[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=4\\ a_1=2\\ r=\frac{1}{3} \end{cases}[/tex]
[tex]\bf S_4=2\left( \cfrac{1-\left( \frac{1}{3} \right)^4}{1-\frac{1}{3}} \right)\implies S_4 = 2\left( \cfrac{1-\frac{1}{81}}{\frac{2}{3}} \right)\implies S_4 = 2\left( \cfrac{\frac{80}{81}}{~~\frac{2}{3}~~} \right) \\\\\\ S_4=2\left( \cfrac{40}{27} \right)\implies S_4=\cfrac{80}{27}\implies S_4=2\frac{26}{27}[/tex]
Answer:
80/27.
Step-by-step explanation:
Sum of n terms = a1 * (1 - r^n) / (1 - r)
Sum of 4 terms = 2 * (1 -(1/3)^4) / ( 1 - 1/3)
= 2 * 80/81 / 2/3
= 160 / 81 * 3/2
= 480/ 162
= 80/27 (answer
Cinemark Theater has three categories for ticket prices. Adult tickets
sell for $6.50 after 3pm or $3.25 for a matinee (before 3pm), and Under 12
tickets sell for $3 at any time. The theater has a maximum capacity of 408
seats. What is the greatestamount that could be collected at:
a) an 8pm showing?
b) a 1pm showing?
c) Explain how much you think would be collected at a
matinee showing of a children's movie.â
is a common external tangent to circles W and Y. What is the distance between the two centers of the circles? Round to the nearest hundredth. (Hint: Draw segment connecting the centers of the two circles, and then draw a segment, , so that YS + SZ = YZ and .)
Answer:
[tex]WY=42.8\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle WYS
Applying the Pythagoras Theorem
[tex]WY^{2}=WS^{2}+YS^{2}[/tex]
we have that
[tex]WS=XZ=42\ units[/tex]
[tex]YS=YZ-WX=19-11=8\ units[/tex]
substitute
[tex]WY^{2}=42^{2}+8^{2}[/tex]
[tex]WY^{2}=1,828[/tex]
[tex]WY=42.8\ units[/tex]
solve
[tex]tan(a) - 1 = 0[/tex]
[tex]\tan a-1=0\\\tan a =1\\\\a=\dfrac{\pi}{4}+k\pi, k\in\mathbb{Z}[/tex]
Which expression is equivalent to -32 to 3/5 power
Answer:
8
Step-by-step explanation:
We are given the following expression and we are to find the simplest form of this expression:
[tex] - 3 2 ^ { \frac { 3 } { 5 } } [/tex]
First of all, we will factor the coefficient:
[tex] 3 2 = 2 ^ 5 [/tex]
Rewriting it as:
[tex] - ( 2 ^ 5 ) ^ { \frac { 3 } { 5 } }[/tex]
Applying the exponent rule [tex](a^b)^c = a^{bc}[/tex] to get:
[tex]-2^{5.\frac{3}{5}}=-2^3[/tex]
[tex]-2^3=-8[/tex]
I picked true but it told me it was incorrect, I looked it up and it says true, so is this statement really true or not?
Answer:
False
Step-by-step explanation:
What the attached image says that if two solids with equal heights and base areas are cut by any parallel plane to their bases then sections of equal area (volume) would be produced in them
What square root of 9 is less than 2 squared
The square root of 9 is 3, but the negative square root of 9, which is -3, is less than 2 squared (4). Therefore, the answer to the question is -3.
Explanation:The square root of 9 is 3. We denote the square root symbolically as √9 = 3. However, if we're looking for which square root of 9 is less than 2 squared (which is 4), we consider that every positive number has two square roots: one positive and one negative. The negative square root of 9 is -3, which is indeed less than 4. Therefore, the square root of 9 that is less than 2 squared is -3.
Learn more about Square Root here:
https://brainly.com/question/1540542
#SPJ2
High population density can cause increases in competition for resources, such as food and shelter. The table shows the number of zebras living in four different regions.
