Determine if the figures below are similar. If they are, identify the similarity statement.E70F50GK5060L
Answers
We have the following triangles:
And we need to determine if they are similar by identifying the similarity statement.
To determine that similarity statement, we can proceed as follows:
1. Check the measures of the internal angles of the triangles. We need to remember that the sum of the internal angles of a triangle is 180 degrees. Then we have:
2. We can see that to find the angles in the first triangle, EFG, and in the second triangle, JKL, we have that the sum of the three angles must be 180 degrees, and we obtained the other angles as follows:
[tex]\begin{gathered} \text{ Triangle EFG}\rightarrow50+70+x=180 \\ \\ x=180-(50+70)=180-120=60 \\ \\ \text{ Triangle JKL}\rightarrow50+60+y=180 \\ \\ y=180-(50+60)=180-110=70 \end{gathered}[/tex]3. Then we can redraw the triangles as follows:
4. Now, since we can see that, at least, two of the angles of the triangles are congruent (then the third one is also congruent, that is, has the same measure), we also have that to prove that if two triangles are similar it is sufficient that two of the corresponding angles of one triangle are congruent to the two corresponding angles of the other triangle, and this is known as the Angle-Angle method for proving similar triangles, then we can conclude that:
Triangle EFG is similar to triangle JKL by the Angle-Angle method.
Therefore, in summary, we have that:
Triangle EFG is similar to Triangle JKL by Angle-Angle similarity
[tex]\text{ Triangle EFG \textasciitilde Triangle JKL by Angle-Angle similarity}[/tex]
[Last option]
Related Questions
In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If 11,000 students participated in the poll, how many chose green?Orange 13%Pink 7%Blue 10%Red 24%Purple 10%Green 36%
Answers
Total of 11,000 students
Green 36%
how many chose green?
Chose green = 11000 * 36/100 = 3960
36% of 11,000 is 3960
Answer:
3,960 students chose green
GWhich inequalities have no solution? Check all of the boxes that apply.XX-3x -3x–4 + x>-2 + xX-2
Answers
For every number x, x = x, not x < x. So, the inequality x < x has no solution.
Since -3x = -3x for every real number, the inequality
[tex]-3x\leq-3x[/tex]holds for every real number, that is, every number is a solution.
Consider the inequality
[tex]-4+x>-2+x[/tex]Subtract x on both sides gives -4 > -2, which is not possible.
Hence the inequality - 4 + x > - 2 + x has no solution.
Consider the inequality
[tex]x-2Subtract x on both sides gives -2 < 3, which is true.Every real number is a solution of the inequality. Hence the inequality has solution.
Thus the inequalities with no solution are: x < x and -4+x>-2+x
A tank is in the shape of a cylinder of radius 15 cm and height 50 cm.Work out the volume of the tank.
Answers
Answer: [tex]11250\pi \\[/tex] cm^3
Step-by-step explanation:
This could be solved with integral calculus or simple arithmetic.
If you need to show the work in calculus, let me know, otherwise, here's the easiest way to reach the answer:
Volume of a solid is equal to the area of its 2D projection multiplied by its height, assuming that it's uniform throughout its entire height. Fortunately, a cylinder is uniform throughout its height.
What is a cylinder's 2D projection? A circle!
Area of a circle = [tex]\pi r^{2}[/tex]
r = 15
Area = 225pi cm^2
Now, we multiply the area of the 2D projection by the height of the cylinder.
225pi * 50 = 11250pi cm^3
I am asked to graph f(x) = (- 1/x-2) -1
Answers
Answer
[tex]f(x)=-\frac{1}{x-2}-1[/tex]An air plane can cruise at 640mph. How far can it fly in 3/2 Ths of an hour?
Answers
Answer: 960 miles
3/2 of an hour would be 1 hour and 30 min or an hour and a half
640mph (mph = miles per hour)
1/2 of an hour is 30 minutes so its 640 miles in half so 320
now all you gotta do is add it
so 640 + 320 = 960
I need help with my pre-calculus homework, please show me how to solve them step by step if possible. The image of the problem is attached. These are 2 parts of the same question.
