Geometry B Unit 5: Area - Lesson 10: Area Unit Test
1. What is the area of the trapezoid? The diagram is not drawn to scale.
72 cm^2
2. Given the regular polygon, what is the measure of each numbered angle?
m∡1 = 36°; m∡2 = 72°
3. What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.
5/2 and 25/4
4. What is the area of a regular pentagon with a side of 12 in.? Round the answer to the nearest tenth.
247.7 in.2
5. Name the minor arc and find its measure.
AB; 162°
6. What is the circumference of the given circle in terms of pi_symbol?
28pi in.
7. What is the area of the given circle in terms of pi?
10.89pi m^2
8. What is the area of a sector with a central angle of 185° and a diameter of 6.4 m? Round the answer to the nearest tenth.
16.5 m^2
9. What is the area of the shaded region in the given circle in terms of pi_symbol and in simplest form?
(270 pi + 81 Root 3) m^2
A spherical ball of wax with a radius of 4 inches is melted and poured into a container shaped like a rectangular prism with a 6 inch x 6 inch base. What is the height of the melted wax in the new shape?
A 3-lb force acting in the direction of the vector (3,-1) moves an object just over 9 ft from point (0,5) to (6,-2). Find the work done to move the object to the nearest foot-pound
Answer: The Work done to move the object is [tex]=23.15 \text { foot pounds }[/tex]
Step-by-step explanation:
Given;
Force F=3 [tex]l b s[/tex]
Vectors of F= (3,-1)
Moves object to a distance=9 [tex]f t s[/tex]
Let A and B be the displacements Vectors
A= (0,-5)
B= (6,-2)
To Find:
Work done in foot-pounds
Solution:
Work done [tex]W=F \times D[/tex]
Direction of force vector= (3,-1) (i, j)
=3i-j
Unit of force vector [tex]=\sqrt{3^{2}+\left(-1^{2}\right)}[/tex]
[tex]=\sqrt{9+1}[/tex]
Force vector=(Force/Unit Vector)Direction of force vectors
F=[tex]3 / \sqrt{10} \times(3 i-j)[/tex]
Direction of motion vector= (B-A)
= (6,-2)-(0,-5) x i,j)
=(6-0),(-2-5) x (i, j)
=(6,-7) x (i, j)
=6i-7j
Unit of motion vector [tex]=\sqrt{6^{2}+\left(-7^{2}\right)}[/tex]
[tex]=\sqrt{36+49}[/tex]
[tex]=\sqrt{85}[/tex]
Motion Vector= (Distance moved by the object/Unit motion vector) × (Direction of motion vectors)
[tex]D=9 / \sqrt{85} \times(6 i-7 j)[/tex]
Workdone [tex]W=F \times D[/tex]
[tex]= [3/ \sqrt{10} \times (3i-j)] \times [9/ \sqrt{85} \times (6i-7j)][/tex]
[tex]= [3/ \sqrt{10} \times 9/ \sqrt{85}] \times [(3i-j) \times(6i-7j)][/tex]
[tex]= [3/3.1623 \times 9/9.2195] \times [(3\times6) + ((-1) \times (-7))][/tex]
[tex]= [0.94867 \times 0.97619] \times [18+7][/tex]
[tex]=23.15 \text { foot pounds }[/tex]
Result:
Work done to move an object [tex]=23.15 \text { foot pounds }[/tex]
Answer:
[tex]W = 25.617\,lbf\cdot ft[/tex]
Step-by-step explanation:
The work done to move the object is:
[tex]W = F \cdot s \cdot \cos \alpha[/tex]
The angle of the force with respect to change in the position vector is:
[tex]\alpha = \tan^{-1}\left(-\frac{7}{6} \right) - \tan^{-1}\left(-\frac{1}{3} \right)[/tex]
[tex]\alpha \approx 18.415^{\textdegree}[/tex]
The magnitude of the work done is:
[tex]W = (3\,lbf)\cdot (9\,ft)\cdot \cos 18.415^{\textdegree}[/tex]
[tex]W = 25.617\,lbf\cdot ft[/tex]
The length of a rectangle is 5 yd less than three times the width, and the area of the rectangle is 28 yd2 . find the dimensions of the rectangle.
The dimensions of the rectangle are width = 4 yds and length = 7 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the length of a rectangle is 5 yds less than three times the width,
The area of the rectangle is 28 yds square.
