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2 years ago

14

Ian earns x dollars a month. He received a 10% raise in his paycheck. Which expression represents Ian’s new monthly paycheck?

1 answer:

Citrus2011 [14]2 years ago

8 0

Paycheck is 10%

The expression is

$\\ \rm\Rrightarrow x+(1+0.10)x$

$\\ \rm\Rrightarrow x+1.10x$

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Associative Property of Addition to enter an equivalent expression. 5 + (a + b)

Lynna [10]

Step-by-step explanation:

=a+b+5 this is the answer

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3 years ago

A basketball player made 36 free throws in 16 games. Find the ratio of free throws to games.

andriy [413]

Any ratio simply takes the form (A/B)

Let throws = T , games = G

T = 36

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4 years ago

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The 4th and the last terms of an A.P. are 11 and 89 respectively. If there are 30 terms in the A.P., find the A.P. and its 23rd

Natali5045456 [20]

$\underline{\underline{\large\bf{Given:-}}}$

$\red{\leadsto}\:$ $\textsf{}$ $\sf Number \: of \:terms \: in \: A.P,n = 30$

$\red{\leadsto}\:$ $\textsf{}$ $\sf Fourth \: term ,a_4 = 11$

$\red{\leadsto}\:$ $\textsf{}$ $\sf last\:term, a_{30} = 89$

$\underline{\underline{\large\bf{To Find:-}}}$

$\orange{\leadsto}\:$ $\textsf{ }$ $\sf The \: A.P.$

$\orange{\leadsto}\:$ $\textsf{ }$ $\sf 23rd\: term, a_{23}$

$\\$

$\underline{\underline{\large\bf{Solution:-}}}\\$

The nth term of A.P is determined by the formula-

$\green{ \underline { \boxed{ \sf{a_n = a+(n-1)d}}}}$

where

$\sf a = first \:term$
$\sf a_n = nth \: term$
$\sf n = number \:of \:terms$
$\sf d = common \: difference$

Since ,

$\sf a_4 = 11$

$\longrightarrow$ $\sf a+(4-1) d= 11$

$\longrightarrow$ $\sf a+3d= 11\_\_\_(1)$

$\sf a_{30}= 89$

$\longrightarrow$ $\sf a+(30-1)d=89$

$\longrightarrow$ $\sf a+29d= 89\_\_\_(2)$

<u>Subtracting equation (1) from equation(2)</u>

$\begin{gathered}\\\implies\quad \sf a+29d-(a+3d) = 89-11 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a+29d-a-3d = 78 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a-a+29d-3d = 78 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 26d = 78 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf d = \frac{78}{26} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf d = 3 \\\end{gathered}$

Putting the value of d in equation (1) -

$\begin{gathered}\\\implies\quad \sf a+3(3) = 11 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a = 11-9 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a = 2 \\\end{gathered}$

First term of A.P, a = 2

Second term of A.P., $\sf a_2= 2+(2-1)\times 3$

$\quad\quad\quad\sf =2+3$

$\quad\quad\quad\sf =5$

Third term of A.P., $\sf a_3= 2+(3-1)\times 3$

$\quad\quad\quad\sf =2+6$

$\quad\quad\quad\sf =8$

$\longrightarrow$ Thus , The A.P is 2,5,8,. . . . . .

<u>Now,</u>

$\begin{gathered}\\\implies\quad \sf a_n = a+(n-1)d \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a_{23 }= 2+(23-1)\times 3 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a_{23} = 2+22 \times 3 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a_{23} = 2+66 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a_{23} = 68 \\\end{gathered}$

$\longrightarrow$ Thus , 23rd term is 68.

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3 years ago

Which ordered pair is a solution of the equation? − 4 x + 7 = 2 y − 3 −4x+7=2y−3

Maru [420]

Answer:

The equation is

−4x+7=2y−3

Which can be rewritten as

2y−3 = -4x +7

2y = -4x + 10

y = -2x + 5

The equation represents the line shown in the image below.

Any point that belongs to the line is an ordered pair that represents a solution

To find any ordered pair that satisfies the equation, we place an arbitrary value for x and find the corresponding y value with the equation.

For example

x = 0 ,

y = -2(0) + 5 = 5

(0,5) is an ordered pair

x = 1 ,

y = -2(1) + 5 = 3

(1,3) is an ordered pair

x = 2 ,

y = -2(2) + 5 = 1

(2,1) is an ordered pair

And so on

6 0

3 years ago