Algebra 2 Final Exam -kiwi
Solve the following quadratic equation by using the quadratic formula: x²+x=11
x= (−1 ± 3√5/2)
Which point lies on the circle centered at the origin with √5 ?
(-1, 2)
Perform the indicated operation: (1−i/−2+2i)
(-1/2)
Perform the indicated operation: (−10i/−3+2i)
(-20/13)+(30/13 i)
Factor the following: x²−5x−6.
(x−6)(x+1)
Factor the following: y²−9y+18.
(y−6)(y−3)
Perform the following operation: (−10+3i/7−7i)
(−13−7i/14)
Simplify (−8−6i)+(−2−5i)
-10 - 11i
Simplify: (−8+7i)−(−5+3i)
-3 + 4i
Simplify the following radical expression as an exact value: √8 ⋅ √18 ⋅ 5√4
120
Jessica has some round stickers. Each sticker has a radius of 2 cm. She is trying to cover as much of a sheet of paper that is 24 cm by 33 cm as possible without any overlap and modification of the stickers. How much of the bare paper will be visible around the stickers?
188.81 square cm
Perform the given operation: (11+i√12)−(−8+i√3)
19+i√3
Which of the following ratios is equivalent to (1/2)?
1:1
A ball has a density of 0.5 g/mL and a mass of 125 grams. What is the volume of the ball?
250 mL
A hula hoop has a radius of 19 inches. What is the length of the arc subtending 1/4 of the hoop?
29.8 inches
Simplify the following: (160x⁷)^(1/4)
2x⋅(10x³)^(1/4)
How many radians are in a circle?
2π
The rectangular pool above has a length of 32 feet, width of 18 feet, and depth of 6 feet. How much water can it hold?
3,456 cubic feet
What is the total volume of a pair of dice with side length 12 millimeters?
3,456 mm³
-Upper:400; Yes= ?, No=100 -Lower:600; Yes=450, No= ? Students at a high school were polled regarding whether or not they would like to change the vending options at the school. Use the tree diagram to determine how many upper-classmen responded "yes".
300
Ian orders an ice cream cone filled to the top with ice cream, with 1 perfectly round scoop of ice cream on top. The cone and the scoop of ice cream both have a radius of 1.8 inches, and the height of the cone is 4.5 inches. What is the total volume of ice cream Ian receives?
39.7 cubic inches
Solve the given quadratic inequality algebraically. x²−11x+28 < 0
4 < x < 7
The graph below shows the number of employees needed at a daycare based on the number of children present. How many employees are needed if there are 18 children?
4 employees
Simplify the following expression. Assume all variables are positive. 128 ^(1/3)
4 ∛2
A farm has 6 chickens, 4 ducks, 2 pigs and 4 cows. If an animal is chosen at random, find P(Cow U C-name).
5/8
The graph of this function is shifted how many units left or right and shifted how many units up or down? f(x)=(−2/3)(x−7)³−5
7 units Right; 5 units Down
Let Q (in grams) represent the mass of a quantity of carbon-14, which has a half-life of 5730 years. The quantity present after t years is Q(t)=10⋅(1/2)^(t/5730). Determine the quantity present after 2000 years.
7.851 grams
*Do You Text* Chart Yes: No: Total: Under 30: (A) (5) (60) Over 30: (C) (B) (40) Total: (D) (25) (100) According to the table, -- should be the value of D.
75
What is the sum of the first 8 terms of the geometric series: 3+6+12+24+...
765
A new toy hits the local store. Sales (in hundreds) increase at a steady rate for several months, then decrease at about the same rate. This can be modeled by the function S(m)=−0.625∣m−8∣+5 In what month(s) were 400 toys sold?
7th and 10th
Evaluate the expression without using a calculator: 16^(3/4)
8
Ted buys wood to build his guitars. Find the number of blocks of mahogany that Ted can afford to buy if he wishes to spend a total of $5000 this month, mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each.
8
A rectangle's length is 1.5 times its width. The perimeter of the rectangle is four more than 3 times the length. What are the dimensions of the rectangle?
8 x 12
Covington, Georgia has a total area of 13.9 square miles and a population of 11,547 people. What is the population density of the city?
