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Varvara68 [4.7K]

3 years ago

15

at its highest point, the elevation of a city is 5791 ft above sea level. At its lowest point, the elevation of another city is

6 ft below sea level. Find the difference

1 answer:

Nat2105 [25]3 years ago

8 0

5785 feet between the top and sea level hope this helps

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The numerator of a fraction is 15 less than twice its denominator. If the numerator is increased by 5 and the denominator is inc

denis-greek [22]

Answer:

7/11

Step-by-step explanation:

Let d represent the original denominator. Then the original numerator is ...

2d-15

The new numerator is ...

(2d-15) +5

and the new denominator is ...

d+7

The ratio of these is 2/3, so we have ...

$\dfrac{2d-15+5}{d+7}=\dfrac{2}{3}\\\\3(2d-10)=2(d+7) \quad\text{cross multiply}\\\\4d=44 \quad\text{add 30-2d}\\\\d=11\\\\2d-15=2(11)-15=7$

The original fraction is 7/11.

7 0

3 years ago

What is the area of this composite

padilas [110]

Step-by-step explanation:

It's 27

Your welcome!!!!

6 0

4 years ago

Which expression is equivalent to <img src="https://tex.z-dn.net/?f=%20-3%5E%7B-4%7D%20" id="TexFormula1" title=" -3^{-4} " alt=

galben [10]

I'm back lol

-3^(-4) = -(1/3)^4 = -1/81

5 0

3 years ago

Read 2 more answers

Help me simplify this

stepan [7]

Do you want the whole solution simplified or the alternative form?

5 0

3 years ago

Can anyone help me out with this?

bogdanovich [222]

${\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}$

$\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}$

$\bullet \sf \: {(a + b)}^{ab}$

<u>Putting value of a as 3 and b as -2, we get</u><u> </u><u>:</u>

$\longrightarrow \sf \: {( 3 + (- 2))}^{3 \times - 2}$

$\longrightarrow \sf \: {( 3 - 2)}^{3 \times - 2}$

$\longrightarrow \sf \: {( 1)}^{ - 6}$

• <u>Using negative Exponents Law</u>

$\longrightarrow \sf \dfrac{1}{ {1}^{6} }$

$\longrightarrow \sf \dfrac{1}{ 1 \times 1 \times 1 \times 1 \times 1 \times 1 }$

$\longrightarrow \sf \dfrac{1}{ 1 }$

$\longrightarrow \sf \purple{1}$

${\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}$

$\star\:{\underline{\underline{\sf{\red{Solution:}}}}}$

$\bullet \sf \: \dfrac{ {8}^{ - 1} \times {5}^{3} }{ {2}^{ - 4}}$

$\longrightarrow \sf \: {8}^{ - 1} \times {5}^{3} \times \dfrac{1}{{2}^{ - 4}}$

<u>• Using negative Exponents Law</u>

$\longrightarrow \sf \: {8}^{ - 1} \times {5}^{3} \times {2}^{4}$

$\longrightarrow \sf \: {8}^{ - 1} \times 5 \times 5 \times 5 \times {2}^{4}$

$\longrightarrow \sf \: {8}^{ - 1} \times 125 \times {2}^{4}$

$\longrightarrow \sf \: {8}^{ - 1} \times 125 \times 2 \times 2 \times 2 \times 2$

<u>• Using negative Exponents Law</u>

$\longrightarrow \sf \: \dfrac{1}{ \cancel{8}_{4}} \times 125 \times \cancel{2}_{1} \times 2 \times 2 \times 2$

$\longrightarrow \sf \: \dfrac{1}{ \cancel4_{2}} \times 125 \times \cancel{2}_{1} \times 2 \times 2$

$\longrightarrow \sf \: \dfrac{1}{ \cancel2} \times 125 \times \cancel{2} \times 2$

$\longrightarrow \sf \: 125 \times 2$

$\longrightarrow \sf \red{ 250}$

${\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}$

$\star\:{\underline{\underline{\sf{\green{Solution(1):}}}}}$

$\bullet \sf \dfrac{ \sqrt{32} + \sqrt{48} }{ \sqrt{8} + \sqrt{12} }$

$\longrightarrow \sf \dfrac{ \sqrt{4 \times 4 \times 2} + \sqrt{4 \times 4 \times 3} }{ \sqrt{2 \times 2 \times 2} + \sqrt{2 \times 2 \times 3} }$

