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Darya [45]
2 years ago
11

7u<42 solve the inequality for U

Mathematics
2 answers:
MAVERICK [17]2 years ago
6 0
<h3>Answer:</h3>

u<6

<h3>Solution:</h3>
  • In order to solve this inequality, we need to divide both sides by 7.
  • Remember, our goal is to find the value of u.
  • We know that 7u is less than 42.
  • So, divide both sides by 7:
  • u<6
  • So u is less than 6.
  • This also means that the numbers less than 6 will satisfy the inequality (make it true).

Hope it helps.

Do comment if you have any query.

stiks02 [169]2 years ago
4 0

Answer: u<6

Step-by-step explanation:

Isolate u by dividing both sides of the inequality by 7

\frac{7u}{7} < \frac{42}{7} \\u < 6

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The profit function for the first version of the device was very similar to the profit function for the new version. As a matter
NeTakaya

Answer:

a) - Compressing the P(new) function by a scale of 0.5 about the y axis.

- Moving the P(new) function down by 104 units.

b) The two simplified functions for P(original)

-0.08x² + 10.8x – 200.

-0.16x² + 21.6x – 504.

Step-by-step explanation:

Complete Question

An electronics manufacturer recently created a new version of a popular device. It also created this function to represent the profit, P(x), in tens of thousands of dollars, that the company will earn based on manufacturing x thousand devices: P(x) = -0.16x² + 21.6x – 400.

a. The profit function for the first version of the device was very similar to the profit function for the new version. As a matter of fact, the profit function for the first version is a transformation of the profit function for the new version. For the value x = 40, the original profit function is half the size of the new profit function. Write two function transformations in terms of P(x) that could represent the original profit function.

b. Write the two possible functions from part a in simplified form.

Solution

The equation for the new profit function is

P(x) = -0.16x² + 21.6x – 400

At x = 40, the original profit function is half the size of the new profit function

First, we find the value of the new profit function at x = 40

P(x) = -0.16(40)² + 21.6(40) – 400 = 208

Half of 208 = 0.5 × 208 = 104

P(original at x = 40) = P(new at x = 40) ÷ 2

Since we are told that P(original) is a simple transformation of the P(new)

P(original) = P(new)/2 = (-0.16x² + 21.6x – 400)/2 = -0.08x² + 10.8x – 200 ... (eqn 1)

Or, P(original) = 104

-0.16x² + 21.6x – 400 = 104

P(original) = -0.16x² + 21.6x – 400 - 104 = -0.16x² + 21.6x – 504.

So, the two functions that are simple transformations of P(new) to get P(original) are

-0.08x² + 10.8x – 200

Obtained by compressing the P(new) function by a scale of 0.5 about the y axis.

And

-0.16x² + 21.6x – 504.

Obtained by moving the P(new) function down by 104 units.

Hope this Helps!!!

4 0
3 years ago
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