apply the distribution property to produce an equivalent expression 2(7g + 7)

Answer:

Vertex form:

[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]  

Step-by-step explanation:

Given: [tex]f(x)=8x^2+4x[/tex]

We need to write in vertex form.

Vertex form:

[tex]y=a(x-h)^2+k[/tex]

vertex: (h,k)

[tex]f(x)=8x^2+4x[/tex]

Step 1: Take out 8 common from each term

[tex]f(x)=8(x^2+\frac{1}{2}x)[/tex]

Step 2:  Add and subtract square of half of coefficient of x

[tex]f(x)=8(x^2+\frac{1}{2}x+\frac{1}{16}-\frac{1}{16})[/tex]

Step 3: Factor the term inside parentheses

[tex]f(x)=8(x^2+2\cdot \frac{1}{4}\cdot x+(\frac{1}{4})^2)-8\cdot \frac{1}{16})[/tex]

[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]                   [tex]\because (a^2+2ab+b^2)=(a+b)^2[/tex]

Hence, The vertex form of f(x)

[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]  

The cost of the cell phone plan over x months is represented by the equation y = 35x + 43.85. For 9 months, the total cost is $359.85, and for a 1-year contract, the total annual cost is $463.85.

The total monthly cost of the cell phone plan for x months of service can be represented by the linear equation y = 35x + 18.85 + 25. Here, y represents the total cost, x represents the number of months, 35 is the cost per month, 18.85 is the cost of the cell phone, and 25 is the one-time activation fee. The equation simplifies to y = 35x + 43.85, since the cost of the phone and the activation fee is a one-time charge, independent of the number of months.

For x = 9 months of service, the ordered pair is (9, y), where y = 35(9) + 43.85. Therefore, the ordered pair associated with x = 9 is (9, 359.85).

If you sign a 1-year contract, which is 12 months, you will pay y = 35(12) + 43.85, which results in a total cost of $463.85 for the year.

For the function f(x, y) = 9 + xy - x - 2y in the triangular region, the maximum value is 9 at point (1,0), and the minimum value is 1 at point (1,4). The critical point does not lie within the triangle region.

To find the absolute maximum and minimum values of the multivariate function f(x, y) = 9 + xy − x − 2y on the triangular region with vertices (1, 0), (5, 0), and (1, 4), we first locate the critical points within the region by solving the system of first order partial derivative equations.

Notice that (2,1) is not in the triangle region, so there's no critical point in the interior of the triangle. The maximum and minimum must occur somewhere on the boundary, i.e., the lines connecting (1, 0), (5, 0), and (1, 4).

After using these points in the function, we get the following:

The maximum value is 9 when (x,y) are (1,0) and the minimum value is 1 when (x,y) are (1,4).

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Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

We have that:

Lynne owns 12 games.

Of those

5 are sports games

3 are educational

What fraction of the games are either sport games or educational games?

[tex]f = \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

The transaction time is 24 hours or one business day.

Dylan made his credit card payment at noon on the payment due date. According to Consumer Protection Law, how much time does the bank have to credit the payment to his account? So, it is the same day/date or within 24 hours.

Final answer:

Banks are typically required to credit card payments to the customer's account by the end of the business day on which the payment was made, according to Consumer Protection Law. This ensures consumers are not unfairly charged late fees if payments are made on the due date.

Explanation:

The question concerns the timeframe within which a bank is required to credit a payment to a customer's account, according to Consumer Protection Law. If Dylan made his credit card payment at noon on the payment due date, the bank is typically required to credit the payment to his account by the end of that business day.

This requirement ensures that consumers are not unfairly penalized with late fees if they make their payment on the due date. It's essential for consumers to understand the specific policies of their credit card issuer and the relevant consumer protection laws to avoid any unnecessary charges. Timely payments are crucial for maintaining good credit health and avoiding additional fees.

Introducing vehicles costing less than $5,000 will alter the supply curve by adding a new segment for lower-priced cars, likely leading to an increase in the quantity supplied for this market segment. This reflects market segmentation and aligns with the demand for cheaper vehicles.

The introduction of cars less than $5,000 into the salesman's inventory may affect the distribution of car sales. When discussing economic models, a supply curve (such as curve So) indicates the quantity of goods that sellers are willing to supply at various prices. According to the scenario provided, Point J on the supply curve So shows that if the price is $20,000, the quantity supplied will be 18 million cars. However, if the price drops to below $5,000, this will most likely introduce a new segment on the supply curve, as the current supply data relates to higher-priced vehicles.

Introducing lower-cost cars will attract a different consumer base, often overlooked in premium markets. This could lead to an increase in the quantity supplied of cheaper cars, as the demand for this segment is likely to be different from premium cars. If the projection of selling 200 cars in 10 years holds true, it will introduce a new point on the supply curve, which will represent cars at a lower price point and possibly a higher quantity compared to the original supply curve for higher-priced cars.

It cannot be determined from the given information whether the overall effect will pull market equilibrium towards the lower end, but it introduces the concept of market segmentation where different products and prices can co-exist, catering to different consumer needs and preferences.

The probability that the marble is blue on the second draw, given that the first marble was replaced and had the number 6 on it, is 4 out of 7.

The probability that the marble is blue on the second draw, given that the first marble was replaced and had the number 6 on it, can be found using conditional probability.

The probability of drawing a blue marble on the first draw is 4 out of 7 (4 blue marbles out of a total of 7 marbles). Since the first marble was replaced, the probability of drawing a blue marble on the second draw is still 4 out of 7. Therefore, the probability that the marble is blue on the second draw, given that the first marble had the number 6 on it, is also 4 out of 7.

Answer:

The outfielder must throw the ball 125 feet to return it to the pitcher.

Step-by-step explanation:

It is given that On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder.

Now, applying the law of cosines,

[tex]a^2=b^2+c^2-2bccosA[/tex],

Putting b=43, c=162 and A=27°, we have

[tex]a^2=(43)^2+(162)^2-2(43)(162)cos27^{\circ}[/tex]

[tex]a^2=1849+26244-12413.4[/tex]

[tex]a^2=15679.6[/tex]

[tex]a=125.21[/tex]

[tex]a[/tex]≈[tex]125 feet[/tex]

Thus, the outfielder must throw the ball 125 feet to return it to the pitcher.

Answer:

2,3,5,8

Step-by-step explanation:

edge 22

Answer: Hattie Can jump 57 times in 3 minutes so therefore she jumps 19 times per minute. Because if do 57/3 it would give you 19.

Hope this helped!

Answer:

4.51

Step-by-step explanation: