All categories

2 years ago

The length of a rectangle is 7 inches less than twice the width, w, of the rectangle.

Mathematics

1 answer:

Ivan2 years ago

4 0

Answer:

Step-by-step explanation:

Let w represent the width of the rectangle.

The length of a rectangle is 7 inches less than twice the width, w, of the rectangle. It means that the length is (2w - 7) inches

Part A

The function that gives the area as a function of the width is

A(w) = w(2w - 7)

Part B:

If the area of the rectangle is 60 square inches, it means that

w(2w - 7) = 60

2w² - 7w = 60

2w² - 7w - 60 = 0

2w² + 8w - 15w - 60 = 0

2w(w + 4) - 15(w + 4) = 0

2w - 15 = 0 or w + 4 = 0

w = 15/2 or w = - 4

Since w cannot be negative, then

w = 15/2 = 7.5 inches

You might be interested in

Find the missing angle. Find x

dolphi86 [110]

Answer: 20

Reason: They're opposite meaning they are the same when compared to the side

3 0

2 years ago

Find the line through

Kaylis [27]

Answer:

$(\frac{1}{2},\frac{-1}{2},\frac{1}{2})$

Step-by-step explanation:

We have been given the intersection coordinates:

(7,1,-6) and perpendicular to the line x=-1+t ,y=-2+t and z=-1+t

From the condition of perpendicularity we know:

$(7,1,-6)(x,y,z)$

$\Rightarrow 7x+y-6z=0$

Now, we have given x=-1+t , y=-2+t and z= -1+t

$7(-1+t)+(-2+t)-6(-1+t)=0$

$-7+7t-2+t+6-6t=0$

$\Rightarrow -3+2t=0$

$2t=3$

$t=\frac{3}{2}$

Now, substituting t in the given coordinates x,y and z we get:

$x=-1+\frac{3}{2}=\frac{1}{2}$

$y=-2+\frac{3}{2}=\frac{-1}{2}$

And $z=-1+\frac{3}{2}=\frac{1}{2}$

3 0

3 years ago

Read 2 more answers

Which of these relations is a function?<br> I’m I correct??

Vlad1618 [11]

Answer:

the first one on the bottom

Step-by-step explanation:

There is a little trick to find out if it is a function or not. This trick is called the vertical line test. if you can scan the figure with a virtual line and it does not touch more than one side of the figure at one time then it is a function. if it touches more than one side or line of the figure it is not a function.

3 0

2 years ago

The hypotenuse of a right triangle is 8 cm longer than the longer leg. The shorter leg is 17 cm shorter than the longer leg. Fin

balu736 [363]

Answer:

45 cm

Step-by-step explanation:

Let x represent the length of the longer leg. Then the hypotenuse is x+8 and the shorter leg is x-17. The Pythagorean theorem gives the relation between these values as ...

(x +8)^2 = x^2 +(x -17)^2

x^2 +16x +64 = 2x^2 -34x +289 . . . . eliminate parentheses

0 = x^2 -50x +225 . . . . . put in standard form

0 = (x -45)(x -5) . . . . . . . . factor

Solutions to this equation are x=5 and x=45. The value of x must be greater than 17, so the useful solution is x=45.

The length of the longer leg of the triangle is 45 cm.

5 0

3 years ago

Read 2 more answers

Please help asap !!!!!! Which equation has one solution for x?

steposvetlana [31]

Question number b is the correct one