what is the surface area of a rectangular prism whose base is 5 inches by 6 inches and whose height is 5 inches?

Determine the gradient of the straight line 2x-3y+9=0. Find the equation of the straight line through the origin which is perpen

frutty [35]

Answer: 3

x

−

2

y

−

15

=

0

Explanation:

We know that,

the slope of the line

a

x

+

b

y

+

c

=

0

is

m

=

−

a

b

∴

The slope of the line

2

x

+

3

y

=

9

is

m

1

=

−

2

3

∴

The slope of the line perpendicular to

2

x

+

3

y

=

9

is

m

2

=

−

1

m

1

=

−

1

−

2

3

=

3

2

.

Hence,the equn.of line passing through

(

3

,

−

3

)

and

m

2

=

3

2

is

y

−

(

−

3

)

=

3

2

(

x

−

3

)

y

+

3

=

3

2

(

x

−

3

)

⇒

2

y

+

6

=

3

x

−

9

⇒

3

x

−

2

y

−

15

=

0

Note:

The equn.of line passing through

A

(

x

1

,

y

1

)

and

with slope

m

is

y

−

y

1

=

m

(

x

−

x

1

)3

x

−

2

y

−

15

=

0

Explanation:

We know that,

the slope of the line

a

x

+

b

y

+

c

=

0

is

m

=

−

a

b

∴

The slope of the line

2

x

+

3

y

=

9

is

m

1

=

−

2

3

∴

The slope of the line perpendicular to

2

x

+

3

y

=

9

is

m

2

=

−

1

m

1

=

−

1

−

2

3

=

3

2

.

Hence,the equn.of line passing through

(

3

,

−

3

)

and

m

2

=

3

2

is

y

−

(

−

3

)

=

3

2

(

x

−

3

)

y

+

3

=

3

2

(

x

−

3

)

⇒

2

y

+

6

=

3

x

−

9

⇒

3

x

−

2

y

−

15

=

0

Note:

The equn.of line passing through

A

(

x

1

,

y

1

)

and

with slope

m

is

y

−

y

1

=

m

(

x

−

Explanation:

the equation of a line in

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange

2

x

+

3

y

=

9

into this form

⇒

3

y

=

−

2

x

+

9

⇒

y

=

−

2

3

x

+

3

←

in slope-intercept form

with slope m

=

−

2

3

Given a line with slope then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

−

2

3

=

3

2

⇒

y

=

3

2

x

+

b

←

is the partial equation

to find b substitute

(

3

,

−

3

)

into the partial equation

−

3

=

9

2

+

b

⇒

b

=

−

6

2

−

9

2

=

−

15

2

⇒

y

=

3

2

x

−

15

2

←

equation of perpendicular lineExplanation:

the equation of a line in

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange

2

x

+

3

y

=

9

into this form

⇒

3

y

=

−

2

x

+

9

⇒

y

=

−

2

3

x

+

3

←

in slope-intercept form

with slope m

=

−

2

3

Given a line with slope then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

−

2

3

=

3

2

⇒

y

=

3

2

x

+

b

←

is the partial equation

to find b substitute

(

3

,

−

3

)

into the partial equation

−

3

=

9

2

+

b

⇒

b

=

−

6

2

−

9

2

=

−

15

2

⇒

y

=

3

2

x

−

15

2

←

equation of perpendicular line

7 0

3 years ago

Read 2 more answers

Sarah is allowed to watch no more than 10 hours of television each week. Sarah has already watched 6 hours of television. Define

sashaice [31]

Answer:

Inequality = 6 + x ≤ 10

x(Number of hours more of television Sarah can still watch this week) = 4 hours

Step-by-step explanation:

Define a variable, set up an inequality and solve that inequality to determine how many more hours of television Sarah can watch this week.

We are told in the question that:

Sarah is allowed to watch no more than 10 hours of television each week.

This means :

Sarah can watch tv for less than or equal to 10 hours in a week. Sarah has already watched 6 hours of television.

Hence:

The number of hours left that Sarah can watch television in a week is represented as x

Our Inequality Equation =

6hours + x hours ≤ 10 hours

6 + x ≤ 10

Solving the inequality

x ≤ 10 - 6

x ≤ 4 hours

This means Sarah still has no more than (less than or equal to) 4 hours or television left to watch in this week

7 0

3 years ago

Log2+ log8=2<br><br>how do I do it?

soldi70 [24.7K]

Answer:

Step-by-step explanation:

log(2)+log(8) = 2

1.20412≠2

False

8 0

3 years ago

Please help!!! Question is below

Lilit [14]

Answer:

A. Obtuse

Step-by-step explanation:

Well we can cross out C and D just by looking at the triangle because the triangle is not equal and there is no right angle.

Also it is not B an acute because not all the angles are acute.

Hence, the answer is A. Obtuse

8 0

3 years ago

Read 2 more answers

Find the area of the unshaded reason for these two problems

Taya2010 [7]

9514 1404 393

Answer:

a) 96 m²

b) 26,000 ft²

Step-by-step explanation:

The area of the unshaded region is the difference between the overall area of the rectangle and the area of the shaded region. It can also be found directly using the dimensions of the unshaded region.

a) We have the height of the right triangle, but need to know its base. The Pythagorean theorem can help with that. Let the base of the triangle be represented by x. Then ...

x² +16² = 20²

x² = 400 -256 = 144

x = √144 = 12

The area of the unshaded triangle is given by the formula ...

A = (1/2)bh

A = (1/2)(12)(16) = 96 . . . . square meters

__

b) The shaded area at upper left is a square 100 ft on a side. Its area is ...

A = s² = (100 ft)² = 10,000 ft²

The shaded area at upper right is a triangle with base and height 120 ft and 150 ft. Its area is ...

A = (1/2)bh = (1/2)(120 ft)(150 ft) = 9,000 ft²

The area of the overall rectangle is ...

A = LW = (300 ft)(150 ft) = 45,000 ft²

So, the unshaded area is ...

unshaded area = overall area - left shaded area - right shaded area

unshaded area = 45,000 ft² -10,000 ft² -9,000 ft² = 26,000 ft²

7 0

3 years ago