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3 years ago

Suppose y varies directly with x. If y = -4 when x = 8, what is the equation of direct variation?

2 answers:

8 0

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill$

____ [38]3 years ago

6 0

Answer:

k = -1/2

y= -1/2x

Step-by-step explanation:

y = kx

We know y = -4 and x=8

-4 = k*8

Divide each side by 9

-4/8 = 8k/8

-1/2 =k

y= -1/2x

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Could you help plz.

I am Lyosha [343]

Cost of each bags of flour = $2.50

Cost of each bags of butter = $3.75

Solution:

Let f be the bags of flour and b be the pounds of butter.

Cost of 20 bags of flour 16 pound of butter = 110

⇒ 20f + 16b = 110 -------------------- (1)

Cost of 30 bags of flour 12 pound of butter = 120

⇒ 30f + 12b = 120 -------------------- (2)

Equation (1) and (2) are the system of equations.

(2) ⇒ 30f + 12b = 120

Subtract 30f from both sides.

⇒ 12b = 120 – 30f

Divide by 12 on both sides.

$$\Rightarrow b =\frac{120-30f}{12}$ -------------------- (3)

Substitute (3) in (1).

$$20f+16\left(\frac{120-30f}{12}\right)=110$

$$20f+4\left(\frac{120-30f}{3}\right)=110$

$$20f+4(40-10f)=110$

$$20f+160-40f=110$

Subtract 160 from both sides.

$$-20f=-50$

Divide by –20, we get

$$f=\frac{5}{2}$

f = 2.50

Substitute f = 2.5 in equation (3), we get

$$\Rightarrow b =\frac{120-30(2.50)}{12}$

$$b=\frac{15}{4}$

b = 3.75

Cost of each bags of flour = $2.50

Cost of each bags of butter = $3.75

7 0

3 years ago

What's 10 3/4 - 7 1/4?

leva [86]

$10 \frac{3}{4} - 7 \frac{1}{4} \\ \\ \frac{10 \times 4 + 3}{4} -7 \frac{1}{4} \\ \\ \frac{43}{4} - y \frac{1}{4} \\ \\ \frac{43}{4} - \frac{7 \times 4 + 1}{4} \\ \\ \frac{43}{4} - \frac{29}{4} \\ \\ \frac{43-29}{4} \\ \\ \frac{14}{4} \\ \\ \frac{7}{2} \\ \\ 3 \frac{1}{2} \\ \\ Answer: \fbox {3 \ 1/2} \ or \ \fbox {3.5}$