Answers
If a quadrilateral is a parallelogram, then its opposite sides are congruent therefore:
[tex]\begin{gathered} GH\cong JI \\ and \\ GJ\cong HI \end{gathered}[/tex]Using the distance formula:
[tex]\begin{gathered} GH=\sqrt[]{(5-1)^2+(3-1)^2} \\ GH=\sqrt[]{16+4} \\ GH=\sqrt[]{20} \\ JI=\sqrt[]{(0-4)^2+(3-5)^2} \\ JI=\sqrt[]{16+4} \\ JI=\sqrt[]{20} \\ GH\cong JI \end{gathered}[/tex][tex]\begin{gathered} GJ=\sqrt[]{(0-1)^2+(3-1)^2} \\ GJ=\sqrt[]{1+4} \\ GJ=\sqrt[]{5} \\ HI=\sqrt[]{(4-5)^2+(5-3)^2} \\ HI=\sqrt[]{1+4} \\ HI=\sqrt[]{5} \\ GJ\cong HI \end{gathered}[/tex]Step 2:
The diagonals are given by:
[tex]\begin{gathered} JH=\sqrt[]{(0-5)^2+(3-3)}^2 \\ JH=\sqrt[]{25} \\ JH=5 \\ GI=\sqrt[]{(4-1)^2+(5-1)^2} \\ GI=\sqrt[]{9+16} \\ GI=\sqrt[]{25} \\ GI=5 \\ JH=GI \\ 5=5 \\ so\colon \\ JH\cong GI \end{gathered}[/tex]Related Questions
please help!!! only 20 mins left
Answers
The rule of (x, y) → (-x, y), which is reflection over y-axis.
Given that, ΔABC maps to triangle ΔA'B'C'.
What is the reflection on y-axis?When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
The coordinate points of ΔABC are A(-4, 3), B(-3, -3) and C(1, 2) and the coordinate points of ΔA'B'C' are A'(4, 3), B'(3, -3) and C'(-1, 2).
Here, A(-4, 3) → A'(4, 3), x-coordinate is negated and y-coordinate remains same.
Similarly, B(-3, -3) → B'(3, -3) and C(1, 2) → C'(-1, 2) follows the same pattern.
From this, it is clear that the coordinates of triangle ABC is reflected on y-axis.
Therefore, the rule of (x, y) → (-x, y), which is reflection over y-axis.
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Identify a solution to the system of equation
-4x+ 3y=23
x - y =7
Answers
x = - 44 and y = - 51
How are the linear equations solved?
-4x+ 3y=23 ---(1)
x - y =7 ----(2)
4*(2) => 4x- 4y =28 ---- (3)
(3) + (1)
4x- 4y =28 (+)-4x+ 3y=23
- y = 51
y = -51
Substituting y in (2)
x - y =7
x + 51 = 7
x = -44
What are linear equations ?
A linear equation is one in which the variable's maximum power is consistently 1.A one-degree equation is another name for it. A linear polynomial over a field, from which the coefficients are taken, can be reduced to a linear equation by equating it to zero. Due in part to the fact that linear equations are typically good approximations for non-linear systems, linear equations are ubiquitous in all mathematics and their applications in physics and engineering.To learn more about linear equations, refer:
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Answer: x = -2
y = 5
Step-by-step explanation:
-4x+3y=23
x-y= -7
First take x-y= -7 and make it x=-7+y place it into the first equation
-4 (-7+y)+3y = 23
28-4y+3y = 23
28-y = 23
+y +y
28=23+y
-23 -23
5=y
Not that you have y you can replace it into the original
-4x+3(5)=23
-4x+15=23
-15=-15
-4x = 8
x= -2
The answer would be (-2,5)
1. The number of fans produced by a manufacturer in a week can be no more than five times the number of lamps produced by the same manufacturer during the same week. If the number of fans produced this week by the manufacturer was 20, what is the minimum number of lamps produced by the manufacturer this week?
A) 4
B) 5
C) 15
D) 20
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Use inverse matrices to find the solution to the system of equations represented by this matrix equation
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if you replace it in that order, it should give you the answer
[tex]\begin{bmatrix}{2} & {-3} \\ {-3} & {5}\end{bmatrix}[/tex]Given l ∥ m ∥ n, find the value of x.
