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neonofarm [45]
3 years ago
10

For which value of a are all the solutions of 2(x-5)>3x+a less than or equal 5?

Mathematics
1 answer:
saveliy_v [14]3 years ago
6 0
2(x-5)>3x+a \\
2x-10 > 3x+a \\
2x-3x>a+10 \\
-x>a+10 \ \ \ |\times (-1) \\
x

The solutions must be less than or equal to 5.
-a-10 \leq 5 \\
-a \leq 5+10 \\
-a \leq 15 \ \ \ |\times (-1) \\
a \geq -15

All the solutions are less than or equal to 5 for a≥-15.
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Step-by-step explanation:

All equally important without physical health having social health might be harder since you might not be able to interact as well because of illness which would then affect mental. Without mental health your social and physical health would deteriorate and without social health your mental then physical health would deteriorate we need a balanced amount of all of these

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8 0
3 years ago
Please help with the attached question. Thanks
Mademuasel [1]

Answer:

Choice A) F(x) = 3\sqrt{x + 1}.

Step-by-step explanation:

What are the changes that would bring G(x) to F(x)?

  • Translate G(x) to the left by 1 unit, and
  • Stretch G(x) vertically (by a factor greater than 1.)

G(x) = \sqrt{x}. The choices of F(x) listed here are related to G(x):

  • Choice A) F(x) = 3\;G(x+1);
  • Choice B) F(x) = 3\;G(x-1);
  • Choice C) F(x) = -3\;G(x+1);
  • Choice D) F(x) = -3\;G(x-1).

The expression in the braces (for example x as in G(x)) is the independent variable.

To shift a function on a cartesian plane to the left by a units, add a to its independent variable. Think about how (x-a), which is to the left of x, will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by a units, subtract a from its independent variable.

For example, G(x+1) is 1 unit to the left of G(x). Conversely, G(x-1) is 1 unit to the right of G(x). The new function is to the left of G(x). Meaning that F(x) should should add 1 to (rather than subtract 1 from) the independent variable of G(x). That rules out choice B) and D).

  • Multiplying a function by a number that is greater than one will stretch its graph vertically.
  • Multiplying a function by a number that is between zero and one will compress its graph vertically.
  • Multiplying a function by a number that is between -1 and zero will flip its graph about the x-axis. Doing so will also compress the graph vertically.
  • Multiplying a function by a number that is less than -1 will flip its graph about the x-axis. Doing so will also stretch the graph vertically.

The graph of G(x) is stretched vertically. However, similarly to the graph of this graph G(x), the graph of F(x) increases as x increases. In other words, the graph of G(x) isn't flipped about the x-axis. G(x) should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points (x, y)'s that are on the graph of F(x) fit into the expression y = F(x) = 3\sqrt{x - 1}.

5 0
3 years ago
Read 2 more answers
Question 1 of 10
goblinko [34]

Answer:

<h3>22 ÷ 0 = 0 </h3>

<h3>So ur Answer is 0 .</h3>
6 0
3 years ago
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