In order to find the amount of paper that will be needed, we need to calculate the surface area of this rectangular prism.
The faces of this figure are:
- 2 rectangles with dimensions 8 in and 15 in,
- 2 rectangles with dimensions 15 in and 12 in,
- 2 rectangles with dimensions 12 in and 8 in.
Calculating the area of each rectangle, we have:
[tex]\begin{gathered} A_1=8\cdot15=120 \\ A_2=15\cdot12=180 \\ A_3=12\cdot8=96 \end{gathered}[/tex]Now, the surface area is:
[tex]\begin{gathered} S=2A_1+2A_2+2A_3 \\ S=240+360+192 \\ S=792\text{ in}^2 \end{gathered}[/tex]So the amount of paper needed is 792 in².
A 30-m-wide field is how many yard wide?The field is ____ yard wide.( Type a whole number or decimal. Round to three decimal places as needed.)
Given:
30 meter wide field
To determine the field in yards, we convert the given 30 meters into yards.
We must remember that:
1 meter = 1.0936 yards
So,
Therefore, the answer is 32.808 yards.
you want to get rid of the X by elimination in the system below
Hence, the correct option is -3
By how much was the price counted?What was the percentage of the discount?
1.
original price - price with discount = 22-13.26 = 8.74
2.
in order to know the percentage of the discount
first, we need to know the percentage pay
x=percentage pay
(22)(x)=13.26
x=13.26/22= 0.60
the percentage pay 60%
the percentage of the discount is
100%-60%=40%
the percentage of the discount is 40%
Triangle ABC has vertices (1,4), (5,6), and (3, 10). It is reflected across the y-axis, forming Triangle A’B’C’. What are the vertices of the new triangle?
Step 1:
First, write the rule for the transformation across the y-axis
The rule for a reflection over the y -axis is (x,y)→(−x,y).
Meaning value of y remains the same and you will multiply the coordinate of x by negative.
Step 2
Coordinates of pre-image
A = (1 , 4)
B = (5 , 6)
C = (3 , 10)
Step 3:
Find the coordinates of the image using the rule.
A' = (-1, 4)
B' = (-5 , 6)
C' = (-3 , 10)
Final answer
The vertices of the new triangle is
A' = (-1, 4)
B' = (-5 , 6)
C' = (-3 , 10)
the fraction 1-4 is blank to the decimal of 0.25
Answer:
equal
Step-by-step explanation:
1/4 = .25
1÷4=.25
Question:Solve the formula I = Prt to find the principal, P, when I = $272.25, r = 2.2%, and t = 3 years.
Given in the question:
I = $272.25
r = r = 2.2%
t = 3 years
Let's re-equate the formula of Simple Interest to find P in terms of I, r, and t.
[tex]I\text{ = Prt }\rightarrow\text{ P = }\frac{I}{rt}[/tex]Let's plug in the values to find P.
[tex]P\text{ = }\frac{I}{rt}[/tex][tex]P\text{ = }\frac{272.25}{(\frac{2.2}{100})(3)}\text{ = }\frac{272.25}{(0.022)(3)}[/tex][tex]P\text{ = }\frac{272.25}{0.066}[/tex][tex]P\text{ = 4,125 = \$4,125}[/tex]Therefore, the Principal Amount is $4,125.
Use the accompanying Venn Diagram, which shows the cardinality of each region,to answer the question below.How many elements belong to set B?
4 elements
Explanation
to find the number of elements that belong to set B, just count the elements inside the circle B
4 elements (3,5,2,9)
I hope this helps you
Solve for Y2x + = 4a. y = 6x + 12b. y = -6x +12C. y= 6x - 12d. y = -6x - 12
You have the following equation:
2x + y/3 = 4
In order to solve for y, proceed as follow:
2x + y/3 = 4 subtract by 2x both sides
y/3 = 4 - 2x multiply by 3 both sides
y = 3(4 -2x) apply distribution property
y = 3(4) + 3(-2x)
y = 12 - 6x order the expression
y = -6x + 12
Hence the solution for y is:
y = -6x + 12
A person can join The Fitness Center for $50. A member can rent the tennis ball machine for $10 an hour. Write a linear function to model the relationship between the number of hours the machine is rented (x) and the total cost (y).
what is the initial value?
Determine the cost for renting the tennis ball machine for 2 hours? for 5 hours? 0 hours?