Answers
We are given the following triangle:
We need to determine the area of the triangle. To do that we need to determine sides "a" and "b". We will use the sine law to determine the side "b":
[tex]\frac{b}{sin107}=\frac{98}{sin48}[/tex]Now, we multiply both sides by "sin107":
[tex]b=sin(107)\frac{98ft}{sin(48)}[/tex]Solving the operations:
[tex]b=126.11ft[/tex]Now, before determining side "a" we will determine the angle "x" that is opposed to "a". To do that we will use the fact that the sum of the interior angles of a triangle is 180, therefore:
[tex]107+48+x=180[/tex]Adding the values:
[tex]155+x=180[/tex]Now, we subtract 155 from both sides:
[tex]\begin{gathered} x=180-155 \\ x=25 \end{gathered}[/tex]Therefore, the angle opposite to "a" is 25 degrees. Now, we apply the sine law:
[tex]\frac{a}{sin(25)}=\frac{98}{sin(48)}[/tex]Now, we multiply both sides by "sin(25)":
[tex]a=sin(25)\frac{98}{sin(48)}[/tex]Solving the operations:
[tex]a=55.73ft[/tex]Now, we determine the area using the following formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]Where:
[tex]s=\frac{a+b+c}{2}[/tex]Now, we determine the value of "s":
[tex]s=\frac{55.73ft+126.11ft+98ft}{2}[/tex]Solving the operation:
[tex]s=139.92ft[/tex]Now, we substitute the value in the formula for the area:
[tex]A=\sqrt{(139.92ft)(139.92ft-55.73ft)(139.92ft-126.11ft)(139.92ft-98ft)}[/tex]Solving the operations:
[tex]A=2611.43ft^2[/tex]Now, since the search party can cover 300 ft^2/h we can use a rule of 3 to determine the number of hours it takes them to cover 2611.43 ft^2:
[tex]\begin{gathered} 300ft^2\rightarrow1h \\ 2611.43ft^2\rightarrow x \end{gathered}[/tex]Now, we cross multiply:
[tex](300ft^2)(x)=(1h)(2611.43ft^2)[/tex]Now, we divide both sides by 300ft^2:
[tex]x=\frac{(1h)(2611.43ft^2)}{(300ft^2)}[/tex]Solving the operations:
[tex]x=8.7h[/tex]Therefore, it takes 8.7 hours to cover the area. Therefore, the search party won't be able to conclude before the sun goes down.
Which statement is the converse of the conditional statement:
If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
• If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
O If point 8 is not the midpoint, then point B does not bisect line segment AC into two congruent segments.
Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.
O if point B
does not bisect line segment AC into two congruent segments, then point B is not the midpoint.
Answers
Point B is the midpoint if it divides line segment AC into two congruent segmentsIf point B is not the midpoint, then point B does not divide the line segment AC into two congruent segments, which is the statement opposite to the one that has been made.
Which statement is the converse of the conditional statement ?
A point that separates a segment into two congruent segments is the segment's midpoint.The segment is bisected by a point (or segment, ray, or line) that separates it into two congruent segments.Trisecting is the process of dividing a segment into three congruent segments using two points (segments, rays, or lines). A perpendicular bisector is a segment, ray, line, or plane that is perpendicular to another segment at its halfway. The x-coordinate of the midpoint M of the line segment AB is, as we can see from the formula, equal to the arithmetic mean of the x-coordinates of the segment's two endpoints.The midpoint's y-coordinate is also equal to the mean of the endpoints' y-coordinates. Even a unique postulate just for midpoints exists.Midpoint of a Segment Hypothesis.Any line segment will only have one midpoint, neither more nor less. Any line segment with equal measure is referred to as a congruent line segment.Congruent line segments, for instance, refer to the sides of an equilateral triangle since they all have the same length. Line segments that are congruent have the same length.There is a point in a line segment that will divide it into two congruent line segments.The middle is where you are now. A segment bisector runs through the middle of a line segment and divides it into two congruent portions.A segment bisector that intersects the segment at a right angle is called a perpendicular bisector.AB B C A C D E By applying algebraic techniques to solve the midpoint formula for one endpoint, the endpoint formula can be discovered.After performing the necessary algebra, (xa,ya)=((2xmxb),(2ymyb)) (x a, y a) = ((2 x m x b), (2 y m y b)) is the formula for the Endpoint A A of line AB A B.To learn more about mid point refer
https://brainly.com/question/13792388
#SPJ13
Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.10min for calls. Find the model of the total cost of company a's plan. using m for minutes.
