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Ulleksa [173]
3 years ago
13

If

Mathematics
1 answer:
dsp733 years ago
8 0

Answer:

\large\boxed{Q1.\ q(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ q(2)=\dfrac{9}{2}}\\\boxed{Q2.\ t(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ t(0)=\dfrac{7}{2}}

Step-by-step explanation:

\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have}\\\\q(-1)=3\to(-1,\ 3)\\q(3)=5\to(3,\ 5)

\text{Calculate the slope:}\\\\m=\dfrac{5-3}{3-(-1)}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\\\\\text{We have the equation:}\\\\y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the point (-1, 3) to the equation:}\\\\3=\dfrac{1}{2}(-1)+b\\\\3=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}

q(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\q(2)-\text{put x = 2 to the equation:}\\\\q(2)=\dfrac{1}{2}(2)+\dfrac{7}{2}=\dfrac{2}{2}+\dfrac{7}{2}=\dfrac{9}{2}

t(-4)=3\to(-4,\ 3)\\t(4)=4\to(4,\ 4)\\\\m=\dfrac{4-3}{4-(-4)}=\dfrac{1}{8}\\\\y=\dfrac{1}{8}x+b\\\\\text{put the coordinates of the point (4,\ 4):}\\\\4=\dfrac{1}{8}(4)+b\\\\4=\dfrac{1}{2}+b\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}\\\\t(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\t(0)=\dfrac{1}{2}(0)+\dfrac{7}{2}=0+\dfrac{7}{2}=\dfrac{7}{2}

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_______________________________________________________
Explanation:
_____________________________________________
  x + (x + 2) + (x + 4) = -39 ;
_____________________________________________
 in which "x" is one of the integers, 
           "(x + 2)" is the next consecutive odd integer;
           "(x + 4)"  is the third consecutive odd integer.
__________________________________________
By solving for "x", we can solve for each of three (3) consecutive odd integers.
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     x + (x + 2) + (x + 4) = -39  ;
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          1x + 1x + 2 + 1x+ 4 = -39 ;
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                   3x + 6 = -39 ;
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               Subtract  "6" from EACH side of the equation:
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                    3x + 6 − 6  =  -39 <span>− 6 ;
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        to get:   3x = -45 ;
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           Divide EACH side of the equation by "3" ;
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                 3x / 3 = -45 / 3 ;
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        to get:   x = -15 ;
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     x + 4 =  -15 + 4 =  -11 .
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Are: -15, -13, and -11 ;  Consecutive odd integers?  YES!
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Does:  -15 + (-13) + (-11)  =? = -39 ??
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           -15 </span>− 13 <span>− 11 = ? 39 ??  YES!
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Answer: The three consecutive odd integers are:  -15, -13, and -11.
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