Answers
Answer:
[tex]x = \frac{ - 23}{3} [/tex]
Step-by-step explanation:
everything u need is in the picture
Solve tan(x){tan(%) - 1) = 0 O A. x = 5 + 27T7,X = 3 37 + 27 O B. x = -2779,x=37 + X +277, X = +27 2. C. X = +19,X = = tnx +277 O D. X = n,X = x FT 4
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Given the trigonometry equation below,
[tex]\tan (x)(\tan (x)-1)=0[/tex]Solving each part separately
[tex]\begin{gathered} \tan \mleft(x\mright)=0\quad \mathrm{or}\quad \tan \mleft(x\mright)-1=0 \\ x=\tan ^{-1}0\text{ or tan(x)=1} \\ x=\pm n\pi\text{ }or\text{ }x=tan^{-1}1 \\ x=\pm n\pi\text{ or x=45} \\ x=\pm n\pi\text{ or x=}\frac{\pi}{45}\pm n\pi \end{gathered}[/tex]Therefore,
[tex]x=\pm n\pi,\text{ x=}\frac{\pi}{45}\pm n\pi[/tex]Hence, Option D is the correct answer.
The product of the digits of a five-digit number is 6! (factorial). How many such numbers are there
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There are 720 of such numbers that consists of five-digits which their product is 6! by permutation.
What is permutation?The mathematical term permutation can simply be defined as a process of arrangement or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.
We can apply the formula for permutation;
[tex]p(n,r) = \frac{n!}{(n - r)!} [/tex]
where n = total number of object and r = number of objects selected.
We can calculate the arrangement by applying the permutation formula as follows
[tex]p(6,5) = \frac{6!}{(6- 5)!}[/tex]
[tex]p(6,5) = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{1!}[/tex]
[tex]p(6,5) = \frac{720}{1}[/tex]
[tex]p(6,5) = 720[/tex]
Hence, with good application of the formula for permutation, we can say that there are 720 arrangement of such numbers which their product is 6!.
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An attic floor is shaped like a triangle with a height of n yd and a base of 6 yd.Which expression represents the area of the floor? 6n3nn + 63n2
Answers
In order to calculate the area, we can use the formula for the triangle area:
[tex]A=\frac{b\cdot h}{2}[/tex]Where b is the base length and h is the height relative to this base.
So, for b = 6 and h = n, we have:
[tex]\begin{gathered} A=\frac{6\cdot n}{2} \\ A=3n \end{gathered}[/tex]Therefore the correct option is the second one.
Could you please help me with this exercise? Thanks for your help!
Answers
ANSWER
• Distance:, 7.81
,• Midpoint: ,(-4.5, -6)
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean Theorem,
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2_{}}[/tex]In this problem, the points are (-7, -9) and (-2, -3),
[tex]\begin{gathered} d=\sqrt[]{(-7-(-2))^2+(-9-(-3))^2} \\ d=\sqrt[]{(-7+2)^2+(-9+3)^2}\text{ } \\ d=\sqrt[]{(-5)^2+(-6)^2}=\sqrt[]{25+36} \\ d=\sqrt[]{61}\approx7.81 \end{gathered}[/tex]Hence, the distance between P1 and P2 is 7.81 units.
To find the midpoint, we have to find the average between the coordinates of the points,
[tex](x_m,y_m)=\mleft(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\mright)[/tex]The midpoint in this problem is,
[tex](x,y)=\mleft(\frac{-7-2}{2},\frac{-9-3}{2}\mright)=\mleft(\frac{-9}{2},\frac{-12}{2}\mright)=(-4.5,-6)[/tex]Hence, the midpoint between P1 and P2 is (-4.5, -6).
Shiori is working on a stem project and her model is represented by the quadratic function below. She eventually wants to build a 3D model si she needs to understand each part of the function . She is trying to find the coordinate of the vertex of the following function and determine whether the graph opens up or down. F(x)=3x^2-2x-71. What are the coordinates of the vertex of the parabola of the function. There are several wars to determine this answer but state clearly all the steps you look to find the solution.2.Just by looking at the equation (without graphing it) does the graph open up or down(How do you know).3.what does the -7 tell you about the parabola specifically.
Answers
1) To get the vertex of the function, the formulae is given as:
[tex]x=-\frac{b}{2a}[/tex]This gives the x coordinate of the vertex. Where a and b are the coefficients of the 1st and 2nd terms respectiely.
[tex]x=\frac{-(-2)}{2(3)}=\frac{1}{3}=0.333333[/tex]To get the y coordinate, we substitute this x value into the original equation.
[tex]f(x)\text{ = 3(}\frac{1}{3})^2-2(\frac{1}{3})-7=\frac{-22}{3}=-7.333333[/tex]The coordinates of the the vertex (0.33, -7.33)
2) The graph opens upwards. Because the coefficient of the 2nd power of x is a negative number.
