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4 years ago

To Rationalize the denominator of 5-√7/9-√14, you should multiply the expression by which fractions?

Mathematics

2 answers:

beks73 [17]4 years ago

8 0

Answer

9+√14

Explanation

To Rationalize the denominator of 5-√7/9-√14.

To rationalize this we multiply both the denominator and denominator by the conjugate of the denominator.

The denominator is 9-√14 and its conjugate is (9+√14).

(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)

= (5-√7)(9+√14)/(9²-14)

= (45 + 5√14 - 9√7 - √98)/(81-14)

= (45 + 5√14 - 9√7 - √98)/67

= (45 + 5√14 - 9√7 - 7√2)67

This is the rationalized expression.

The denominator is (9-√14) and its conjugate is (9+√14).

ludmilkaskok [199]4 years ago

5 0

Answer:

Its C

Step-by-step explanation:

9+√14

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3 years ago

Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.

just olya [345]

Answer:

Find the answers below

Step-by-step explanation:

Using m<X as the reference angle

Opposite YZ = 7

Adjacent XY = 10

Hypotenuse XZ = √149

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sinX = opp/hyp

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3 years ago

sweet [91]

Answer:

The variable Y represents the number of meters of string in the third yoyo

Step-by-step explanation:

In this equation y stands for the unknown variable. The equation tell you that hope made 3 different yo-yos so the number of yo-yos hope made isn't unknown, meaning, it cant be the first answer. The problem also tells you that hope used a total of 4 meters of string which means that the total number of string used isn't the unknown variable. The number of meters of string in the third yo-yo is the only number that isn't. This makes the number of sting used in the third yo-yo the unknown variable, making it y.

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3 years ago

If f(x) = 5x − 3, which expression represents its inverse function?

tangare [24]

Answer:

$f ^{-1}(x)=\frac{x+3}{5}$

Step-by-step explanation:

To find the inverse of a function f (x) follow the steps below:

1) Make y = f (x)

$y= 5x - 3$

2) Solve for the variable x

$y+3= 5x - 3+3$

$y+3= 5x$

$x=\frac{y+3}{5}$

3) Exchange the variable x with the variable y

$y=\frac{x+3}{5}$

4) Make $y = f ^{-1}(x)$

$f ^{-1}(x)=\frac{x+3}{5}$

Finally, the inverse of the function f (x) is: $f ^{-1}(x)=\frac{x+3}{5}$

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3 years ago

Mr. Harris is packaging items to give to his students. He has 48 pencils and 30 notebooks. He wants each package to contain the

guapka [62]

Answer:

The maximum number of packages that can be made with each package have same number of each item is = 6

Step-by-step explanation:

Given:

Mr. Harris has 48 pencils and 30 notebooks.

To find the number of packages he can make with each package have same number of each item.

Solution:

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Number of notebooks = 30

In order to find the number of packages he can make with each package have same number of each item, we will find the greatest common factor of the given numbers.

To find the G.C.F., we will list down the prime factors of each.

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We find that the G.C.F. = $2\times 3$ = 6

Thus, the maximum number of packages that can be made with each package have same number of each item is = 6

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