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statuscvo [17]
3 years ago
9

Write an equation in point -slope form for the line through the given point with the given slope

Mathematics
1 answer:
Zepler [3.9K]3 years ago
7 0

Answer:

C) y+2=-1/2(x+4)

Step-by-step explanation:

y-y1=m(x-x1)

m=slope & (x1, y1) is a point on the line

m=-1/2

y-(-2)=-1/2(x-(-4))

y+2=-1/2(x+4)

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Write the formula for a function d(x) that describes the distance between the point P and a point (x,y) on the line. You final a
vlabodo [156]

Answer:

d(x) = √[(x - 2)² + (3x - 1)²]

Step-by-step explanation:

The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given as

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, the distance between point (2,0) and a point (x,y)

d = √[(x - 2)² + (y - 0)²]

d = √[(x - 2)² + (y)²]

But the point (x,y) is on the line y = 3x - 1

We can substitute for y in the distance between points equation.

d(x) = √[(x - 2)² + (3x - 1)²]

QED!

6 0
3 years ago
Define Following:consistent equations
mario62 [17]

Answer:

1. Consistent equations

x + y = 3

x + 2·y = 5

2. Dependent equations

3·x + 2·y = 6

6·x + 4·y = 12

3. Equivalent equations

9·x - 12·y = 6

3·x - 4·y = 2

4. Inconsistent equations

x + 2 = 4 and x + 2 = 6

5. Independent equations

y = -8·x + 4

8·x + 4·y = 0

6. No solution

4 = 2

7. One solution

3·x + 5 = 11

x = 2

Step-by-step explanation:

1. Consistent equations

A consistent equation is one that has a solution, that is there exist a complete set of solution of the unknown values that resolves all the equations in the system.

x + y = 3

x + 2·y = 5

2. Dependent equations

A dependent system of equations consist of the equation of a line presented in two alternate forms, leading to the existence of an infinite number of solutions.

3·x + 2·y = 6

6·x + 4·y = 12

3. Equivalent equations

These are equations with the same roots or solution

e.g. 9·x - 12·y = 6

3·x - 4·y = 2

4. Inconsistent equations

Inconsistent equations are equations that are not solvable based on the provided set of values in the equations

e.g. x + 2 = 4 and x + 2 = 6

5. Independent equations

An independent equation is an equation within a system of equation, that is not derivable based on the other equations

y = -8·x + 4

8·x + 4·y = 0

6. No solution

No solution indicates that the solution is not in existence

Example,  4 = 2

7. One solution

This is an equation that has exactly one solution

Example 3·x + 5 = 11

x = 2

3 0
3 years ago
A CHICKEN COOP HOLDS A TOTAL OF 10 HENS OR 20 CHICKS. IF 2/5THS OF THE HENS IN A FULL COOP ARE REMOVED, HOW MANY NEW CHICKS COUL
LiRa [457]

Answer:

8 new chicks can be fitted in the coop.

Step-by-step explanation:

A chicken coop holds 10 hens or 20 chicks.

That means space in the coop for 10 hens = space for 20 chicks

Or space for 1 hen = space for 2 chicks

Now \frac{2}{5}th of the hens were removed from the coop.

So, number of hens removed from the coop = \frac{2}{5}\times 10

= 4 hens

And space for 4 hens in the coop = space for the 8 chicks

Therefore, 8 new chicks can be fitted in the coop.

5 0
3 years ago
Use the modle to find 2x137
Lena [83]
the answer is 2• 137= 274
3 0
3 years ago
Read 2 more answers
ZE and ZF are vertical angles with mZE = 8x + 8 and mZF = 2x +38.<br> What is the value of x?
Dovator [93]

Answer:

Since ZE and ZF are vertical angles, they are congruent.

8x+8 = 2x+38

8 = 2x-8x+38

8 = -6x+38

8-38 = -6x

-30 = -6x

x = -30/-6

x = 5

7 0
3 years ago
Read 2 more answers
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