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solmaris [256]
3 years ago
9

If ab and cd are congruent what is the measure of

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
5 0

Answer:

25°

Step-by-step explanation:

the arcs are congruent, and the radii are the same length, as it would be from any other point in a circle. this means that the angle must be the same.

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Find the roots of the equation x^3-3x^2+x+5
leonid [27]
First observe that x=-1 is a root of the equation. Use long division to divide x^3-3x^2+x+5 by x+1, we find that (x^3-3x^2+x+5)/(x+1)=(x^2-4x+5). Now we need to find the roots of x^2-4x+5.
x^2-4x+5=0, 
x^2-4x+4=-1,
(x-2)^2=i,
x-2=i or -1,
x=2+i or 2-i. 
The three roots are 2+i, 2-i, -1.
5 0
3 years ago
What is the smallest prime number p such that
Ne4ueva [31]

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.

  • p^3 + 4p^2 + 4p

By factorization, we have:

  • = p(p+2)²

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:

  • p₁ = 5 and p₂ = 3

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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8 0
1 year ago
What is 1/8 as a decimal
Vilka [71]

Answer:

1.8

Step-by-step explanation:

1.8

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3 years ago
Four students have summer jobs. The table shows how much each student earns after working a certain number of hours. Which stude
vlada-n [284]

Answer:

C Jacob

Step-by-step explanation:

Alfredo: 157.5/18 = 8.75

Helene: 198/24 = 8.25

Jacob: 142.5/15 = 9.53

Leonna: 111/12 = 9.25

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3 years ago
The school bus Evie rides is scheduled to arrive at her stop at 8:20 a.m. each day. The table below shows the actual arrival tim
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