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4 years ago

Which polynomial represents the area of the rectangle?

Mathematics

2 answers:

docker41 [41]4 years ago

4 0

Area of a rectangle is length times width
length= 4x-6 width= x+1
you end up getting
A) 4x^2 + 2x - 6

Marta_Voda [28]4 years ago

3 0

The answer is 4x^2-2x-6 i just took the answer and got it wrong but i snipped the right ones for yall

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alisha [4.7K]

Answer:

$d=3\sqrt{2}\ units$

Step-by-step explanation:

The complete question is

Line L contains points (3, 5) and (7, 9). Points P has coordinates (2, 10). Find the distance from P to L

step 1

Find the equation of the line L contains points (3,5) and (7,9)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the given values

$m=\frac{9-5}{7-3}$

$m=\frac{4}{4}=1$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=1\\point\ (3,5)$

substitute

$y-5=(1)(x-3)$

isolate the variable y

$y=x-3+5$

$y=x+2$ -----> equation A

step 2

Find the equation of the perpendicular line to the given line L that passes through the point P

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

The slope of the given line L is $m=1$

The slope of the line perpendicular to the given line L is

$m=-1$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=-1\\point\ (2,10)$

substitute

$y-10=-(x-2)$

isolate the variable y

$y=-x+2+10$

$y=-x+12$ ----> equation B

step 3

Find the intersection point equation A and equation B

$y=x+2$ -----> equation A

$y=-x+12$ ----> equation B

solve the system by graphing

The intersection point is (5.7)

see the attached figure

step 4

we know that

The distance from point P to the the line L is equal to the distance between the point P and point (5,7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

(2,10) and (5,7)

substitute

$d=\sqrt{(7-10)^{2}+(5-2)^{2}}$

$d=\sqrt{(-3)^{2}+(3)^{2}}$

$d=\sqrt{18}\ units$

simplify

$d=3\sqrt{2}\ units$

see the attached figure to better understand the problem

6 0

4 years ago

Solve 1/2x-2=9-5x by graphing

melamori03 [73]

Answer:

Step-by-step explanation:

8 0

3 years ago

SOMEONE HELP ME PLEASE!!!!?

Sliva [168]

Answer:

139

Step-by-step explanation:

supplementary angles add up to equal 180

so to find the measure of angle ABC we subtract the given angle from 180

180-41=139

so we can conclude that angle ABC= 139

8 0

3 years ago

Read 2 more answers

Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school.

Reil [10]

Answer:

Step-by-step explanation:

3===o===2=======1========0========-1=======x-2

I know this is backwards, but the question makes the choice of which direction is plus. o represents where anna lives.

Ben should be right at -2 where the x is.

8 0

3 years ago

13 m

Murrr4er [49]

Answer:

The ladder needs to be placed at 5 m from the wall.

Step-by-step explanation:

Pythagoras's Theorem

Being a and b the legs of a right triangle and c its hypotenuse, then

$c^2=a^2+b^2$

The image shows a ladder of length c=13 m as the hypotenuse of the right triangle formed by the height, the ladder, and the ground.

We are given the height up the wall as a=12 m.

We calculate the distance b solving it from the equation above:

$b^2=c^2-a^2$

Substituting:

$b^2=13^2-12^2$

Operating:

$b^2=169-144$

$b^2=25$

Taking the square root:

$b=\sqrt{25}$

b = 5 m

The ladder needs to be placed at 5 m from the wall.

7 0

3 years ago