Given data:
The given function is f(x)=9x^2-180=0
The given expression can be written as,
[tex]\begin{gathered} 9x^2-180=0 \\ 9(x^2-20)=0 \\ (x^2-20)=0 \\ x=\pm2\sqrt[]{5} \end{gathered}[/tex]Thus, option (A) is correct.
The Pentagon building in Washington, D.C., is named because it is in the shape ofa regular pentagon. What is the measure of each interior angle?
The formula to find the sum of the interior angles of a polygon is given below,
[tex]\text{Sum of angles of polygon = (n-2)180}^0[/tex]Number, n, of sides of a regular pentagon is 5 i.e n = 5,
To find the sum of angles in a regular pentagon, substitute for n into the formula above,
[tex]\text{Sum of angles of a pentagon=(5-2)180}^0=3\times180^0=540^0[/tex]To find the measure of each angle of the pentagon, the formula is given below
[tex]\begin{gathered} for\text{ each interior angle=}\frac{Sum\text{ of angles}}{n} \\ \text{Where n = 5} \\ \text{For each interior angle=}\frac{540^0}{5}=108^0 \end{gathered}[/tex]Hence, each interior angle is 108°
solve system of equations by substution { y=3x+19{ y=5x+33
Given:
[tex]\begin{gathered} y=3x+19\ldots\ldots\ldots(1) \\ y=5x+33\ldots\ldots\ldots(2) \end{gathered}[/tex]To solve: The system of equations by substitution
Explanation:
Substituting equation (1) in equation (2), we get
[tex]\begin{gathered} 3x+19=5x+33 \\ 3x-5x=33-19 \\ -2x=14 \\ x=-7 \end{gathered}[/tex]Substitute the x value in equation (1), we get
[tex]\begin{gathered} y=3(-7)+19 \\ y=-21+19 \\ y=-2 \end{gathered}[/tex]Final answers: The solutions are,
[tex]\begin{gathered} x=-7 \\ y=-2 \end{gathered}[/tex]solve for x:
7x=6+5 (3x+3)-x
Answer: x= -3
Step-by-step explanation:
7x = 6+ 15x + 15 - x
7x = 21 + 14x
-7x = 21
x= -3
A large vat has a faucet to allow liquid to enter the vat and a drain to allow liquid to leave the vat.
Each minute, the faucet allows 40 1/5 gallons of liquid to enter the vat, and the drain allows 44 3/4 gallons to leave the vat.
What is the change in the amount liquid in the vat after 12 minute?
After some mathematical operations, the rate of change is -273/5.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).So, the rate of change will be:
12(40⅕) - 12(44¾)Evaluate as follows:
12(40⅕) - 12(44¾)12(201/5) - 12(179/4)12 × 201/5 - 12 × 179/42,412/5 - 5372,412 - 5(537)/52412 - 2,685/5-273/5Therefore, after some mathematical operations, the rate of change is -273/5.
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A teacher asks his students to use the Addition Property of Equalityto write an equation equivalent to x - 9 = 11 Antonio writes* - 9 + 9 + 11 + 9. Stefan writes x - 9+2 -11 + 2 Have bothstudents followed the teacher's instructions? Explain your reasoning
Both students followed the teacher's instruction. The addition property of equality states that if 2 numbers x and y are equal x=y, then, x+a=y+a.
In this case both students applied the property correctly. One of them added 9 to both sides of the equation and the other one added 2 to both sides.
The answer is yes, both followed the teacher's instruction.
