Triangle LMN is a right triangle The measure of angleL,m41, is equal to 35° Triangle LMN is

Write the prime factorization for 65,169

posledela

Let's try to find some primes that divide this number.

The number is not divisible by 2, because it is odd.

The number is divisible by 3 though, because the sum of its digits is:

$6+5+1+6+9=27=3\cdot 9$

So, we can divide the number by 3 and keep going with the factorization:

$65169\div 3 = 21723$

This number is again divisible by 3, because

$2+1+7+2+3 = 15 = 3\cdot 5$

We have

$21723\div 3 = 7241$

This number is no longer divisible by 3. Let's go on looking for primes that divide it: 5 doesn't because the number doesn't end in 0 nor 5. This number is not divisible by 7 or 11 either (just try). It is divisible by 13 though: we have

$7241\div 13 = 557$

And 557 is prime, so we're done. This means that the prime factorization of 65169 is

$3^2\cdot 13 \cdot 557$

8 0

3 years ago

Is y=-9x proportional

icang [17]

Yes, y=-9x is proportional

3 0

3 years ago

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Write down the quadratic equation whose roots are $x = -7$ and $x = 1,$ and the coefficient of $x^2$ is 1. Enter your answer in

pav-90 [236]

<h2>Steps:</h2>

So firstly, since we know that the coefficient of x² is 1, this means that this is our base equation:

y = x² + bx + c

Now, since we know that the roots are -7 and 1, set y = 0 and set x = -7 and 1 and simplify:

$0=(-7)^2+b(-7)+c\\0=49-7b+c\\-49=-7b+c\\\\0=1^2+b(1)+c\\0=1+b+c\\-1=b+c\\\\-49=-7b+c\\-1=b+c$

Now with this, we can set up a system of equations to solve for b and c. For this, I will be using the elimination method. For this, subtract the 2 equations:

$\begin{alignedat}{2}-49&=-7b+c\\-(-1&=b+c)\\-48&=-8b\end{alignedat}$

Now that the c variable has been eliminated we can solve for b. For this, divide both sides by -8 and your first part of your answer is b = 6.

Now that we know the value of b, plug it into either equation to solve for c:

$-49=-7(6)+c\\-49=-42+c\\-7=c\\\\-1=6+c\\-7=c$

<h2>Answer:</h2>

<u>Putting it together, your final answer is x² + 6x - 7 = 0.</u>

4 0

3 years ago

Which statement is true?

Lady_Fox [76]

Answer:

An irrational number may show terminating digits after the decimal

Step-by-step explanation:

Examples of Rational Numbers

Number 9 can be written as 9/1 where 9 and 1 both are integers. 0.5 can be written as ½, 5/10 or 10/20 and in the form of all termination decimals. √81 is a rational number, as it can be simplified to 9 and can be expressed as 9/1. 0.7777777 is recurring decimals and is a rational number

Examples of Irrational Numbers

Similarly, as we have already defined that irrational numbers cannot be expressed in fraction or ratio form, let us understand the concepts with few examples.

5/0 is an irrational number, with the denominator as zero.

π is an irrational number which has value 3.142…and is a never-ending and non-repeating number.

√2 is an irrational number, as it cannot be simplified.

0.212112111…is a rational number as it is non-recurring and non-terminating.

There are a lot more examples apart from above-given examples, which differentiate rational numbers and irrational numbers.

Properties of Rational and Irrational Numbers

Here are some rules based on arithmetic operations such as addition and multiplication performed on the rational number and irrational number.

#Rule 1: The sum of two rational numbers is also rational.

Example: 1/2 + 1/3 = (3+2)/6 = 5/6

#Rule 2: The product of two rational number is rational.

Example: 1/2 x 1/3 = 1/6

#Rule 3: The sum of two irrational numbers is not always irrational.

Example: √2+√2 = 2√2 is irrational

2+2√5+(-2√5) = 2 is rational

#Rule 4: The product of two irrational numbers is not always irrational.

Example: √2 x √3 = √6 (Irrational)

√2 x √2 = √4 = 2 (Rational)

5 0

3 years ago

2 3 + x = 3 what is X solved for

Olegator [25]

Answer:

Obviously its x=3-23=-20.

5 0

3 years ago

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