How many hours did a member rent the tennis ball machine if the total cost was $130?
The linear function to model the relationship between the number of hours the machine is rented (x) and the total cost (y) is 50 + 10h.
The initial value is $50.
The cost of renting for 2 hours is 70
The hours that a member rent the tennis ball machine if the total cost was $130 is 8 hours.
What is an equation to model the relationship?An equation simply means the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the person can join The Fitness Center for $50 and member can rent the tennis ball machine for $10 an hour. Let the number of hours be h
This will be:
= 50 + (10 × h)
= 50 + 10h
The cost for renting for 2 hours will be:
= 50 + 10(2)
= 50 + 20
= 70
When cost is $130, the hours will be:
50 + 10h = 130
Collect like terms
10h = 130 - 50
10h = 80
Divide
h = 80/10
h = 8 hours.
In conclusion, the number of hours is 8 hours.
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1. A linear function that models the relationship between the number of hours the machine is rented (x) and the total cost (y) is f(y) = 50 + 10x.
2. The initial value is $50, which refers to the membership cost.
3. The cost of renting the tennis ball machine for 2 hours is $70.
4. The cost of renting the tennis ball machine for 5 hours is $100.
5. The cost of renting the tennis ball machine for 0 hours is $50.
6. A member who rented the tennis ball machine for 8 hours will pay a total cost of $130.
What is a linear function?
A linear function is a mathematical expression in an equation form, like f(y) = a + bx.
The a is a constant (like a fixed cost) just like the b (the slope). The x is the independent variable while y is the dependent variable.
The fixed cost for joining The Fitness Center = $50
The variable cost of renting the tennis ball machine = $10 per hour
To rent the tennis ball machine for 2 hours, the total cost, y = 50 + 10(2)
= $70
To rent the tennis ball machine for 5 hours, the total cost, y = 50 + 10(5)
= $100
To rent the tennis ball machine for 0 hours, the total cost, y = 50 + 10(0)
= $50
To pay a total cost of $130, the member rented the tennis ball machine for 8 hours, given that the total cost of, 130 = 50 + 10x
= 10x = 80
x = 8 hours
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over the last 3 evenings 85 phone calls were received. the second evening she received 5 fewer calls than the first evening.The third evening she received 4 times as many calls how many did she receive each evening
a =20, b =15, c= 60
1) Writing this we have
1st evening: a
2nd evening: b
3rd evening: c
a +b+ c = 85
b=5 -a
c=4a
2) So rewriting this out as an expression we have:
a + b+ c = 85 Plug into that in terms of "a"
a + 5-a + 4a = 85 Combine like terms
4a +5 = 85 subtract 5 from both sides
4a = 80 Divide both sides by 4
a = 20
2.2) Plug into each formula:
b =a -5
b = 20 -5
b = 15
20+15 + c = 85 Add them up
35 +c = 85 Subtract 35 from both sides
c = 85 -35
c= 60
Or we could have done it:
c = 4b
c= 4* 15
c= 60
3) Hence, the answer is a =20, b =15, c= 60
Please Help!!!!! I will give brainliest and 5 stars!!!!
1. A system of linear functions cannot have only two or three solutions, the possible amounts are: Zero, One and Infinity.
2. This is not true because if the lines do not cross, the system has no solutions.
3. Substitution: Explicit variable, such as:
x = 3, y + 3x = 10.y = 2x + 4, 3x + 2y = 20.Elimination: Non-explicit variable, such as:
x + y = 2, 2x + 3y = 5.x - y = 10, 2x + 5y = 40.What are linear functions?Linear functions have the definition given as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.A system of linear equations is composed by multiple equations, and the number of solutions is defined as follows:
Zero solutions: slopes are multiples and intercepts are not -> the functions do not intersect on the graph.One solution: different slope and intercepts -> the functions intersect once on the graph.Infinitely many solutions: slopes and intercepts are multiples, hence the functions are the same on the graph.There are two ways to solve the systems, given as follows:
Substitution: one of the variables has an explicit definition.Elimination: none of the variables has an explicit definition.More can be learned about linear functions at https://brainly.com/question/24808124
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solve each system of equations below by graphing, please use my graphy = 1/2x - 3y= 3/2x - 1
Answer:
(-2, -4)
Explanation:
To solve the system, we need to graph both equations. So, we will find two points for each line.