In which region is competition for resources most likely the greatest?
Region A
Region B
Region C
Region D
Answer:
The answer is Region C
Step-by-step explanation:
Region C has total population of Zebra as 16,400 divided by the area occupied in square km which is 625. This gives population density of approximately 26 zebras/km square
[tex] \frac{16400}{625} = 26.24[/tex]
If you follow the same procedure for other regions, you will discover that region C has the highest number of Zebras/square km which is 26.
I hope this helped?
The region that would have the greatest competition for resources is Region C.
What is population density?
Population density is the amount of organisms that live in a square feet of an area.
Population density = population / area
Population density in Region A = 1312 / 212 = 6.19Population density in Region B = 630 / 314 = 2Population density in Region C = 16400 / 625 = 26.24Population density in Region D = 17800 / 902 = 19.7To learn more about population density, please check:
https://brainly.com/question/3704320
If rolling a number cube, identify the following events as disjointed or overlapping.
Event A: rolling a prime number
Event B: rolling a number larger than 4
Overlapping events ?
or
disjointed events ?
Answer:
Overlapping events
Step-by-step explanation:
Note that in the question, it specifically specifies that there is only a number cube (or 1 number cube). Note that the two events asked for us to solve is does not conflict at all.
Event A is asking for the probability of you rolling a prime number (1 , 3 , 5), while Event B is asking for the probability of you rolling a number larger than 4 (5 , 6). These two can occur at the same time, and both events can be confirmed by rolling the number 5.
~
Answer:
overlapping events
Step-by-step explanation:
Event A: Rolling a prime
The following are the prime numbers from 1 to 6 (inclusive):
2,3,5
Event B: Rolling a number larger than 4
The following are larger than 4 from 1 to 6 (inclusive):
5,6
Do you see any overlap?
The overlap is 5.
These are overlapping events.
1. Given the functions f(x)=3x-4 and g(x)=4x+10, find the value of x for which f(x) = g(x)
A. 2
B. -2
C. -6
D. -14
Answer:
answer is D
Step-by-step explanation:
3x-4=4x+10
3x=4x+14
-1x=14
x= -14
Answer:
-14
Step-by-step explanation:
It's multiple choice so we could plug in values of x and see which makes f(x)=g(x) true.
What I mean is would could plug in values of x to see which gives us
3x-4=4x+10 is true.
Or we could just solve it.
3x-4=4x+10
Subtract 3x on both sides:
-4=1x+10
-4=x+10
Subtract 10 on both sides:
-14=x
So x=-14 would make f(x)=g(x) hold.
Let's check it and see!
f(-14)=3(-14)-4=-42-4=-46.
g(-14)=4(-14)+10=-56+10=-46.
They have the same value of -46 so x=-14 is certainly going to make f(x)=g(x) be true.
Solve step by step :
(2+2i)(5+3i)
Answer:
(2 + 2i)(5 + 3i) = 4 + 16iStep-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
and i² = -1
(2 + 2i)(5 + 3i) = (2)(5) + (2)(3i) + (2i)(5) + (2i)(3i)
= 10 + 6i + 10i + 6i² = 10 + 6i + 10i + 6(-1)
= 10 + 6i + 10i - 6 combine like terms
= (10 - 6) + (6i + 10i)
= 4 + 16i
Answer:
[tex]\displaystyle 4+16i[/tex]
Step-by-step explanation:
Distributive property: ⇒ A(B+C)=AB+AC
A=2, B=2, C=5, and D=3
[tex]\displaystyle (2*5-2*3)+(2*3+2*5)i[/tex]
Simplify and refine to find the answer.
[tex]\displaystyle2*3+2*5=2*3=6, 2*5=10, 10+6=16[/tex]
[tex]\displaystyle2*5-2*3=2*5=10-2*3=2*3=6, 10-6=4[/tex]
[tex]\displaystyle 4+16i[/tex] , which is our correct answer.
