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Readme [11.4K]
2 years ago
8

Find the equation of the line that passes through (1,4) and is parallel to 3x+y+2=0. Leave your answer in the form y=mx+c.

Mathematics
1 answer:
Mila [183]2 years ago
3 0

Answer:

y = -3x + 7.

Step-by-step explanation:

First find the slope of the given line by converting to intercept form:

3x + y + 2 = 0

y = -3x - 2

So the slope is -3.

Then the line we want has a slope of -3 also (as it is parallel).

y - y1 = m(x - x1)   where m is the slope and (x1, y1) is a point on the line:

m = -3,  x1 = 1 and y1 = 4, so we have:

y - 4 = -3(x - 1)

y = -3x + 3 + 4

y = -3x + 7.

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Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and fou
saw5 [17]

Answer:

height = 14.5 ft

width = length = 3.2 ft

Step-by-step explanation:

Let the side of the square base is a and the height of the box is h.

The material required to make the box is equal to the total surface area of the box.

Area of base = a²

Cost of square base is $ 2 per ft²

So, the cost of making base = 2a²

Area of four walls + area of top = 2 (a² + ah + ah) + a² =  3a² + 2ah

Cost of making walls and the top is $ 1 per ft²

So, the cost of making walls and the top = 1 x ( 3a² + 2ah)

Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah

According to the question

144 = 5a² + 2ah

h = \frac{144-5a^{2}}{2a}     .... (1)

The volume of the box is V = length x width x height

V = a x a x h

V = 72 a - 2.5 a³     from equation (1)

Differentiate both sides with respect to a.

dV/da = 72 - 7.5 a²

Put, it equal to zero for maxima and minima

7.5 a² = 72

a = 3.2 ft

Put in equation (1)

h = \frac{144-5\times 3.2\times 3.2}{2\times 3.2}

h = 14.5 ft

So, the dimensions of the box are

height = 14.5 ft

width = length = 3.2 ft

6 0
3 years ago
How do I find this formula?<br><br> Trapizoid:b1=3 m;b2=4 m;A=7m2
DochEvi [55]
That depends. What are you trying to find? The formula for the perimeter? The formula for the area?
8 0
3 years ago
Read 2 more answers
8{(5*3)+(2*5)+(2*10)=
DerKrebs [107]

Answer:

8(5*3)+(2*5)+(2*10)=360

Step-by-step explanation:

8(15)+(10)+(20)=

8(45)=

6 0
3 years ago
Read 2 more answers
5k + 9 = 89.............
blsea [12.9K]

Answer:

k= 16

Step-by-step explanation:

89-9=80

80/5=16

16=k

5 0
2 years ago
Read 2 more answers
HELP SMART PPL!!!!!!!!!!!!!!!!!
mezya [45]

Answer:

33.75

Step-by-step explanation:

45x0.75=33.75

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3 years ago
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