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7nadin3 [17]
3 years ago
6

An open box is to be made from a flat square piece of material 19 inches in length and width by cutting equal squares of length

x from the corners and folding up the sides. (a) Write the volume V of the box as a function of x. Leave it as a product of factors; you do not have to multiply out the factors.
Mathematics
1 answer:
amm18123 years ago
7 0

Answer:Volume=\left ( 19-2x\right )\left ( 19-2x\right )\left ( x\right )

Step-by-step explanation:

Given

Length is 19 in of original box so required length of square box is 19-2x

as width is also equal to length of box

therefore width=19-2x in.

height of box =x in.

Volume =length\times width\times height

Volume=\left ( 19-2x\right )\left ( 19-2x\right )\left ( x\right )

You might be interested in
Not sure how difficult this would be to solve
mr_godi [17]
F (x) = x^2 - 2x + 1
f (x) = (-2)^2 - 2(-2) + 1
= 4 + 4 + 1
= 9
f (x) = ( 0 )^2 - 2 (0) + 1
= 0 - 0 + 1
= 1
0 = x^2 - 2x + 1
x^2 = 2x - 1 = 1
f (2) = 2^2 - 2(2) + 1
= 4 - 4 + 1
= 1
f (3) = 3^2 - 2(3) + 1
= 9 - 6 + 1
= 3 + 1
= 4

3 0
2 years ago
I need the answers for 6,7,8,9,10,11 pls fast
Natalka [10]

Answer:

6) common denominator = 54

7) common denominator = 80

8) common denominator = 108

9) least common denominator = 10

10) least common denominator = 24

11) common denominator = 21


Step-by-step explanation:

6) common denominator of 1/6 , 1/9

example: A/B where A is de numerator and B is the denominator.

common denominators are numbers that have te same composition

1/6 , 1/9 ⇒ if we want to add this fractions we need to find the common denominator.

therefore: (1/6)*(9/9) , (1/9)*(6/6) ⇒ ((1*9)/(6*9)) . ((1*6)/(9*6)) ⇒ 9/54 , 6/54

the common denominator is 54

7) 3/8 , 3/10

(3*10)/(8*10) , (3*8)/(10*8) ⇒ 30/80 , 24/80

common denominator of this two fractions is 80

Note: We can see that the common denominator can be find just by multiplying the denominators. in 7) 6*9=54 and in 8) 10*8=80. This is because in this cases we are asked just for the common denominator

9) 1/9 , 5/12 ⇒ common denominator = 9*12 = 108

10) Least common denominator of 2/5 , 1/10

in this case is the smmallest number that the denominator have in common:

first, from 2/5: denominator=5

multiples of 5: ⇒5, 10, 15, .........

then from 1/10: denominator=10

multiples of 10 ⇒ 10, 20, 30,....

The least common denominator is the smalles number this two denominators have in common. We can see that this number is 10.

There are other ways because you should also think of it as the minimun common denominator. 5 =5*1 and  10 = 2*5 (minimun expresions)

the least minimun denominator willbe the one that includes all de numbers included in their minimum expresion without making it doble (just the amount of times to make the denominator number in each fraction).

therefore we would know that the least common denominator in this fractions is: 1*2*5 = 2*5 = 10

But just have fun and make it simple

10. least common denominator for: 5/6 , 3/8

first: 5/6 ⇒ denominator: 6, so ⇒ 6, 12, 18, 24, 30, 36.....

then: 3/8 ⇒ denominator: 8, so ⇒ 8, 16, 24. 32, 40....

least common denominator for this fractions is ⇒24

or also:

5/6 ⇒ denominator is 6 ⇒ 6=2*3

3/8 ⇒ denominator is 8 ⇒ 8=2*2*2

least common denominator for this fractions is ⇒ 2*2*2*3 =24

11. common denominator of: 1/3 , 2/7

because in this case 3 and 7 are in their minimum expresion ⇔ 3=1*3 & 7=1*7

we can jus find the common denominator by multiplying both denominators:

7*3=21

Hope it helps.

8 0
3 years ago
A 15 ft ladder makes a 52° angle with the ground. How far will the top of the ladder be above the ground.
levacccp [35]

Answer:

11.820 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

Sin = Opposite/Hypotenuse

The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...

sin(52°) = height/(15 ft)

Multiplying by the denominator gives you ...

height = (15 ft)·sin(52°) ≈ 11.820 ft

___

You may need to round this number appropriately.

5 0
3 years ago
Use fractions strips to find the difference. Write your answer in simplest form 4/5 - 1/2
jarptica [38.1K]

Answer:

3/10

Step-by-step explanation:

4/5-1/2

8/10-5/10

3/10

8 0
3 years ago
Can somone pls help me with this I have a C- in math and I really need help also a like show work on each one plsss
Lady bird [3.3K]

Answer:

1. \frac{3}{8}

2. \frac{1}{4}

3a. -\frac{1}{4}

3b. 3

3c. -\frac{4}{5}

4. m = \frac{y_1 - y_2}{x_1-x_2}\\

Step-by-step explanation:

1.

Rises 6 inches for every horizontal change of 16 inches

Slope = rise/run

Slope = 6/16

Slope = 3/8

2.

Rises 3 feet for every horizontal change of 12 feet

Slope = rise/run

Slope = 3/12

Slope = 1/4

3a.

m = \frac{y_1 - y_2}{x_1-x_2}

m = \frac{3-2}{-2-2}

m = \frac{1}{-4}

m = -\frac{1}{4}

3b.

m = \frac{y_1 - y_2}{x_1-x_2}\\

m = \frac{-1 - 2}{-1-0}

m = \frac{-3}{-1}

m = 3

3c.

m = \frac{y_1 - y_2}{x_1-x_2}\\

m = \frac{1 - (-3)}{-1-4}\\

m = \frac{4}{-5}\\

m = -\frac{4}{5}

4.

m = \frac{y_1 - y_2}{x_1-x_2}\\

7 0
3 years ago
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