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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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Then, for 1 shirt, it would be: 4 2/3 / 3 1/2

Fabric for 1 shirt = 14/3 / 7/2
We can re-write it as: 14/3 * 2/7 = 4/3 yards

In short, Final answer would be 4/3 or 1 1/3 yards

Hope this helps!
7 0
4 years ago
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guajiro [1.7K]

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3 years ago
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Step-by-step explanation:

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5 0
3 years ago
I need help with this anybody know it?<br> 3(2n-7)=9
Ksivusya [100]

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5

Step-by-step explanation:

3(2n-7)=9

^        ^

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6 0
4 years ago
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Lana71 [14]

\bf \begin{array}{ccll} \stackrel{blueberries}{lbs}&\stackrel{jam}{cup}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{3}{4}&\frac{1}{2}\\\\ b&1 \end{array}\implies \cfrac{\quad \frac{3}{4}\quad }{b}=\cfrac{\quad\frac{1}{2} \quad }{1}\implies \cfrac{\quad \frac{3}{4}\quad }{\frac{b}{1}}=\cfrac{\quad\frac{1}{2} \quad }{\frac{1}{1}}

\bf \cfrac{3}{4}\cdot \cfrac{1}{b}=\cfrac{1}{2}\cdot \cfrac{1}{1}\implies \cfrac{3}{4b}=\cfrac{1}{2}\implies 6=4b\implies \cfrac{6}{4}=b\implies \cfrac{3}{2}=b

6 0
4 years ago
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