3) The -7 tells us that the graph cuts the vertical axis at -7.
Choose the figure that accurately represents the following relation on the Cartesian coordinate plane? {(-2,-2),(2,-3),(4,-1),(5,-6),(6,-8),(6,9)}
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Recall that, in a point (a,b), the first entry represents the x-entry, and the second entry represents the y-entry, and its graph is as follows:
Therefore, the graph of the given relation is:
Answer:
(Solve the problem down below & simplify the answer. Round to the nearest hundredth as needed.)
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From the given information, we know that the decreasing function values is
[tex]V(t)=3600(3^{-0.15t})[/tex]and we need to find the time t when V(t) is equal to $1200. Then by substituting this values into the function, we have
[tex]1200=3600(3^{-0.15t})[/tex]By dividing both sides by 3600, we get
[tex]3^{-0.15t}=\frac{1200}{3600}=\frac{1}{3}[/tex]So we have the equations
[tex]3^{-0.15t}=\frac{1}{3}[/tex]From the exponents properties, we know that
[tex]3^{-0.15t}=\frac{1}{3^{0.15t}}[/tex]so we have
[tex]\frac{1}{3^{0.15t}}=\frac{1}{3}[/tex]or equivalently,
[tex]3^{0.15t}=3[/tex]This means that
[tex]0.15t=1[/tex]Then, by dividing both sides by 0.15, we obtain
[tex]t=\frac{1}{0.15}=6.6666[/tex]So, by rounding to the nearest hundreadth, the answer is 6.67 years
In the distribution shown, state the mean and the standard deviation. Hint: The vertical lines are 1 standard deviation apart.
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We are given a distribution graph.
The mean of the distribution is the center that is 125.
[tex]\operatorname{mean}=\mu=125[/tex]The standard deviation is given by
[tex]std=\sigma=153-125=28[/tex]Therefore, the mean of the distribution is 125 and the standard deviation is 28.
Find the equation of a line perpendicular to y +1 = -x that passesthrough the point (-8, 7).
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Two lines are perpendicular if the product of their slopes is equal to -1.
Find the slope of the given line. Then, use that result to find the slope of a line perpendicular to it. Use the slope of the line perpendicular to the given line to find the equation of the one that passes through the point (-8,7).
To find the slope of the given line, write it in slope-intercept form by isolating y:
[tex]\begin{gathered} y+1=-x \\ \Rightarrow y=-x-1 \end{gathered}[/tex]The coefficient of x is -1. Then, the slope of the given line is -1.
Let m be the line perpendicular to y+1=-x.
Since the product of the slopes of perpendicular lines is equal to -1, then:
[tex]\begin{gathered} -1\times m=-1 \\ \Rightarrow m=\frac{-1}{-1} \\ \therefore m=1 \end{gathered}[/tex]The equation of a line with slope m that passes through the point (a,b) in slope-point form is:
[tex]y=m(x-a)+b[/tex]Replace m=1, a=-8 and b=7 to find the equation of the line perpendicular to y+1=-x that passes through the point (-8,7):
[tex]\begin{gathered} y=1(x-(-8))+7 \\ \Rightarrow y=(x+8)+7 \\ \therefore y=x+15 \end{gathered}[/tex]Therefore, the equation of the line perpendicular to y+1=-x that passes through (-8,7) is:
[tex]y=x+15[/tex]If g(x) = 5x, h(x) = √x , find the composition. (g . h)(0)
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The composition (g . h)(0) has a value of 0
How to evaluate the composite function?The definitions of the functions are given as
g(x) = 5x and h(x) = √x
To find the composition (g . h)(o), we make use of
(g . f)(x) = g(x) * h(x)
This can also be expressed as
(g . f)(x) = h(x) * g(x)
Substitute g(x) = 5x and h(x) = √x
So, we have
(g . f)(x) = 5x * √x
Substitute 0 for x
So, we have the following equation
(g . f)(0) = 5 x 0 * √0
Evaluate the product
So, we have the following equation
(g . f)(0) = 0
Hence, the value of the composition is 0
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A fish tank in the shape of a rectangular prism has a volume of 24 cubic feet. The length of the fish tank is 2 feet less than twice the width w, and the height is 1 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the fish tank in feet. Your answer should be in the form of a polynomial equals a constant.
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Answer in the form of a polynomial equals a constant:
2w^3-4w^
If 5 books of equal weight, weigh 1.755 kilograms, how many books will weigh 1.404 kilograms?