830.72 people per square mile
Simplify the following radical expression as an exact value: 4 ∜128
8⋅ ∜8
A triangular pyramid has a triangular base with height of 1.5 inches and base length of 4 inches, and height of 9 inches. What is the volume?
9 cubic inches
Find the length of the arc on a circle with a radius of 7 centimeters and a central angle of 74 degrees.
9.04 centimeters
Simplify: (−5−8i)(−6+8i)
94 + 8i
Which of the following is NOT an equivalent expression to *Area of sector= (πr²θ/360)* ?
Area of a sector= (2πrθ/360)
*Have you read HP* Chart Male: Female: Total: Have read: (19) (24) (43) Have not read: (57) (84) (141) Total: (76) (108) (184) Reading Harry Potter and gender are independent.
False
P(A) = 2/3 P(B) = 2/3 P(A ∩ B) = 2/3 A and B are independent.
False
The domain of the graph of this equation is (−3.0249,+∞). y=−x³+10x²+x−3
False
The domain of the graph of this equation is (−∞,11). y=−3x³+10x²−13x+11
False
The graph of this equation is an upside down parabola. y=x³+11x²−5x−1
False
The graph of this function is shifted 7 units left and shifted 5 units up. f(x)=(−2/3)(x−7)²−5
False
The graph of y=3x⁵−4x²+2 has a y−intercept at 3.
False
The range of the graph of this equation is (−1.9,∞). y=x⁴−4x³+143x²−97x+2
False
f(x)=3x−7 and g(x)=(1/3)x+7 are inverses of each other.
False
What operation would you use to find the mass of an object given its density and volume?
Mass = (Density)(Volume)
-purple line, seems to open up, very blurry- View the graph below. Decide what type of symmetry, if any, it has.
No Symmetry
How many real and imaginary solutions does the equation x²−3x=−2x−7 have?
No real solutions; 2 imaginary solutions
Which expression represents the probability of the union of not A and not B?
P(A′∪B′)
*HH* : *Both* : *C* : *Neither* : -WJC -BHO -GWB -RWR -JFK -RMN -JEC -GRF -WHT -DDE -LBJ -HST -WGH -GHB -FDR -HCH If a student (represented by initials) was chosen at random, find P(HH | C').
P(HH | C') = 1/2
Find the point that partitions the segment AB with coordinates A(-2, 4) and B(7, -2) in the ratio 1:2.
P: (1, 2)
Given points X(-1, 2) and Y(7, 14), find the coordinates of the point P on the directed line segment that partitions XY in the ratio 1:3.
P: (1, 5)
HH= Section 1 Intersection= Section 2 C= Section 3 Outside= Section 4 Which section or sections represent what is not in set HH?
Sections 3 and 4.
Find the zeros: f(x)=x⁴−2x³+x²
The solutions are 0 and 1.
Find the zeros: f(x)=x³+4x
The solutions are 0 and ±2i.
Find the roots of the equation below by graphing. Give answers to the nearest tenth.. x²−3x=7
The zeros are -1.5 and 4.5
P(A) = 5/6 P(B) = 4/5 P(A ∩ B) = 2/3 A and B are independent.
True
The graph of this equation is shifted 3 units to the right and 5 units up. y=−4(x−3)³+5
True
The graph of this equation rises on the right. y=x³+5x²−3x+1
True
The range of the graph of this equation is [1.8974,∞). y=x⁴−4x³+143x²−97x+2
True
Which is NOT true of the construction of an angle bisector?
When you're finished, you have a line that bisects your segment
The city of Covington is placing a statue in a triangular grassy area bounded by sidewalks on all 3 sides. If the city wants the statue to be an equal distance from all 3 sides of the grassy area, where should they place it?
at the incenter of the triangle
Give the center and radius of the circle defined by the following equation:(x − 1)²+ y² = 5
center = (1, 0) radius = √5
A prism with a heart-shaped base is sliced parallel to the base. What shape is formed?
heart
The 3D object above is sliced parallel to the base. What shape is formed?
hexagon
Given a triangle with coordinates X(2, -1), Y(-5, -4), and Z (-2, 3), what type of triangle is it?
isosceles
Paige knows that a certain shape is a rectangle. She has found the slope of one side to be 2/3. What is the slope of the opposite side? What are the slopes of the other two sides?
