Name the inequality!

The length of a paper clip chain is directly proportional to the number of paper clips. If a chain with 65 paper clips has a len

Ghella [55]

Answer:

The length of a paper clip chain is directly proportional to the number of paper clips. If a chain with 65 paper clips has a length of 97.5 inches then the length of chain with 14 paper clips is 21 inches.

Solution:

Given that the length of a paper clip chain is directly proportional to the number of paper clips. Directly propotional means when the length of paper clip increases, then the number of paper clips also increases in same ratio.

Hence, by above definition, we get

$\frac{l_{1}}{l_{2}} = \frac{n_{1}}{n_{2}}$ ------- eqn 1

From question, for a chain with 65 paper clips has a length of 97.5 inches, we get

$l_{1} = 97.5 \text { and } n_{1} = 65$

Similarly, for a chain with 14 paper clips with length to be found, we get

$n_{2}=14 \text { and } l_{2} = ?$

Now by using eqn 1, we can calculate the length of 14 paper clips is,

$\frac{97.5}{65}=\frac{l_{2}}{14}$

Rearranging the terms we get,

$l_{2 }= \frac{97.5 \times 14}{65}$

$l_{2}=21 \text { inches }$

Hence the length of chain with 14 paper clips is 21 inches.

3 0

3 years ago

How many solutions can be found for the linear equation 3(x/2 + 5 ) - 6 = ( 9x + 18 ) / 3

I am Lyosha [343]

answer: it would be one solution, becasue the variables are different and the constants dont matter, since the variables are different

5 0

3 years ago

Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. When company comes she makes 96 fluid ounces of coffee. H

Komok [63]

The answer is B. 48 x 2 = 96, 30 x 2 = 60.

6 0

3 years ago

Jasmine is in charge purchasing tubes of silicone sealant, used for finishing restroom facilities. She finds that she is able to

Georgia [21]

The question attached is:

Is Jasmine correct about the silicone sealant cones?

If you think Jasmine is correct to explain, why.

Answer:

Jasmine is correct about the silicone sealant cones

Step-by-step explanation:

Given that:

Jumbo cone of sealant has a top diameter of 12 inches and a height of 14 inches, Suppose Jasmine orders or demands for two regular cones of regular sealant, definitely, that will be equal to the Jumbo cone of sealant.

This is because the top diameter when put together in a Jumbo cone will give an actual result as a Jumbo cone, for as much as 6 × 2 = 12 inches (top diameter) and 7 × 2 = 14 inches (height).

8 0

3 years ago

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −3 and a local minimum value of 0 at

Vinvika [58]

The formula is f(x) = a x ^ 3 + b x ^ 2 + c x + d
f '(x) = 3ax^2 + 2bx + c.
f(- 3) = 3 ==> - 27a + 9b - 3c + d = 3
f '(- 3) = 0 (being a most extreme) ==> 27a - 6b + c = 0.
f(1) = 0 ==> a + b + c + d = 0
f '(1) = 0 (being a base) ==> 3a + 2b + c = 0.
-
Along these lines, we have the four conditions
- 27a + 9b - 3c + d = 3
a + b + c + d = 0
27a - 6b + c = 0
3a + 2b + c = 0
Subtracting the last two conditions yields 24a - 8b = 0 ==> b = 3a.
Along these lines, the last condition yields 3a + 6a + c = 0 ==> c = - 9a.
Consequently, we have from the initial two conditions:
- 27a + 9(3a) - 3(- 9a) + d = 3 ==> 27a + d = 3
a + 3a - 9a + d = 0 ==> d = 5a.
Along these lines, a = 3/32 and d = 15/32.
==> b = 9/32 and c = - 27/32.
That is, f(x) = (1/32)(3x^3 + 9x^2 - 27x + 15).

8 0

3 years ago