Answer:
The two numbers are 28 and 7.
Step-by-step explanation:
Let the first number be x
Let the second number be y
The difference of x and y is x-y=21
The quotient of two numbers is x/y = 4
x-y =21 (This is equation 1)
x/y=4 (This is equation 2)
By solving equation 2 we will get the value of x.
x/y=4
x=4y (Lets call it equation 3)
Now, put the value of x(equation 3) in (equation 1)
x-y=21
4y-y=21
3y=21
y=21/3
y=7
Now put the value of y in equation 3 to get the value of x
x=4y
x=4(7)
x=28
Solution Set {(x,y)(28,7)}
Answer:
3.9 to nearest tenth.
Step-by-step explanation:
Using the theorem of intersecting chords:
9 * y = 5 * 7
y = 35/9
= 3.888...
The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
Learn more about prime numbers here:
brainly.com/question/145452
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Answer: 8
Step-by-step explanation:
Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.
Total marbles other than green = 8
Total marbles other than green and yellow = 6
Then the number of sets of seven marbles include at least one yellow one but no green ones:-
Number of sets of seven marbles include at least one yellow one but no green ones = 8
I think the answer is 1d.