opposite side: 2/3 other sides: -3/2
A quadrilateral is formed by the points A(1, -1), B(0, 3), C(5, 5), and D(6, 1). Plot the points and use the distance formula to find the lengths of all 4 sides. What type of quadrilateral is this?
parallelogram
Which of the following constructions must you know how to do in order to construct a circumscribed circle for a given triangle?
perpendicular bisector
Which of the following is NOT used in geometric constructions?
protractor
What geometric figure best describes the large building in the photo?
pyramid
A triangle whose sides are all different lengths is a(n) ________ triangle.
scalene
Which of these is NOT a method for proving that a quadrilateral is a parallelogram?
show that one pair of opposite sides is parallel and the other is not parallel
What shape is a soccer ball?
sphere
What shape is used to describe a marble?
sphere
Area is expressed in ______ units, while volume is expressed in ______ units.
square; cubic
Simplify the expression. Assume all variables are positive. t ⋅ t^(-1/5)
t^(4/5)
Which of the following is always true about opposite angles of a cyclic quadrilateral?
they add up to 180 degrees
Which of the following is NOT true of a perpendicular bisector?
to construct it, we have to draw two arcs using the intersection points as centers
What type of quadrilateral has one pair of opposite sides that are parallel, and one pair of opposite sides that are not parallel?
trapezoid
What shape best describes the figure above?
triangular prism
Solve the given quadratic inequality algebraically. x²−11x+28 ≥ 0
x ≤ 4 or x ≥ 7
Solve the given quadratic inequality algebraically. x²−2x−15 ≥ 0
x ≤ −3 or x ≥ 5
Which of the following is the correct factorization of ...x⁵+x³−2x ?
x(x²+2)(x−1)(x+1)
Solve the following quadratic equation by completing the square: 4x²−4x−2=0
x= (1/2) ± (√3/2)
Solve the following quadratic equation by using square roots: (1/4)(x+1)²−16=0
x=−9; x=7
A rectangle's length is 1.25 times its width. Its perimeter is 3 times the length plus one. What are the dimensions of the rectangle?
1.33 x 1.67
A six sided die is rolled and a coin is tossed. Find P(1 and H).
1/12
A six sided die is rolled and a coin is tossed. Find P(T | 6).
1/2
A six sided die is rolled and a coin is tossed. Find P(odd and T).
1/4
P(A) = 1/2 P(B) = 1/3 If A and B are independent, what is P(A ∩ B)?
1/6
A sector of a circle has a central angle measure of 310 degrees. If the radius of the circle is 2 feet, what is the area of the sector?
10.82 square feet
A circle has a diameter of 10 centimeters. If a sector with a central angle of 50 degrees is cut out, what is the area of this sector?
10.91 square centimeters
In a survey, 70 out of 84 people from the north prefer professional football over college football. 120 people from the south were asked the same question. In order for favorite type of football and region to be independent, -- people in the south would have to prefer professional football
100
-Upper:400; Yes= ?, No=100 -Lower:600; Yes=450, No= ? Students at a high school were polled regarding whether or not they would like to change the vending options at the school. Use the tree diagram to determine how many students were polled.
1000
Emily went to a local shop to purchase some round rugs. Each rug has a radius of 3 feet. She is trying to cover as much of the floor of her 18 foot by 20 foot living room as possible without any overlap of the rugs. How much of the bare floor will be visible around the rugs?
105.5 square feet
What is the mass of a cylinder of lead with a radius of 1 centimeter and a height of 3 centimeters, given that the density of lead is 11.4 (g/cm³) ?
107.39 grams
A cylinder has a volume of 33 cubic inches. What is the volume of a cone with the same radius and height?
11 cubic inches
Find the perimeter of trapezoid WXYZ with vertices W(2, 3), X(4, 6), Y(7, 6), and Z(7,3). Leave your answer in simplest radical form.
11+√13 units
Given rectangle ABCD with vertices A(1, 4), B(3, 6), C(6, 3), and D(4, 1), what is the area of ABCD? Leave your answer in simplified radical form.
12 square units
Find the perimeter of a triangle with vertices A(3, 1), B(2, -1), and C(-3, 2). Leave your answer in decimal form, rounded to the nearest hundredth.
14.15 units
Evaluate the expression without using a calculator: (−64)^(2/3)
16
A rectangle has the following vertices: A(-1, 9), B(0, 9), C(0, -8), D(-1, -8). What is the area of rectangle ABCD?
