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larisa [96]
3 years ago
14

The total number of toothpicks also forms a sequence: 4, 12, 24, 40, ... What rule describes this sequence?

Mathematics
1 answer:
astraxan [27]3 years ago
4 0
<span> rule describes this sequence is 
</span><span> an = 2 ( n^2 + n )

n = 1

</span> an = 2 ( 1^2 + 1 )
 an = 2 ( 1 + 1 )
 an = 2 ( 2 )
 an =  4

n = 2

 an = 2 ( 2^2 + 2 )
 an = 2 ( 4 + 2 )
 an = 2 ( 6 )
 an =  12

n = 3

 an = 2 ( 3^2 + 3 )
 an = 2 ( 9 + 3 )
 an = 2 ( 12 )
 an =  24

n = 4

 an = 2 ( 4^2 + 4 )
 an = 2 ( 16 + 4 )
 an = 2 ( 20 )
 an =  40
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Beulah used 3/5 pounds of dough, 3/4 pound of sugar, &amp; 2/3 pounds of sprinkles to make donuts. How many pounds of donuts did
andre [41]

Number of pounds of dough used = 3/5 pounds.

Number of pounds of sugar used = 3/4 pounds

Number of pounds of sprinkles used = 2/3 pounds.

Total number of pounds of donuts = Number of pounds of dough used + Number of pounds of sugar used + Number of pounds of sprinkles used.

Plugging values.

Total number of pounds of donuts = 3/5 + 3/4 + 2/3.

We need to add all those fractions.

In order to add fracions, we need to find common denominator (lcd).

We have 5,4 and 3 in denominators.

Least common denominator(lcd) of 5, 4 and 3 is 60.

We need to make each denominator equals 60.

Multiplying first fracion by 12 in top and bottom, we get

3*12/5*12 = 36/60

Multiplying first fracion by 5 in top and bottom, we get

3*15/4*15 = 45/60

Multiplying first fracion by 20 in top and bottom, we get

2*20/3*20 = 40/60.

Therefore,

3/5 + 3/4 + 2/3 = 36/60 + 45/60 + 40/60

               =  121/60

Let us convert 121/60 into mixed fraction.

Dividing 121 by 60 we get quotient =2 and remainder =1.

So, the mixed fraction is 2 1/60.

Therefore, Beulah made total 2 1/60 pounds of donuts.

4 0
3 years ago
the area of a triangle is 124 square units. what would it's new area be if its base was half as long and its height was three ti
Montano1993 [528]
To solve this problem you must apply the proccedure shown below:

 1. You have that the formula for calculate the area of a triangle is:

 A=bh/2

 Where A is the area of the triangle, b is the base of the triangle and h is the height of the triangle.

 bh/2=124
 bh=124x2
 bh=248

 2. The problem asks for the new area of the triangle <span>if its base was half as long and its height was three times as long. Then, you have:

 Base=b/2
 Height=3h

 3. Therefore, when you substitute this into the formula for calculate the area of a triangle, you obtain:

 A'=bh/2

 (A' is the new area)

 A'=(b/2)(3)/2
 A'=3bh/4

 4. When you substitute bh=248 into </span>A'=3bh/4, you obtain:
<span>
 A'=186 units</span>²
<span>
 The answer is: </span>186 units²
3 0
3 years ago
What is the value of x? Enter your answer, as a decimal, in the box.<br><br> ___ cm
lora16 [44]

Answer

50.6

Step-by-step explanation:

I'm not sure how to do it, but I took the quiz and it said this was the correct answer


6 0
3 years ago
Find the area of a circle with the circumference 18(pi)
JulsSmile [24]

Answer:

D 81 pi units^2

Step-by-step explanation:

The circumference of a circle  is given by

C = 2 * pi *r

18 pi = 2 * pi *r

Divide each side by 2 * pi

18 pi / (2 pi) = 2 pi * r/ (2 pi)

9 = r

Now we can find the area.  Area is given by

A = pi r^2

A = pi * 9^2

A = 81 pi units^2

5 0
3 years ago
Read 2 more answers
Which are the solutions of x² = 19x + 12​
Sever21 [200]

Answer:

\{x=\frac{19-\sqrt{409} }{2}\ , \  x=\frac{19+\sqrt{409} }{2}\}

Step-by-step explanation:

x² = 19x + 12

⇔ x² - 19x - 12 = 0

Calculating the discriminant :

b² - 4ac = (-19)² - 4×1×(-12) = 409

The discriminant is positive ,then the equation has two solutions.

x=\frac{19-\sqrt{409} }{2} \ \ or\ \ x=\frac{19+\sqrt{409} }{2}

4 0
2 years ago
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