I don't understand. I get an answer that doesn't exist. The question is to multiply in a+bi form. (5/2 + 2i)(1/4 - 6i)
Given the below
[tex](\frac{5}{2}+2i)(\frac{1}{4}-6i)[/tex]Multiplication of the vectors in the a+bi form gives
Applying the complex arithmetic rule below
[tex](a+bi)(c+di)=(ac-bd)(ad+bc)i[/tex]The expansion of the vectors gives
[tex](\frac{5}{2}+2i)(\frac{1}{4}-6i)=\frac{5}{2}(\frac{1}{4}-6i)+2i(\frac{1}{4}-6i)[/tex]Opening the brackets
[tex]\begin{gathered} (\frac{5}{2}+2i)(\frac{1}{4}-6i)=\frac{5}{2}(\frac{1}{4}-6i)+2i(\frac{1}{4}-6i) \\ =\frac{5}{8}-\frac{30}{2}i+\frac{2}{4}i-12i^2 \\ \text{Where i}^2=-1 \\ =\frac{5}{8}-\frac{30}{2}i+\frac{2}{4}i-12(-1) \\ ==\frac{5}{8}+12-\frac{30}{2}i+\frac{2}{4}i \end{gathered}[/tex]Simplifying the above expression
[tex]\begin{gathered} =\frac{5+96}{8}+\frac{-60i+2i}{4}=\frac{101}{8}+\frac{-58}{4}i \\ =\frac{101}{8}+\frac{-29}{2}i=\frac{101}{8}-\frac{29i}{2} \\ (\frac{5}{2}+2i)(\frac{1}{4}-6i)=\frac{101}{8}-\frac{29i}{2} \end{gathered}[/tex]Hence, the answer is
[tex]=\frac{101}{8}-\frac{29i}{2}[/tex]Write the inequality shown by the Shaded region in the graph with the boundary line 4x + 3y = -3
ANSWER
[tex]y\text{ }\leq\text{ -}\frac{4}{3}x\text{ - 1}[/tex]EXPLANATION
We want to write the inequality represented by the shaded region of the graph.
The boundary line of the graph is given as:
4x + 3y = -3
Let us put this in slope-intercept form:
=> 3y = -4x - 3
=> y = -(4/3)x - 1
Now that we have the equation in that form, we have to consider a few things:
=> The line used to represent the boundary line is a solid line. This means that the inequality we need has either a less than/equal to or a greater than/equal to sign.
=> The shaded region is on the left hand side of the boundary line. This means that the inequality represented is less than or equal to.
Therefore, the inequality represented by the shaded region is:
[tex]y\text{ }\leq\text{ -}\frac{4}{3}x\text{ - 1}[/tex]Savings ($)
200
160
120
80
40
O
5 10 15 20 25
Time (weeks)
Find the constant of proportionality and write an equation for the relationship
The constant of proportionality is
The equation for the relationship is
For the given graph related to savings on y-axis and time on x-axis, the constant of proportionality is equal to 4, and the equation representing the relationship between the savings and the time is given by y = 4x.
As given in the question,
From the graph,
y-axis represents the savings in dollars
x-axis represents the time in seconds
Let us consider savings represents by y and time represents by x.
Form the graph we can see that,
When x = 10 ⇒ y = 40
when x = 15 ⇒ y = 60
Graph represents the straight line so it is linear function.
y = 40
⇒ y= 4(10)
⇒ y= 4x
⇒y ∝ x
⇒Constant of proportionality 'k' = 4
Now, for the equation consider two coordinates on the graph,
(x₁ , y₁) = (10, 40)
(x₂ , y₂) = (15, 60)
( y-y₁)/ (x-x₁) = (y₂ -y₁) / (x₂ - x₁)
⇒( y- 40)/(x-10) = (60 -40)/ (15-10)
⇒ y-40 = 4(x-10)
⇒y = 4x
Therefore, for the given graph related to savings on y-axis and time on x-axis, the constant of proportionality is equal to 4, and the equation representing the relationship between the savings and the time is given by y = 4x.
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A bag of Mand Ms contains 5 yellow, 11 red, 4 green, 12 blue and 7 brown candies.What is the probability that a red or brown candy is pulled from the bag?A. 18/39B. 18/78C. 9/20D. 77/1521
In this question, we need to find the probability of pulling a red or brown candy from a bag.
We know that the bag contains the next amount of candies:
• 5 yellow candies
,• 11 red candies
,• 4 green candies
,• 12 blue candies
,• 7 brown candies
Therefore, in total, we have 39 candies.
Then the probability of pulling a red candy is:
[tex]P(\text{red)}=\frac{11}{39}[/tex]The probability of pulling a brown candy is:
[tex]P(\text{brown)}=\frac{7}{39}[/tex]Now, we know that the general formula for the probability of two events is given by:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]However, in this case, we do not have any probability that both events happen at the same time - in other words, they are mutually exclusive events. Therefore, we have:
[tex]\begin{gathered} P(R\cup B)=P(R)+P(B)-P(R\cap B) \\ P(R\cup B)=\frac{11}{39}+\frac{7}{39}=\frac{18}{39} \\ P(R\cup B)=\frac{18}{39} \end{gathered}[/tex]Therefore, in summary, the probability that a red or brown candy is pulled from the bag is 18/39 (option A.)
