All categories

3 years ago

What is the product of a,b, and c?

Mathematics

1 answer:

Yuri [45]3 years ago

6 0

Answer:

$abc = - \frac{16}{3}$

Step-by-step explanation:

${x}^{ - 2} {y}^{3} \sqrt[3]{ 64{x}^{5} {y}^{3} } = a {x}^{b} {y}^{c} \\ \\ {x}^{ - 2} {y}^{3} \times 4 \times {x}^{ \frac{5}{3} } \times y= a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5}{3} - 2 } {y}^{3 + 1} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5 - 6}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{ - 1}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ a = 4 \\ \\ b = - \frac{1}{3} \\ \\ c = 4 \\ \\ abc = 4 \times ( - \frac{1}{3} ) \times 4 \\ \\ = 16 \times ( - \frac{1}{3} ) \\ \\ abc = - \frac{16}{3}$

You might be interested in

Layla read 1 book in 4 months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTIO

kirza4 [7]

Answer:

1/4

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Solve x2 + 14x = −24 by completing the square.

Aleks04 [339]

Option A

The solution set of the equation is {-12, -2}

<h3><u>Solution:</u></h3>

Given equation is:

$x^2 + 14x = -24$

We have to find the solution set of this equation by completing the square

First, rearrange the equation so that only zero will be on the right side:

$x^2 + 14x + 24 = 0$ ----- eqn 1

<em><u>The general form of quadratic equation is:</u></em>

$ax^2 + bx + c = 0$ where $a \neq 0$

On comparing the given eqn 1 with general quadratic equation, we get

a = 1

b = 14

c = 24

In completing the square, we take half of coefficient of middle term "x" and then square it. Then we add it on both sides of the equation

So to complete the square, add $(\frac{b}{2})^2$ to both sides of the equation

$x^2 + 14x + 24 + (\frac{14}{2})^2 = (\frac{14}{2})^2$

$x^2 + 14x + 24 + 7^2 = 7^2\\\\x^2 + 14x + 24 + 49 = 49$

$x^2 + 14x + 24 + 49 = 49\\\\x^2 + 14x + 49 = 49 - 24\\\\x^2 + 14x + 49 = 25\\\\(x + 7)(x + 7) = 25\\\\(x + 7)^2 = 25$

Take square root on both sides

$x + 7 = \sqrt{25}$

$x+7=\pm 5$

Now make two equations

x + 7 = + 5 and x + 7 = -5

x = +5 - 7 = -2

x = -2

And,

x + 7 = -5

x = -5 - 7 = -12

x = -12

Therefore, the solution set of the equation is {-12, -2} and option A is correct

6 0

3 years ago

Read 2 more answers

What is an equation of the line that passes through the point (6,1) and is perpendicular to the line 2x+3y=18?

Rudiy27

Answer

y = 3/2x -8

Step-by-step explanation:

The first thing you should do is change the equation into slope intercept form. Subtract 2x from both sides to get: 3y = -2x + 18. Divide all parts of the equation by 3 to get your equation in slope intercept: y = -2/3x + 6. One thing you should know when finding the slope of a perpendicular line is that it is the opposite reciprocal. So, the slope is going to be 3/2. This is your current equation: y = 3/2x + b. Plug in the point to the equation, it should look like this: 1 = 3/2(6) + b. Multiply 3/2 by 6 to get 9. This is what it should look like: 1 = 9 + b. Then, subtract 9 from both sides of the equation to get your y-intercept of -8. Go back to your other equation and plug in -8 for b. This is your final equation: y = 3/2x -8.

3 0

3 years ago

Which value cannot represent the probability of an event occurring? StartFraction 1 over 100 EndFraction 0. 29 85% Three-half.

Serjik [45]

Every value{0.01, 0.29, 85%} can represent the probability of an event occurring except option d that is 1.5.

Given to us,

a.) $\dfrac{1}{100}$

b.) 0.29

c.) 85%

d.) $\dfrac{3}{2}$

The probability help us to know about the probability of specific events occurring.

For a sure event, the probability is always 1,

while for an event that will never happen the probability is always 0.

Thus, probability(p), $\bold{1 \geq p\geq 0}$ .

Now looking at the options,

a.) $\dfrac{1}{100}$ = 0.01

b.) 0.29

c.) 85% = 0.85

d.) $\dfrac{3}{2}$ = 1.5

Now comparing each option with $\bold{1 \geq p\geq 0}$ .

Therefore, the only option which is not feasible is option d that is 1.5.

Hence, every value{0.01, 0.29, 85%} can represent the probability of an event occurring except option d that is 1.5.

To know more visit:

brainly.com/question/795909

3 0

2 years ago

Read 2 more answers

What is the equation of the line (in slope-intercept form) that passes through the given point and is

Otrada [13]

keeping in mind that perpendicular lines have negative reciprocal slopes, hmmmm what's the slope of the equation above anyway?

$\bf x+y=6\implies y = \stackrel{\stackrel{m}{\downarrow }}{-1}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{-1}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{1}\implies 1}}$

so we're really looking for the equation of a line whose slope is 1 and runs through (-5,-6).

$\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-6})~\hspace{10em} \stackrel{slope}{m}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{1}[x-\stackrel{x_1}{(-5)}] \\\\\\ y+6=1(x+5)\implies y+6=x+5\implies y=x-1$

6 0

3 years ago