Answers
Based on the monthly fee charged by Company A and the charges per minute for calls, the model for the total cost of Company A's plan is Total cost = 20 + 0.05m.
How to find the model?The model to find the total cost of Company A's plan will incorporate the monthly fee paid as well as the amount paid for each minute of calls.
The model for the cost is therefore:
Total cost = Fixed monthly fee + (Variable fee per minute x Number of minutes)
Fixed monthly fee = $20
Variable fee per minute = $0.05
Number of minutes = m
The model for the total cost of Company A's plan is:
Total cost = 20 + 0.05m
Find out more on models at https://brainly.com/question/28308768
#SPJ1
The required equation that represents the total cost of Company a's plan is x = 20 + 0.5m.
As of the given data, Company A has a monthly fee of $20 and charges $.05/min for calls. An equation that represents the total cost of Company a's plan is to be determined.
Here,
Let x be the total cost of the company and m be the number of minutes on a call.
According to the question,
Total charges per minute on call = 0.5m
And a monthly fee = $20
So the total cost of company a is given by the arithmetic sum of the sub-charges,
X = 20 + 0.5m
Thus, the required equation that represents the total cost of Company a's plan is x = 20 + 0.5m.
Learn more about modals here:
https://brainly.com/question/28742310
#SPJ1
A gumball machine contains 5 blue gumballs and 4 red gumballs. Two gumballs are purchased, one after the other, without replacement.
Find the probability that the second gumball is red.
Answers
===================================================
Work Shown:
5 blue + 4 red = 9 total
A = P(1st is red, 2nd is red)
A = P(1st is red)*P(2nd is red, given 1st is red)
A = (4/9)*(3/8)
A = 12/72
B = P(1st is blue, 2nd is red)
B = P(1st is blue)*P(2nd is red, given 1st is blue)
B = (5/9)*(4/8)
B = 20/72
C = P(2nd is red)
C = A+B
C = 12/72 + 20/72
C = 32/72
C = 4/9
The sign points at the smaller number. True or False. Example 2 < 100 True False
Answers
When working with inequalities you have to remember that:
The symbol "<" indicates that the number on the left is smaller than the number on the right, then, for example:
[tex]85<90[/tex]This indicates that 85 is less than 90.
The symbol ">" indicates that the number of the left is greater than the number on the right, for example:
[tex]70>54[/tex]This indicates that 70 is greater than 54.
Now for the given statement:
[tex]2<100[/tex]"The sign points at the smaller number"
The expression indicates that 2 is less than 100, so the statement is true.
Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
I need the equation
Answers
Here is the completed table:
Number of phones manufactured Total cost of Manufactured phones
0 $400
1 $525
2 $650
3 $775
The equation that represents the total cost is C = $400 + $125p .
What is the total cost?The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.
Total cost = fixed cost + total variable cost
Total cost = fixed cost + (variable cost x total output)
C = $400 + ($125 x p)
C = $400 + $125p
Total cost when 0 phones are made = $400 + $125(0) = $400
Total cost when 1 phone are made = $400 + $125(1) = $525
Total cost when 2 phones are made = $400 + $125(2) = $650
Total cost when 3 phones are made = $400 + $125(3) = $775
To learn more about total cost, please check: https://brainly.com/question/14927680
#SPJ1
although the actual amount varies by the season and time of the day the average volume of water that flows over the false each second is 2.9 x 10 to the 5th power gallons how much water flows over the falls in an hour write the result in scientific notation hint 1 hour equals 3600 second
Answers
We were told that volume of water that flows over the fall each second is 2.9 x 10^5 gallons.
Recall, 1 hour = 3600 seconds
If 1 second = 2.9 x 10^5 gallons, then
3600 seconds = 3600 x 2.9 x 10^5
= 1.044 x 10^9 gallons
Thus, 1.044 x 10^9 gallons of water will flow over the falls in an hour.
One of the legs of a right triangle measures 13 cm and the other leg measures
2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest
tenth.
