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Dennis_Churaev [7]
2 years ago
13

Write a polynomial to represent the larger rectangle and the smaller rectangle.

Mathematics
1 answer:
nikdorinn [45]2 years ago
4 0

Answer:

See answers below.

Step-by-step explanation:

<u>Large Rectangle:</u><u> </u>  length x width = (x + 3)(x - 4) =

                                        x² - 4x + 3x - 12

                                           x² - x - 12

<u>Smaller Rectangle:</u>  length x width = (x)(3) = 3x

<u>Shaded Region: </u>shaded area =  lg. rectangle minus small rectangle

                             A = (x² - x - 12) - 3x  

                             A = x² - 4x - 12

<u>Solve for x, if shaded reion's area is 48 square units: </u>      

                          48 = x² - 4x - 12

                                  x² - 4x - 12 -48 = 0

                                  x² - 4x - 60 = 0

                                  (x - 10)(x + 6) = 0

                                   x - 10 = 0   or   x + 6 = 0

                                   x = 10    or    x = -6

                                               But x represents a length, so x cannot be -6.

                                  x = 10

                                     

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Second, let's now multiply what we have in the fraction. (5 × 8 = 40) and (12 × 13 = 156). Doing so will create a new fraction for us to use.
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Third, now obviously, we can simplify the fraction we just got into lower terms. To do that, we have to collect the greatest common factor (GCF) of both the numerator and denominator and list their factors to find the common factor that is the greatest.

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156

Out of the listed factors, which of those are the common ones? 1, 2, and 4 are the common factors. Since we are looking for the greatest common factor, it would be 4 since that is the higher number out of the commons. The GCF is 4.

Fourth, we can now divide our numerator (40) and our denominator (156) by the GCF we just found out, which was 4. 
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Answer in fraction form: \fbox {-10/39}
Answer in decimal form: \fbox {-0.2564}
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Answer:

<u>m</u><u> </u><u>is</u><u> </u><u>-</u><u>2</u><u> </u><u>and</u><u> </u><u>c</u><u> </u><u>is</u><u> </u><u>-</u><u>1</u>

Step-by-step explanation:

• Let's first phrase out the general equation of a line

{ \rm{y = mx + c}}

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[ remember that a general line equation must be in slope - intercept form as shown above ]

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→ <em>r</em><em>e</em><em>m</em><em>e</em><em>m</em><em>b</em><em>e</em><em>r</em><em> </em><em>t</em><em>o</em><em> </em><em>a</em><em>p</em><em>p</em><em>l</em><em>y</em><em> </em><em>"</em><em>s</em><em>u</em><em>b</em><em>j</em><em>e</em><em>c</em><em>t</em><em> </em><em>m</em><em>a</em><em>k</em><em>i</em><em>n</em><em>g</em><em> </em><em>k</em><em>n</em><em>o</em><em>w</em><em>l</em><em>e</em><em>d</em><em>g</em><em>e</em><em>"</em>

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{ \rm{m \:  \dashrightarrow \:  - 2}} \\  \\ { \rm{c \:  \dashrightarrow \:  - 1}}

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