For y = 1/2x - 3
If x = 0
y = 1/2(0) - 3 = -3
If x = 2
y = 1/2(2) - 3
y = 1 - 3 = -2
For y = 3/2x - 1
If x = 0
y = 3/2(0) - 1 = -1
If x = 2
y = 3/2(2) - 1
y = 3 - 1 = 2
Therefore, we have the points (0, -3) and (2, -2) for the first equation and the points (0, -1) and (2, 2) for the second equation. Now, we can graph the lines as:
The lines intersect at (-2, -4), so the solution of the system is (-2, -4)
Identify the property that justifies each step asked about in the answer area below.Line 1:(xz)yLine 2:x(zy)Line 3:x(yz)Line 1 to Line 2:Line 2 to Line 3:
Line 1 to line 2) This property,
[tex](xz)y=x(zy)[/tex]is called associativity.
Line 2 to line 3) The property used here is this:
[tex]xy=yx[/tex]It is called commutativity.
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Letmidpoint (2,9), endpoint (1, -3)
Given this is a one of the endpoints of the segment:
[tex](1,-3)[/tex]You know that the midpoint is:
[tex](2,9)[/tex]By definition, the formula for finding the midpoint of a segment is:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where:
- The coordinates of the midpoint are:
[tex](x_m,y_m)[/tex]- And the coordinates of the endpoints are:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]In this case, you can set up that:
[tex]\begin{gathered} x_m=2 \\ y_m=9 \\ \\ x_1=1 \\ y_1=-3 \end{gathered}[/tex]Then, you can set up this equation to find the x-coordinate of the other endpoint:
[tex]2=\frac{1+x_2}{2}[/tex]Solving for:
[tex]x_2[/tex]You get:
[tex](2)(2)=1+x_2[/tex][tex]\begin{gathered} 4-1=x_2 \\ x_2=3 \end{gathered}[/tex]Set up the following equation to find the y-coordinate of the other endpoint:
[tex]9=\frac{-3+y_2}{2}[/tex][tex](9)(2)=-3+y_2[/tex][tex]\begin{gathered} 18+3=y_2 \\ y_2=21 \end{gathered}[/tex]Hence, the answer is:
[tex](3,21)[/tex]Please look at the picture for accurate description thank you in advance
Given:
Height of person 5.3 ft.
Distance between person and tree is 34 feet
In triangle ABC
BC=34
Angle = 71
[tex]\begin{gathered} \tan \theta=\frac{\text{ perpendicular}}{\text{ base}} \\ \tan \theta=\frac{AB}{BC} \\ \tan 71=\frac{AB}{34} \\ AB=34\times\tan 71 \\ AB=98.7431 \end{gathered}[/tex]So height of tree is person height + AB
[tex]\begin{gathered} =98.7431+5.3 \\ =104.0431 \end{gathered}[/tex]So height of tree is 104
Determine if the following set is a function or not.
In an ordered pair (x,y), x represents the domain, and y is the range.
Gather up all of the domain, the domain is
{-10, -3, 4, 7, 12}
The range is
{-2, 3, 4, 3, 3} ----> {-2, 3, 4} (the same multiple sets counts as one)
A function can be defined as either one-to-one, or many-to-one BUT NOT one-to-many.
Draw a diagram representing the domain mapping to a range.
Based on the diagram, we have mappings of one-to-one [-10 maps to 2, 4 maps to 4, based on the ordered pair (-10,-2) and (4,4)],
and many-to-one [-3, 7, and 12 maps to 3, based on the ordered pair (-3,3), (7,3), and (12,3)]
Since there are no one-to-many mappings, we can conclude that the set is a function.
