a laundry detergent box measures 12 inches by 8 inches by 2.5 inches. What is the volume of the two boxes?

#5 Antonio and Abby had the same nimber of paperclips. After Antonio gave 30 paperclips to Abby, Abby had twice as many papercli

Kay [80]

Answer:

#5: 180 paperclips in total.

#6: 126 stamps in total.

#7: Elena should give Lucy 15 colored pencils.

Step-by-step explanation:

This explanation solves each question by setting a single unknown, $x$ .

Let $x$ the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.

Initially:

Antonio: $x$ paperclips;
Abby: $x$ paperclips.

Antonio gives $30$ paperclips to Abby. After that,

Antonio: $(x - 30)$ paperclips;
Abby: $x + 30$ paperclips.

Abby now possess twice as many paperclips as Antonio does. In other words,

$2(x - 30) = x + 30$ .

By the distributive property:

$2x - 60 = x + 30$ .

Substract $x - 60$ from both sides

$x = 30 - (-60) = 90$ .

Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.

Similarly, let $x$ be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.

Initially:

Emily: $x$ stamps;
Jasmine: $x$ stamps.

After Emily gives $42$ stamps to Jasmine:

Emily: $x-42$ stamps;
Jasmine: $x+42$ stamps.

Jasmine now possesses twice as many stamps as Emily does. In other words,

$2(x-42) = x+42$ .

$x = 42 + 2\times 42 = 126$ .

Jasmine used to possess 126 stamps. Now she possesses $126 + 42 = 168$ stamps after receiving $42$ stamps from Emily.

Let the number of pencils that Elena needs to give to Lucy be $x$ .

Initially:

Elena: 60 pencils;
Lucy: 26 pencils.

After Elena gives $x$ pencils to Lucy:

Elena: $60 - x$ pencils;
Lucy: $26 + x$ pencils.

Elena should now possess four more pencils than Lucy does. In other words,

$\underbrace{60 - x}_{\text{Elena's}} = \underbrace{(26 + x)}_{\text{Lucy's}} +4$ .

$2x = 30$ .

$x = 15$ .

8 0

3 years ago

Algebra Find the value of n :<br><br> n × 0.2 = 0.08

noname [10]

Answer:

0.4

Step-by-step explanation:

n × 0.2=0.08

n = 0.08÷0.2

n = 0.4

6 0

2 years ago

Read 2 more answers

Write an equation for each linear function described. Show your work. The graph of the function passes through the point (2,1),

svp [43]

Step-by-step explanation:

As

The graph of the function passes through the point (2,1), and

y increases by 4 when x increases by 1.

so

x y

2 1

3 5

4 9

5 13

6 17

and so on

From the table:

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(2,\:1\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)$

$m=\frac{5-1}{3-2}$

$m=4$

As the slope-intercept form of the line is

$y=mx+b$

putting m=4 and any point, let say (2, 1) to find y-intercept 'b'.

$1=\left(4\right)2+b$

$8+b=1$

$8+b-8=1-8$

$b=-7$

So putting $b=-7$ and $m=4$ in the slope-intercept form of the line

$y=\left(4\right)x+\left(-7\right)$

$y=4x-7$

Therefore, the equation for the linear function will be:

$y=4x-7$

8 0

3 years ago

A highway engineer specifies that a certain section of roadway covering a horizontal distance of 2km should have a downgrade of

Zigmanuir [339]

Answer:

$0.16km$

Step-by-step explanation:

A highway engineer wants to compute the change in elevation of a section of road. The horizontal distance of this section of road is 2km and downgrade is 8%

The slope formula is given by

$m=\frac{rise}{run}=\frac{x}{y}$

m = 8% = 8/100

run = y = 2km

$m =\frac{x}{y}$

$\frac{8}{100} =\frac{x}{2}$

$\frac{2*8}{100} =x$

$x=\frac{16}{100} =0.16km$

Verification:

$m=\frac{0.16}{2}= 0.08=8%$ %

3 0

3 years ago

Read 2 more answers

What is the zeros of the quadratic function y=x^2+14x+24

777dan777 [17]

Step-by-step explanation:

${x}^{2} + 14x + 24 = 0 \\ {x}^{2} + 12x + 2x + 24 = 0 \\ x(x + 12) + 2(x + 12) = 0 \\ (x + 12)(x + 2) = 0\\ x = - 12 \\ x = - 2$

6 0

3 years ago