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4 years ago

Solve for a.5a−5−15=3a+6+4

Mathematics

1 answer:

taurus [48]4 years ago

5 0

Answer:

Step-by-step explanation:

5a - 5 - 15 = 3a + 6 + 4 combine like terms

5a + (-5 - 15) = 3a + (6 + 4)

5a - 20 = 3a + 10 add 20 to both sides

5a = 3a + 30 subtract 3a from both sides

2a = 30 divide both sides by 2

a = 15

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6 ( p + 6 ) − 3 ( p + 3 )

MAXImum [283]

Answer:

3p +27

Step-by-step explanation:

6( p+6) - 3(p+3)

Distribute

6p +36 - 3p -9

Combine like terms

6p -3p +36-9

3p +27

4 0

3 years ago

Read 2 more answers

A ball is thrown vertically upwards from the ground. It rises to a height of 10m and then falls and bounces. After each bounce,

Citrus2011 [14]

${\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}$

(i)

$\sf{a_n = 20 \times {( \frac{2}{3} )}^{n - 1} }$

(ii)

$\sf S_n = 60 \{1 - { \frac{2}{3}}^{n} \}$

Step-by-step explanation:

$\underline\red{\textsf{Given :-}}$

height of ball (a) = 10m

fraction of height decreases by each bounce (r) = 2/3

$\underline\pink{\textsf{Solution :-}}$

(i) We will use here geometric progression formula to find height an times

${\blue{\sf{a_n = a {r}^{n - 1} }}} \\ \sf{a_n = 20 \times { \frac{2}{3} }^{n - 1} }$

(ii) here we will use the sum formula of geometric progression for finding the total nth impact

$\orange {\sf{S_n = a \times \frac{(1 - {r}^{n} )}{1 - r} }} \\ \sf S_n = 20 \times \frac{1 - ( { \frac{2}{3} })^{n} }{1 - \frac{2}{3} } \\ \sf S_n = 20 \times \frac{1 - {( \frac{2}{3}) }^{n} }{ \frac{1}{3} } \\ \sf S_n = 3 \times 20 \times \{1 - ( { \frac{2}{3}) }^{n} \} \\ \purple{\sf S_n = 60 \{1 - { \frac{2}{3} }^{n} \}}$

4 0

2 years ago

For a science report, Doug is measuring widths of mushrooms with a ruler that divides inches as shown. To determine each width,

Serga [27]

From the 3 options listed, both $5.25$ in and $6.5$ in could be measures found using a ruler with eighth inches marked, because those decimals can be written in terms of eighth fractions.

$5.25 $in $ \rightarrow (5 + 0.25) $in $ \rightarrow (5 + \frac{2}{8} ) $in$ \\ 
6.5 $in $ \rightarrow (6 + 0.5) $in $ \rightarrow (5 + \frac{4}{8} ) $in$$

The other option, $7.1$ in, is not a possibility because 0.1 cannot be written as a fraction of 8 that is marked on the ruler.