Answers
If 5 books of equal weight, weigh 1.755 kilograms, then the number of books will weight 1.404 kilogram is 4 books
The 5 books are equal weights
The weight of 5 books = 1.755 kilograms
Then the weight of one book = The weight of 5 books / 5
Substitute the values in the equation
The weight of one book = 1.755/5
= 0.351 kilograms
To find the number of books we have to use division again
The number of books will weight 1.404 kilograms = 1.404 / The weight of one book
=1.404/0.351
= 4 books
Hence, If 5 books of equal weight, weigh 1.755 kilograms, then the number of books will weight 1.404 kilogram is 4 books
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Find f(g(3)).f(x)=2x-5g(x) = 1 + x²f(g(3)) = [?]
Answers
To find the value of the given composition of functions you follow the next steps:
1. Find g(3):
[tex]\begin{gathered} g(3)=1+3^2 \\ g(3)=1+9 \\ g(3)=10 \end{gathered}[/tex]2. Find f(g(3)) or f(10):
[tex]\begin{gathered} f(g(3))=f(10) \\ f(g(3))=2(10)-5 \\ f(g(3))=20-5 \\ f(g(3))=15 \end{gathered}[/tex]Then, f(g(3)) is equal to 15Scientific notation of 100+6*10^2
Answers
Answer: The answer is 700
Step-by-step explanation:
is that the answer you're looking for?
Answer:
7e2
Step-by-step explanation:
10^2=100
100*6=600
600+100=700
there are 2 zeros in 700 so
7e2
In a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle. find the measure of all 3 angles. Hint: the angles of a triangle add up to 180.
Answers
The three angles of the triangle are 22.5, 67.5 and 90 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides.
The sum of angles in a triangle is 180 degrees.
Therefore, the angles of the triangle can be found as follows;
In the triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle.
Therefore,
let the smallest angle = x
Therefore, the three angles are as follows;
x3x45 + 2xTherefore,
x + 3x + 45 + 2x = 180
6x + 45 = 180
6x = 180 - 45
6x = 135
divide both sides by 6
x = 135 / 6
x = 22.5
Therefore, the three angles are as follows;
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Identify the pre-image and the image. Then determine if the transformation is a rigid motion or not
Answers
The pre-image is the figured formed by the points VWUST and the image is V'W'U'S'T'.
To produce the image from the pre-image a rotation is performed around the point (2, -2). A rotation doesn't change the dimensions of the figure, therefore it is not a rigid motion.
Choose the equation that represents a line that passes through points (−3, 2) and (2, 1)
5x + y = −13
5x − y = 17
x − 5y = −13
x + 5y = 7
Answers
The equation that represents a line that passes through points (−3, 2) and (2, 1) is x + 5y = 7.
How to find the equation of a line?The equation of the line passes through the points (−3, 2) and (2, 1). The equation of the line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope using (−3, 2) and (2, 1)
m = slope = 1 - 2 / 2 + 3
m = - 1 / 5
Therefore,
slope = - 1 / 5
Let's find the y-intercept of the line using (2, 1)
y = - 1 / 5 x + b
1 = - 1 / 5 (2) + b
b = 1 + 2 / 5
b = 5 + 2/ 5
b = 7 / 5
Therefore, the equation of the line can be represented as follows:
y = - 1 / 5 x + 7 / 5
5y = -x + 7
5y + x = 7
x + 5y = 7
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I dont know how to answer this pls help
Answers
The hedgehog's total change in weight is -2.5 ounces.
What is the total change in weight?A relationship is proportional if the ratio of the variables is constant. The variables can either increase or decrease at a constant rate. A proportional relationship can be modelled with a linear equation.
Ratio = change in weight / days of hibernation
-0.18 / 9 = -0.02
-0.56 / 28 = -0.02
-1.44 / 76 = -0.02
-1.96 / 98 = -0.02
Weight when the day of hibernation is 125 = number of days x ratio
125 x -0.02 = -2.5
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c(n) = -6 (-1/3) *n-1What is the 2nd term in the sequence ?
Answers
We are given the following sequence
[tex]c(n)=-6(-\frac{1}{3})^{n-1}[/tex]We are asked to find the 2nd term of the above sequence
Let us substitute n = 2 into the given sequence
[tex]\begin{gathered} c(2)=-6(-\frac{1}{3})^{2-1} \\ c(2)=-6(-\frac{1}{3})^1 \\ c(2)=6\cdot\frac{1}{3} \\ c(2)=2 \end{gathered}[/tex]Therefore, the 2nd term of the given sequence is 2
You are dressing a mannequin for a clothingstore display. You have 4 types of shoes, 5necklaces, 10 tops, and 7 bottoms to choosefrom. How many distinct outfits can youcréate? >
Answers
Given:
• Types of shoes = 4
,• Number if necklaces = 5
,• Number of tops = 10
,• Number of bottoms = 7
Let's find how many distinct outfits you can create.
