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3 years ago

Simplify the radical expression.

Mathematics

1 answer:

tresset_1 [31]3 years ago

5 0

To simplify this fraction, multiply the entire fraction by the conjugate of the denominator. The conjugate of a square root and a number being added to it would be the number subtracted from the square root. In other words, the conjugate of $\sqrt{a} + b$ would be $\sqrt{a} - b$ .

Applying that information to our fraction shown here, the conjugate of the denominator would be $\sqrt{3} - 4$ . We will multiply both the numerator and denominator of our original fraction by this expression to obtain our answer, as shown below.

$\Big(\dfrac{1}{\sqrt{3} + 4}\Big)\Big(\dfrac{\sqrt{3} - 4}{\sqrt{3} - 4}\Big)$

$\dfrac{\sqrt{3} - 4}{3 - 16}$

$\dfrac{4 - \sqrt{3}}{13}$

Our answer is $\boxed{\dfrac{4 - \sqrt{3}}{13}}$ .

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Evaluate x^0+ y^0 for x = 3 and y = 2. 0 1 5 2

stiks02 [169]

Answer:

Step-by-step explanation:

x^0+ y^0

Let x = 3 and y = 2

3^0 + 2^0

Raised to the 0 power is 1

1 + 1

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3 years ago

Determine which of the following logarithms is expanded correctly.

ziro4ka [17]

Answer:

A) log(jk2y = 7log i + 2logk

Step-by-step explanation:

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3 years ago

A baseball is hit and its height is given by h = 29.4t – 4. 9t^2, where h is the

ioda

Answer:

44.1m

Step-by-step explanation:

we are given a quadratic function which represents the height and time of a baseball

$\displaystyle h = 29.4t - 4.9 {t}^{2}$

we want to figure out maximum height of

the baseball

since the given function is a quadratic function so we have a parabola

which means figuring out the maximum height is the same thing as figuring out the maximum y coordinate (vertex)

to do so we can use some special formulas

recall that,

$\displaystyle \rm t= \frac{ - b}{ 2a}$

$\displaystyle H_{\text{max}}=f(t)$

notice that, our given function is not in standard form i.e

$\displaystyle f(x) = a {x}^{2} + bx + c$

let's make it so

$\displaystyle h = - 4.9 {t}^{2} + 29.4t$

therefore we got

our a is -4.9 and b is 29.4

so substitute:

$\displaystyle\rm t= \frac{ -( 29.4)}{ 2 \cdot - 4.9}$

remove parentheses and change its sign:

$\displaystyle\rm t= \frac{ -29.4}{ 2 \cdot - 4.9}$

simplify multiplication:

$\displaystyle\rm t= \frac{ -29.4}{ - 9.8}$

simplify division:

$\displaystyle \: t = 3$

so we have figured out the time when the baseball will reach the maximum height

now we have to figure out the height

to do so

substitute the got value of time to our given function

$\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot {3}^2$

simplify square:

$\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot 9$

simplify mutilation:

$\displaystyle H_{\text{max}}=88.2-44.1$

simplify substraction:

$\displaystyle H_{\text{max}}=44.1$

hence,

the maximum height of the baseball is 44.1 metres

4 0

3 years ago

Read 2 more answers

Scenario: A tiger is running at a speed of 15 miles per hour. It's food , an antelope is 5 miles away running at a speed of 5 mi

alekssr [168]

Oh naw i cant do math

6 0

3 years ago

Using the work shown on the left, What is the cubed root of 4/ the square root of 2 in simplest radical form

krek1111 [17]

Answer:

⁶√2

Step-by-step explanation:

∛4 = (2^2)^1/3 = 2^2/3

So ∛4 / √2

= 2^2/3 / 2^1/2

= 2^1/6

= ⁶√2

5 0

3 years ago