Simplify 6th root of 12 divided by product of cubic root of 2 and square root of 3

The volume of a piece of wood is 620cm3. Its density is 0.85g/cm3. Work out its mass

asambeis [7]

Answer:

527 grams

Step-by-step explanation:

Use the density formula, d = m/v

Plug in the density and volume, then solve for m (mass):

d = m/v

0.85 = m/620

527 = m

So, the mass is 527 grams

3 0

2 years ago

Fred walked a trail at 2 mph. Paul started 30 minutes later on the same trail and walked at a pace of 3 mph. Create a system of

spayn [35]

Answer:

$y=2x\\y=3(x-\frac{1}{2})$

Paul will catch Fred after $1\ hours$ at a distance $3\ miles$ .

Step-by-step explanation:

Distance is represented by $y$ and the time is represented by $x$ . Here after $x$ hours(when Fred started) the distance covered by Fred and Paul is same that is $y$ .

For Fred:

time= $x$

distance= $y$

Speed $=2\ mph$

$Distance=speed\times time\\y=2\times x \\y=2x$

Paul:

Since Fred started 30 minutes earlier, so Paul's travel time will be 30 minutes less than that of Fred.

Time $=x-\frac{1}{2}$

Speed $=3\ mph$

Distance $=y\\$

$y=3\times (x-\frac{1}{2})\\y=3(x-\frac{1}{2})$

Hence system of equation

$y=2x\\y=3(x-\frac{1}{2})$

Solution of this system of equations gives the time, when Paul will catch Fred and distance covered by each of them.

$y=2x\\y=3(x-\frac{1}{2})\\\\2x=3x-\frac{3}{2}\\x=\frac{3}{2}\\\\y=2x\\y=2\times \frac{3}{2}\\y=3$

Time taken by Paul $=x-\frac{1}{2}=\frac{3}{2}-\frac{1}{2}=1$

Hence Paul will catch Fred after $1\ hours$ at a distance $3\ miles$ .

3 0

3 years ago

( 7k^8m) ( k^13m^7)÷(14k^20 m^9)

guapka [62]

Answer:

k=9

Step-by-step explanation:

Here's how to solve this equation

Step 1: -7(k+9)=9(k-5)-14k

Step 2: -7k-63=(9k-45)-14k

Step 3: -7k-63=-5k-45

Step 4: -7k=-5k+18

Step 5: -2k=18

Solution: k=-9

Good luck on your assignment, hope this helps

8 0

2 years ago

Which function represents g(x), a reflection of f(x) = On a coordinate plane, 2 exponential functions are shown. g (x) decreases

Vanyuwa [196]

Answer:

$g(x)=\frac{1}{2}(3^{-x})$

Step-by-step explanation:

Given:

The graph of function $f(x)\ and\ g(x)$ are given.

The equation for $f(x)$ is given as:

$f(x)=3^x$

Now, the graph of $g(x)$ is a reflection of $f(x)$ .

The graph of $g(x)$ passes through the point (-1, 1.5) [second quadrant] and crosses the y-axis at (0, 0.5).

As evident from the graph, the functions $f(x)\ and\ g(x)$ are reflections about the y-axis.

We know the transformation rule for reflection about the y-axis as:

$f(x)\to f(-x)\\\\\therefore 3^x\to3^{-x}....(\textrm{Reflection about y-axis})$

Now, the y-intercept of the function $y=3^{-x}$ is obtained by plugging in $x=0$ . This gives,

$y=3^0=1$

So, the y-intercept is at (0, 1). But the graph of $g(x)$ crosses the y-axis at (0, 0.5). As we observe, the coordinate rule for the transformation can be written as:

(0, 1) → (0, 0.5)

$(x,y)\to (x,\frac{1}{2}y)$