Can you please help me figure out how to do this?
Given
[tex]f(x)=2x^2-4x-3[/tex]
Procedure
[tex]\begin{gathered} f(-1)=2\cdot(-1)^2-4\cdot(-1)-3 \\ f(-1)=2+4-3 \\ f(-1)=3 \end{gathered}[/tex]
The answer would be f(-1) = 3
the area of the shaded circular sector is equal to 30. The radius of the circle is 10. Find the measure of the central angle (in degrees)
Given:
There are given that the area of the shaded circular sector is:
[tex]30\pi[/tex]Explanation:
To find the central angle, we need to use the formula of area of the sector:;
So,
From the formula of area of the sector:
[tex]Area\text{ of sector=}\frac{central\text{ angle}}{360^{\circ}}\times\pi r^2[/tex]Then,
Put the value of area and radius into the above formula;
So,
[tex]\begin{gathered} Area\text{ of sector=}\frac{central\text{ angle}}{360^{^{\circ}}}\times\pi r^2 \\ 30\pi=\frac{centralangle}{360}\pi\times(10)^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 30\pi=\frac{centralangle}{360}\pi(10)^{2} \\ 3=\frac{centralangle}{36} \\ central\text{ angle=36}\times3 \\ central\text{ angle=108}^{\circ} \end{gathered}[/tex]Final answer:
hence, the central angle is 108 degrees.
how can I find which statements can be deducted from the picture
The following statements can be deduced by knowing some previous knowledge from Parallelism.
2) Examining and commenting
∠1 ≅ ∠2 FALSE This is a linear pair. So they are supplementary angles, not congruent ones.
∠5≅ ∠7 TRUE Vertical Angle Theorem states that they are congruent ones.
m∠7≅ m∠4 True Linear pair a+ b are supplementary as well.
∠1 ≅ ∠7 True Corresponding Angles are always congruent.
≅
у20f15(4,12)10g(4,6)(-2,0)(0,25) 2,4,(3,5)(2,0)0,47Use the graph off and g.Find (gof)(2).ما
The first step is to find the fuctions, f(x) and g(x)
Since function f(x) is represented by the curve, it's a quadratic function. The curve cuts the x axis at x = 2 and x = - 2. Thus, the factors are (x + 2) and (x - 2). The quadratic function would be
(x + 2)(x - 2)
= x^2 - 2x + 2x - 4
f(x) = x^2 - 4
Since the function g(x) is represented by a straight line, it is a linear function. We would represent the function in the slope intercept form which is expressed as
y = mx + c
where
m = slope
c = y intercept
To find slope, the formula is
m = (y2 - y1)/(x2 - x1)
From the given points,
when x1 = - 2, y1 = 0
when x2 = 2, y2 = 4
m = (4 - 0)/(2 - - 2) = 4/(2 + 2) = 4/4
m = 1
the y intercept is the value of y when x = 0. Thus, c = 2
The function is
g(x) = x + 2
To find (g o f)(x), we would substitute function f into function g. Thus,
gof(x) = x^2 - 4 + 2
gof(x) = x^2 - 2
To find gof(2), we would substitute x = 2 into gof(x). It becomes
gof(2) = 2^2 - 2 = 4 - 2
gof(2) = 2
Kennedy goes to a store an buys an item that costs xx dollars. She has a coupon for 35% off, and then a 7% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Kennedy paid at the register.
We are given that an item has a cost xx.
