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aliina [53]
3 years ago
5

There are ___ nuts are in the smallest possible container.

Mathematics
1 answer:
NARA [144]3 years ago
8 0
Small is the blank which is th answer
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The number 35 has the property that when its digits are both increased by 2, and
seropon [69]

Answer: The sum is 127

Step-by-step explanation:

A 2-digit number N = ab can be written as (where a and b are single-digit numbers)

a*10 + b.

Now, we want that:

(a + 2)*(b + 2) = a*10 + b.

So we must find all the solutions to that equation such that a can not be zero (if a = 0, then the number is not a 2-digit number)

We have:

(a + 2)*(b + 2) = a*b + 2*a + 2*b + 4 = a*10 + b

a*b + 2*b - b + 4 = a*10 - a*2

a*b + 4 + b = a*8

a*b + 4 + b - a*8 = 0.

Now we can give one of the variables different values, and see if the equation has solutions:

>a = 1:

1*b + 4 + b - 8 = 0

2*b - 4 = 0

b = 4/2 = 2

Then the number 12 has the property.

> if a = 2:

2*b + 4 + b -16 = 0

3b -12 = 0

b = 12/3 = 4

The number 24 has the property.

>a = 3 is already known, here the solution is 35.

>a = 4.

4*b + 4 + b - 8*4 = 0

5*b + 4 - 32 = 0

5*b = 28

b = 28/5

this is not an integer, so here we do not have a solution.

>if a = 5.

5*b + 4 + b - 8*5 = 0

6b + 4 - 40 = 0

6b - 36 = 0

b = 36/6 = 6

So the number 56 also has the property.

>if a = 6

6*b + 4 + b - 8*6 = 0

7b + 4 - 48 = 0

7b - 44 = 0

b = 44/7 this is not an integer, so here we do not have any solution.

>if a = 7

7*b + 4 + b -8*7 = 0

8b -52 = 0

b = 52/8 = 6.5 this is not an integer, so we here do not have a solution.

>if a = 8

8*b + 4 + b -8*8 = 0

9*b + 4 - 64 = 0

9*b = 60

b = 60/9 this is not an integer, so we here do not have any solution:

>if a = 9

9*b + 4 + b - 8*9 = 0

10b + 4 - 72 = 0

10b -68 = 0

b = 68/10 again, this is not an integer.

So the numbers with the property are:

12, 24, 35 and 56

And the sum is:

12 + 24 + 35 + 56 =  127

8 0
3 years ago
Find the distance between the point (-3,5,8) and (8,12,2)
Nitella [24]
Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points.
8 0
3 years ago
Find the value of 15c1
Natali [406]

Answer:

The simple answer is 15 only

8 0
3 years ago
What's a good app to use to study for the driving permit​
Sergio [31]

Answer:DMV Genie

Step-by-step explanation:

DMV Genie is the new gold standard in driver education, the only program recommended by DMVs, top driving schools and independent instructors. It's the highest rated driver's ed study tool on the market, and millions of drivers already know it. Check out the reviews to see what your fellow applicants have to say.

6 0
3 years ago
Read 2 more answers
What is the area of this trapezoid?
Ivanshal [37]

Answer: 357 cm²

Step-by-step explanation: In this problem, were asked to find the area of the trapezoid shown. Remember that a trapezoid is a quadrilateral with one pair of parallel sides. The formula for the area of a trapezoid is shown below

The b's are the bases or the parallel sides and the h represents the height.

So in the trapezoid shown, the bases are 15 cm and 27 cm and the height is 17 cm.

Plugging this information into the formula, we have .

Next, the order of operations tells us that we must simplify inside the parentheses first. 15 cm + 27 cm is 42 cm and we have

1/2 × 42 cm is 21 cm and we have (21 cm)(17 cm) which is 357 cm².

So the area of the trapezoid shown is 357 cm².

5 0
3 years ago
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