Solve the polynomial equation by factoring and then using the zero product principal
Given: The polynomial below
[tex]x^3+2x^2=9x+18[/tex]To Determine: The factored form of the equation using the zero product principle
Step 1: Put all the terms to the left hand side of the equation
[tex]\begin{gathered} x^3+2x^2=9x+18 \\ x^3+2x^2-9x-18=0 \end{gathered}[/tex]Step 2: Group the equation into and factorize
[tex]\begin{gathered} (x^3+2x^2)-(9x-18)=0 \\ x^2(x+2)-9(x+2)=0 \\ (x+2)(x^2-9)=0 \end{gathered}[/tex]Step 3: Expand the difference of two squares
[tex]\begin{gathered} a^2-b^2=(a-b)(a+b) \\ x^2-9^2=x^2-3^2=(x-3)(x+3) \end{gathered}[/tex]Step 4: Replace the difference of two squares with its equivalence
[tex]\begin{gathered} x^3+2x^2=9x+18 \\ x^3+2x^2-9x-18=0 \\ (x+2)(x^2-9)=0 \\ (x+2)(x-3)(x+3)=0 \end{gathered}[/tex]Step 5: Use the zero product principle to determine the solution set
[tex]\begin{gathered} (x+2)(x-3)(x+3)=0 \\ x+2=0,or,x-3=0,or,x+3=0 \\ x=-2,or,x=3,or,x=-3 \end{gathered}[/tex]Hence,
The factored form is (x + 2)(x - 3)(x + 3) = 0
The solution set is x = -2, 3, -3
Find the ratio of the length of the longest side to the length of the shortest side. Write the ratio as a fraction in lowest terms.1.2 meters0.8 meter0.8 meter1.2 meters
A ratio may be written as a:b or, in fraction form, a/b.
To obtain the ratio in fraction, divide the longest side by the shortest side. Thus, we get the following.
[tex]\frac{1.2}{0.8}[/tex]To determine the lowest term, eliminate the decimal point by multiplying the numerator and the denominator by 10.
[tex]\frac{1.2}{0.8}\cdot\frac{10}{10}=\frac{12}{8}[/tex]Divide the numerator and the denominator by the greatest common factor (GCF) of 12 and 8, which is 4.
[tex]\frac{12\div4}{8\div4}=\frac{3}{2}[/tex]Therefore, the ratio in fraction form is
[tex]\frac{3}{2}[/tex]What is the distance between (4, 3) and (9, 15) on the coordinate plane? Select two that apply. 13 units V 169 units V144 units 12 units 5 units
Explanation
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Step 1
Let
P1=(4,3)
P2=(9,15)
replace
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{distance}=\sqrt[]{(9-4)^2+(15-3)^2} \\ \text{distance}=\sqrt[]{(5)^2+(12)^2} \\ \text{distance}=\sqrt[]{25+144^{}} \\ \text{distance}=\sqrt[]{169} \\ \text{also} \\ \text{distance}=13 \end{gathered}[/tex]I hope this help you
solve for x perimeter of the rectangle is 100to x - 8 + x + 4 + 2x - 8 + x + 4 = 100 solve for x
The perimeter of rectangle is 100.
The formula for the perimeter of rectangle is
[tex]P=2(l+w)[/tex]The length of the rectangle is 2x-8 and width of the rectangle is x+4.
The perimeter is
[tex]100=2(2x-8+x+4)[/tex][tex]50=3x-4[/tex][tex]3x=54[/tex][tex]x=18[/tex]Hence the value of x is 18.
The length is
[tex]2\times18-8=36-8=28[/tex]The width is
[tex]18+4=22[/tex]The correct options are 22 and 28.
I need help with this 2Identify the graph with point (0, -8, 5)
Explanation:
Cartesian coordinate system
A point can be defined in the Cartesian coordinate system with 3 real numbers: x, y, z. Each number corresponds to the signed minimal distance along with one of the axis (x, y, or z) between the point and plane, formed by the remaining two axes. The coordinate is negative if the point is behind the coordinate system origin.
The points is given below as
[tex](0,-8,5)[/tex]Hence,
The final answer is
The probability of being dealt a club and a diamond is
There are a total of 52 cards in a standard deck.
There are 13 club cards and 13 diamond cards.
The probability of getting a club card is given by
[tex]P(club)=\frac{\text{number of club cards}}{\text{total number of cards}}=\frac{13}{52}[/tex]The probability of getting a diamond card is given by
[tex]P(diamond)=\frac{\text{number of diamond cards}}{\text{total number of cards}}=\frac{13}{52}[/tex]The probability of getting a club and diamond is given by
"And" means to multiply the probabilites
[tex]\begin{gathered} P(club\; \; and\; \; diamond)=P(club)\times P(diamond) \\ P(club\; \; and\; \; diamond)=\frac{13}{52}\times\frac{13}{52} \\ P(club\; \; and\; \; diamond)=\frac{169}{2704}=\frac{1}{16} \end{gathered}[/tex]Therefore, the probability of getting a club and diamond is 1/16
I need help and I need to right answer please
As you can see, figures ABC and A'B'C' have the same sides and the same orientation about the origin, then the they only differ by their position, a translation is a transformation that let us change the position of a figure without affecting its shape or its size, in this case ABC moved 3 units down and 1 unit left, for this reason the sequence of transformations is:
(x, y) -> (x - 1, y - 3)
Then, the second option is the correct answer
spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute.Find the rates of change of the radius when r=30 centimeters and r=85 centimeters.Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant.
