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dmitriy555 [2]
3 years ago
13

The sumof the angle measures of any triangle is 180 degrees. Suppose that one angle in a triangle has a degree for 6x-9 and anot

her has a degree measures 9x+1. Write an expression for the degree measure of the third angle in the triangle.
Mathematics
1 answer:
vovikov84 [41]3 years ago
6 0
Remark
No matter what kind of triangle it is, the angles must add up to 180, just as you said.

Suppose we say 
A = 6x - 9
B = 9x + 1
C = y          We need an expression for C or y.

A + B + C = 180
6x - 9 + 9x + 1 + y = 180   Collect the like terms on the left.
6x + 9x + 1 - 9 + y = 180
15x - 8 + y = 180               Add 8 to both sides.
15x + y = 180 + 8
15x + y = 188                    Subtract 15x from both sides.
y = 188 - 15x <<<<<<<<< Answer
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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);
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  • 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.
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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).

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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}.

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