the product of the first three prime numbers is how much less than the sum of thew nest three prime numbers

Mathematics

1 answer:

Ivan3 years ago

4 0

The product of the first 3 prime numbers is 1 less than the sum of the next 3 prime numbers.

First we need to multiply the first 3 prime numbers together. The first 3 prime numbers are 2, 3, and 5.

2 * 3 * 5 = 30.

Next we need to add the next 3 prime numbers. The next 3 prime numbers are 7, 11, and 13.

7 + 11 + 13 = 31

Now we can subtract our first total from our second.

31 - 30 = 1

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Three consecutive vertices of a parallelogram are (– 2, 1); (1, 0) and (4, 3). Find the coordinate of the fourth vertex and find

antiseptic1488 [7]

Answer:

D(1,4) - the fourth vertex, the area is equal to 12

Step-by-step explanation:

A(2,-1), B(1,0),C(4,3), They are consecutive, we need to find the point D, find the midpoint of AC (O)

xo= (xA+xc)/2 x0= (-2+4)/2=1

y0=(yA+yC)/2 y0= (1+3)/2=2

0(1,2)

O is the midpoint of BD, so let's find the vertex D

X0= (xB+xD)/2 1= (1+xD)/2 xD=1

y0= (yB+yD)/2 2= (0+yD)/2 yD=4

D(1,4)

the vector DA is (-2-1, 1-4)= (-3,-3)

the vector DC is (4-1, 3-4)= (3,-1)

The modul of DC is sqrt ((-3)^2+(-3)^2)= 3*sqrt2(the length of the side Dc)

The modul of DA is sqrt (3^2+(-1)^2)= sqrt10(the length of the side DA)

cosD= (-3*3+(-3)(-1))/3*sqrt2*sqrt10=-6/3*2*sqrt5=-1/sqrt5

sinD= sqrt (1- 1/5)=2/ sqrt5

S=3sqrt2*sqrt10*2/sqrt5= 12

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6.083 would be the answer

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A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formu

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Questions:

A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?

Answer:

32 units of fabrics

Step-by-step explanation:

Given

$a = \sqrt{f + 4} - \sqrt{36 - f}$