Jacob is saving to buy an MP3 player that costs $195. He earns $225 a week at a part-time job. His expenses are $180 a week. If he currently has saved $55, how many more weeks will it be before he can buy the MP3 player? (SHOW WORK)
Answer:
approximately 3 ....to be exact 3.1 weeks
Step-by-step explanation:
he earns 225 a week we know that right? and he has to take out 180 to pay for things... so right there you have 225-180=45 so that's 45 dollars a week he has. the MP4 player is 195 and he already has 55 dollars saved so 195-55= 140 so he still needs 140 dollars to buy it the question now is how many weeks will it take for him to save up to 140 dollars? you simply take 140÷45 (bc that's what he gets each week) and it should = 3.1
Answer: 3.1
Step-by-step explanation:
1. 225 a week in pay
2. 180 take out of pay
3. 225-180=45 a week from paycheck
4. Mp3 cost 195.00
5. 55.00 money saved
6. 195-55=140
7. 140÷45 after rounding 3.1
There is the answer
13. Pizza Perfection sold 93 pizzas on Monday, 67 pizzas on Tuesday, 78 pizzas on Wednesday, 44 pizzas on Thursday, and 123 pizzas on Friday. On average, how many pizzas did they sell per day?
A. 83
B. 63
C. 81
D. 82
Add all of the number of pizzas together
93+67+78+44+123
160+245
405
Divide by 5 because there are 5 numbers
405/5=81
81 pizzas
Answer: 81 pizzas -C.
What is the simplified form of the following expression? 5sqrt 8-sqrt18-2sqrt2
Answer:
5 sqrt2.
Step-by-step explanation:
sqrt8 = sqrt4 * sqrt2 = 2 sqrt2
sqrt18 = sqrt9 * sqrt2 = 3 sqrt2
So simplifying:
5sqrt 8 - sqrt18 - 2 sqrt2
= 5*2sqrt2 - 3 sqrt 2 - 2 sqrt2
= 10 sqrt2 - 5 sqrt2
= 5 sqrt2 (answer).
For this case we must simplify the following expression:
[tex]5 \sqrt {8} - \sqrt {18} -2 \sqrt {2}[/tex]
Rewriting we have:
[tex]8 = 2 * 2 * 2 = 2 ^ 2 * 2\\18 = 9 * 2 = 3 ^ 2 * 2\\5 \sqrt {2 ^ 2 * 2} - \sqrt {3 ^ 2 * 2} -2 \sqrt {2} =[/tex]
We have that by definition of properties of roots and powers it is fulfilled:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]5 * 2 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -5 \sqrt {2} =\\5 \sqrt {2}[/tex]
Answer:
[tex]5 \sqrt {2}[/tex]
please help!!!
The number of Indian, Malay, and Chinese pupils in a school is in the ratio of 1 : 3 : 6. If there are 360 more Malay pupils than Indian pupils, how many Chinese pupils are in the school?
Answer:
1080
Step-by-step explanation:
looking at the ratio of 1 : 3 : 6, we can say that the pupils are divided into 1 + 3 + 6 = 10 "parts".
Indian are 1 part, Malay are 3 parts, and Chinese are 6 parts.
So 3x (3 parts of malay) is 360 more than 1x (1 part of Indian). Thus:
3x - 360 = x
2x = 360
x = 180
We know chinese is 6 parts, or 6x, so Chinese would be 6 (180) = 1080
Hence, there are 1080 chinese pupils
The paragraph below comes from the rental agreement Susan signed when she opened her account at Super Video.
“All rentals are due back by midnight of the due date as printed on the transaction receipt. Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late. Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. The Customer will not be required to return the product once the total balance is paid.”
Susan went into her local Super Video to rent a movie last week. When she had made her choice, she approached the checkout counter where the clerk asked for her ID, scanned her movies and asked for $5.83. Susan gave her a $10 bill and the clerk gave her $4.17 as change as she said, “Thank you, have a good day!”.
