You start at (3, 0). You move right 1 unit and left 2 units. Where do you end?

A cube has a volume of 512 mm^3. If all sides of the cube are divided by 4, what will the resulting volume be?

pshichka [43]

$\bf \textit{volume of a cube}\\\\
V=s^3\qquad \boxed{s=\frac{s}{4}}\implies V=\left( \cfrac{s}{4} \right)^3\implies V=\cfrac{s^3}{4^3}\implies V=s^3\cdot \cfrac{1}{4^3}
\\\\\\
V=s^3\cdot \cfrac{1}{64}\impliedby \frac{1}{64}\textit{ of the original volume, if the original was 512}
\\\\\\
512\cdot \cfrac{1}{64}\implies \cfrac{512}{64}$

3 0

3 years ago

Professor Turner wrote the expression below on the chalkboard for his team at the Research Center. He asked the scientists there

Lynna [10]

Answer:

12x + 18y + 6z + 4x - 4z

Step-by-step explanation:

Given the expression : 3(4x + 6y + 2z) + 4(x – z)

To eliminate the parenthesis ; we use the distributive property :

3(4x + 6y + 2z) + 4(x – z) becomes ;

3*4x + 3*6y + 3*2z + 4*x + 4*-z

12x + 18y + 6z + 4x - 4z

Hence,

12x + 4x + 18y + 6z - 4z

16x + 18y + 2z

6 0

3 years ago

8.45 At some point in the season, the Unicorns had won 60% of their basketball games. After that point, they won 8 more games an

ololo11 [35]

Answer:

The total number of games won by Unicorn is 40.

Step-by-step explanation:

We are given with a word problem
We are asked to find the number of unicorns played during the season
We can do this in two steps

Step 1: Finding the win percentage

Step 2: Finding the number of unicorns played during the season

Step 1 of 2

Let the number of games played by unicorn be x.The unicorn won 60% of the first x-10 games That is $\frac{60}{100} \times(x-10)$

Combining the 8 games we get,

$\begin{gathered}\frac{60}{100}(x-10)+8=\frac{60}{100} \times x-\frac{60}{100} \times 10+8 \\0.6 x-6+8=0.6 x+2\end{gathered}$

Step 2 of 2

The unicorn totally won 65% of the games played.

That is $\frac{65}{100} \times x=0.65 x$

Equating both the equation gives

$\begin{gathered}0.6 x+2=0.65 x \\2=0.65 x-0.6 x \\2=0.05 x \\\frac{2}{0.05}=x \\40=x\end{gathered}$

5 0

2 years ago

5y + 3 = 4y - 9 what is y?

Elena L [17]

$y = - 12$

Step-by-step explanation:

$5y - 4y = - 9 - 3 \\ y = - 12$

6 0

3 years ago

A clothing store has a going-out-of business sale. They are selling pants for $8.99 and shirts for $3.99. You can spend as much

astraxan [27]

Answer:

Let x represents the number of pants and y represents the number of shirts.

As per the statement:

Since, a clothing store are selling pants for $8.99 and shirts for $3.99

then;

total number of Pants cost is, $8.99x and total number of Shirt cost is, $3.99

Also, it is given that: You can spend as much as $60 and want to buy at least two pairs of pants.

then, we have the equation of inequality;

$8.99x + 3.99y \leq 60$ ;......[1] where x, y are natural number.

x-intercept:

Substitute the value y= 0 in [1] and solve for x;

$8.99x + 3.99(0) \leq 60$

$8.99x \leq 60$

Simplify:

$x \leq 6.667$

Since, x is in natural number;

$x \leq 7$

Similarly.

For y-intercept:

Substitute the value x= 0 in [1] and solve for x;

$8.99(0) + 3.99y \leq 60$

$3.99y \leq 60$

Simplify:

$y \leq 15.037$

$y \leq 15$

Therefore, we have

$8.99x + 3.99y \leq 60$ ;

$2\leq x\leq 7$ and $0\leq y\leq 15$

8 0

3 years ago

You start at (3, 0). You move right 1 unit and left 2 units. Where do you end?​

You start at (3, 0). You move right 1 unit and left 2 units. Where do you end?