Solve the quadratic equation y2 - 5y = -4 by factoring.

Final answer:

To convert 8.25 × 10³ into an ordinary number, move the decimal point 3 places to the right, resulting in 8250. Similarly, for dividing powers of ten, subtract the exponents and divide the coefficients accordingly.

Explanation:

To convert 8.25 × 10³ to an ordinary number, you need to understand how powers of ten work in scientific notation. The exponent on the 10 indicates how many places to move the decimal point. Since the exponent is positive, you will move the decimal point to the right. For 8.25 × 10³, you move the decimal 3 places to the right, giving us 8250.

Now, addressing the division example of 2.4 × 10¹³ divided by 8 × 10⁷, we use the rule that when dividing powers of 10, we subtract the exponents. This gives us 10¹³/10⁷ = 10⁶ (13 minus 7 equals 6). Then we divide the coefficients (2.4 divided by 8 equals 0.3) to get the final answer of 0.3 × 10⁶, or 3 × 10⁵ when we adjust the coefficient to have a single digit before the decimal point.

Answer:

b

Step-by-step explanation:

The data set that matches the description best is Option C where both the median and the mean are 8, indicating a centrality of data around 8. This is the system, in other measures like range and mode, showing that if another measurement was taken, it would likely be around 8.

The set of data described - data is around 8 and another measurement would also probably be around 8, can be best represented by Option C. In this option, the median is 8 and the mean is also 8. This signifies that the data is centered around 8 meaning, the typical value in the data set is around 8 and the average of all values is 8. If another measurement were to be taken at random, the most likely result would be close to this central value of 8.

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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.

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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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:

Equation of line passing through the point (a,b) and having slope m is given by :

 →   [tex]\frac{y-b}{x-a}=m[/tex]  

Equation of X axis is , y = 0

i.e slope , m= 0

Any line parallel to x axis have slope = 0

Equation of line passing through the point (1,5)  and parallel to X axis is given by :

→ y - 5 = m( x -1)

As , m=0

→ y -5 = 0× (x-1)

→ y- 5= 0

→ y = 5 [ Final Answer]

multiply the cost of each by the amount needed

124 *11 = $1,364 ( total cost)

 1364 is less than 1400 so they do have enough money

Answer:

The answer is D

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

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:

Quick answer 5.

Start with what is inside the brackets.

5*0 = 0

10/2 - 3(0) Anything times 0 is 0. the three disappears.

10/2 = 5 And that is your answer.

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.

Learn more about Factors here:

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Hope this helps

I made the graph myself

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

To know more about an equation of the line follow

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