$\longrightarrow \sf \dfrac{ \sqrt{ {4}^{2} \times 2} + \sqrt{ {4}^{2} \times 3} }{ \sqrt{ {2}^{2} \times 2} + \sqrt{ {2}^{2} \times 3} }$

$\longrightarrow \sf \dfrac{ 4\sqrt{ 2} + 4 \sqrt{ 3} }{ 2\sqrt{ 2} +2 \sqrt{ 3} }$

$\longrightarrow \sf \dfrac{ \cancel{ 4}_{2}(\sqrt{ 2} + \sqrt{ 3}) }{ \cancel{2}(\sqrt{ 2} + \sqrt{ 3}) }$

$\longrightarrow \sf \dfrac{ 2 \: \cancel{(\sqrt{ 2} + \sqrt{ 3}) } }{ \cancel{(\sqrt{ 2} + \sqrt{ 3})} }$

$\longrightarrow \sf \green{2}$

$\star\:{\underline{\underline{\sf{\blue{Solution(2):}}}}}$

$\bullet \sf \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{80} + \sqrt{48} - \sqrt{45} - \sqrt{27} }$

$\begin{gathered} \longrightarrow \sf \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{4 \times 4 \times 5} + \sqrt{4 \times 4 \times 3} - \sqrt{3 \times 3 \times 5} - \sqrt{3 \times 3 \times 3} } \end{gathered}$

$\begin{gathered}\longrightarrow \sf \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{ {4}^{2} \times 5} + \sqrt{ {4}^{2} \times 3} - \sqrt{ {3}^{2} \times 5} - \sqrt{ {3}^{2} \times 3} } \end{gathered}$

$\longrightarrow \sf \dfrac{ \sqrt{5} + \sqrt{3} }{4 \sqrt{ 5} + 4 \sqrt{ 3} - 3\sqrt{ 5} - 3\sqrt{ 3} }$

$\longrightarrow \sf \dfrac{ \sqrt{5} + \sqrt{3} }{4 \sqrt{ 5} - 3\sqrt{ 5} + 4 \sqrt{ 3} - 3\sqrt{ 3} }$

$\longrightarrow \sf \dfrac{ \cancel{ \sqrt{5} + \sqrt{3}} }{ \cancel{\sqrt{ 5} + \sqrt{ 3} } }$

$\longrightarrow \blue{1}$

${\large{\textsf{\textbf{\underline{\underline{Answers :}}}}}}$

• Question 1 - $\purple{1}$

• Question 2 - $\red{250}$

• Question 3(1) - $\green{2}$

• Question 3(2) - $\blue{1}$

${\large{\textsf{\textbf{\underline{\underline{ Concept \: :}}}}}}$

<u>★</u><u> </u><u>Negative</u><u> Exponents Law -</u>

$\bullet \sf \: {a}^{ - m} = \dfrac{1}{ {a}^{m} }$

★ $\sqrt{32}$ can be written as $4 \sqrt{2}$

‣ $\sqrt{48}$ can be written as $4 \sqrt{3}$

‣ $\sqrt{8}$ can be written as $2 \sqrt{2}$

‣ $\sqrt{12}$ can be written as $2 \sqrt{3}$

‣ $\sqrt{80}$ can be written as $4 \sqrt{5}$

‣ $\sqrt{48}$ can be written as $4 \sqrt{3}$

‣ $\sqrt{45}$ can be written as $3 \sqrt{5}$

‣ $\sqrt{27}$ can be written as $3 \sqrt{3}$

★ <u>During Addition and Subtraction</u>

• minus (-) minus (-) gives plus (+)

• minus (-) plus (+) gives minus (-)

• plus (+) minus (-) gives minus (-)

• plus (+) plus (+) gives plus (+)

• Also the sign of the resultant term depends upon the sign of the largest number.

${\large{\textsf{\textbf{\underline{\underline{ Note \: :}}}}}}$

• Swipe to see the full answer.

$\begin{gathered} {\underline{\rule{330pt}{3pt}}} \end{gathered}$

5 0

2 years ago