Which of the following events invalidates the contract Susan signed with Super Video?
a.
Susan rented the wrong movie.
b.
The clerk gave Susan the wrong amount of change.
c.
The clerk asked Susan for her ID rather than her membership card.
d.
The clerk completed the transaction without giving Susan a receipt or otherwise informing her of the due date.
Answer:
option D
Step-by-step explanation:
As per the contract:
"All rentals are due back by midnight of the due date as printed on the transaction receipt. "
In given case clerk did not give any transaction receipt.
so option D is correct
The clerk completed the transaction without giving Susan a receipt or otherwise informing her of the due date !
Answer:
d
Step-by-step explanation:
i just did the test
What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?
Consider the line7X-6Y=-5
Answer:
See below in bold.
Step-by-step explanation:
Convert the equation into slope-intercept form:
7x - 6y = -5
6y = 7x + 5
y = (7/6) x + 5/6
- so the slope is 7/6.
The slope of a line parallel to this has the same slope 7/6.
The slope of a line perpendicular to this has a slope of - 1 / 7/6
= -6/7.
Answer:
Step-by-step explanation:
calculate the slope of given line :
7X-6Y=-5
6y = 7x+5
y=7/6 x +5/6
the slope is : 7/6
the slope of a line parallel to this lineis 7/6 ( same slope )
the slope of a line perpendicular to this line is : a when : a× 7/6= - 1
so : a = -6/7
Find the measure of each side indicated round to the nearest 10th
Answer:
20) 30°; 21) 21,1; 22) 6,2
Step-by-step explanation:
For the first image, you have to do csc⁻¹ 2 [OR sin⁻¹ ½] because you are solving for an angle measure. When evaluated, you get 30°.
For the second image, you have to do 13sec 52° = x [OR 13\cos 52° = x]. When evaluated, you get an approximate measure of 21,1.
For the third image, you have to do 6csc 75° = x [OR 6\sin 75° = x]. When evaluated, you get an approximate measure of 6,2.
Extended information on Trigonometric Ratios
O\H = sin θ
A\H = cos θ
O\A = tan θ
H\A = sec θ
H\O = csc θ
A\O = cot θ
I am joyous to assist you anytime.
Help! I need help on this
Check the picture below.
now we simply plug all those three sides in Heron's Area Formula.
[tex]\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=5.8\\ b=9.75\\ c=7.39\\ s=11.47 \end{cases} \\\\\\ A=\sqrt{11.47(11.47-5.81)(11.47-9.75)(11.47-7.39)} \\\\\\ A=\sqrt{11.47(5.66)(1.72)(4.08)}\implies A\approx \sqrt{455.5839955} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 21.3444~\hfill[/tex]
Answer:
area of triangle ABC is 21.39 square units.
C is the correct option.
Step-by-step explanation:
We know the formula for the area of the triangle ABC in terms of sine. The formulas are
[tex]A=\frac{1}{2}ab\sin C\\\\A=\frac{1}{2}ac\sin B\\\\A=\frac{1}{2}bc\sin A[/tex]
In the given triangle, we hae
b = 9.75
c = 7.39
A = 36.43°
Therefore, area of triangle ABC is given by
[tex]A=\frac{1}{2}bc\sin A\\\\\frac{1}{2}\cdot9.75\cdot7.39\sin36.43\\\\A=21.39[/tex]
Hence, area of triangle ABC is 21.39 square units.
C is the correct option.
is 0.777777 a repeating decimal ?
Answer: no
Step-by-step explanation:
How many triangles are there that satisfy the conditions a = 13, b= 6, a=6°?
Answer:
did this problem came with a chart becuase i dont know what youre talkin about
Step-by-step explanation:
Answer:
1 triangle will satisfy the condition.
Step-by-step explanation:
I Need The Answer Plz I’m Failing Plz
Answer:
M<A is less than or equal to 90°
Step-by-step explanation:
If it is less than or equal to, then the first statement has to be false, that it is greater. This means the statement is negated because they can't work together.
