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WINSTONCH [101]
3 years ago
5

What is the equation for passing through (-2,2) and (5,3)

Mathematics
1 answer:
Reil [10]3 years ago
5 0
\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~{{ -2}} &,&{{ 2}}~) 
%  (c,d)
&&(~{{ 5}} &,&{{ 3}}~)
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}\implies 
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{3-2}{5-(-2)}\implies \cfrac{3-2}{5+2}\implies \cfrac{1}{7}

\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=\cfrac{1}{7}[x-(-2)]
\implies 
y-2=\cfrac{1}{7}(x+2)
\\\\\\
y-2=\cfrac{1}{7}x+\cfrac{2}{7}\implies y=\cfrac{1}{7}x+\cfrac{2}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{16}{7}
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3 years ago
Dude is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25
pshichka [43]

Number of pounds of macadamia nuts is 8 pounds and number of pounds of almonds is 4 pounds.

<u>Step-by-step explanation:</u>

Step 1:

Given total pounds of mixture = 12 pounds, cost of macadamia nuts per pound = $9, cost of almonds per pound = $5.25, total cost of mixture per pound = $7.75.

Let number of pounds of macadamia nuts be x and number of pounds of almonds be 12-x.

Step 2:

Form an equation using the above information.

⇒ 9x + 5.25 (12-x) = 12 × 7.75

⇒ 9x + 63 - 5.25x = 93

⇒ 9x - 5.25x = 30

⇒ 3.75x = 30

⇒ x = 8

Number of macadamia nuts is 8 pounds.

Step 3:

Calculate number pounds of almonds

⇒ Number of pounds of almonds = 12 - x = 4 pounds.

5 0
2 years ago
3 l = _____ dl<br><br> A. 0.3<br> B. 0.03<br> C. 300<br> D. 30
Andru [333]

Answer: The correct option is D, i.e.,30.

Explanation:

It the given equation we have two units l and dl.

Where l represents the liter and dl represents the deciliter. These are the volume units.

We know that,

1 liter = 10 deciliter

It means,

1 l = 10 dl

Multiply both sides by 3,

1\times 3 l = 10\times 3 dl

3 l = 30 dl

Therefore, the correct option is D and 3 l = 30 dl.

6 0
3 years ago
If a caterer charges a fixed cost for preparing a dinner plus an additional cost for each person served. You know that the cost
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