First, we will calculate the 35% discount on the total price. To do that we will subtract 35% of the initial cost from the initial cost
To calculate the 35% we multiply the price by 35/100, like this:
[tex]xx\times\frac{35}{100}[/tex]Now we subtract this from the initial price, which was "xx". Subtracting we get:
[tex]P_d=xx-xx\times\frac{35}{100}[/tex]This is the cost with the discount. Now, we will add to this the tax of 7%. First, we calculate the 7% of the price with the discount by multiplying it by 7/100, like this:
[tex](xx-xx\times\frac{35}{100})\times\frac{7}{100}[/tex]Now, we add this to the price with the discount, like this:
[tex]T=(xx-xx\times\frac{35}{100})+(xx-xx\times\frac{35}{100})\times\frac{7}{100}[/tex]Now, we can simplify. We start by using the distributive property on the second parenthesis:
[tex]T=xx-xx\times\frac{35}{100}+xx\times\frac{7}{100}-xx\times\frac{35}{100}\times\frac{7}{100}[/tex]Now we solve the product of 35/100 by 7/100, we get:
[tex]T=T=xx-xx\times\frac{35}{100}+xx\times\frac{7}{100}-xx\times\frac{49}{2000}[/tex]Now we take xx as a co
Inderstanding ocabulary Are 23 and 24 adjacent angles? Explain. 1. 2. 3. 4 3 4 3 4 3 . Reasoning Does every angle have a complement? Explain. ises For more exercises, see Extra Skills and Word Problem me a pair of vertical and adjacent angles in each figure. Find m21.
By definition, two angles are adjacent if they share one side and the vertex.
To determine if ∠3 and ∠4 are adjacent, you have to look at each image and determine if they share the vertex and one side:
1.
In this image ∠3 and ∠4 share, the vertex but they do not share one side, this indicates that these angles are not adjacent.
2.
In this image ∠3 and ∠4 share the vertex and one side (blue line), which indicates that they are adjacent angles.
3.
In this image ∠3 and ∠4 share one side (blue line) but each angle has its own vertex (green dots). You cannot conclude these angles are adjacent.
4.
Two angles are complementary of they add up to 90º, they don't necesarly have to be adjacent.
Any acute angle, meaning, any angle that measures less than 90º, has a complement.
For example, you have the following angles:
- If both ∠1 and ∠2 are acute angles and complementary, then we know that they add up to 90º:
[tex]\angle1+\angle2=90º[/tex]-For example, ∠1= 46º, then you can determine the measure of ∠2 as follows:
[tex]\begin{gathered} \angle2=90º-\angle1 \\ \angle2=90-46 \\ \angle2=44º \end{gathered}[/tex]Both ∠1=46º and ∠2=44º are acute and add up to 90º
-If one of the angles is a right angle, for example, ∠2=90º, then no matter what measure does ∠1 take, they will never add up to 90º.
We can say that right angles do not have a complement.
-If one of the measures of the angles is more than 90º (it is an obtuse angle), let's say, for example, ∠1= 124º, no matter what measure ∠2 has, if you add both angles, they will never add up to 90º.
So we can say that obtuse angles have no complements.
In conclusion, not all angles can have a complement, only acute angles have complements.
The perimeter of a rectangle is 32 meters and the length is 4 meters longer than width
Given:
The perimeter of a rectangle is 32 meters and the length is 4 meters longer than the width
Let, x = the length of the rectangle
And, y = the width of the rectangle
So, we have the following system of equations:
[tex]\begin{gathered} 2x+2y=32\rightarrow(1) \\ x-y=4\rightarrow(2) \end{gathered}[/tex]We will use the method of substitution to solve the system
So, from equation 2:
[tex]x=y+4\rightarrow(3)[/tex]substitute with (x) from equation (3) intp eqaution (1)
[tex]2(y+4)+2y=32[/tex]solve the equation to find (y):
[tex]\begin{gathered} 2y+8+2y=32 \\ 4y+8=32 \\ 4y=32-8 \\ 4y=24 \\ y=\frac{24}{4}=6 \end{gathered}[/tex]Now, substitute with (y) into equation (3) to find (x):
[tex]x=y+4=6+4=10[/tex]So, the answer will be:
The length of the rectangle = 10 m
The width of the rectangle = 6 m
Find the domain and range. Select the correct symbols to indicate interval notation.If a number is not an integer then round to the nearest hundredth.
Remember that
The Domain is the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).
The Range is the set of all output values, which are the y-coordinate of each ordered pair (the second number in each pair).
so
In this problem
The domain is the interval [-5,3)
The range is the interval [0,2]
Solve the inequalityNine times c is less than -15.