To find the number of distinct outfits you can create, we have:
[tex]\begin{gathered} n=4*5*10*7 \\ \\ n=1400 \end{gathered}[/tex]Therefore, the number of distinct outfits you can create is 1400.
ANSWER:
1400
the side opposite the right angle measures 8 in. what is the measurement of the side opposite of the 60 degree angle (draw and label the triangle before solving)
Answers
1) The best way to tackle this question is by sketching out the triangle:
2) Considering that 60º angle we can write out the following trig ratio:
[tex]\begin{gathered} \sin (60^{\circ})=\frac{x}{8} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{8} \\ 2x=8\sqrt[]{3} \\ x=\frac{8\sqrt[]{3}}{2} \\ x=4\sqrt[]{3} \end{gathered}[/tex]Note that if we had drawn the 60º angle to the lowe right in that triangle we would find the same measure, by using the cosine of (30º) instead.
And that's the answer
need help for mathhh
Answers
Using implicit differentiation, the rates are given as follows:
2. dV/dt = 144π cm³/sec.
3. dh/dt = 2/5π cm/s.
4. dr/dt = -0.2/π cm/day.
What is the rate of change of the volume of an sphere?The volume of an sphere of radius r is given by the following equation:
[tex]V = \frac{4}{3}\pi r^3[/tex]
Applying implicit differentiation, differentiating both variables relative to t, the rate of change is given as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
For item 2, the parameters are given as follows:
[tex]\frac{dr}{dt} = 2, r = 4[/tex]
Hence the rate is given as follows:
dV/dt = 4π x 4² x 2 = 144π cm³/sec.
For item 4, the parameters are:
[tex]\frac{dV}{dt} = -0.2, r = 5[/tex]
Negative because the orange is shrinking.
Hence the rate of the radius can be found as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]-0.2 = 4\pi (5)^2\frac{dr}{dt}[/tex]
dr/dt = -0.2/100π
dr/dt = -0.2/π cm/day.
What is the rate of change of the volume of an cylinder?The volume of a cylinder of radius r and height h is given as follows:
[tex]V = \pi r^2h[/tex]
The rate of change of the volume as a function of time is given by:
[tex]\frac{dV}{dt} = 2\pi rh\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]
For item 3, the parameters are given as follows:
[tex]r = 5, \frac{dV}{dt} = 10, \frac{dr}{dt} = 0[/tex]
The radius is of 5 as r² = 25, due to the area of the base.
Hence the rate of change of the height is found as follows:
[tex]\frac{dV}{dt} = \pi r^2\frac{dh}{dt}[/tex]
10 = 25π dh/dt
dh/dt = 10/25π
dh/dt = 2/5π cm/s.
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Find the indicated angle 0. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 120 and c = 136. Round your answer to two decimal places.)
Answers
Base on the given data, the triangle is shown below.
Apply law of sine to this triangle implies,
[tex]\sin \theta=\frac{a}{c}[/tex]Given that, a=120 and c=136. Thefore, the given equation becomes,
[tex]\begin{gathered} \sin \theta=\frac{120}{136} \\ \sin \theta=0.88 \end{gathered}[/tex]Take the inverse to find the the measure of indicated angle.
[tex]\begin{gathered} \theta=\sin ^{-1}0.88 \\ \theta=61.64 \end{gathered}[/tex]Therefore, the angle is 61.64 degree.
All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having a vowel written on it?
Answers
Let:
A = Get a paper having a vowel written on it
N = Total number of letters = 11
a = Number of vowels = 4
so:
[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{4}{11} \\ P(A)\approx0.36 \end{gathered}[/tex]Answer:
36%
get me some help with it she of them
Answers
We are given the following expression:
[tex](6+4i)(9-11i)[/tex]Using the distributive property:
[tex](6)(9)+(6)(-11i)+(4i)(9)+(4i)(-11i)[/tex]Solving the products:
[tex]54-66i+36i-44i^2[/tex]Now we use the following property:
[tex]i^2=-1[/tex]Substituting:
[tex]54-66i+36i+44[/tex]Adding like terms:
[tex]98-22i[/tex]Since we can't simplify any further this is the answer.