Which equation represents a line which is parallel to the line y= -2/3x + 1?

PLAYSTOP6The volume of the solid iscubic feet. Use the formula V = Bh. All angles are 90°.9 ft.6 ft.ft.3 ft.2 ft.2ft.

ira [324]

Volumen of A Solid

Given a solid with a shape of a constant base B and height H, the volume is:

V = BH

The height of the solid is 1 1/4 ft. We need to calculate the area of the base.

The base consists of a larger rectangle from which has been taken a smaller rectangle.

The larger rectangle has dimensions of 9 ft by 6 ft, thus its area is:

A1 = 9 ft * 6 ft = 54 square ft

The smaller rectangle has dimensions of 2 1/2 ft by 4 ft.

The second dimension was calculated as the difference between 9 ft and 2 ft plus 3 ft. (9 ft - 3 ft - 2 ft = 4 ft).

The area of the smaller rectangle is:

A2 = 2 1/2 * 4

The mixed fraction 2 1/2 is converted to improper fraction:

2 1/2 = 2 + 1/2 = 5/2

Thus, the area is:

A2 = 5/2 * 4

A2 = 10 square feet

The area of the base is A1 - A2 = 54 square feet - 10 square feet = 44 square feet

B = 44 square feet.

Now for the volume:

V = 44 square feet * 1 1/4 feet

Again the mixed fraction is converted to a single fraction:

1 1/4 = 1 + 1/4 = 5/4

V = 44 square feet * 5/4 feet

V = 55 cubic feet

3 0

1 year ago

The sum of three consecutive even numbers is 114. what is the smallest of the three numbers?

saul85 [17]

Answer:

36

Step-by-step explanation:

Let's let n be any number.

If we multiply n by 2, we get 2n. Since anything multiplied by 2 is even, 2n must be even. Therefore, let 2n be our first number.

So, the consecutive even number will be (2n+2) followed by (2n+4).

We know that their sum must be 114. Therefore, we can write the following equation:

$(2n)+(2n+2)+(2n+4)=114$

Solve for n. Combine like terms on the left:

$6n+6=114$

Subtract 6 from both sides:

$6n=108$

Finally, divide both sides by 6. Therefore, the value of n is:

$n=108/6=18$

Therefore, our first even number is 2n or 2(18) which equates to 36.

And the consecutive even numbers will be 38 and 40.

So, the smallest of them, the first term, is 36.

4 0

3 years ago

Read 2 more answers

Solve for n 0=-5n-2n

iris [78.8K]

0 = -5n - 2n
0 = -7n |divide both sides by (-7)

n = 0

4 0

3 years ago

If (x + 2) is a factor of x3 − 6x2 + kx + 10, k =

ch4aika [34]

Answer:

The value of k is -11

Step-by-step explanation:

If (x+2) is a factor of x3 − 6x2 + kx + 10:

Then,

f(x)=x3 − 6x2 + kx + 10

f(-2)=0

f(-2)=(-2)³-6(-2)²+k(-2)+10=0

f(-2)= -8-6(4)-2k+10=0

f(-2)= -8-24-2k+10=0

Solve the like terms:

f(-2)=-2k-22=0

f(-2)=-2k=0+22

-2k=22

k=22/-2

k=-11

Hence the value of k is -11....

5 0

3 years ago

Calcula y comprueba las ecuaciones: porfavor alguienn la nesesito pliss a) 2X = 6 b) 10 + Z = 20 c) P + 9 = 11 d) 3X + 8 = + 29

Alexeev081 [22]

Answer:

a) x = 3

b) z = 10

c) p = 2

d) x = 7

e) u = 1

Step-by-step explanation:

a) 2x = 6

Despejamos x dividiendo por 2 a amabos lados de la eacuacion.

(2/2)x = 6/2

x = 3

Si remplazamos x en la ecuación original:

2(3)=6

6 = 6

Queda demostrado.

b) 10 + z = 20

Despejamos z restando 10 en amabos lados de la eacuacion.

10-10+z = 20-10

z = 10

Si remplazamos z en la ecuación original:

10 + 10=20

20 = 20

Queda demostrado.

c) p + 9 = 11

Despejamos p restando 9 en amabos lados de la eacuacion.

p + 9 - 9 = 11-9

p = 2

Si remplazamos p en la ecuación original:

2 + 9 = 11

11 = 11

Queda demostrado.

d) 3x + 8 = 29

Despejamos x restando 8 en amabos lados de la eacuacion y luego divideindo por 3 en ambos lados de la ecuación.

3x+8-8 = 29-8

3x = 21

(3/3)x = 21/3

x = 7

Si remplazamos x en la ecuación original:

3(7) + 8 = 29

21 + 8 = 29

29 = 29

Queda demostrado

e) 2u + 8 = 10

Despejamos u restando 8 en amabos lados de la eacuacion y luego divideindo por 2 en ambos lados de la ecuación.

2u+8-8 = 10-8

2x = 2

(2/2)x = 2/2

x = 1

Si remplazamos x en la ecuación original:

2(1) + 8 = 10

2 + 8 = 10

10 = 10

Queda demostrado

Espero te haya sido de ayuda!

5 0

3 years ago