Nine times c is less than -15.
Can be written as
[tex]\begin{gathered} 9c<-15 \\ \Rightarrow \\ \frac{9c}{9}<\frac{-15}{9} \\ \Rightarrow c<\frac{-5}{3} \\ \Rightarrow c<-1\frac{2}{3} \end{gathered}[/tex]May I please get help with this. I don’t know the definitions of each, therefore I cannot state weather each of them are true or false
Quadrilateral: Plane figure that has four sides. All squares are quadrilaterals but not every quadrilateral is a square.
1- False
A square is considered as a rhombus because all the sides are equal in length, the diagonals are perpendicular to each other and bisecs opposite angles. Then, a square is a rhombus but as not all the rhombus has right angles not every rhombus is a square
2- False
A square is a parallelogram (quadrilateral with two pairs of parallel sides) with four sides of equal length. Then, every square is a parallelogram
3- True
A square is considered as a rhombus with right angles. Then, every rhombus with foru right angles is a square.
4-True
Factorise the following quadratic:
e² - 17e + 70
Answer:
Step-by-step explanation:
I think you're supposed to use the quadratic formula Samanth
Know it?
-b ± [tex]\sqrt{b^{2}-4ac }[/tex] / (2a)
so for starters, let me mention, that if 4ac happens to be greater than [tex]b^{2}[/tex] contrary to what all math teacher say, about not being able to taking the square of a negative number, you can, but you just end up with a complex number in the form of A + Bi , where 'i' represents [tex]\sqrt{-1}[/tex] anyway,
for the given equation
A = 1
B = -17
C = 70
{ -(-17) ± [tex]\sqrt{(-17)^{2}-4*1*70 }[/tex] } / (2*1)
{ 17 ± [tex]\sqrt{289-280}[/tex] } / 2
wow, now i'm glad I mentioned about the 4ac being greater :P
it was close, huh
{ 17 ± [tex]\sqrt{9}[/tex] } / 2
{ 17 ± 3 } /2
let's take each case now, the plus and then the minus
{ 17+3 } /2
20 /2
10
now the minus
{17 - 3 } / 2
14 /2
7
now that i've done all that work, I think we could have just done this by inspection :P
(e-7)(e-10)
anyway, hope that helps, ask if you have any questions :)
HELP ASAP!!! THE BEST ANSWER GETS BRAINLIST! (15 POINTS)
(07.05A HC)
The following table shows the values of y for different values of x:
x y
0 -5
1 0
2 5
Which statement best explains whether the table represents a linear function or a nonlinear function?
It represents a linear function because its points are on a straight line.
It represents a linear function because its points are not on a straight line.
It represents a nonlinear function because its points are on a straight line.
It represents a nonlinear function because its points are not on a straight line.
The first choice is the correct answer.
It represents a linear function because its points are on a straight line
You have a rectangular backyard that is 90 feet wide. It has an area of 10,800 square feet. You are putting a fence along one length of the yard.Use the formula for the area of a rectangle A = l * w, where I is the length, and w is the width. Find the length of your backyard.
ANSWER:
120 feet
STEP-BY-STEP EXPLANATION:
We hve the following:
A = 10800 ft²
w = 90 ft
The area of a rectangle is the product between the length and the width, we do not know the length but we do know the area, therefore, we calculate the length as follows:
[tex]\begin{gathered} A=w\cdot l \\ \\ \text{ We replacing} \\ \\ 10800=90\cdot l \\ \\ l=\frac{10800}{90} \\ \\ l=120\text{ ft} \end{gathered}[/tex]The length of your backyard is equal to 120 feet
10. f(x) = 2x+5 if x < 4 1x² + 3x if x 24 LX D = R =
The domain of the given piecewise function are all the values that x can take.
These are:
x < -4 and
[tex]x\ge-4[/tex]It can be written as:
[tex](-\infty,\infty)[/tex]The range is:
[tex](-\infty,-3)\cup\lbrack-\frac{9}{4},\infty)[/tex]What is the domain of the following function?A) {-6, -2, 1, 5, 7, 8}B) {-2, 7}C) {-6, 1, 5, 8}D) all Real numbers
In this problem, we have that
The domain or input values are the data set {-6, 1, 5, 8}
The range or output values are the data set [-2,7]
therefore
The answer is the option CAre there any extraneous solutions? If yes, write the solution in the box, if no write "none"). x=
Given:
[tex]\sqrt[]{x+1}+2=4[/tex]x=3 is the only solution for the given equation.