Given the equation A=250(1.1)t, you can determine that the interest is compounded annually and the interest rate is 10%. Suppose the interest rate were to change to being compounded quarterly. Rewrite the equation to find the new interest rate that would keep A and P the same.
What is the approximate new interest rate?
Convert your answer to a percentage, round it to the nearest tenth, and enter it in the space provided, like this: 42.53%
Final answer:
To find the new interest rate compounded quarterly, divide the annual interest rate by the number of compounding periods per year.
Explanation:
To rewrite the equation to find the new interest rate, we need to consider the compounding frequency. Currently, the interest is compounded annually. To find the new interest rate compounded quarterly, we need to divide the annual interest rate by the number of compounding periods per year.
So, for an interest rate of 10%, the quarterly interest rate would be 10% divided by 4, which is 2.5%.
Therefore, the approximate new interest rate, compounded quarterly, would be 2.5%.
The new interest rate when compounded quarterly that would keep the future value (A) and the present value (P) the same is approximately 9.38%.
To find the new interest rate when the interest is compounded quarterly instead of annually, we need to use the compound interest formula and equate the two expressions for A.
Given:
[tex]A = 250(1.1)^_t[/tex] (interest compounded annually)
[tex]A = P(1 + r/m)^_(mt)[/tex] (compound interest formula)
Where:
A = Future value
P = Present value (250)
r = Annual interest rate
m = Number of times interest is compounded per year
t = Time in years
Step 1: Equate the two expressions for A.
[tex]250(1.1)^t = 250(1 + r/m)^_{(mt)}[/tex]
Step 2: Substitute m = 4 (interest compounded quarterly).
[tex](1.1)^t = (1 + r/4)^_{(4t)}[/tex]
Step 3: Solve for r.
[tex](1 + r/4)^4 = 1.1[/tex]
[tex]1 + r/4 = (1.1)^_{(1/4)}[/tex]
[tex]r/4 = (1.1)^_(1/4)} -1[/tex]
[tex]r= 4((1.1)^_(1/4)} -1)[/tex]
r ≈ 0.0938 or 9.38%
210 donuts can be made in 10 hours how many can be made in 3 hours
Answer:
63 donuts
Step-by-step explanation:
210 donuts -> 10 hours
x donuts -> 3 hours
This is already setup for a proportion:
[tex]\frac{210}{x}=\frac{10}{3}[/tex]
Cross multiply:
[tex]3(210)=10x[/tex]
Simplify:
[tex]630=10x[/tex]
Divide both sides by 10:
[tex]\frac{630}{10}=x[/tex]
Simplify:
[tex]63=x[/tex]
63 donuts can be made in hours.
The division is one of the four fundamental arithmetic operations. The number of donuts that can be made in 3 hours time period is 63 donuts.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that 210 donuts can be made in 10 hours. Therefore, the number of donuts that can be made per hour are:
Number of donuts per hour = 210 donuts / 10 hour
= 21 donuts / hour
Now, the number of donuts that can be made in 3 hours are,
Number of donuts = 21 donuts / hour × 3 donuts
= 63 donuts
Hence, the number of donuts that can be made in 3 hours time period is 63 donuts.
Learn more about Division:
https://brainly.com/question/369266
#SPJ2
Write the slope-intercept form of the equation that passes through the point (-2, 3) and is parallel to the line y = -6x - 9 y = 1/6x - 1 y = 6x - 9 y = -6x - 1 y = -6x - 9
Answer:
y = -6x - 9Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
Parallel lines have the same slope.
===========================================
We have y= -6x - 9 → m = -6
Put the value of a slope and the coordinates of the point (-2, 3) to the equation of a line:
3 = -6(-2) + b
3 = 12 + b subtract 12 from both sides
-9 = b → b = -9
Finally:
y = -6x - 9
What is the area of the polygon below?
A. 147 square units
B. 111 square units
C. 156 square units
D. 120 square units
Area of the given polygon is required.