Answers
Answer:
13.2 cm
Step-by-step explanation:
Use Pythagorean Theorem
Hypotenuse^2 = (leg1)^2 + (leg2)^2
H^2 = 13^2 + 2^2
= 169 + 4
H^2 = 173
H = sqrt (173) = 13.2 cm
Simplify. -(-6w + x - 3y)
Answers
Answer: 6w - x + 3y
Step-by-step explanation:
A number cube labelled 1 to 6 is rolled 276 times. Predict how many times a 5 will show.
Answers
All the outcomes of the cube are equally probable, therefore, it is expected to have all the outcomes after 6 rolls. To find the amount of times we're supposed to get one of the outcomes, we multiply the amount of rolls by the probability of this outcome.
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. We have one number five out of six possible numbers, therefore, the probability of getting a 5 is:
[tex]P(5)=\frac{1}{6}[/tex]Therefore, in 276 rolls we're going to get the following amount of 5's:
[tex]276\times P(5)=\frac{276}{6}=46[/tex]5 will show 46 times.
since birth hakem has had a savings account that started at $3,000 and had been growing at a rate of 13% per year the amount of money in the account can be modeled by the equation y equals P =(1.13)^ Z where why is the value of the count is the number of years and pee was original deposit amount is it possible for hakem account to grow to $31812 11.42 in hakem lifetime?( try to figure out the bounds of the perameter)
Answers
Solution
For this case we have the following formula:
[tex]y=3000(1.13)^x^{}[/tex]And we want to find the value for t in order to have y = 3181211.42 , solving for y we got:
[tex]3181211.42=3000(1.13)^x[/tex]and solving for x we got:
[tex]\ln (\frac{3181211.42}{3000})=x\cdot\ln (1.13)[/tex][tex]x=56.99\approx57[/tex]for this case we need 57 years to reach the amount so then assuming that a person lives about 80 years , then is possible
yes
the length of a rectangle is 2 inches more than the width. The area is 24 square inches. Find the dimensions
Answers
Given:
length(l) = width(w) + 2
[tex]\text{Area}=24[/tex][tex]l\times w=24[/tex][tex](w+2)w=24[/tex][tex]w^2+2w-24=0[/tex][tex](w+6)(w-4)=0[/tex][tex]w=4\text{ or -6}[/tex]Negative not possible.
[tex]\text{width(w)}=4\text{ inches}[/tex][tex]\text{length(l)}=w+2[/tex][tex]\text{length of the rectangle=4+2}[/tex][tex]\text{length of the rectangle=}6\operatorname{cm}[/tex]Find the first four terms of the sequence given by the following
Answers
1) In this question, we need to resort to that Explicit formula, with the first term so that we can find the terms:
[tex]\begin{gathered} a_n=54+8(n-1) \\ a_1=54+8(1-1) \\ a_1=54 \\ \\ a_2=54+8(2-1) \\ a_2=54+8 \\ a_2=62 \\ \\ a_3=54+8(3-1) \\ a_3=54+8(2) \\ a_3=54+16 \\ a_3=70 \\ \\ a_4=54+8(4-1) \\ a_4=54+8(3) \\ a_4=78 \\ \end{gathered}[/tex]2) As we can see, this is an Arithmetic sequence. And the answer is:
[tex]54,62,70,78[/tex]Select all the true statements about this graph A. The graph is nonlinearB. The function increases at the same rateC. The rate decreases after x = 2.D. The graph is a functionE. The graph is increasing in two intervals.SELECT ALL ANSWER CHOICES THATS RIGHT
Answers
In the graph the points are connected by the straight lines, so graph is linear graph. In nonlinear graph the points are connected by the curve. So option A is incorrect.
The slope of the line changes after x=2. The inclination of line with positive x axis is different before and after x=2. So the function not increases at same rate. Then option B is incorrect.
The rate is given by the slope of line. The inclination of line with positive x axis increase after x=2, so rate increases not decreases. Then option C is incorrect.
The graph of a straight line is function or not a function can be inspected by vertical line test.
If we draw a vertical line, then the vertical line intersect the line only once, so the graph is function. Option D is correct.
The value of y increases with increase in value of x but increase in value of y with x is different for two lines. So graph is increasing in two intervals. Option E is also correct.
Thus option D and E is only true for given graph.
what is the conjugate of the denominator of the expression 9i/-2+7i
Answers
The answer is D.