Answer
Explanation
Given:
A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute means
[tex]\frac{dV}{dt}=800\text{ }cm^3\text{/}min[/tex](a) The rates of change of the radius when r = 30 centimeters and r = 85 centimeters is calculated as follows:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ \frac{dV}{dr}=\frac{4}{3}\times3\pi r^{3-1} \\ \\ \frac{dV}{dr}=4\pi r^2 \\ \\ But\frac{\text{ }dV}{dr}=\frac{dV}{dt}\div\frac{dr}{dt} \end{gathered}[/tex]So when r = 30, we have
[tex]\begin{gathered} \frac{dV}{dr}=4\pi(30)^2 \\ \\ \frac{dV}{dr}=4\times\pi\times900 \\ \\ \frac{dV}{dr}=3600\pi \\ \\ From\text{ }\frac{dV}{dr}=\frac{dV}{dt}\div\frac{dr}{dt} \\ \\ Putting\text{ }\frac{dV}{dt}=800,\text{ }we\text{ }have \\ \\ 3600\pi=800\div\frac{dr}{dt} \\ \\ \frac{dr}{dt}=\frac{800}{3600\pi}=\frac{800}{3600\times3.14} \\ \\ \frac{dr}{dt}=0.071\text{ }cm\text{/}min \end{gathered}[/tex]Therefore, the rate of change of the radius when r = 30 is dr/dt = 0.071 cm/min.
For when r = 25 cm, the rate of change is:
[tex][/tex](1 point) Rework problem 4 from section 2.2 of your text, involving the choice of officers for acommittee. For this problem, assume that you have a committee of 10 members, and that youmust choose a parliamentarian, and secretary.msIn how many ways can these selections be made?
There are 90 possible ways the selection can be made
Here, we want to know the number of ways the choice can be made from 10 members
Firstly, we want to select 1 parliamentarian from 10 members; then after the selection we will select a secretary from the remaining nine
As pertaining selections, selecting r items from a total n , can be calculated by the use of the combinatorial formula as follows;
[tex]\begin{gathered} ^nC_r\text{ = }\frac{n!}{(n-r)!r!_{}} \\ \\ \text{Also, we have;} \\ ^nC_1\text{ = n} \end{gathered}[/tex]So, we have 10 ways to select an item from 10 items, we also have 9 ways to select an item from 9 items
So, the total possible number of ways would be;
[tex]10\times\text{ 9 = 90 ways}[/tex]Triangle a is reflected in the x-axis to give triangle b traingle b is reflected in the y-axis to give triangle a describe fully the transformation that maps a onto c
Triangle A is transformed into triangle C, and all of the vertices' signs are modified.
Is a reflection over the x-axis positive or negative?Thus, we get the conclusion that when a point is mirrored along the x-axis, the x-coordinate stays constant while the y-coordinate deviates from zero. So, M' is the image of the point M (h, k) (h, -k). Guidelines for determining a point's x-axis reflection: I Maintain the x-coordinate, or abscissa.
Thus, the reflection in the x-xis:
The entire x-component is unaltered.
The sign of each y-component is changed from - to + and vice versa.
then, the reflection in the y-xis:
The entire y-component is unaltered.
Every x-component has its sign altered from - to + and vice versa.
Triangle A is transformed into triangle C, and all of the vertices' signs are modified.
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8.The outfield fencing for a Minor League field forms a circular sector with home plate as thecenter. (See the figure at the top of page 681.) The fence is placed at a uniform distance of2130 ft from home plate. The boundaries of the fence, which extends partway into foulterritory, create an angle of 110 degrees with home plate. At $21 per foot, how much willthe fence cost? (Round to the nearest $10.)
The Solution.
