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Afina-wow [57]
3 years ago
7

If (1, 2) and (3, 4) lie on the same line, give the slope-intercept equation of the line.

Mathematics
1 answer:
Masja [62]3 years ago
3 0
The slope of the line is  (4-2) / (3-1) = 2/2 = 1 
y - y1 = x - x1 
here x1 = 1 and y1 = 2 :-
y - 2 = x - 1
y = x + 1 <---- Answer
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8 0
3 years ago
A piece of cardboard measures 10 ft by 10 ft. Four equal squares of size x are removed from the corners. After removing the squa
Gnesinka [82]

Answer:

The value of x would be \frac{5}{3}

Step-by-step explanation:

Given,

The dimension of the cardboard = 10 ft by 10 ft,

∵ After removing four equal squares of size x ( in ft ) from the corners,

The dimension of the resultant box would be,

Length = ( 10 - 2x ) ft,

Width = ( 10 - 2x ) ft,

Height = x ft,

The volume of box,

V=(10-2x)\times (10 - 2x)\times x=x(10-2x)^2 = x(100 - 40x + 4x^2)=100x - 40x^2 + 4x^3

Differentiating with respect to x,

V'=100 - 80x + 12x^2

Again differentiating with respect to x,

V''=-80 + 24x

For maxima or minima,

V'=0

\implies 100 - 80x + 12x^2 = 0

\implies 3x^2 - 20x + 25=0

By quadratic formula,

x=\frac{20\pm \sqrt{20^2-4\times 3\times 25}}{6}

x=\frac{20\pm \sqrt{400 - 300}}{6}

x=\frac{20\pm \sqrt{100}}{6}

x=\frac{20\pm 10}{6}

\implies x = \frac{10}{6}=\frac{5}{3}\text{ or } x = 5

For x = 5/3, V'' = negative,

While for x = 5, V'' = Positive,

Hence, the value of x would be 5/3 ft for maximising the volume.

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3 years ago
HVAC technician average salary = $28/hour with a one-year Tech school certification costing an average of $7,500. What would you
Juli2301 [7.4K]

Answer:

56,000

Step-by-step explanation:

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3 years ago
PLS HELP WILL BE MARKED BRAINLIEST
zmey [24]

Answer:

-23, 5

Step-by-step explanation:

JK = 14 and K = -9

J could be on the left or the right of -9

Add 14 to -9

14+-9 = 5

So J could be at 5

Subtract 14 from -9

-14-9 = -23

8 0
3 years ago
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