17 square units
Many students from Europe come to the United States for their college education. From 1980 through 1990, the number S (in thousands), of European students attending a college or university in the U.S. can be modeled by S=0.05(t³−11t²+45t+277), where t=0 corresponds to 1980. In what year were there 31.35 thousand European students attended a U.S. college or university?
1990
What is the slope of a line parallel to -6x + 3y = 5?
2
A club consists of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve and Samuel). Find P(Girl | K-name)
2/3
What is the slope of a line perpendicular to 3x + 2y = 7?
2/3
A club consists of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve and Samuel). Find P(K-name | girl)
2/5
*Do You Text* Chart Yes: No: Total: Under 30: (A) (5) (60) Over 30: (C) (B) (40) Total: (D) (25) (100) According to the table, -- should be the value of B.
20
*Do You Text* Chart Yes: No: Total: Under 30: (A) (5) (60) Over 30: (C) (B) (40) Total: (D) (25) (100) According to the table, -- should be the value of C.
20
Find the perimeter of quadrilateral ABCD with vertices A(0, 4), B(4, 1), C(1, -3), and D(-3, 0).
20 units
Perform the indicated operation: (−3+2i√48)(−5−4i√12)
207−16i√3
Simplify the following: 4(150x²y)^(1/2)
20x √6y
Give the center and radius of the circle (x+2)²+(y−4)²=36
center: (-2, 4) radius: 6
A plane slices through a cone parallel to the base. What shape is the cross-section?
circle
What shape is formed when a plane slices through a sphere at any angle?
circle
Kim is constructing the circumscribed circle about a triangle she drew. What is the center of this circle called?
circumcenter
Arc length is a fraction of a circle's _____________.
circumference
Arc length is to ____________ as central angle is to 360 degrees.
circumference
An equilateral triangle is rotated around an axis bisecting the triangle. What shape is formed?
cone
Nate is constructing a tangent line to a circle he drew from a point outside the circle. Once he has the circle and the point drawn, what is his next step?
connect the center of the circle to the point outside the circle
Ed is constructing the perpendicular bisector of a segment on his paper. He just finished labeling the points of intersection of the two arcs that he drew. What is his next step?
construct the line connecting the two points
A quadrilateral inscribed in a circle is called a _________________.
cyclic quadrilateral
Laurie is constructing an angle bisector. She sketched her angle, then opened her compass to a radius length less than the length of the rays that make up the angle. What should be her next step?
draw an arc, using the vertex as the center
A piece of wood measures 4 in x 6 in x 3 in and has a mass of 80 grams. What is its density?
1.1 (grams/in³)
What are the y-intercepts of the following polynomial equation? y=−2x⁴−2x²−3x+6x³+(3/4)
(0,0.75)
The points A(-3, -4) and B(5, 0) form a line segment. Find the coordinates of the point P that partitions segment AB in a 2:3 ratio.
(0.2, -2.4)
Perform the following operation: (−2+8i/4+2i)
(2+9i/5)
What is the vertex of the graph of y=3x²−12x+13 ?
(2, 1)
What is the vertex of the graph of y=(1/4)(x−2)²+6 ?
(2, 6)
What is the vertex of the graph of y=(−1/2)(x+2)(x−6)?
(2, 8)
What point is 2/3 of the distance from point A(3, 1) to point B(3, 19)?
(3, 13)
Which of these points lies on the circle with center (2, 3) and radius 2?
(4, 3)
Ian's home is represented by the point (4, 4) on the coordinate grid. Joe's home is represented by the point (10, 6) on the coordinate grid. They want to meet at a diner is halfway between their houses (i.e., divides the line from Ian's house to Joe's house in a 1:1 ratio). What are the coordinates of the diner?
(7, 5)
Simplify the following radical as an exact value: √(7/3) ⋅ √(14/3)
(7√2/3)
Factor the following quadratic expression completely: 64x²−121
(8x + 11)(8x - 11)
A student wants to write an expression for, "all of the elements which are not in set A but are in set B". Which expression below matches the statement?
(A′∩B)
A student wants to write an expression for, "all of the elements which are not in set A combined with those elements not in set B". Which expression below matches the statement?