Let the width of the rectangle is x
So the length of the rectangle = 3x - 5
The area of a rectangle = x × (3x - 5)
28 = 3x² - 5x
3x² - 5x - 28 = 0
(3x + 7)(x - 4) = 0
3x + 7 = 0 and and x - 4 = 0
x = -7/3 and x = 4
Take x = 4 as the width
So the length of the rectangle = 3(4) - 5 = 12 - 5 = 7
Therefore, the dimensions of the rectangle are width = 4 yds and length = 7 yds.
Learn more about the Area of the rectangle here:
brainly.com/question/20693059
#SPJ5
Please help me idk this
Answer:
1 13/20
Step-by-step explanation:
You want the total of distances walked to be the length of the hike:
2 1/10 + 1 1/4 + (left to walk) = 5
Then the amount left to walk is the difference ...
left to walk = 5 - 2 1/10 - 1 1/4
___
You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.
5 - 2 1/10 - 1 1/4
= (5 -2 -1/10) - 1 1/4
= 2 9/10 - 1 1/4
= (2 -1) + (9/10 -1/4)
= 1 + (9/10 -1/4)
= 1 + (18/20 - 5/20)
= 1 13/20 . . . miles left to walk
___
Using a calculator:
5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20
ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)
Solve for x in the image below
The value of x in the equation given is 8
Using the equations given for our Calculation;
7/8 - 1/x = 3/4Take the L.C.M of 8 and x ; which is 8x
(7x - 8) / 8x = 3/4
Now we cross multiply;
4(7x - 8) = 3 * 8x
open the bracket
28x - 32 = 24x
28x - 24x = 32
4x = 32
x = 8
Hence, the value of x = 8
Learn more on equations: https://brainly.com/question/2972832
#SPJ2
On a highway, Nick's car uses 12.5 gallons of gas to travel 240 miles. The gas tank in Nick's car holds 20 gallons of gas. How far can Nick's car travel on a highway using a full tank of gas?
Answer:
Nick's car can travel 384 miles using a full tank of gas.
Step-by-step explanation:
The antarctic peninsula is less than 700 miles from what continent
At a high school 7 student volunteer for a committtee how many different 5 person committees can be chosen
Using the combination formula, 21 different 5-person committees can be chosen from a group of 7 students.
To determine how many different 5-person committees can be chosen from a group of 7 students, we use the concept of combinations, specifically the combination formula which is defined as:
C(n, k) = n! / [k! * (n - k)!]
where n is the total number of items to choose from, k is the number of items to choose, and the exclamation point represents a factorial, which is the product of all positive integers up to that number.
Applying this to the given problem, we have:
C(7, 5) = 7! / [5! * (7 - 5)!]
This simplifies to:
C(7, 5) = (7 * 6) / (2 * 1)
Therefore, C(7, 5) = 21.
There are 21 different 5-person committees that can be formed from 7 students.
Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would Tammy take to do the job alone?
3 hrs.
4 hrs.
6 hrs.
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura.
The equations are given as,
T + J + L = 1 + 20/60
T + J + L = 1.333 ....1
J = 2T ....2
J = 2 + L ....3
The rate for Laura, Tammy, and Jeri will be given as,
Laura DATA:
Time = x hr/job ; Rate = 1/x job/hr
Jeri DATA:
Time = x+2 hr/job ; Rate = 1/(x+2) job/hr
Tammy DATA:
Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr.
Together DATA:
Time = 4/3 hr/job ; Rate = 3/4 job/hr
The equation is given as,
Rate + Rate + Rate = Together rate
1/x + 1/(x+2) + 2/(x+2) = 3/4
Multiply the equation by 4x(x+2) to get:
4(x+2) + 4x + 8x = 3x(x+2)
16x + 8 = 3x^2+6x
3x^2-10x-8 = 0
3x^2-12x+2x-8 = 0
3x(x-4)+2(x-4) = 0
(x-4)(3x+2) = 0
x = 4, - 2/3
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
PLEASE HELP: Question above ☝☝☝
I'm actually pretty sure it's B
Can someone show me how to do this?
16! / 4! 12!
Jesse earns $420 a week, and he works 5 days a week. What is his daily wage?
