step-by-step explanation:
2x12=24
5x12=60
60+24=84 total vehicles
60 of them are trucks.
Suppose you are going to graph the data in the table below. What data should be represented on each axis, and what would be the
appropriate increments?
Reporting periods Sales
d out of 2
Flag
an
Jan-Mar., 2010
$100,000
Apr.-Jun., 2010
$55,000
Jul.-Sep., 2010
$45,000
Oct-Dec., 2010
$110,000
Jan. --Mar., 2011
$330,000
Apr.-Jun., 2011
$800,000
Jul.-Sep., 2011
$242,000
Oct-Dec., 2011
$150,000
Answer:
the months would be the x axis and the numbers would be the y axis and the increments could start at 45k and have to go up to 800k don't forget the years with the months
63 divided by 3456 ?
18% of the cars in the parking lot are blue.If there are 150 cars in the parking lot,how many cars are blue
Answer:
Step-by-step explanation:
14
An investor flips a house, selling it for $88,000. If her profit was 30%, how much did she pay for the house originally? Round to two decimal places.
Answer:
She paid $67692.31 for the house originally.
Step-by-step explanation:
Let the initial cost of the house be [tex]x[/tex] dollars.
Given:
Selling price of the house (S.P) = $88000
Profit made = 30% of 'x' = [tex]0.30x[/tex]
We know that,
Profit = Selling Price - Original price
[tex]0.30x = 88000 - x[/tex]
Adding [tex]x[/tex] on both sides, we get:
[tex]0.30x+x = 88000\\\\1.3x=88000[/tex]
Dividing both sides by 1.3, we get:
[tex]x = 88000/1.3\\\\x = \$ 67692.307[/tex]
Rounding to 2 decimal places, we get:
[tex]x=\$67692.31[/tex]
Therefore, she paid $67692.31 for the house originally.
Can somebody help me with solve this question
Answer:
f⁻¹(y) = y^(-7/17)
Step-by-step explanation:
f(x) = x^(-17/7)
To find the inverse, switch x and y, and solve for y.
x = y^(-17/7)
x^(-7/17) = y
Therefore, f⁻¹(y) = y^(-7/17).
Which of the following shows (2x + y) 4 (4 is small) In expanded notation?
Answer:
8x+4y
Step-by-step explanation:
so use the distributive property and multiply 4 into (2x+y), so you get
(2x*4) + (y*4) = 8x + 4y
hope this helped
In Ms. Henrick's class, there are 10 boys and 12 girls. What is the ratio of boys to girls? Express your answer as a fraction in simplest form.
Answer:
5:6
Step-by-step explanation:
the ratio before would be 10/12 so you would have to divide both sides by 2 so you would get 5/6.Hope this helped
14.) Mr. Lovell was playing cards with his son. In the first round he earned 52
points. In the second round he lost 20 points. How would you write this as
an addition problem?
Answer:
That would be;
+52-20
Step-by-step explanation:
From the first part, he gained/earned 52 points
This is a positive so we have + 52
In the second round , he lost 20
This is a negative so we have - 20
Writing this as an addition problem, it will be;
+52-20
Sharon has a new beaded necklace. 72 out of the 80 beads on the necklace are blue. What
percentage of beads on Sharon's necklace are blue?
Write your answer using a percent sign (%).
Answer:
90%
Step-by-step explanation:
Step 1:
72/80 = x /100 Proportion
Step 2:
80x = 7200 Multiply
Step 3:
x = 7200 ÷ 80 Divide
Answer:
90%
Hope This Helps :)
Answer:
Sharon bought a necklace with 90% blue beads.
Step-by-step explanation:
We are given that Sharon's necklace has 80 beads. We are also given that of those 80 beads, 72 of them are blue.
Therefore, we can set up a ratio of blue beads to total beads in order to find out the relationship.
[tex]\displaystyle \frac{72}{80}=\frac{36}{40}=\frac{18}{20}=\frac{9}{10}[/tex]
Then, using the fraction we receive as a result, we can convert this to a decimal.
[tex]\displaystyle \frac{9}{10} = 0.9[/tex]
After we complete this calculation, we can multiply our decimal by 100 in order to obtain the relationship in percentage form.
[tex]0.9 \times 100 = 90\%[/tex]
Of the 80 beads, 90% were blue beads.