(A′∪B′)
A student wants to write an expression for, "all of the elements which are in sets A and B (not just A or just B)". Which expression below matches the statement?
(A∩B)
If A={2,4,6,8,10,12} and B={3,6,9,12,15} then A∩B is
(A∩B)={6,12}
A student wants to write an expression for, "all of the elements which are in set A AND all of the elements in set B". Which expression below matches the statement?
(A∪B)
If A={2,4,6,8,10,12} and B={3,6,9,12,15} then (A∪B) is
(A∪B)={2,3,4,6,8,9,10,12,15}
What does the rational form of the ratio a:b look like?
(a/a+b)
Factor the following polynomial by grouping 4x³−4x²−9x+9.
(x−1)(2x−3)(2x+3)
What is the equation of a circle with radius 2 and center (3, 1)?
(x−3)²+(y−1)²=4
Factor the following polynomial by any method. x²−6x+8
(x−4)(x−2)
Factor the following polynomial by grouping x³−5x²−9x+45.
(x−5)(x−3)(x+3)
What is the sum of the first 7 terms of the geometric series: -8 + (-4) + (-2) + (-1) + (−1/2)+...
-15.875
What is the slope of a line parallel to 3x + y = 7
-3
Perform the given operation: (1+5i)−(5+3i)
-4 + 2i
For the function below, find f(-6). f(x)=−2∣x²−10∣−1
-53
Simplify: (−6+7i)−(3+2i)
-9 + 5i
A farm has 6 chickens, 4 ducks, 2 pigs and 4 cows. If an animal is chosen at random, find P(Cow | 2 legs).
0
What is the density, in grams/cubic inch, of a substance with a mass of 6 grams filling a rectangular box with dimensions 2 in x 6 in x 3 in?
0.17
What is the density of a piece of metal that has a mass of 25 grams and a volume of 29.4 cubic centimeters?
0.85 (grams/cm³)
-Rectangle with shaded corners that are x by x- A baker is folding up open-topped boxes to package up her baked goods. She has flat, rectangular pieces of cardboard that are 10 inches by 6 inches. She wants to maximize the volume of the box. What size squares should she cut from the corners of the cardboard?
1.21 inches
To prove a quadrilateral is a trapezoid, what must we show?
1. one pair of opposite sides parallel 2. one pair of opposite sides NOT parallel (different slopes)
Joe is building a rectangular pool in his yard. He knows that the perimeter of the pool must be 88 feet, but he wants the surface of the pool to have the largest possible area. What length and width should Joe choose for the pool?
22 ft x 22 ft
A box of cereal has the following dimensions: 12 inches x 7.5 inches x 2.5 inches. What is the volume of the box of cereal?
225 cubic inches
Perform the indicated operation: (−3+2i)(−5−4i)
23+2i
The "body" of a soda can (in between the lid and the bottom) is a cylinder. If the body is about 4.5 inches tall with a diameter of about 2.6 inches, what is the volume of soda the body of the can is able to hold?
23.89 cubic inches
A cereal box has a height of 10 inches, a length of 8 inches, and a width of 2 inches. What is the surface area of the cereal box?
232 square inches
P(A) = 1/2 P(A ∩ B) = 1/5 What will P(B) have to be for A and B to be independent?
4/10
What is the slope of a line perpendicular to 3x + 4y = -2?
4/3
*Do You Snapchat* Chart Yes: No: Total: Under 30: (35) (A) (40) Over 30: (20) (40) (B) Total: (C) (D) (100) According to the table, -- should be the value of D.
45
Mai is kayaking on a river that has a current of 2 miles per hour. If r represents her rate in calm water, then (r + 2) represents her rate with the current, and (r - 2) represents her rate against the current. Mai kayaks 2 miles downstream and then back to her starting point. Use the formula for time, t=(d/r), where d is the distance, to write a simplified expression for the total time it takes Mai to complete the trip.
4r/(r+2)(r-2) hours
Simplify the following radical expression as an exact value: √810 + √240 − √250
4√10 + 4√15
Find the area of a triangle with vertices A(3, 1), B(2, -1), and C(-2, 1). Leave your answer in decimal form, rounded to the nearest hundredth.
