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3 years ago

Prime factors of 625

Mathematics

1 answer:

ipn [44]3 years ago

3 0

$625=5\cdot 5\cdot 5\cdot 5\\ 625={ 5 }^{ 4 }$

${ 5 }^{ 4 }$ is 625's prime factor

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15 less than a number tripled is equivalent to the difference of the same number and 12

Nitella [24]

Step-by-step explanation:

x = number

3x - 15 = (x - 12)×-4 or (12-x)×-4

3x - 15 = -4x + 48 or -48 + 4x

7x = 63, x = 9 or

33 = x

4 0

3 years ago

Prove that root 7 is irrational by the method of contradiction

Alchen [17]

Let assume that $\sqrt7$ is a rational number. Therefore it can be expressed as a fraction $\dfrac{a}{b}$ where $a,b\in\mathbb{Z}$ and $\text{gcd}(a,b)=1$ .

$\sqrt7=\dfrac{a}{b}\\\\7=\dfrac{a^2}{b^2}\\\\a^2=7b^2$

This means that $a^2$ is divisible by 7, and therefore also $a$ is divisible by 7.

So, $a=7k$ where $k\in\mathbb{Z}$

$(7k)^2=7b^2\\\\49k^2=7b^2\\\\7k^2=b^2$

Analogically to $a^2=7b^2$ ------- $b^2$ is divisible by 7 and therefore so is $b$ .

But if both numbers $a$ and $b$ are divisible by 7, then $\text{gcd}(a,b)=7$ which contradicts our earlier assumption that $\text{gcd}(a,b)=1$ .

Therefore $\sqrt7$ is an irrational number.

8 0

3 years ago

Given: 2x + 30 = -4(5x -2);<br> Prove: x = -1

Lady_Fox [76]

2x + 30 = -20x + 8
2x + 20x = 8 - 30
22x = -22
x = 1

6 0

3 years ago

Please solve the questions

Wewaii [24]

Answer:

Step-by-step explanation:

For a

2 + x = 15

x = 15 -2

x = 13

For B

x - 12 = 14

x = 12 + 14

x = 26

For C

3x = 12

x = 12/3

x = 4

Hope it helps:)

5 0

3 years ago

I don’t know the answer or how to do this, help!

makvit [3.9K]

Answer:

Step-by-step explanation:

y = x^2 - x - 12

y = (x-4)×(x+3) that means x it either 4 or -3

y = x + 3

for x = 4 ➡ y = 3+4 ➡7

for x = -3 ➡ y = -3 + 3➡0

(the answer key is most probably faulty there's no way for y to be 0 in both scenarios)

6 0

3 years ago