The functions for the total cost per month for data use are linear in each of the given options.
Correct responses;
1. A(1) = 60, B(1) = 35
2. A(7.5) = 60, B(7.5) = 100
3. The monthly charge for Option A fixed. The monthly charge for Option B includes a fixed monthly fee and $10 per gigabyte used.
4. Please find attached the combined graph of Option A and Option B. Option B is more affordable when the (extra) data usage is less than 3.5 gigabytes each month.
The amount of gigabytes of data the student would have for $50 is 2.5 gigabytes.
What is an expression?Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given parameters are;
Both plans data allowance per month = 2 gigabytes
The monthly cost for each option is;
Option A: A(x) = 60 = Constant
Option B: B(x) = 10·x + 25
Solution:
1. The values of A(1) and B(1) are;
A(1) = 60
B(1) = 10 × 1 + 25 = 35
Therefore;
A(1) = $60
B(1) = $35
2. The values of A(7.5), and B(7.5) are;
A(7.5) = 60
B(7.5) = 10 × 7.5 + 25 = 100
A(7.5) = $60
B(7.5) = $100
3. The description of each data plan are;
Option A
The data plan of option A has a fixed charge of $60
Option B
The charges on the data plan on option B consist of a fixed monthly charge of $25, and $10 per gigabyte of data used.
4. Please find attached the graph of the functions of Option A and Option B. From the graph, the most affordable plan to use based on the data usage is;
Option B; If the data used a month, x < 3.5 gigabytes
Option A; If the data used a month, x > 3.5 gigabytes
Either Option A or Option B if the data usage per month is exactly 3.5 gigabytes
The amount the student budgets per month = is $50
By using Option B, we have;
B(x) = 10·x + 25 = 50
10·x = 50 - 25 = 25
x = 25 / 10 = 2.5
At $50, the amount of gigabytes the student can get is x = 2.5 gigabytes
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What is the vertex form of Y X² 8x 3?.
The vertex form of the quadratic function is f(x) = x² + 8x + 3 is (x + 4)² = y +13.
The term Vertex form of a quadratic equation refers as
=> (x - h)² = 4a (y - k) form or in another written as,
=> (y - k)² = 4a (x - h) form depending on whether the square is on x-term or y-term respectively.
Here we have given quadratic function is that is written f(x) = x² + 8x + 3
And in the given equation square term is for x.
As we all know that equation must be reduced to (x - h)² = 4a (y - k) form.
Then here we know that we have
=> y = f(x) = x² + 8x + 3
Now we have to completing the square,
=> y = (x² + 8x +16) -16 + 3
Then it can be written by using the factorize the expression
=> y = (x + 4)² -13
Now we have to rewrite the expression, then we get,
=> y + 13 = (x + 4)²
Then resulting vertex form of the expression as,
=> (x + 4)² = y +13
Complete Question:
What is the vertex form of f(x) = x² + 8x + 3?
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Ngela practice the piano for 2 1/2 hour on friday 2 1/3 hour on aturday and unday 3 2/3 hour how long angela practice the piano over the weekend
Angela practiced piano during the weekend for 6 hours.
According to the question,
Amount Angela spent on Saturday = [tex]2\frac{1}{3}[/tex]
Amount Angela spent on Sunday = [tex]3\frac{2}{3}[/tex]
To find out the total amount spent on both days of the weekend =
The amount that Angela spent on Saturday + the amount that Angela spent on Sunday
= [tex]2\frac{1}{3}[/tex] (otherwise expressed as 7/3) + [tex]3\frac{2}{3}[/tex] (otherwise expressed as 11/3)
[tex]= \frac{7}{3} + \frac{11}{3}[/tex]
[tex]= \frac{7 + 11}{3}[/tex] ( using addition)
= [tex]\frac{18}{3}[/tex] = 6 hours
Noted, Friday’s value was not added because it didn’t fall on the weekend.
The denominators of both fractions are the alike (3), thereby it was used to factor out the numerators (7) and (11), and subsequently arrive at the final answer which is 6 hours.
So, Angela practiced for 6 hours.
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What property of a regular hexagon makes this construction correct?
Step 1
: Draw a circle. Mark a point on it. Set the compass to the length of the radius.
Step 2
: Starting from the point on the circle, draw an arc that intersects the circle and mark the point of intersection.
Step 3
: From that point of intersection, draw another arc that intersects the circle.
Step 4
: Repeat until you have made 6 arcs.
Step 5
: Connect the 6
points to form a regular hexagon.
Answer:
the compass was used to locate all 6 vertices
What is associative property of rational numbers?.
The associative property of rational numbers shows that addition and multiplication are associative with rational numbers. For x,y,z,p,r,q∈Q
(x + y) + z = x + (y + z)p × (q × r) = (p × q) × rThe associative property of rational numbers is defined as on adding or multiplying any three rational numbers leaves the same result no matter how the numbers are grouped. But if the order of the numbers in subtraction or division changes, the result will also change.
For addition : A, B, C belong to rational numbers (A + B) + C = A + (B + C). For example, (1/3 + 1/3) + 1/2 = 1/3 + (1/3 + 1/2)
= 7/6. Addition is said to be associative for rational numbers.
For multiplication: Multiplication is expressed as (A × B) × C = A × (B × C). For example: (1/3 × 1/4) × 1/2 = 1/4 × (1/3 × 1/2)
= 1/24 = 1/24. It turns out that multiplication is associative for rational numbers. However, division and subtraction operations do not follow the associative properties of rational numbers.
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In 2010, the population of a city was 93,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 4%. How much did the population grow from 2010 to 2015, to the nearest 100 people?
Answer:
I think its 8
Step-by-step explanation:
Because from 2010 to 2015 population grew by 8•/• that mean 8 people per 100
Ozzie has a Visa with a $2000 limit and a balance of $450; a store credit card with a $500 limit and a $200 balance; and a joint card with his mom with a $5000 limit and a $700 balance.
What’s Ozzie’s credit utilization on:
a. His Visa?
b. His store credit card?
c. The joint card with his mom?
What’s Ozzie’s overall credit utilization?
Ozzie works extra hours one week and receives an extra $75 in his paycheck. Which debt should he put that money toward? Why?
The values of the credit utilization are
Visa = 22.5%Store credit = 40%With his mum = 14%Overall = 13.5%He should pay highest interest debt first
How to determine Ozzie’s credit utilization?a. His Visa?
Here, we are given that
$2000 limit and a balance of $450
So, we have
Ozzie's credit utilization on his Visa is
Utilization = (450/2000) * 100 = 22.5%
b. His store credit card?
Here, we are given that
$500 limit and a $200 balance
So, we have
Ozzie's credit utilization on his store credit card is
Utilization = (200/500) * 100 = 40%
c. The joint card with his mom?
Using the same formula, we have
Ozzie's credit utilization on the joint card with his mom is (700/5000) * 100 = 14%
Overall credit utilization
This is calculated as:
Ozzie's overall credit utilization is the sum of his balances divided by the sum of his credit limits
So, we have
Utilization = (450 + 200 + 700) / (2000 + 500 + 5000) = 13.5%.
Which debt should he put that money toward? Why?The debt with the highest interest rate first. This is because high-interest debt will cost more in the long run, so paying it off sooner will save money on interest charges.
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