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4 years ago

Can someone give me the answer and explain plz

Mathematics

2 answers:

Bezzdna [24]4 years ago

5 0

Answer:

$\boxed{\sf - ({x}^{2} + 9x + 9 )}$

Step-by-step explanation:

$\sf Simplify \: the \: following: \\ \sf \implies - 2(4 {x}^{2} + 6) + (7 {x}^{2} - 9x + 3) \\ \\ \sf - 2(4 {x}^{2} + 6) = - 8 {x}^{2} - 12 : \\ \sf \implies - 8 {x}^{2} - 12 + 7 {x}^{2} - 9x + 3 \\ \\ \sf Grouping \: like \: terms : \\ \sf \implies ( - 8 {x}^{2} + 7 {x}^{2} ) - 9x + ( - 12 + 3) \\ \\ \sf 7{x}^{2} - 8 {x}^{2} = - {x}^{2} : \\ \sf \implies - {x}^{2} - 9x + ( - 12 + 3) \\ \\ \sf 3 - 12 = - 9 : \sf \implies - {x}^{2} - 9x - 9 \\ \\ \sf Factor \: - 1 \: out \: of \: - {x}^{2} - 9x - 9: \\ \sf \implies - ({x}^{2} + 9x + 9 )$

s2008m [1.1K]4 years ago

5 0

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{ - {x}^{2} - 9x - 9}}}}}$

Step-by-step explanation:

$\sf{ - 2(4 {x}^{2} + 6) + (7 {x}^{2} - 9x + 3)}$

When there is a ( + ) in front of an expression in parentheses, there is no need to change the sign of each term in the expression. That means, the expression remains the same. Also, remove the unnecessary parentheses

⇒ ${ \sf{ - 2(4 {x}^{2} + 6) + 7 {x}^{2} - 9x + 3}}$

Distribute -2 through the parentheses

⇒ $\sf{ - 2 \times 4 {x}^{2} + ( - 2) \times 6 + 7 {x}^{2} - 9x + 3}$

⇒ $\sf{ - 8 {x}^{2} + ( - 12) + 7 {x}^{2} - 9x + 3}$

We know that , $\sf{( + ) \times ( - ) = ( - )}$

⇒ $\sf{ - 8 {x}^{2} - 12 + 7 {x}^{2} - 9x + 3}$

Collect like terms

⇒ $\sf{ - 8 {x}^{2} + 7 {x}^{2} - 9x - 12 + 3}$

The negative and positive terms / integer are always subtracted but possess the sign of the bigger term / integer

⇒ $\sf{ - {x}^{2} - 9x - 12 + 3}$

Subtract 3 from 12

⇒ $\sf{ - {x}^{2} - 9x - 9}$

Hope I helped!

Best regards! :D

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Percentage of the votes did John got overall is 25 %

Solution:

Given, Vivenne, John and nassim ran for 6th grade class president.

Vivenne got four votes for every 3 votes that John got.

Nassim got two votes for every vote that Vivenne got.

Now, ratio of vivenne votes to john votes = 4 : 3

a : b can be written in fraction as $\frac{a}{b}$

$\rightarrow \frac{\text {vivenne votes}}{\text {john votes}}=\frac{4}{3} \rightarrow(1)$

Now, ratio of nassim votes to vivenne votes = 2 : 1

$\rightarrow \frac{\text {nassim votes}}{\text {vivenne votes}}=\frac{2}{1} \rightarrow(2)$

Now, multiply the above two fractions,

$\begin{array}{l}{\rightarrow \frac{\text {vivenne votes}}{\text {john votes}} \times \frac{\text {nassim votes}}{\text {vivenne votes}}=\frac{4}{3} \times \frac{2}{1}} \\\\ {\rightarrow \frac{\text {nassim votes}}{\text {john votes}}=\frac{8}{3} \rightarrow(3)}\end{array}$

Now, add (1) and (3),

$\begin{array}{l}{\rightarrow \frac{\text {vivenne votes}}{\text {john votes}}+\frac{\text {nassim votes}}{\text {john votes}}=\frac{4}{3}+\frac{\mathrm{s}}{3}} \\\\ {\rightarrow \frac{\text {vivenne votes+nassim votes}}{\text {john votes}}=\frac{4+8}{3}}\end{array}$

We know that total votes = vivenne votes+nassim votes+john votes

Hence substitute "vivenne votes+nassim votes = total votes - john votes "

Hence we get,

$\begin{array}{l}{\rightarrow \frac{\text {total votes}-\text {john votes}}{\text {john votes}}=\frac{12}{3}} \\\\ {\rightarrow \frac{\text {total votes}}{\text {john votes}}-\frac{\text {john votes}}{\text {john votes}}=4} \\\\ {\rightarrow \frac{\text {total votes}}{\text {john votes}}-1=4} \\\\ {\rightarrow \frac{\text {total votes}}{\text {john votes}}=5} \\\\ {\rightarrow \frac{\text {john votes}}{\text {total votes}}=\frac{1}{5}}\end{array}$

Multiplying 100 on both sides,

$\rightarrow \frac{\text {john votes}}{\text {total votes}} \times 100=\frac{1}{5} \times 100$

The above expression is the formula used to calculate John vote percentage

Hence John votes percentage = 25%

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