There is no other solutions for the given equation.
So none is the final answer.
George is making an elaborate meal. he can only cook one thing at a time in his microwave oven. his turkey takes 65 minutes; the pie takes 15 minutes; rolls take 60 seconds; and his coffee takes 45 seconds to heat. how much time does he need to cook the meal? when does he need to start in order to complete the cooking at 4:00pm?
operator nameEXPLANATION
STEP 1: Find the time taken to cook the meal.
The amount of time does George needs to cook the meal is the sum of all the time it would take to cook each of the individual meal
Therefore,
[tex]\begin{gathered} \text{Total time=65mins+15mins+60secs+45secs} \\ =80\min utes\text{ 105 secs} \\ This\text{ can be rewritten as:} \\ =60\text{ mins+ 20mins +60secs +45secs} \\ \sin ce\text{ 60 mins=1hr and 60 secs = 1min} \\ \text{This gives;} \\ =1\text{hour 21mins 45secs} \end{gathered}[/tex]STEP 2: Find the time he needs to start to cook the meal.
The right time to start cooking the meal is simply subtracting 1hour 21 mins 45 secs from 4.00 pm
1) Remove 1hour from 4.00 pm =3.00pm
2) Remove 21 mins from 3.00pm=2.39 pm
3)Remove 21 secs from 2.39pm= 2.38pm 15secs
Therefore the right time for George to start cooking is 15secs after 2.38pm
is f(-2) negative?which values of x is >0which values of x if f(x) =0
We know that a function is greater than 0 when the graph of the function is above the x-axis.
Meaning that if the function is below the x-axis the function is taking negative values.
For that reason we can say that:
A) f(-2) is positive because the graph at that point is above the x-axis
B) the function is greater than 0 o values greater than -3 until 5, in interval notation it will be (-3,5]
c) We can say that the function is equal to 0 when x=-3 because at that point the graph is exactly crossing the x-axis
How can we find the solutions for an equation like 6 cos x = 2 in the interval 0 to 2π?
Answer:
[tex]x=\arccos(1/3), 2\pi-\arccos(1/3)[/tex]
Step-by-step explanation:
[tex]6\cos x=2 \\ \\ \cos x=1/3 \\ \\ x=\arccos(1/3), 2\pi-\arccos(1/3)[/tex]
If a single card is drawn from a standard 52-card deck, in how many ways could it be a diamond or a face card (a face card is a Jack, Queen, or King)?A. 4B. 21C. 22D. 13
The number of diamond cards is 13.
The number of face card is 12.
There are 3 face cards which are of diamond.
Thus, total number of non-face diamond cards is 13-3=10.
Thus, the requred number of ways are =12+10=22.
Thus, option (C) is correct.
Write the sum of the first three terms in the binomial expansion, expressing the result in simplified form.(x – 4y)^7
ANSWER:
[tex](x-4y)^7=x^7-28x^6y+336x^5y^2\ldots[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]\mleft(x-4y\mright)^7[/tex]In this case we can apply the binomial theorem, which is the following:
[tex](a+b)^n=\sum ^n_{i\mathop=0}(\frac{n!}{i!(n-i)!}a^{n-i}\cdot b^i[/tex]we replace and calculate for the first three terms:
[tex]\begin{gathered} 1st=\sum ^7_{i\mathop{=}0}(\frac{7!}{0!(7-0)!}x^{7-0}\cdot(-4y)^0=1\cdot x^7\cdot1=x^7 \\ 2nd=\sum ^7_{i\mathop{=}1}(\frac{7!}{1!(7-1)!}x^{7-1}\cdot(-4y)^1=7\cdot x^6\cdot-4y^1=-28x^6y \\ 3rd=\sum ^7_{i\mathop{=}2}(\frac{7!}{2!(7-2)!}x^{7-2}\cdot(-4y)^2=21\cdot x^5\cdot16y^2=336x^5y^2 \end{gathered}[/tex]