A. $84
B. $415
C. $60
D. $425
**MARKING BRAINLIEST IF RIGHT AND IF YOU SHOW WORK**
3. Use the Fermi process to estimate the number of bricks needed to fill an empty bathtub. Show your work.
My teacher said you can use approximate dimensions of the bricks and bathtub. He said use the easiest ones so that it will be easy to solve.
You are looking at two different houses. house #1 would have a daily 5-mile commute to work, while house #2 would have a daily 20-mile commute. how much more co2 would you produce annually if you buy house #2? (hint: driving 1 mile produces 1.1 lb of co2 and you work 240 days/year.)
Answer:
B: 3960 lb
Step-by-step explanation:
vhslearning
Lines that are not in the same plane are called _____ lines. A.perpendicular B.transversal C.skew D.parallel
Lines that are not in the same plane are called skew lines.
What is a line?"A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely."
Given, two lines are not in the same plane.
Here, perpendicular lines, transversal lines, and parallel lines should be in the same plane.
Two lines are called skew lines are two lines if they do not intersect and are not parallel.
Therefore, skew lines are not in the same plane.
Learn more about lines here: https://brainly.com/question/2506929
#SPJ2
Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9 A) (x - 1 6 )2 = 71 36 B) (x - 1 3 )2 = 71 36 C) (x - 1 6 )2 = - 71 36 Eliminate D) (x - 1 3 )2 = - 71 36
PLEASE HELP!!! ASAP!!!!!!!!!!!!!!! 10 POINTS
Expand the number 1800 into its corresponding exponential form.
2^3 · 3^2 · 5^2
9^2 · 100
8 · 9 · 25
2^2 · 3^3 · 5^2
Select expression equal to ^3√320
4
4^3√5
5^3√4
5^3√5
The recursive rule for a sequence is shown. an=an−1+7 a1=17 what is the explicit rule for this sequence?
The explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
The recursive rule is given as:
[tex]a_n=a_{n-1}+7[/tex]
[tex]a_1 = 17[/tex]
The above shows that the sequence is an arithmetic sequence.
Start by calculating a2
We have:
[tex]a_n=a_{n-1}+7[/tex]
Substitute 2 for n
[tex]a_2=a_1+7[/tex]
This gives
[tex]a_2 = 17 + 7[/tex]
[tex]a_2 = 24[/tex]
So, we have:
a1=17
a2 = 24
The common difference (d) is:
d =a2 - a1
d = 24 - 17
d = 7
The explicit rule is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 17 + (n - 1) * 7[/tex]
Expand
[tex]a_n = 17 - 7 + 7n[/tex]
[tex]a_n = 10 + 7n[/tex]
Hence, the explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
Read more about arithmetic sequence at:
https://brainly.com/question/6561461
Which path is a Hamiltonian circuit?
Which of the following is not an example of like terms? A. 2 and –6 B. 2b and –6b C. 2b and 2 D. 2b^2 and 6b^2
Anyone know?
A. 99
B. 100
C. 121
D. Cannot be determined
Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.
By being congruent, the corresponding angles and sides are equal.
Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].
By using [tex]\angle A = \angle F[/tex]
So, [tex]100^\circ = \angle 1[/tex]
Therefore, the measure of angle 1 is 100 degrees.
So, Option B is the correct answer.
Evaluate the expression
A. arctan ( - \sqrt{3} )
B. Arctan ( - \sqrt{3} )
Pls help i need this asap!
The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.
A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.
To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.
B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.
Learn more about trigonometric functions here:
https://brainly.com/question/1542663
#SPJ6
Find the equation of the line that passes through (-2,5) and is parallel toy= -1/3x+2
Help please??????????
Phil is offered a 3-year contract with a law firm. His first year earnings would be $81,000 with an annual raise of 15%.
What would Phil's total earnings be over the term of the contract?
Enter your answer, rounded to two decimal places, in the box.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%. Phil's total earnings would be over the term of the contract is $281272.5.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%.
First year
= $81000
Second year
1.15 x ($81000)
= $93150
Third year
1.15 x ($93150)
= $107122.50
Phil's total earnings would be over the term of the contract
= $81000 + $93150 + $107122.50
= 281272.5
Learn more about addition here;
https://brainly.com/question/545875
#SPJ2
He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?
What is the answer to the jones family plans a trip to the amusement park...
Select the equations that are equivalent to the equation y – 2 = 3(x + 6). Select all that apply.
y = 3x + 20
y = 3x + 6
2x - y = -3
3x - y = -20
How would I write #3