write the slope intercept equation for the line that passes through (-8,11) and is perpendicular t 2x -7y=14

Answer:  The correct option is (A) b < 4000.

Step-by-step explanation:  Given that the public library has fewer than 4,000 books.

We are to select the inequality that describes the number of books in the library.

The number of books in the library is represented by b.

According to the given information, the inequality hat describes the number of books in the library is given by

Thus, (A) is the correct option.

Let a = car's age in years and v = value of car.

v = 25000(1 - 0.17)^a 

v = 25000(0.83)^a 

v = 25000(0.83)^a 

We need to find a.

Let v = 10,000

10,000 = 25000(0.83)^a

The value of a is about 4.91758.

Round off to the nearest whole number we get 5.

Answer is after more than 4 years but less than 6 and 8.

Final answer:

Using the given scale ratio on the map and setting up a proportion with the real distance to the capital, then solving, we get that the state capital is represented as being 3.5 inches from the border on this map.

Explanation:

The subject of this question is applied mathematics, specifically ratios. The scale on the map is given as 1/4 in : 18 mi. This means that for every 1/4 inch on the map, it represents 18 miles in reality. To figure out how far the capital is from the border on the map, you'll implement this scale ratio.

First, you make a fraction with the scale, with the real distance (18 miles) on top and the map distance (1/4 inch) on the bottom. Then, you set up a proportion with this fraction equal to another fraction consisting of the real distance to the capital on top (252 miles) and an unknown distance on the map at the bottom, which we can represent as x.

The fraction then looks like this: 18/0.25 = 252/x. Solving for x gives you x = (0.25*252)/18 = 3.5. Therefore, the state capital is represented as being 3.5 inches from the border on this map.

Learn more about Map Scale here:

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There are 2,880 different casts that can be created from those who auditioned.

To calculate the number of different casts that can be created, we need to multiply the number of options for each role.

For the lead female role, there are 5 options.

For the lead male role, there are 3 options.

For the best friend role, there are 8 options.

For the mother role, there are 4 options.

For the father role, there are 2 options.

For the humorous aunt role, there are 3 options.

To find the total number of possiblecasts, we multiply the number of options for each role:

5 x 3 x 8 x 4 x 2 x 3 = 2,880

Therefore, there are 2,880 different casts that can be created from those who auditioned.

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Answer:

p(2a) - q(a) = -2a² + 2a + 9

Step-by-step explanation:

Given;

p(x) = x + 9 and q(x) = 2x² + 3x,

we can replace 2a and a for p(x) and q(x).

p(2a) = 2a + 9 and q(a) = 2a² + 3a are the substituted values.

Now we can evaluate p(2a) - q(a):

p(2a) - q(a) = (2a + 9) - (2a² + 3a)

= 2a + 9 - 2a² - 3a

= -2a² + 2a + 9

p(2a) - q(a) = -2a² + 2a + 9

Hope this helps!