The functions f(x) and g(x) are shown on the graph.f(x)=x^2What is g(x)?A. g(x)=(x+3)^2B. g(x)=(x-3)^2C. g(x)=(1/3x)^2D. g(x)=3x^2
Answers
Given:
[tex]f(x)=x^2[/tex]Let's find g(x).
From the given graph, we can see the graph of g(x) is compressed horizontally from f(x).
Thus, to find g(x) aply the transformation rules for function.
We have:
Horizontal compression of b units ==> f(bx)
Given the point on g(x):
(x, y) ==> (2, 12)
Let's solve for the value of the compressed factor.
We have:
[tex]\begin{gathered} 12=b(2)^2 \\ \\ 12=b4 \\ \\ \text{Divide both sides by 4:} \\ \frac{12}{4}=\frac{b4}{4} \\ \\ 3=b \\ \\ b=3 \end{gathered}[/tex]This means the graph of f(x) was compressed horizontally by a factor of 3 to get g(x).
Thus, to write the function for g(x), we have:
[tex]g(x)=3x^2[/tex]ANSWER:
[tex]D\text{.}g(x)=3x^2[/tex]INT. ALGEBRA: Write an equation that passes through (-10,-30) and is perpendicular to 12y-4x=8
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
Answers
The equation of the perpendicular line is y = -3x - 60
How to determine the line equation?The equation is given as
12y - 4x = 8
Make y the subject
12y= 4x + 8
y = 1/3x + 2/3
The point is also given as
Point = (-10, -30)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 1/3
This means that the slope of 12y - 4x = 8 is 1/3
So, we have
m = 1/3
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -3
The equation of the perpendicular lines is then calculated as
y = m(x - x₁) +y₁
Where
m = -3
(x₁, y₁) = (-10, -30)
So, we have
y = -3(x + 10) - 30
Evaluate
y = -3x - 30 - 30
y = -3x - 60
Hence, the perpendicular line has an equation of y = -3x - 60
Read more about linear equations at
brainly.com/question/4074386
#SPJ1
Point (7, 2) is translated up 2 units and left 5 units. Where is the new point located?(12, 4)(9, -3)(2,0)(2, 4)
Answers
The new point is located at (2,4)
Here, we want to get the result of a translation
2 units up simply mean, we are adding 2 to the y-axis value
5 units left mean we are subtracting 5 from the x-axis value
We can represent the translation as;
[tex]\begin{gathered} (x,y)\rightarrow\text{ (x-5 , y+2)} \\ =\text{ (7-5,2+2) = (2,4)} \end{gathered}[/tex]using the given quadratic function f(x)=x^2+2x-15, find the following information"Coordinates of x- intercept(zero) as ordered pairs"
Answers
the given expression is
f(x) = x^2 + 2x - 15
we will find x intercept by putting f(x) = 0
x^2 + 2x - 15 = 0
x^2 + 5x - 3x - 15 = 0
x(x +5) -3(x + 5) = 0
(x +5) (x -3) = 0
x = -5 & x = 3
so the ordered pairs are
(-5, 0) and (3, 0)
How do I simplify my answer of 42i^2+32i+6 when the original problem was (2-6i)(3-7i)
Answers
Given problem is
[tex](2-6i)(3-7i)[/tex]Now,
[tex]\begin{gathered} (2-6i)(3-7i)=42i^2-14i-18i+6 \\ =42i^2-32i+6 \end{gathered}[/tex]We know that
[tex]i^2=-1[/tex]Using this face,
[tex]\begin{gathered} 42i^2-32i+6=-42-32i+6 \\ =-32i-36 \end{gathered}[/tex]Hence, the simplified form is
[tex]-32i-36[/tex]1 a) is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.
Answers
First, we count the number of boxes.
We have: 4,8,12,16
(a)Now:
• 8-4=4
,• 12-8=4
,• 16-12=4
Since the difference is the same, the sequence is an arithmetic sequence.
(b)In the sequence
First term, a =4
Common difference, d=4
The nth term of an arithmetic sequence is:
[tex]\begin{gathered} U_n=a+(n-1)d \\ =4+4(n-1) \\ =4+4n-4 \\ =4n \end{gathered}[/tex]The explicit formula for the above sequence, f(n)= 4n.
