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3 years ago

What is the value of a+b?

Mathematics

1 answer:

MissTica3 years ago

6 0

Answer:

125

Step-by-step explanation:

$a = \frac{1}{2} \times 90 \degree \\ \\ a = 45 \degree \\ \\ b =\frac{1}{2} (360\degree - 200\degree) \\ \\ b = 80\degree \\ \\ a + b = 45 + 80 \\ \\ a + b = 125 \degree$

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3 years ago

Solve the proportion = 2x+? 2x+2 for x.

bonufazy [111]

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3 years ago

Simplify the following surds : 1) 2√21 × √27 ÷ √343 2) 7√5 × √125 ÷ 2√27

ludmilkaskok [199]

Answer:

1) $\frac{18}{7}$

2) $\frac{175\sqrt{3}}{18}$

Step-by-step explanation:

* Lets explain how to simplify a square root

∵ $2\sqrt{21}$ × $\sqrt{27}$ ÷ $\sqrt{343}$

∵ $\sqrt{21}=\sqrt{3}$ × $\sqrt{7}$

∴ $2\sqrt{21}$ = $2\sqrt{3}$ × $\sqrt{7}$

∵ $\sqrt{27}$ = $\sqrt{3}$ × $\sqrt{3}$ × $\sqrt{3}$

∵ $\sqrt{3}$ × $\sqrt{3}$ = 3

∴ $\sqrt{27}$ = $3\sqrt{3}$

∴ $2\sqrt{21}$ × $\sqrt{27}$ =

$2\sqrt{3}$ × $\sqrt{7}$ × $3\sqrt{3}$

∵ $\sqrt{3}$ × $\sqrt{3}$ = 3

∵ 2 × 3 × 3 = 18

∴ $2\sqrt{21}$ × $\sqrt{27}$ = $18\sqrt{7}$

∵ $\sqrt{343}$ = $\sqrt{7}$ × $\sqrt{7}$ × $\sqrt{7}$

∵ $\sqrt{7}$ × $\sqrt{7}$ = 7

∴ $\sqrt{343}$ = $7\sqrt{7}$

∵ $2\sqrt{21}$ × $\sqrt{27}$ ÷ $\sqrt{343}$ =

$18\sqrt{7}$ ÷ $7\sqrt{7}$

∵ $\sqrt{7}$ ÷ $\sqrt{7}$ = 1

∴ $2\sqrt{21}$ × $\sqrt{27}$ ÷ $\sqrt{343}$ =

$\frac{18}{7}$

∵ $7\sqrt{5}$ × $\sqrt{125}$ ÷ $2\sqrt{27}$

∵ $\sqrt{125}$ = $\sqrt{5}$ × $\sqrt{5}$ × $\sqrt{5}$

∵ $\sqrt{5}$ × $\sqrt{5}$ = 5

∴ $\sqrt{125}$ = $5\sqrt{5}$

∴ $7\sqrt{5}$ × $\sqrt{125}$ =

$7\sqrt{5}$ × $5\sqrt{5}$

∵ $\sqrt{5}$ × $\sqrt{5}$ = 5

∴ $7\sqrt{5}$ × $\sqrt{125}$ = 7 × 5 × 5 = 175

∵ $2\sqrt{27}$ = $2\sqrt{3}$ × $\sqrt{3}$ × $\sqrt{3}$

∵ $\sqrt{3}$ × $\sqrt{3}$ = 3

∴ $2\sqrt{27}$ = $6\sqrt{3}$

∴ $7\sqrt{5}$ × $\sqrt{125}$ ÷ $2\sqrt{27}$ =

175 ÷ $6\sqrt{3}$ = $\frac{175}{6\sqrt{3}}$

∵ $\frac{175}{6\sqrt{3}}$ not in the simplest form because

the denominator has square root

∴ Multiply up and down by $\sqrt{3}$

∴ $\frac{175}{6\sqrt{3}}$ = $\frac{175\sqrt{3}}{6\sqrt{3}*\sqrt{3}}$

∴ $\frac{175}{6\sqrt{3}}$ = $\frac{175\sqrt{3}}{18}$

∴ $7\sqrt{5}$ × $\sqrt{125}$ ÷ $2\sqrt{27}$ =

$\frac{175\sqrt{3}}{18}$

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3 years ago

Solve the equation below. Show all your steps 5x−8=17

skelet666 [1.2K]

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kotykmax [81]

Answer:

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4 years ago

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