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ad-work [718]
2 years ago
14

Identify the slope and y-intercept of the line for each equation: y = 1/4x + 5

Mathematics
1 answer:
Tasya [4]2 years ago
6 0

Answer:

the given equation is

y= 1÷4x +5

now,

slope = 1÷4

and

y intercept= - 5÷ 1÷4

= -5÷ 4

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nikklg [1K]
The area is 80 just time 10 and 2 and 4
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3 years ago
Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software,
vichka [17]

Answer:

A(-1,0) is a local maximum point.

B(-1,0)  is a saddle point

C(3,0)  is a saddle point

D(3,2) is a local minimum point.

Step-by-step explanation:

The given function is  

f(x,y)=x^3+y^3-3x^2-3y^2-9x

The first partial derivative with respect to x is  

f_x=3x^2-6x-9

The first partial derivative with respect to y is  

f_y=3y^2-6y

We now set each equation to zero to obtain the system of equations;

3x^2-6x-9=0

3y^2-6y=0

Solving the two equations simultaneously, gives;

x=-1,x=3  and y=0,y=2

The critical points are

A(-1,0), B(-1,2),C(3,0),and D(3,2).

Now, we need to calculate the discriminant,

D=f_{xx}(x,y)f_{yy}(x,y)-(f_{xy}(x,y))^2

But, we would have to calculate the second partial derivatives first.

f_{xx}=6x-6

f_{yy}=6y-6

f_{xy}=0

\Rightarrow D=(6x-6)(6y-6)-0^2

\Rightarrow D=(6x-6)(6y-6)

At A(-1,0),

D=(6(-1)-6)(6(0)-6)=72\:>\:0 and f_{xx}=6(-1)-6=-18\:

Hence A(-1,0) is a local maximum point.

See graph

At B(-1,2);

D=(6(-1)-6)(6(2)-6)=-72\:

Hence, B(-1,0) is neither a local maximum or a local minimum point.

This is a saddle point.

At C(3,0)

D=(6(3)-6)(6(0)-6)=-72\:

Hence, C(3,0) is neither a local minimum or maximum point. It is a saddle point.

At D(3,2),

D=(6(3)-6)(6(2)-6)=72\:>\:0 and f_{xx}=6(3)-6=12\:>\:0

Hence D(3,2) is a local minimum point.

See graph in attachment.

3 0
3 years ago
Henry draws an obtuse triangle how many obtuse angles does Henry's triangle have? Please eye help
Travka [436]
The sum of all three angles in any triangle is always 180 degrees. So in obtuse triangle there is only one obtuse angle (more than 90 degrees). If we have for example an obtuse angle of 91 degrees, then two other angles have to fit in 89 degrees which makes it impossible for any of them to be obtuse.
8 0
3 years ago
Evaluate the expression for y=-14
Daniel [21]
Y=0-14 i think is the amswer
5 0
4 years ago
What is the area of the irregular polygon below
garik1379 [7]

Answer:

The answer is 121.5 sq. units.

Step-by-step explanation:

To find the answer,

Area of Pentagon: About 61.5 sq. units

Area of Rectangle: 60 sq. units

61.95 + 60 = 121.5 sq. units

Thanks, I hope I got this right!

3 0
3 years ago
Read 2 more answers
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