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navik [9.2K]
3 years ago
10

Show that (x+1)(x+3)(x+5) can be written in the form ax3+bx2+cx+d where a b c and d are all positive intergers

Mathematics
1 answer:
Sophie [7]3 years ago
7 0

Answer:

Step-by-step explanation:

(x+1)(x+3)(x+5), multiply first two parenthesis

(x² +3x +x +3)(x+5), combine like terms

(x² +4x +3) (x+5), multiply the parenthesis

(x³ +5x² +4x² +20x +3x +15), combine like terms

x³ +9x² +23x +15 is in the form ax³ +bx² +cx +d

a=1, b=9, c=23, d=15 are all positive integers

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Is 5 1/2 bigger then 5 3/8
Liono4ka [1.6K]

1/2 and 3/8

equivalent

1/2 = 4/8

so 4/8 is greater than 3/8

Answer

5 1/2 is bigger than 5 3/8

6 0
3 years ago
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How do you convert binary numbers to decimal numbers
telo118 [61]
An easy method of converting decimal to binary number equivalents is to write down the decimal number and to continually divide-by-2 (two) to give a result and a remainder of either a “1” or a “0” until the final result equals zero.
5 0
3 years ago
A radio arm saw has a circular cutting blade with a diameter of 10 inches and it spins at 2000rpm if there are 12 cutting teeth
FinnZ [79.3K]

Answer:

12565.11 teeth approximately cut cross the cutting surface per seconds.

Step-by-step explanation:

Since the diameter is 10inches, the circumference of the arm saw is 10π (circumference is πd where d is diameter).

The number of teeth on the cutting blade can be gotten by multiplying the diameter by 12 since we have 12 teeth per inch on the arm saw

Number of teeth on saw = 12 x 10π = 120π.

To get the number of teeth that cross the cutting surface in 2000rpm we multiple it by the total number of teeth in just one rpm.

So we have 2000 x 120π. But since we are asked to find it in revolution per seconds then 2000r/m = 2000r/60s ≈ 33.33

Therefore, we have

33.33 x 120π ≈ 12565.11 teeth

7 0
3 years ago
100 POINTS + BRAINLIST
mojhsa [17]

Problem 1

Since point P is the tangent point, this means angle OPT is a right angle

angle OPT = 90 degrees

Let's use the Pythagorean theorem to find the missing side 'a'

a^2 + b^2 = c^2

a^2 + 7^2 = 12^2

a^2 + 49 = 144

a^2 = 144 - 49

a^2 = 95

a = sqrt(95)

a = 9.7467943

a = 9.7

----------------

Let's use the sine and arcsine rule to find angle y

sin(angle) = opposite/hypotenuse

sin(y) = 7/12

y = arcsin( 7/12 )

y = 35.6853347

y = 35.7

The value of y is approximate. Make sure your calculator is in degree mode. Arcsine is the same as inverse sine or \sin^{-1}

====================================================

Problem 2

Focus on triangle OHP. This may or may not be a right triangle. The goal is to test if it is or not.

We use the converse of the Pythagorean theorem to check.

Recall that the converse of the Pythagorean theorem says: If a^2+b^2 = c^2 is a true equation, then the triangle is a right triangle. The value of c is always the longest side. The order of a and b doesn't matter.

In this case we have

  • a = 7
  • b = 13
  • c = 16

Which leads to

a^2 + b^2 = c^2

7^2 + 13^2 = 16^2

49 + 169 = 256

218 = 256

We get a false equation at the end, since both sides aren't the same number, which means the original equation is false.

We don't get a^2 + b^2 = c^2 to be true, therefore this triangle is not a right triangle.

Consequently, this means angle OPH cannot possible be 90 degrees (if it was then we'd have a right triangle). Therefore, point P is not a tangent point.

You follow the same basic idea for triangle OQH and show that point Q is not a tangent point either. Or you could use a symmetry argument to note that triangle OPH is a mirror reflection of triangle OQH over the line segment OH. This implies that whatever properties triangle OPH has, then triangle OQH has them as well for the corresponding pieces.

7 0
2 years ago
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Simplify a polynomial: (3x–4y)²–(3x–4y)(3x+4y)
Vika [28.1K]

Step-by-step explanation:

(3x-4y)×(3x-4y-(3x+4y))

(3x-4y)×(3x-4y-3x-4y)

(3x-4y)×(-8y)

-8y×(3x-4y

8 0
3 years ago
Read 2 more answers
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