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3 years ago

14

yesterday a recycling center collected 679 cans.the center collected 225 fewer bottles than cans,and 178 fewer newspaper bundles

than bottles.how many newspaper bundles did the center collect yesterday?

1 answer:

ahrayia [7]3 years ago

5 0

276 because 679-225= 154 and 154-178=276

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–18 + 15x = 3(4x – 6) + 3x

svp [43]

First we need to combine like terms:

-18 + 15x = 12x - 18 + 3x

-18 + 15x = 9x - 18

-18 = 9x - 18 - 15x

-18 = -6x - 18

0 = -6x (the 18's cancel)

0 / -6 = x

0 = x

5 0

3 years ago

Read 2 more answers

A square park measures 170 feet along each side. Two paved paths run from each corner to the opposite corner and extend 3 feet i

Cerrena [4.2K]

Answer:

The total area, in square feet, taken by the paths is 2,004

Step-by-step explanation:

see the attached figure with lines to better understand the problem

I can divide the figure into four right triangles, one small square and four rectangles

step 1

Find the area of the right triangle of each corner of the path

The area of the triangle is

$A=(1/2)(b)(h)$

substitute the given values

$A=(1/2)(3)(3)=4.5\ ft^2$

step 2

Find the hypotenuse of the right triangle

Applying Pythagoras Theorem

Let

d -----> hypotenuse of the right triangle

$d^{2}=3^{2}+3^{2}$

$d^{2}=18$

$d=\sqrt{18}\ ft$

simplify

$d=3\sqrt{2}\ ft$

The hypotenuse of the right triangle is equal to the width of the path

step 2

Find the area of the small square of the path

The area is

$A=b^{2}$

we have

$b=3\sqrt{2}\ ft$ ----> the width of the path

substitute

$A=(3\sqrt{2})^{2}$

$A=18\ ft^2$

step 3

Find the length of the diagonal of the square park

Applying Pythagoras Theorem

Let

D -----> diagonal of the square park

$D^{2}=170^{2}+170^{2}$

$D^{2}=57,800$

$D=\sqrt{57,800}\ ft$

simplify

$D=170\sqrt{2}\ ft$

step 4

Find the height of each right triangle on each corner

The height will be equal to the width of the path divided by two, because is a 45-90-45 right triangle

$h=1.5\sqrt{2}\ ft$

step 5

Find the area of each rectangle of the path

The area of rectangle is $A=LW$

we have

$W=3\sqrt{2}\ ft$ ----> width of the path

Find the length of each rectangle of the path

$L=(D-2h-d)/2$

where

D is the diagonal of the park

h is the height of the right triangle in the corner

d is the width of the path (length side of the small square of the path)

substitute the values

$L=(170\sqrt{2}-2(1.5\sqrt{2})-3\sqrt{2})/2$

$L=(170\sqrt{2}-3\sqrt{2}-3\sqrt{2})/2$

$L=(164\sqrt{2})/2$

$L=82\sqrt{2}\ ft$

Find the area of each rectangle of the path

$A=LW$

we have

$W=3\sqrt{2}\ ft$

$L=82\sqrt{2}\ ft$

substitute

$A=(82\sqrt{2})(3\sqrt{2})$

$A=492\ ft^2$

step 6

Find the area of the paths

Remember

The total area of the paths is equal to the area of four right triangles, one small square and four rectangles

so

substitute

$A=4(4.5)+18+4(492)=2,004\ ft^2$

therefore

The total area, in square feet, taken by the paths is 2,004

3 0

3 years ago

112338 rounded to the nearest thousands

dlinn [17]

112000 because the thousands is where the two is placed

8 0

3 years ago

Read 2 more answers

The average age of 40 students of a class is 15 years. An 18 year-old student left the class and a new student was admitted. As

cluponka [151]

Answer:

Answer:age of new student is 13.4 years

Step-by-step explanation:

SUM of ages all 40 students =average age times 40

=15*40=600

after leaving 18 years old student

SUM of ages of 39 students will be 600-18=582

after adding new student with age x

SUM of ages of 40 students will become 582+x

and the average would be (582+x)/40

which is given as 14.885

so we get equation

(582+x)/40=14.885

582+x=14.885*40=595.4

x=595.4-582

x= 13.4

age of new student is 13.4 years

Hope it will help you

Please mark as brainliest answer

6 0

3 years ago

Read 2 more answers

What is the area of the circle below?<br> 10 ft

azamat

Answer:

<h3>Circle</h3>

Solve for area

A=π r^2

r =Radius

<h2>You about this first: </h2>

The circumference of a circle is its perimeter or distance around it. It is denoted by C in math formulas and has units of distance, such as millimeters (mm), centimeters (cm), meters (m), or inches (in). It is related to the radius, diameter, and pi using the following equations: C = πd. C = 2πr.

Step-by-step explanation:

Hope it is helpful....

8 0

3 years ago