The area of the polygon is A. [tex]147\ \text{square units}[/tex]
The polygon is a rectangle with one corner of the rectangle removed.
The removed area is a square.
The area of the complete rectangle is
[tex]13\times 12=156\ \text{square units}[/tex]
Area of the removed square
[tex]3\times 3=9\ \text{square units}[/tex]
The area of the polygon is
[tex]156-9=147\ \text{square units}[/tex]
Learn more:
https://brainly.com/question/11466123?referrer=searchResults
I Need Help Answer Plz I Need It Badly!!!
Answer: Yes it is.
Step-by-step explanation: So we are already told that segment AC is congruent to segment DC. They both have a right angle, as indicated by the angle symbol, and they share side-length BC.
According to the Hypotenuse-Leg Theorem, two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles. AC and DC are hypotenuses and they are congruent. And BC, the shared side, is a corresponding congruent leg. And since they are both right triangles, we then know that the HL Theorem applies.
The coordinates G(7, 3), H(9, 0), I(5, -1) form what type of polygon?
an obtuse triangle
Answer:
Is an acute triangle
Step-by-step explanation:
we have
[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]
so
The polygon is a triangle
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Remember that
If applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex] -----> is a right triangle
[tex]c^{2}>a^{2}+b^{2}[/tex] -----> is an obtuse triangle
[tex]c^{2}<a^{2}+b^{2}[/tex] -----> is an acute triangle
where
c is the greater side
step 1
Find the distance GH
[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]
substitute
[tex]d=\sqrt{(0-3)^{2}+(9-7)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(2)^{2}}[/tex]
[tex]GH=\sqrt{13}\ units[/tex]
step 2
Find the distance HI
[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]
substitute
[tex]d=\sqrt{(-1-0)^{2}+(5-9)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(-4)^{2}}[/tex]
[tex]HI=\sqrt{17}\ units[/tex]
step 3
Find the distance GI
[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]
substitute
[tex]d=\sqrt{(-1-3)^{2}+(5-7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(-2)^{2}}[/tex]
[tex]GI=\sqrt{20}\ units[/tex]
step 4
Let
[tex]c=GI=\sqrt{20}\ units[/tex]
[tex]a=HI=\sqrt{17}\ units[/tex]
[tex]b=GH=\sqrt{13}\ units[/tex]
Find [tex]c^{2}[/tex] ------> [tex]c^{2}=(\sqrt{20})^{2}=20[/tex]
Find [tex]a^{2}+b^{2}[/tex] ----> [tex](\sqrt{17})^{2}+(\sqrt{13})^{2}=30[/tex]
Compare
[tex]20 < 30[/tex]
therefore
Is an acute triangle
Can someone help me with this don’t mind the 11 it’s not apart of the problem
let's firstly convert the mixed fractions to improper fractions and then add.
[tex]\bf \stackrel{mixed}{2\frac{7}{10}}\implies \cfrac{2\cdot 10+7}{10}\implies \stackrel{improper}{\cfrac{27}{10}}~\hfill \stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{27}{10}+\cfrac{17}{2}\implies \stackrel{\textit{using an LCD of 10}}{\cfrac{(1)27+(5)17}{10}}\implies \cfrac{27+85}{10}\implies \cfrac{112}{10}\implies \cfrac{56}{5}\implies 11\frac{1}{5}[/tex]
which number should be added to the expression x^2-8x to change it into a perfect square trinomial?
a. -16
b. -4
c. 4
d. 16
The perfect square [tex](x-a)^2[/tex] can be expanded as follows:
[tex](x-a)^2=x^2-2ax+a^2[/tex]
So, we have to think of the term [tex]-8x[/tex] as [tex]-2ax[/tex], which implies [tex]a=4[/tex].
Thus, we have to add [tex]a^2[/tex], i.e. 16, to complete the perfect square:
[tex](x-4)^2 = x^2-8x+16[/tex]
What is the probability of the spinner landing on 2? please respond fast