(c)18th term
f(18)= 4 x 18
=72
The 18th term is 72.
Graph the exponential function.f(x)=4(5/4)^xPlot five points on the graph of the function,
Answers
We are required to graph the exponential function:
[tex]f(x)=4(\frac{5}{4})^x[/tex]First, we determine the five points which we plot on the graph.
[tex]\begin{gathered} \text{When x=-1, }f(-1)=4(\frac{5}{4})^{-1}=3.2\text{ }\implies(-1,3.2) \\ \text{When x=0, }f(0)=4(\frac{5}{4})^0=4\text{ }\implies(0,4) \\ \text{When x=1, }f(1)=4(\frac{5}{4})^1=5\implies(1,5) \\ \text{When x=2, }f(2)=4(\frac{5}{4})^2=6.25\implies(2,6.25) \\ \text{When x=3, }f(3)=4(\frac{5}{4})^3=7.8125\text{ }\implies(3,7.8125) \end{gathered}[/tex]Next, we plot the points on the graph.
This is the graph of the given exponential function.
i have questions on a math problem. i can send when the chats open
Answers
The random sample is determined as the simplest forms of collecting data from the total population.
Under random sampling, each member of the subset carries an equal opportunity of being chosen as a part of the sampling process.
So according to the question given
Assign each person of the population a number. Put all the numbers into bowl and choose ten numbers.
is the random sample because every person carries an equal opportunity of being chosen from the total population.
Hence the correct option is A.
with regard to promoting standards of excellence, lafasto and larson (2001) identified three rs that help improve performance: require results, review results, and ______.
Answers
With regard to promoting standards of excellence, Lafasto and Larson (2001) identified three Rs that help improve performance:
require results, review results, and Reward Results.What did the Larson and LaFasto 1989 study capture?
The LaFasto and Larson Model investigated team effectiveness. It is founded on the premise that, while individuals might be highly competent and talented, teams solve the most challenging issues.
It doesn't matter how skilled an individual is if they can't operate as part of a team.
They studied the traits of 75 highly successful teams. They discovered that high standards of excellence were a critical component in team performance.
Learn more about performance:
https://brainly.com/question/27953070
#SPJ1
For each quadratic expression below, drag an equivalent expression to its match
Answers
1. Given the expression:
[tex]\mleft(x+2\mright)\mleft(x-4\mright)[/tex]You can use the FOIL method to multiply the binomials. Remember that the FOIL method is:
[tex](a+b)\mleft(c+d\mright)=ac+ad+bc+bd[/tex]Then, you get:
[tex]\begin{gathered} =(x)(x)-(x)(4)+(2)(x)-(2)(4) \\ =x^2-4x+2x^{}-8 \end{gathered}[/tex]Adding the like terms, you get:
[tex]=x^2-2x-8[/tex]2. Given:
[tex]x^2-6x+5[/tex]You have to complete the square:
- Identify the coefficient of the x-term". In this case, this is -6.
- Divide -6 by 2 and square the result:
[tex](\frac{-6}{2})^2=(-3)^2=9[/tex]- Now add 9 to the polynomial and also subtract 9 from the polynomial:
[tex]=x^2-6x+(9)+5-(9)[/tex]- Finally, simplifying and completing the square, you get:
[tex]=(x-3)^2-4[/tex]3. Given the expression:
[tex]\mleft(x+3\mright)^2-7[/tex]You can simplify it as follows:
- Apply:
[tex](a+b)^2=a^2+2ab+b^2[/tex]In this case:
[tex]\begin{gathered} a=x \\ b=3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} =\lbrack(x)^2+(2)(x)(3)+(3)^2\rbrack-7 \\ =\lbrack x^2+6x+9\rbrack-7 \end{gathered}[/tex]- Adding the like terms, you get:
[tex]=x^2+6x+2[/tex]4. Given:
[tex]x^2-8x+15[/tex]You need to complete the square by following the procedure used in expression 2.
In this case, the coefficient of the x-term is:
[tex]b=-8[/tex]Then:
[tex](\frac{-8}{2})^2=(-4)^2=16[/tex]By Completing the square, you get:
[tex]\begin{gathered} =x^2-8x+(16)+15-(16) \\ =(x-4)^2-1 \end{gathered}[/tex]Therefore, the answer is: