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2 years ago

Please help!!!!

Mathematics

1 answer:

Solnce55 [7]2 years ago

8 0

Answer:

c) ( $(6-\sqrt{12} )(6+\sqrt{12} ) = 24$

d) ( $(3+\sqrt{8} )(3-\sqrt{8} ) = 1$

Step-by-step explanation:

Given that the binomial expression

( $(6-\sqrt{12} )(6+\sqrt{12} )$

Multiply

( 36 + 6√12 -6√12 -(√12)²)

= ( 36 -12)

= 24

c) ( $(6-\sqrt{12} )(6+\sqrt{12} ) = 24$

Given that the binomial expression

( $(3+\sqrt{8} )(3-\sqrt{8} )$

Multiply

= 9 - 3√8 + 3√8 -(√8)²

= 9 - 8

= 1

d) ( $(3+\sqrt{8} )(3-\sqrt{8} ) = 1$

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A factory dumps an average of 2.43 tons of pollutants into a river every week. if the standard deviation is 0.88 tons, what is t

vovikov84 [41]

25.8%
First, determine how many standard deviations from the norm that 3 tons are. So:
(3 - 2.43) / 0.88 = 0.57/0.88 = 0.647727273
So 3 tons would be 0.647727273 deviations from the norm. Now using a standard normal table, lookup the value 0.65 (the table I'm using has z-values to only 2 decimal places, so I rounded the z-value I got from 0.647727273 to 0.65). The value I got is 0.24215. Now this value is the probability of getting a value between the mean and the z-score. What I want is the probability of getting that z-score and anything higher. So subtract the value from 0.5, so 0.5 - 0.24215 = 0.25785 = 25.785%
So the probability that more than 3 tons will be dumped in a week is 25.8%

5 0

2 years ago

Which of the following statements is false?

kramer

Option D

The sum of two irrational numbers is always rational is false statement

<em><u>Solution:</u></em>

<h3><u>The sum of two rational numbers is always rational</u></h3>

"The sum of two rational numbers is rational."

So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.

For example:

$\frac{1}{4} + \frac{1}{5} = \frac{9}{20}$

rational number + rational number = rational number

Hence this statement is true

<h3><u>The product of a non zero rational number and an irrational number is always irrational</u></h3>

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational.

Any other situation, however, of a rational times an irrational will be irrational.

A better statement would be: "The product of a non-zero rational number and an irrational number is irrational."

So this statement is correct

<h3><u>The product of two rational numbers is always rational</u></h3>

The product of two rational numbers is always rational.

A number is said to be a rational number if it is of the form p/q,where p and q are integers and q ≠ 0

Any integer is a rational number because it can be written in p/q form.

Hence it is clear that product of two rational numbers is always rational.

So this statement is correct

<h3><u>The sum of two irrational numbers is always rational</u></h3>

"The sum of two irrational numbers is SOMETIMES irrational."

The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.

Thus this statement is false

5 0

3 years ago

Please help and show work if you can

laila [671]

Answer:

25. a = 60

26. a = 17

Step-by-step explanation:

In these two problems we are going to use a property of parallelograms that says: opposite angles have equal measure

so we have

25.

$6a+10=130\\\\6a=130-10\\\\6a=120\\\\a=60$

and for 26 we have

$4a-4=2a+30\\\\4a=2a+30+4\\\\4a=2a+34\\\\4a-2a=34\\\\2a=34\\\\a=17$

6 0

3 years ago

Find two additional roots of P(x)=0.<br><br> 13+sqrt 3 and 7i

vova2212 [387]

So, x = 13, x = √3 and x =7i.

now, recall that for an EVEN radical, there are two possible roots, namely is say √3 is say hmmm some value "a", that means that a*a = √3, however, -a*-a is also √3, therefore, ±√3 are two valid values, and therefore -√3 is another one.

now.... keep in mind that, complex solutions or roots, never come all by their lonesome, their sister is always with them, the conjugate, so, for 7i or namely 0 + 7i, her sister is always around, 0 - 7i, which is the other root.

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3 years ago

Solve for x and y:<br> x+y=5 x−y=a <br> PLEASE I NEED MY ANSWER TILL TOMORROW MORNING!

KengaRu [80]

Answer:

x= $\frac{a+5}{2}$ y=5- $\frac{a+5}{2}$

Step-by-step explanation:

x+y=5

y=5-x

x-y=a

x-(5-x)=a

2x-5=a

2x=a+5

x= $\frac{a+5}{2}$

x+y=5

$\frac{a+5}{2}$ +y=5

y=5- $\frac{a+5}{2}$

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3 years ago

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