Representing the problem in a diagram, we get
To find the length of the boundaries of the fence, we shall use the formula below:
[tex]\begin{gathered} \text{Length}=\frac{\theta}{360}\times2\pi r \\ \text{Where }\theta=110^o \\ \pi=3.14 \\ r=2130\text{ ft} \end{gathered}[/tex]Substituting these values in the formula, we get
[tex]\begin{gathered} \text{Length}=\frac{110}{360}\times2\times3.14\times2130 \\ \\ \text{ =}\frac{11\times3.14\times2130}{18}=4087.23\text{ fe}et \end{gathered}[/tex]We were told that each foot cost $21.
So, the cost of the fence is
[tex]\frac{4087.23}{21}=\text{ \$194.63}\approx\text{ \$190}[/tex]Therefore, the correct answer is $190
help students understand how fractions and decimal numbers are related. Her teacher showed her on the ruler that 0.5 is equivalent to circumference of a circle, Whiet number below will give him the approximate value of ? A 300 B. 3.14 0.5 C. 328 liquip D. 3.43 Inches 1 2 11 What decimal number is equivalent to 12 Question 3 Which of the following numbers rational? A 1 78 A 0.31311 B. 1 1875 C 1.875 C v16 D. 1.75 D. 27
The measuring rule shows lines graded between each unit.
Each unit has four lines between them which means each line is a quarter, or 1/4 or 0.25 of each unit.
When the ruler indicates 0.5, that is shown as two quarters, or one half (that is 1/2).
Therefore when the ruler indicates
[tex]\begin{gathered} 1\frac{7}{8} \\ \text{That can be broken down into } \\ 1+\frac{2}{8}+\frac{2}{8}+\frac{2}{8}+\frac{1}{8} \\ \text{Note that }\frac{2}{8}\text{ is equivalent to }\frac{1}{4} \\ \text{Also }\frac{1}{4}\text{ is equivalent to 0.25} \\ \frac{1}{8}\text{ is half of }\frac{1}{4},\text{ and that is equivalent to half of 0.25} \\ \text{Therefore, we now have} \\ 1+0.25+0.25+0.25+0.125 \\ =1.875 \end{gathered}[/tex]The correct answer is 1.875
A car that originally cost $3,668 in 1955 is valued at $62,125 if in excellent condition, which is1 times as much as a car in very nice condition—if you can find an owner willing to part with one for any price.What would be the value of the car in very nice condition? (Do not round intermediate calculations.)Value of the car
Let
x ----> value of the car in very nice condition
we know that
1 3/4 x=62,125 ----> linear equation that represent this situation
Solve for x
but first
Convert mixed number to an improper fraction or decimal number
1 3/4=1+3/4=1+0.75=1.75
substitute
1.75x=62,125
x=62,125/1.75
x=35,500
therefore
the answer is $35,500Use the composite figures below to mark each statement as true or false. Justify your choices.A.The area of figure A can be found by determining the sum of the area of the rectangle and the area of a semicircle.B. The area of figure b can be found by decomposing the figure into a square and parallelogram.C. Figure b has a total area of 29.75 M2.D.The area of figure a is 45.99 m2 more than the area of figure B.
Answer
A. True
In figure A, there are two semicircles and a rectangle.
Area of the composite figure = Area of a circle + area of a rectangle
Two semicircles give a complete circle, therefore the area of a circle is given by
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where r is the radius }=\frac{4}{2}=2\text{ m} \\ \Rightarrow A=3.14\times2^2 \\ A=3.14\times4 \\ A=12.56m^2 \end{gathered}[/tex]The area of the rectangle in figure A is given by
A = length x width
A = 7 x 4
A = 28 m²
Therefore, the area of the composite figures = 12.56 m² + 28 m² = 40.56 m²
B. True
Note: label the figure from A - G and join line D to C as shown below.
Area of the composite figure = Area of parallelogram ABCE + Area of square CDFG
Note: Area of parallelogram = base x height
Area of a square = length x length
[tex]\begin{gathered} \text{Area of Composite figure }=(5\times3.5)+(3.5\times3.5) \\ =17.5+12.25 \\ =29.75m^2 \end{gathered}[/tex]C. True
D. False, area of figure A is 40.56 m², and area of figure B is 29.75 m². Therefore, the area of figure A is 10.81 m² NOT 45.99 m². more than the area of figure B