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2 years ago

Solve the formula 27a + 1/3 * b = 4 for a.

Mathematics

2 answers:

Aneli [31]2 years ago

4 0

Answer:

a = 4/27 - b/81

Step-by-step explanation:

27a + 1/3 * b = 4

Subtract the term with b from both sides.

27a = 4 - 1/3 *b

Divide both sides by 27.

a = 4/27 - 1/81 * b

a = 4/27 - b/81

Afina-wow [57]2 years ago

4 0

Answer:

$\large\boxed{a=\dfrac{12-b}{81}}$

Step-by-step explanation:

$27a+\dfrac{1}{3}b=4\qquad\text{multiply both sides by 3}\\\\(3)(27a)+3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}b=(3)(4)\\\\81a+b=12\qquad\text{subtract}\ b\ \text{from both sides}\\\\81a=12-b\qquad\text{divide both sides b 81}\\\\a=\dfrac{12-b}{81}$

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2 years ago

Read 2 more answers

Inessa ran 3 laps in 8 minutes. How long would it take her to run 10 laps at this pace? (This is proportions)

Degger [83]

Answer:

26.6 minutes

Step-by-step explanation:

Set up a proportion

3/8 = 10/x

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3 years ago

Five less than a number Y is under 20

vodomira [7]

Answer:

Y - 5 < 20

Step-by-step explanation:

5 less than Y translates to:

Y - 5

Under 20 translates to:

< 20

Therefore your answer is

Y - 5 < 20

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2 years ago

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Prove the divisibility:<br><br>45^45·15^15 by 75^30

garri49 [273]

Answer:

$3^{75}$ .

Step-by-step explanation:

We have been an division problem: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(9*5)^{45}=9^{45}*5^{45}$

$15^{15}=(3*5)^{15}=3^{15}*5^{15}$

$75^{30}=(15*5)^{30}=15^{30}*5^{30}$

Substituting these values in our division problem we will get,

$\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}$

$\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}$

$\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}$

$\frac{3^{105}*5^{60}}{3^{30}*5^{60}}$

$\frac{3^{105}}{3^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{105}}{3^{30}}=3^{105-30}$

$3^{105-30}=3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

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3 years ago

Afan pays $875 for 3 premium seat tickets. Another fan pays $2125 for 8 premium seat tickets. Write a linear model for the cost

grandymaker [24]

The equation is : C=250t +125 where C is the cost and t represent the number of tickets purchased.

Step-by-step explanation:

Let the cost of premium seat ticket be C

Let the number of tickets a fan buys to be t

Then, presenting the information as ordered pairs of coordinates (x,y) will be;

Fan 1, (3,875)

Fan 2, (8,2125)

Plot the ordered pairs as coordinates on a graph tool, find the slope of the linear graph and equation in slope intercept form as;

m=Δy/Δx

m=2125-875/8-3

m=1250/5

m=250

Equation of the graph,

Δy/Δx=250

y-875/x-3 =250

y-875=250(x-3)

y-875=250x-750

y=250x-750+875

y=250x+125

C=250t +125 where C is the cost and t represent the number of tickets purchased

Learn More

Slope-intercept form equation: brainly.com/question/11016508

Keyword : slope-intercept form,cost

#LearnwithBrainly

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3 years ago