What is the degree of 10a^5b^4

Emma starts at one end of a 45-mile-long bike trail. After

aleksley [76]

Answer:

She has already reached the end of the trail.

Step-by-step explanation:

216 is a greater number than 45 miles

8 0

3 years ago

Veronica works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20

MArishka [77]

<u>Answer:</u>

The range of the amount Veronica makes each hour if she can only work a total of 8 hours is 20 ≤ x ≤ 29.55

<u>Solution: </u>

Let us assume that Veronica worked x hours

The starting pay is $\$20$

Each hour increase is $5\%$

So the function is $f(x)=20(1.05)^{x}$

Now if she works 8 hours, she will earn, $= 20(1.05)^8$

$\Rightarrow 20\times1.477 = 29.55$

So, the range will be 20 ≤ x ≤ 29.55

4 0

4 years ago

If √3 = 1.732, then √[(√3-1)/(√3+1)] is equal to

adelina 88 [10]

Step-by-step explanation:

<h3><u>Given Question :-</u></h3>

$\sf \: \sqrt{3} = 1.732, \: then \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} }$

$\red{\large\underline{\sf{Solution-}}}$

Given expression is

$\rm :\longmapsto\: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} }$

<em>On rationalizing the denominator, we get </em>

$\rm \: = \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \dfrac{ \sqrt{3} - 1}{ \sqrt{3} - 1} }$

$\rm \: = \: \sqrt{\dfrac{ {( \sqrt{3} - 1)}^{2} }{( \sqrt{3} + 1)( \sqrt{3} - 1)} }$

$\boxed{ \tt \: (x - y)(x + y) = {x}^{2} - {y}^{2} \: }$

<em>So, using this, we get </em>

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{ {( \sqrt{3})}^{2} - {(1)}^{2} } }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{ 3 - 1} }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{2} } \times \dfrac{ \sqrt{2} }{ \sqrt{2} }$

$\rm \: = \: \dfrac{(1.732 - 1) \sqrt{2} }{2}$

$\rm \: = \: \dfrac{0.732 \times \sqrt{2} }{2}$

$\rm \: = \: 0.366 \sqrt{2}$

Hence,

$\rm :\longmapsto\: \boxed{ \rm{ \: \: \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} } = 0.366 \sqrt{2} \: \: \: }}$

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<h2>More Identities to know :- </h2>

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)² = (a - b)² + 4ab

(a - b)² = (a + b)² - 4ab

(a + b)² + (a - b)² = 2(a² + b²)

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)

3 0

3 years ago

Need help due tonight v

Yuri [45]

Answer:

number 2

Step-by-step explanation:

from the original equation you can multiple the m to the x's first.

y-y1=mx-mx1

if you moved mx1 to left the sign will change from - to +

so you y- y1+mx1= mx

then to get x

(y- you + mx1 )/ m = x

hope it helps

7 0

3 years ago

What methods do you know that can be used to solve a quadratic equation?

zhuklara [117]

Answer: If the quadratic equation has real, rational solutions, the quickest way to solve it is often to factorise into the form (px + q)(mx + n), where m, n, p and q are integers. This is especially true where the coefficient of x2 is 1.

Example 1 - Solve x2+7x+12=0

Step-by-step explanation:

that's the only one I remember

8 0

3 years ago

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