What's the answer too x+7/7x+35*x^2-3x-40/x-8

Answers

Answer 1

Answer: $(x+7)/(7x+35)\cdot(x^2-3x-40)/(x-8)=(*)\n\nx^2-3x-40=0\na=1;\ b=-3;\ c=-40\n\Delta=b^2-4ac;\ x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\Delta=(-3)^2-4\cdot1\cdot(-40)=9+160=169;\ \sqrt\Delta=√(169)=13\n\nx_1=(3-13)/(2\cdot1)=(-10)/(2)=-5;\ x_2=(3+13)/(2\cdot1)=(16)/(2)=8\n\nx^2-3x-40=(x+5)(x-8)\n\n(*)=(x+7)/(7(x+5))\cdot((x+5)(x-8))/(x-8)=(x+7)/(7)=(x)/(7)+(7)/(7)=(1)/(7)x+1\n\nD:x\neq-5\ \wedge\ x\neq8$

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What composite number is greater than 1000 whose prime factorization contains 1 prime number that does not repeat 1 prime number that repeats three times and 1 prime number that repeats twice?

Answers

Final answer:

The composite number sought is 12250 which is greater than 1000. Its prime factorization includes the prime numbers 2 (that does not repeat), 5 (that repeats thrice), and 7 (that repeats twice).

Explanation:

The subject is looking for a composite number greater than 1000, whose prime factorization contains 3 types of prime numbers: one that does not repeat, the second repeats three times, and the third repeats twice. We have many prime numbers but to get a number greater than 1000, let’s use larger prime numbers for instance 2, 5 and 7. Let's calculate the composite number with these primes:

2^1 * 5^3 * 7^2 = 2 * 125 * 49 = 12250

Therefore, 12250 is a composite number greater than 1000 whose prime factorization contains 1 prime number(2) that does not repeat, 1 prime number(5) that repeats three times and 1 prime number(7) that repeats twice.

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Fourteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?

Answers

What is the probability?

The probability is a measure of the likelihood of an event to occur.
P(A) is the probability of an event, n(A) is the number of favorable outcomes and n(S) is the total number of events in the sample space.
The probability that a randomly selected item is not defective is P(A) = n(A)/n(S).

We are given that a total of 100 digital video recorders (DVRs) out of these 14 are defective.

The probability of randomlyselect an item that is defective,

P(A) = n(A)/n(S)

P(A) = 14/100

P(A) = 7/50

The probability of randomlyselecting an item that is not defective,

P(A) = 1-(7/50)

P(A) = (50-7)/50

P(A) = 43/50

Hence, the probability of randomly selecting an item that is not defective is 43/50.

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P(non-defective) = 43/50
First, you subtract 14 from 100 to get the number of non-defective video recorders.
Then, you reduce the fraction of 86/100 to 43/50.

find the volume of the cone shown as a decimal rounded to the nearest tenth hight is 16th and radius is 8 yd?

Answers

$H=16\n\nr=8\n\nV=(1)/(3)\pi r^2H\n\nV=(1)/(3)\pi\cdot8^2\cdot16=(1024)/(3)\pi$

Write an equation of proportionality: Sue traveled 1200 miles in 4 hours. *

Answers

Answer:

1200 ÷ 4 = 300

Step-by-step explanation:

Solve using logs 5^(3x-6)=125

Answers

$5 ^(3x-6) =125 \n \n 5 ^(3x-6) =5^3 \n \n3x-6 =3 \ \ |+6 \n \n3x=3+9 \n \n3x=12 \ \ /:3 \n \nx=(12)/(3) \n \nx= 3$

There are multiple chickens and rabbits in a cage. There are 72 heads and 200 feet inside the cage. How many chickens and how many rabbits?

Answers

Given:
heads = 72
feet = 200
Chicken = c
Rabbit = r

c + r = 72
2c + 4r = 200

c = 72 - r

2c + 4r = 200
2(72-r) + 4r = 200
144 - 2r + 4r = 200
2r = 200 - 144
2r = 56
r = 56/2
r = 28

c = 72 - r
c = 72 - 28
c = 44

There are 44 chicken and 28 rabbits.

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A ball is thrown into the air with an upward velocity of 44 ft/s. Its height h in feet after t seconds is given by the function . What is the height of the ball after 2 seconds?