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MrMuchimi
2 years ago
14

Choose the equation below that represents the line passing through the point (2, -5) with a slope of -3.

Mathematics
1 answer:
mash [69]2 years ago
4 0
The point-slope form: y-y_0=m(x-x_0)

m=-3;\ (2;-5)\to x_0=2;\ y_0=-5

subtitute

y-(-5)=-3(x-2)\\\\y+5=-3x+6\ \ \ \ \ |subtract\ 5\ from\ both\ sides\\\\\boxed{y=-3x+1}
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Line segment 19 units long running from (x,0) ti (0, y) show the area of the triangle enclosed by the segment is largest when x=
Debora [2.8K]
The area of the triangle is

A = (xy)/2

Also,

sqrt(x^2 + y^2) = 19

We solve this for y.

x^2 + y^2 = 361

y^2 = 361 - x^2

y = sqrt(361 - x^2)

Now we substitute this expression for y in the area equation.

A = (1/2)(x)(sqrt(361 - x^2))

A = (1/2)(x)(361 - x^2)^(1/2)

We take the derivative of A with respect to x.

dA/dx = (1/2)[(x) * d/dx(361 - x^2)^(1/2) + (361 - x^2)^(1/2)]

dA/dx = (1/2)[(x) * (1/2)(361 - x^2)^(-1/2)(-2x) + (361 - x^2)^(1/2)]

dA/dx = (1/2)[(361 - x^2)^(-1/2)(-x^2) + (361 - x^2)^(1/2)]

dA/dx = (1/2)[(-x^2)/(361 - x^2)^(1/2) + (361 - x^2)/(361 - x^2)^(1/2)]

dA/dx = (1/2)[(-x^2 - x^2 + 361)/(361 - x^2)^(1/2)]

dA/dx = (-2x^2 + 361)/[2(361 - x^2)^(1/2)]

Now we set the derivative equal to zero.

(-2x^2 + 361)/[2(361 - x^2)^(1/2)] = 0

-2x^2 + 361 = 0

-2x^2 = -361

2x^2 = 361

x^2 = 361/2

x = 19/sqrt(2)

x^2 + y^2 = 361

(19/sqrt(2))^2 + y^2 = 361

361/2 + y^2 = 361

y^2 = 361/2

y = 19/sqrt(2)

We have maximum area at x = 19/sqrt(2) and y = 19/sqrt(2), or when x = y.
3 0
3 years ago
What is the solution of 2y + 3x - 6y ÷ 3x?
pentagon [3]

Answer:

=−2xy+3x+2y

Step-by-step explanation:

this is what i get in calculating

3 0
2 years ago
A designer enlarged both the length and the width of a rectangular carpet by 60 percent. The new carpet was too large so the des
Snowcat [4.5K]

x= length, y=width

Both the length and width were increased by 60% so now they are:

1.6x and 1.6y

Then they were both reduced by 25% so now they are 75%(100-25) of their previous size so they are:

0.75(1.6x) and 0.75(1.6y)

Their area would be length * width so it would be:

0.75(1.6x) * 0.75(1.6y)

Simplified this would be:

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Simplified more it would be :

1.44xy which is also 144% of xy which is a 44% increase of the original area (xy)


So the answer is:

44%



5 0
3 years ago
Which of the following equations cannot be solved using real numbers?
dsp73

Answer:

x²+4=0

Step-by-step explanation:

x²=-4

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4 0
3 years ago
If f(x)=7x and g(x)=6x-3,find (f*g)(x)
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(f\cdot g)(x)=f(x)\cdot g(x)\\\\
(f\cdot g)(x)=7x(6x-3)=42x^2-21x

7 0
3 years ago
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