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3 years ago

Rearrange w= 3(2a + b) - 4 to make a the subject

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

8 0

Answer:

$\boxed{a = \frac{w}{ 6} - \frac{b}{2} + \frac{2}{3} }$

Step-by-step explanation:

$Solve \: for \: a: \\ = > w=3(2a+b)-4 \\ \\ w=3(2a+b)4 \: is \: equivalent \: to \: 3(2a+b)-4= w: \\ = > 3(2a+b) - 4=w \\ \\ Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ = > (3 \times 2a) + (3 \times b) - 4 = w \\ = > 6a+3b - 4=w \\ \\ Subtract \: 3b - 4 \: from \: both \: sides: \\ = > 6a + 3b - 4 - (3b - 4)=w - (3b - 4) \\ = > 6a = w - 3b + 4 \\ \\ Divide \: both \: sides \: by \: 6: \\ = > \frac{ \cancel{6}a}{ \cancel{6}} = \frac{w - 3b + 4}{6} \\ = > a = \frac{w}{6} - \frac{3b}{6} + \frac{4}{6} \\ = > a = \frac{w}{ 6} - \frac{b}{2} + \frac{2}{3}$

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3 years ago

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If you know the names of the remaining nine students in the spelling bee, what is the probability of randomly selecting an orde

rjkz [21]

The probability of getting the correct order in the spelling bee is 1 chance in 362,880.

This is a permutation problem. Our goals is to find the total number of ways that the 9 students can be ordered.

For the first spot there are 9 choices, then 8 choices, then 7 choices....

We need to evaluate:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

Another way to write this is: 9!

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3 years ago

The height of a trapezoid can be expressed as x – 4, while the bases can be expressed as x + 4 and x + 9. if the area of the tra

AlexFokin [52]

Answer: 19 cm

<u>Step-by-step explanation:</u>

$A_{trapezoid}=\frac{b_{1}+b_{2}}{2}*h$

99 = $\frac{(x+4 + x+9}{2}*(x - 4)$

99 = $\frac{(2x + 13}{2}*(x - 4)$

198 = (2x + 13)(x - 4)

198 = 2x² + 5x - 52

0 = 2x² + 5x - 250

0 = 2x²- 20x + 25x - 250

0 = 2x(x - 10) + 25( x - 10)

0 = (2x + 25)(x - 10)

0 = 2x + 25 or 0 = x - 10

$-\frac{25}{2}$ = x or x = 10

Since length cannot be negative, $-\frac{25}{2}$ can be disregarded

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3 years ago

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What is 22.5% written as a fraction in simplest form?

murzikaleks [220]

Answer:

9/40

Step-by-step explanation:

Write down the percent divided by 100 like this:

22.5/100

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As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,

(22.5*10)(100*10)= 225/1000

Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(225,1000) = 25.

225 ÷ 25/ 1000÷25 = 9/40

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3 years ago

Find 10 partial sums of the series. (round your answers to five decimal places.) ∞ 15 (−4)n n = 1

nikklg [1K]

Given

$\Sigma_{n=1}^\infty15(-4)^n$

The first 10 partial sums are as follows:

$S_1=\Sigma_{n=1}^{1}15(-4)^n=15(-4)=\bold{-60} \\ \\ S_2=\Sigma_{n=1}^{2}15(-4)^n=\Sigma_{n=1}^{1}15(-4)^n+15(-4)^2 \\ =-60+15(16)=-60+240=\bold{180} \\ \\ S_3=\Sigma_{n=1}^{3}15(-4)^n=\Sigma_{n=1}^{2}15(-4)^n+15(-4)^3 \\ =180+15(-64)=180-960=\bold{-780} \\ \\ S_4=\Sigma_{n=1}^{4}15(-4)^n=\Sigma_{n=1}^{3}15(-4)^n+15(-4)^4 \\ =-780+15(256)=-780+3,840=\bold{3,060} \\ \\ S_5=\Sigma_{n=1}^{5}15(-4)^n=\Sigma_{n=1}^{4}15(-4)^n+15(-4)^5 \\ =3,060+15(-1,024)=3,060-15,360=\bold{-12,300}$

$S_6=\Sigma_{n=1}^{6}15(-4)^n=\Sigma_{n=1}^{5}15(-4)^n+15(-4)^6 \\ =-12,300+15(4,096)=-12,300+61,440=\bold{49,140}$

The rest of the partial sums can be obtained in similar way.

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3 years ago