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REY [17]
2 years ago
15

Estimate the perimeter and the area of the shaded figure to the nearest whole number.

Mathematics
2 answers:
BigorU [14]2 years ago
7 0

Answer:

Perimeter:

about \: 12 \: \: units

Area:

about \: 21 \: {units} ^{2}

Step-by-step explanation:

The perimeter of this shape would be the value of all the sides added together. The sides measure: 4 units, 4 units, 1 unit, 1 unit, 1 unit, 1 unit. Therefore the perimeter is: 12 units

4 + 4 + 1 + 1 + 1 + 1 = 12

To find the area of the shape we have to split it into a square and 2 triangles. The formula to find the area of a square is

a = length \times width \: or \:  {(side)}^{2}

All sides of a square are equal and the side measures 4 units, hence the area is

{4} ^{2} = 16

The formula to find the area of a triangle is

\frac{1}{2} base \:  \times height

Both triangles are equal and as such after finding the area of one triangle you can just multiply it by 2. The base is 3 units and the height is 1.5 units.

\frac{1}{2} b \times h \\  \frac{1}{2} (3) \times 1.5 \\ 1.5 \times 1.5 = 2.25 \\ 2.25 \times 2 = 4.5

area \: or \: square \:  + area \: of \: 2 \: triangles \\ 16 + 4.5 = 20.5 \: or \: 21  (whole\: number)

soldier1979 [14.2K]2 years ago
5 0

Answer:

Step-by-step explanation:

The area and perimeter of the given shaded figure are respectively 33.12 unit² and 20.56 units.

Area and perimeter-based problem:

What information do we have?

Radius of semi-circle = 8 / 2 = 4 unit

Length of remain Rectangle = 8 unit

Width of remain Rectangle = 2 unit

Perimeter of shaded figure = πr + (l + 2b)

Perimeter of shaded figure = (3.14)(4) + [4 + (2)(2)]

Perimeter of shaded figure = 12.56 + 4 + 4

Perimeter of shaded figure = 20.56 units

Area of shaded figure = πr²/2 + lb/2

Area of shaded figure = (3.14)(4)²/2 + (8)(2)/2

Area of shaded figure = (3.14)(8) + 8

Area of shaded figure = 25.12 + 8

Area of shaded figure = 33.12 unit²

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1. which data set represents an increasing, linear function? (1 point)
GenaCL600 [577]
#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D

Explanation
#1)  If the data set is linear, the slope will be constant throughout the entire data set.  For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set.  The set is also increasing; as x increases, y increases as well.

#2)  Substituting 4 for y and 1 for x, 
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t.  Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term.  If the common difference is 2, this means that 2 was added each time.  This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2

Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5

Add 5 to both sides:
6+5 = d-5+5
11 = d

#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)

Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6

Add 1 to both sides:
y-1+1 = 3x+6+1
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#14) If two lines are parallel, they have the same slope.  The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped).  The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2.  The only one with this slope is D.

#16)  The two equations are not the same, so there are not infinitely many solutions.  The variables do not both cancel, so there is at least one solution.  This only leaves one solution as the answer.

#19)  Using 1 for 7 and 4 for x, we check each equation.  The only one that comes out correct is D.
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3 years ago
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