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guapka [62]
3 years ago
6

The sum of three consecutive integers is 222. What is the smallest of these integers?

Mathematics
1 answer:
Anna71 [15]3 years ago
5 0

Answer:

73

Step-by-step explanation:

x+(x+1)+(x+2)=222

x+x+1+x+2=222

3x+3=222

3x=222-3

3x=219

x=219/3

x=73

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A rectangle is twice as long as it is wide and has the same perimeter as a square whose area is 36 square feet larger than that
Korvikt [17]

Answer:

  • rectangle: 12 ft × 24 ft
  • square: 18 ft square

Step-by-step explanation:

You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.

<h3>Setup</h3>

Let x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).

This area is the product of length and width. The expression factors as ...

  rectangle area = x² -36 = (x +6)(x -6)

<h3>Solution</h3>

If we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:

  (x +6) = 2(x -6)

  18 = x . . . . . . . . . add 12-x to both sides

This is the side length of the square. The rectangle dimensions are ...

  x+6 = 18+6 = 24 . . . . feet long

  x -6 = 18 -6 = 12 . . . . feet wide

The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.

__

<em>Additional comment</em>

The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.

The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.

<em>Alternate solution</em>

Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².

The difference is 36 square feet, so we have ...

  9/4x² -2x² = 36 = x²/4   ⇒   x = √(36·4) = 6·2 = 12 . . . . width of rectangle

8 0
1 year ago
What is the area of the composite figure? (6π 4) cm2 (6π 16) cm2 (12π 4) cm2 (12π 16) cm2
raketka [301]

The area of the considered composite figure is given by: Option: 6π + 16 cm²

<h3>How to calculate the surface area of a composite figure?</h3>

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

\text{Area of composite figure} = \sum (\text{Area of composing figures})

That ∑ sign shows "sum"

For this case, the missing image is attached below.

As visible, the area of the figure = Sum of area of those 3 semi circles + Area of that square(its square because it has 4 equal sides in which adjacent sides are perpendicular) in between.

The side of the square is of 2+2=4 cm( as half of its side is 2 cm), thus, Area of that square = 4² = 16 cm²

All those 3 semicircles has radius = 2 cm

Since radius is same, so area of those 3 semicircle is same = \dfrac{\pi r^2}{2} = \dfrac{\pi (2)^2}{2} = 2 \pi\: \rm cm^2

Thus, we get:

Area of the composite figure = 2 \pi +2 \pi +2 \pi  + 16 \: \rm cm^2 = 6 \pi+ 16 \: \rm cm^2

Learn more about area of a composite figure here:

brainly.com/question/10254615

6 0
3 years ago
Help with geometry? Will give brainliest!<br> spam answers will be reported
Anastasy [175]
I got 110 because 35+35=70 and 180-70=110. I added 35 to 35 because it says that AB=AD, so they should make congruent angles. So add the 35+35 and work from there.
3 0
3 years ago
4. A sports car accelerates from rest to a final velocity of 64 m/s at a rate of 12.3
Ivanshal [37]

Answer:

t = 5.2\ s

Step-by-step explanation:

Given

a= 12.3m/s^2 --- acceleration

v = 64m/s --- final velocity

u =0m/s --- initial velocity (it is 0, because the car starts from rest)

Required

Determine the time taken

This will be solved using Newton's first equation of motion:

v = u + at

Substitute values for v, u and a

64 = 0 + 12.3*t

64 = 12.3t

12.3t = 64

Make t the subject

t = \frac{64}{12.3}

t = 5.2\ s

<em>Hence, the time taken is approximately 5.2 seconds</em>

6 0
3 years ago
Four friends are collecting canned goods for charity Ron collects 10 more than 3 times as many cans as jasmine barry collects tw
FromTheMoon [43]
Jasmine + ron =alicia + barry
Ron collects 3jasmine+10 more than jasmine
barry collects 2 jamsine
alicia collects 10 barry = 20 jasmine
4jasmine+10=22 jasmine
10=18 jasmine
jasmine = 1.8
ron =15.4
alicia=32
barry=3.2
6 0
4 years ago
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