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Naddik [55]
3 years ago
6

A rectangle has vertices at these coordinates. (−6, 3), (−6, 5), (2, 3) What are the coordinates of the fourth vertex of the rec

tangle?
Mathematics
1 answer:
Anna35 [415]3 years ago
7 0

Answer:

(2, 5).

Step-by-step explanation:

The length of the line joining the first 2 points = (5 - 3) = 2 units. This is a vertical line because the 2 x coordinates  ( -6 and - 6) are equal.

The line joining ( -6 , 3) and (2 , 3) is horizontal and is 2 - -6 = 8 units long.

Because we have a rectangle the point we need to find must have x coordinate of 2 and the y coordinate will be 2 more than the y coordinate 3.

.So it is  (2, 5),

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Simplify this rational expression. 2x^2+5x+3/2x^2-x-3
Murljashka [212]

Answer:

2x+3/2x-3

Step-by-step explanation:

firstly we make two steps to simplify this question.

1st step: simplify 2x^{2} +5x+3

to simplify this we use factorization

2x^{2} +2x+3x+3

2x(x+1) +3(x+1)

(2x+3) (x+1)        .....(1)

2nd step:simplify 2x^{2} -x-3

2x^{2} +2x-3x-3

2x(x+1)-3(x+1)

(2x-3)(x+1)          .....(2)

now dividing (1) and  (2), we get the answer

2x+3/2x-3

5 0
3 years ago
PLEASE HELP WILL GIVE BRAINLIEST the number of students at north middle school is 1240 and is decreasing by 25 students per year
Nikolay [14]

Answer:

-88

Step-by-step explanation:

Let N(x) be the number of students at NMS for a certain number of years.

Let S(x) be the number of students at SMS for a certain number of years.

Let x be the number of years.

N(x)=1240-25x

S(x)=800-30x

When # of students is equal, N(x)=S(x). Therefore, we are looking for the value of x (# of years) when 1240-25x=800-30x

Subtract 1240 from each side

-25x=-440-30x

Add 30x

5x=-400

x=-88 years

Check your numbers.

6 0
3 years ago
An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest
vitfil [10]
Exponential decay is a very common process especially when we are talking about radioactive materials. So, there is already a common formula for this type of behavior which is written below:

A = Pe^-rt
where
A is the amount left after time t
P is the initial amount at t=0
r is the rate

Substituting the values,
A = (780 g)(e^-0.163*16)
A = 57.5 g
8 0
4 years ago
Find the 12th term of the sequence -15,-9,-3, 3
Reika [66]
First term (a) = -15
common difference(d)= -9-(-15)
= -9+15=6
So,
12th term(a12)= a +(n-1)d
= -15+(12-1)×6
= -15 + 11×6
= -15+66
= 51
4 0
3 years ago
Consider the surface f (x comma y comma z )f(x,y,z)equals=negative 2 x squared plus 2 y squared minus 3 z squared plus 3 equals
trapecia [35]

Answer:

a) (8,8,-6)

b) 4x+4y+3z = -3

Step-by-step explanation:

a)

The surface is given by the equation  

f(x,y,z) = 0 where

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

The gradient of this function is the vector

(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})=(-4x,4y,-6z)

If we evaluate it in the point P = (-2,2,1) we obtain the point

(8,8,-6)

b)

The vectors with their tails at P are of the form  

(-2,2,1)-(x,y,z) = (-2-x, 2-y, 1-z)

as they must be orthogonal to the gradient, they must be orthogonal to the vector (8,8,6) so their inner product is 0

(-2-x,2-y,1-z)\cdot(8,8,6)=0\Rightarrow -16-8x+16-8y+6-6z=0\Rightarrow 4x+4y+3z=-3

and the equation of the desired plane is

4x+4y+3z = -3

3 0
4 years ago
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