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Dennis_Churaev [7]
3 years ago
13

What is the equation of the line that contains point ( -2,1) and has a slope of 4

Mathematics
1 answer:
marshall27 [118]3 years ago
6 0

Answer:

y=4x+7

Step-by-step explanation:

it's in the picture

please mark as brainliest

You might be interested in
In the diagram below, AC and CB, AB and CD, and m(angle)A=33 degrees. Find M(angle)B
hoa [83]

Answer:

15°.

Step-by-step explanation:

1. Angles ADC and CDB are supplementary, thus

m∠ADC+m∠CDB=180°.

Since m∠ADC=115°, you have that m∠CDB=180°-115°=65°.

2. Triangle BCD is isosceles triangle, because it has two congruent sides CB and CD. The base of this triangle is segment BD. Angles that are adjacent to the base of isosceles triangle are congruent, then

m∠CDB=m∠CBD=65°.

The sum of the measures of interior angles of triangle is 180°, therefore,

m∠CDB+m∠CBD+m∠BCD=180° and

m∠BCD=180°-65°-65°=50°.

3. Triangle ABC is isosceles, with base BC. Then

m∠ABC=m∠ACB.

From the previous you have that m∠ABC=65° (angle ABC is exactly angle CBD). So

m∠ACB=65°.

4. Angles BCD and DCA together form angle ACB. This gives you

m∠ACB=m∠ACD+m∠BCD,

m∠ACD=65°-50°=15°.

Have a good Day!

7 0
2 years ago
I will mark brainlist and 20 extra points
grandymaker [24]
(X1=1, y1=7) and (x2= -4, y2 =-8)

Slope = ( y2-y1)/(x2-x1)= (-8-7)/(-4-1)= -15/-5=3

Slope is 3
5 0
3 years ago
Read 2 more answers
What is the area of the triangle?
fomenos

Answer:

1012.5

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Gail ran 4610 miles on Saturday and 6810 miles on Sunday. How many miles did Gail run over the weekend?
VMariaS [17]

Answer:

He ran 11,420 miles on the weekend.

Step-by-step explanation:

It's simple: add 4610 and 6810 to get 11,420

hope this helped!

8 0
2 years ago
A plane with equation xa+yb+zc=1 (a,b,c>0)together with the positive coordinate planes forms a tetrahedron of volume V=16abcF
soldier1979 [14.2K]

Question not well presented.

See correct question presentation below

A plane with equation (x/a) + (y/b) + (z/c) = 1, where a,b,c > 0 together with the positive coordinate planes form a tetrahedron of volume V = (1/6)abc. Find the plane that minimizes V if the plane is constrained to pass through the point P(2,1,1).

Answer:

The plane is x/6 + y/3 + z/3 = 1

Step-by-step explanation:

Given

Equation: (x/a) + (y/b) + (z/c) = 1 where a,b,c > 0

Minimise, V = (1/6) abc subject to

the constraint g = 2/a + 1/b + 1/c = 1

First, we need to expand V

V = (abc)/6

Possible combinations of V taking 2 constraints at a time; we have

(ab)/6, (ac)/6 and (bc)/6

Applying Lagrange Multipliers on the possible combinations of V, we have:

∇V = λ∇g

This gives

<bc/6, ac/6, ab/6> = λ<-2/a², -1/b², -1/c²>

If we equate components on both sides, we get:

(a²)bc/12 = -λ = a(b²)c/6 = ab(c²)/6

Solving for a, b and c;

First, let's equate:

(a²)bc/12 = a(b²)c/6 -- divide through by abc, we have

a/12 = b/6 --- multiply through by 12

12 * a/12 = 12 * b/6

a = 2 * b

a = 2b

Then, let's equate:

(a²)bc/12 = ab(c²)/6 -- divide through by abc, we have

a/12 = c/6 --- multiply through by 12

12 * a/12 = 12 * c/6

a = 2 * c

a = 2c

Lastly, we equate:

a(b²)c/6 = ab(c²)/6 -- divide through by abc, we have

b/6 = c/6 --- multiply through by 6

6 * b/6 = 6 * c/6

b = 2

Writing these three results, we have

a = 2b; a = 2c and b = c

Recalling the constraints;

g = 2/a + 1/b + 1/c = 1

By substituton, as have

2/(2c) + 1/c + 1/c = 1

1/c + 1/c + 1/c = 1

3/c = 1

c * 1 = 3

c = 3

Since a = 2c;

So, a = 2 * 3

a = 6

Similarly, b = c

So, b = 3

So, the plane: (x/a)+(y/b)+(z/c)=1;

By substituton, we have

x/6 + y/3 + z/3 = 1

Hence, the plane

So the plane is x/6 + y/3 + z/3 = 1

5 0
2 years ago
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