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expeople1 [14]
3 years ago
7

Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form? Y – 6 = y minus 6 equals St

artFraction 5 Over 2 EndFraction left-parenthesis x minus 2 right parenthesis.(x – 2) y – 6 = negative StartFraction 2 Over 5 EndFraction. (x – 2) y + 6 = y plus 6 equals StartFraction 2 Over 5 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2) y + 6 = y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)
Mathematics
1 answer:
Tanya [424]3 years ago
8 0

Answer:

Step-by-step explanation:

The standard way of writing equation of a line in a point-slope form is as given;

y - y0 = m(x-x0)

m is the slope of the line

(x0,y0) is a point on the line.

Given the point (-2,-6), in order to determine with of the equation that correctly uses the point, we will substitute the point into the formula and get the necessary equation.

y - y0 = m(x-x0)

y - (-6) = m(x-(-2))

y+6 = m(x+2)

Since we are not given the slope, let's assume the slope is 5/2

The equation becomes y+6 =5/2(x+2). Option D is correct

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Find a formula for the sum of the first n even positive integers.
melisa1 [442]
So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
{k}^{2}  + k
so let us test the equation
for the first 3 even number there sums will be
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by our equation 3^2+3=12
gave us the same answer so our equation is correct
7 0
3 years ago
A company has a budget of $280,000 for computing equipment. Tablets cost $500 each, laptops cost $2000 each, and servers cost $5
Kazeer [188]

Answer:

The number of tablets  200

the number of laptops  40

and, the number of servers 20

Step-by-step explanation:

Let the number of tablets be 'x'

the number of laptops be 'y'

and, the number of servers be 'z'

According to the given question

Total budget = $280,000

Tablets cost = $500 each

laptops cost = $2000 each

servers cost = $5000 each

Thus,

500x + 2000y + 5000z = 280,000 ..............(1)

also,

x = 5y  ................(2)

and,

y = 2z  

or

z = \frac{\textup{y}}{\textup{2}}   ............(3)

substituting y from 2 and 3 in equation 1,  we get

(500 × 5y) + (2000 × y) + (5000 × \frac{\textup{y}}{\textup{2}} ) = 280,000

or

2500y + 2000y + 2500y = 280,000

or

7000y = 280,000

or

y = 40

substituting y in equation 2, we get

x = 5 × 40 = 200

substituting y in equation 3 we get

z = \frac{\textup{40}}{\textup{2}}

or

z = 20

hence,

the number of tablets  200

the number of laptops  40

and, the number of servers 20

7 0
3 years ago
Find the y-intercept of the line on the graph.
Naya [18.7K]

Answer:

2

Step-by-step explanation:

7 0
3 years ago
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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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8 0
2 years ago
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