5 square units
The graph of this function is shifted how many units left or right and shifted how many units up or down? f(x)=−3(x+5)³+2
5 units Left; 2 units Up
You are pouring juice into a cylindrical cup with a 2 inch radius and height of 8 inches. If you want to fill it exactly half full, how many cubic inches of juice should you pour in?
50.3 cubic inches
Perform the following operation: (1+5i) + (5+3i)
6+ 8i
*Do You Snapchat* Chart Yes: No: Total: Under 30: (35) (A) (40) Over 30: (20) (40) (B) Total: (C) (D) (100) According to the table, -- should be the value of B.
60
Evaluate the expression without using a calculator: (∜256)³
64
A student wants to write an expression for, "all of the elements which are not in set A". Which expression below matches the statement?
A'
Find the zeros: f(x)=x³+14x−8x²−1. Round to the nearest hundredth.
The zeros are 0.08, 2.45, and 5.48.
*Do you own a smartphone* Chart Male: Female: Total: Yes: (27) (24) (51) No: (81) (72) (153) Total: (108) (96) (204) Owning a smartphone and gender are independent
True
A polynomial function with a degree of 0 is called a Constant Function.
True
A polynomial function with a degree of 3 is called a Cubic Function.
True
A polynomial function with a degree of 5 is called a Quintic Function.
True
A rough sketch of y=x³−4x²+3x is "S" shaped.
True
The density of air is approximately 1.225 kg/m³ . What is the volume of a soccer ball if the mass of the air it contains is 0.08 kg?
V = 0.07 cubic meters
Which of the following constructions must you know how to do in order to construct an inscribed circle for a given triangle?
angle bisector
In order to prove that a quadrilateral is a square specifically, we must show that it possess the properties of both a ________ and a _________.
rectangle; rhombus
Solve the following quadratic equation by completing the square: 4x²−7x+83=0
x= (7/8) ± i(√1279/8)
Factor and solve the given quadratic equation: 4x²+9=0.
x= ± (3/2)i
Solve the following quadratic equation by using square roots: (3/4)(x+1)²+16=0
x= −1 ± 2i√3
Solve completely by factoring. 8x²+5x−4=2x²−8x+1
x=(−5/2); x=(1/3)
What is the axis of symmetry of the graph of y=(1/4)(x−2)²+6 ?
x=2
Solve the following quadratic equation by using the quadratic formula: x²+2x−9=0
x=−1 ±√10
Solve the following by factoring: 2x²+7x−4=0
x=−4; x=(1/2)
Solve the following quadratic equation by using square roots: 2(x+3)²=8
x=−5; x=−1
Factor and solve the given quadratic equation: x²+13x+42=0.
x=−7; x=−6
Which of the following is the correct factorization of x⁴−x³−6x² ?
x²(x−3)(x+2)
-Center at (0,3) and radius of 4- What is the equation of this circle?
x²+(y−3)²=16
Find the equation of the line parallel to y = 2x - 4 that runs through the point (-2, 4).
y = 2x + 8
Find the equation of the line that has a y-intercept of 1 and is perpendicular to the graph of the line 2x + y = 4.
y= (1/2)x+1
Give the equation of the line perpendicular to the line through (3, 2) and (-2, 4) that passes through the point (1, 1).
y= (5/2)x−(3/2)
A college with a graduating class of 4000 students in the year 2010 predicts that its graduating class will grow 5% per year. Write an exponential function to model the number of students y in the graduating class t years after 2010.
y=4000(1.05)^t
Does the point (2, 2) lie on the circle (x−4)²+(y−2)² = 4?
yes; when you plug the point in for x and y, you get a true statement
Choose all the situations that are independent
~ A die is thrown and the same die is thrown again. ~ Die is thrown and a coin flipped. ~ Two cards are drawn (with replacement).
Choose all the situations that are independent.
~ Two marbles are pulled from a deck (with replacement) ~ A coin is tossed 10 times.
Use the Rational Root Theorem to list all of the possible Rational Zeros of the following equation: t³−13t²+65t−105=0
±1, ±3, ±5, ± 7, ±15, ±21, ±35, and ±105
How many radians are in a semicircle?
π
Solve the given quadratic inequality algebraically. x²−6x−16 ≤ 0
−2 ≤ x ≤ 8
Perform the indicated operation: (3+7i)(8+4i)
−4+68i
Perform the given operation: (1+i√12)+(−8+i√48)
−7+6i√3
