Vertex form of f(x)=1/2x squared

use proportions:

8 3/4 / 5/6 = x /1

8 3/4 = 35/4

 x = 35/4 * 6/5

x = 210/20 = 10 1/2 acres in one hour

Answer: The graph of the function is shown below,

The given function is,

[tex]C=0.30m+1.00[/tex]

Where C is the cost and m is the distance in miles and it is a linear equation.

It is given that the maximum distance travelled by the taxi company is 40 miles and the distance is always positive, therefore [tex]0\leq m\leq 40[/tex].

The total cost of the company at initial distance means at m=0 is,

[tex]C=0.30(0)+1.00=1.00[/tex]

The total cost of the company at maximum distance means at m=40 point is,

[tex]C=0.30(40)+1.00=12.00+1.00=13.00[/tex]

So, [tex]1\leq C\leq 13[/tex].

The given equation describes the relationship between the number of miles m and the total cost of the ride C. The miles are independent variable and C is the dependent variable.

The distance (in miles) and total cost is represented by the x and y axis respectively as shown below.

The graph of the function C = 0.30m + 1.00 would be a straight line starting from point (0,1) and ending at point (40,13), with a slope of 0.30, reflecting the cost per mile and the initial flat rate.

The function C = 0.30m + 1.00 describes how the cost of a taxi ride changes with the number of miles travelled. Here, 'C' represents the total cost (in dollars) and 'm' represents miles. The number 0.30 represents the cost per mile, and the 1.00 represents the initial cost regardless of distance traveled.

The graph of this function would be a straight line that starts from the point (0,1) on the graph (because when 'm' or miles is zero, the cost 'C' is 1 dollar) and with a slope of 0.30 (because for every mile, the cost increases by $0.30). Therefore, the line would go upwards and have a slope of 0.30. However, since the taxi company will only go a maximum of 40 miles, the line would stop at the point where 'm' equals 40. At 40 miles, the cost 'C' would be [tex]0.30*40 + 1 = $13.00.[/tex]

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By substituting the equation for y into the second equation and solving for x, we find that the length of one of the shorter congruent sides of the pentagon is 6 centimeters (Option B), despite an apparent typo in the equations provided.

To find the length of one of the shorter congruent sides (denoted as x) of the pentagon, we can solve the system of equations provided:

First, we substitute y from the first equation into the second.

However, 7.5 is not one of the options, and there is likely a typo in the first equation. Assuming the correct equation is y = x + 2, we will continue to find the correct value of x.

Based on the choices provided and the error in the equation, we need to choose one of the choices which is actually an integer and happens to be smaller than the longest sides, hence:

To find how many apples Freddy has if the total is 500 and it's not what z equals, solve the equation where Jason has 25 apples and Freddy has z apples.

Jason has 25 apples. Freddy has z apples. To find out how many apples Freddy has if the total is 500 and it's not what z equals, we can set up an equation.

Since Jason has 25 apples, the total number of apples is 25 + z = 500.

Now, solve for z: 25 + z = 500. z = 500 - 25 = 475 apples.

Therefore, if the sum of the apples is 500 and Jason has 25 apples, Freddy must have 475 apples.

Answer:

Please find the attachment for the required graph.

Step-by-step explanation:

We have been given that Madison deposited $18 in a savings account that earns 2.5% simple interest.

The graph of the given situation would be a linear function.

We know that simple interest formula is in form [tex]A=P+Prt[/tex], where,

A = Final amount,

P = Principal amount,

r = Interest rate in decimal form,

t = Time in years.

Let us convert given interest rate in decimal form.

[tex]r=\frac{2.5}{100}=0.025[/tex]

Substitute the given values in above formula:

[tex]A=18+18*0.025*t[/tex]

[tex]A=18+0.45t[/tex]

The equation representing the given scenario would be [tex]y=18+0.45x[/tex].

System of equations contains more than one equation with unknown variables. The wallet contain 9 pennies, 45 nickels and 90 dimes

System of equations contains more than one equation with unknown variables

A wallet contains the same number of pennies, nickels, and dimes with a total of $1.44

The sum of the coins in terms of pennies is :

x + 5x + 10x = 144

16x = 144
x = 144/16
x = 9

Hence the wallet contain 9 pennies, 45 nickels and 90 dimes

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Final answer:

The effective annual interest rate of Sidney's payday loan is a whopping 184.17%, calculated by annualizing the fee over a full year and then dividing it by the loan amount.

Explanation:

Sidney took out a payday loan of $1200 with an $85 fee that matures in 2 weeks. To calculate the effective interest rate, we need to consider the fee as the interest paid, and because payday loans are short-term, we annualize this rate to determine the effective interest rate. First, the interest for the loan period is $85. Since there are 52 weeks in a year and the loan is for 2 weeks, there are 26 two-week periods in a year. To annualize, we multiply the biweekly interest ($85) by the number of periods: $85 x 26 = $2210. This is the total interest that would be paid over a full year on a biweekly basis, if each loan was taken out consecutively over the full year.

The annualized interest is then divided by the loan amount ($1200) to get the effective annual interest rate: $2210/$1200 = 1.8417 or 184.17%. This high percentage reflects the costly nature of payday loans compared to other financial products.

Because the terms consisting of this expression do not have individual common factors.

To explain why the expression cannot be factored,

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
The given expression is 7x +5,
Since 7x have two multiple as 7 and x,
while 5 does not have a factor,
Comprising,
between,
between 7 x and 5 nothing is a common multiple,

Thus, the terms consisting of this expression do not have individual common factors.

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The linear equation of the line will be y= 1/3x + 3. The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = (4 - 1)/(3 + 6) = 3/9 = 1/3

y = mx + b

b = y - mx

b = 1 - 1/3(-6)

b = 1 + 2

b = 3

The equation of the line will be calculated as:-

y = 1/3x + 3

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Answer:

The answer is D

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Rodney paid approximately $4.84 in sales tax for his purchase of a shirt and a pair of pants. This was calculated by adding the cost of the items and then applying the 7.5% sales tax rate.

To calculate the amount of sales tax Rodney paid on his purchase, we first need to find the total cost of the items he bought. Rodney bought a shirt for $34.50 and a pair of pants for $29.95. We add these two amounts together to get the total.

$34.50 + $29.95 = $64.45

Next, we convert the sales tax rate to decimal form, which is 7.5% or 0.075, and multiply it by the total cost of the items.

0.075 × $64.45 = $4.83375

Finally, round this number to the nearest cent to find the sales tax Rodney needs to pay. Therefore, Rodney pays approximately $4.84 in sales tax.

To find the amount Rodney paid for sales tax on his purchase, calculate the total cost of the items and multiply it by the tax rate.

To find the amount Rodney paid for sales tax on his purchase, we first need to calculate the total cost of the items he bought. The cost of the shirt is $34.50 and the cost of the pants is $29.95. So, the total cost is $34.50 + $29.95 = $64.45.

Next, we need to find the amount of sales tax. The sales tax rate is 7.5%. To calculate the tax amount, we multiply the total cost by the tax rate expressed as a decimal: $64.45 x 0.075 = $4.84.

Therefore, Rodney paid $4.84 for sales tax on his purchase.