Answers
Answer:
a. [tex](x - 3)^2 + 16[/tex]
b. [tex]8(x -7)^2[/tex]
c. [tex](a^2 - 1)(7x - 6)[/tex] or [tex](a+1)(a-1)(7x-6)[/tex]
d. [tex](x^2-4)(x^2+3)[/tex] or [tex](x-2)(x+2)(x^2+3)[/tex]
e. [tex](a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})[/tex]
Step-by-step explanation:
[tex]a.\ (x + 1)^2 - 8(x - 1) + 16[/tex]
Expand
[tex](x + 1)(x + 1) - 8(x - 1) + 16[/tex]
Open brackets
[tex]x^2 + x + x + 1 - 8x + 8 + 16[/tex]
[tex]x^2 + 2x + 1 - 8x + 24[/tex]
Collect Like Terms
[tex]x^2 + 2x - 8x+ 1 + 24[/tex]
[tex]x^2 - 6x+ 25[/tex]
Express 25 as 9 + 16
[tex]x^2 - 6x+ 9 + 16[/tex]
Factorize:
[tex]x^2 - 3x - 3x + 9 + 16[/tex]
[tex]x(x -3)-3(x - 3) + 16[/tex]
[tex](x - 3)(x - 3) + 16[/tex]
[tex](x - 3)^2 + 16[/tex]
[tex]b.\ 8(x - 3)^2 - 64(x-3) + 128[/tex]
Expand
[tex]8(x - 3)(x - 3) - 64(x-3) + 128[/tex]
[tex]8(x^2 - 6x+ 9) - 64(x-3) + 128[/tex]
Open Brackets
[tex]8x^2 - 48x+ 72 - 64x+192 + 128[/tex]
Collect Like Terms
[tex]8x^2 - 48x - 64x+192 + 128+ 72[/tex]
[tex]8x^2 -112x+392[/tex]
Factorize
[tex]8(x^2 -14x+49)[/tex]
Expand the expression in bracket
[tex]8(x^2 -7x-7x+49)[/tex]
Factorize:
[tex]8(x(x -7)-7(x-7))[/tex]
[tex]8((x -7)(x-7))[/tex]
[tex]8(x -7)^2[/tex]
[tex]c.\ 7a^2x - 6a^2 - 7x + 6[/tex]
Factorize
[tex]a^2(7x - 6) -1( 7x - 6)[/tex]
[tex](a^2 - 1)(7x - 6)[/tex]
The answer can be in this form of further expanded as follows:
[tex](a^2 - 1^2)(7x - 6)[/tex]
Apply difference of two squares
[tex](a+1)(a-1)(7x-6)[/tex]
[tex]d.\ x^4 - x^2 - 12[/tex]
Express [tex]x^4[/tex] as [tex]x^2[/tex]
[tex](x^2)^2 - x^2 - 12[/tex]
Expand
[tex](x^2)^2 +3x^2- 4x^2 - 12[/tex]
[tex]x^2(x^2+3) -4(x^2+3)[/tex]
[tex](x^2-4)(x^2+3)[/tex]
The answer can be in this form of further expanded as follows:
[tex](x^2-2^2)(x^2+3)[/tex]
Apply difference of two squares
[tex](x-2)(x+2)(x^2+3)[/tex]
[tex]e.\ a^{4n} -b^{4n}[/tex]
Represent as squares
[tex](a^{2n})^2 -(b^{2n})^2[/tex]
Apply difference of two squares
[tex](a^{2n} -b^{2n})(a^{2n} +b^{2n})[/tex]
Represent as squares
[tex]((a^{n})^2 -(b^{n})^2)(a^{2n} +b^{2n})[/tex]
Apply difference of two squares
[tex](a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})[/tex]
Related Questions
Solve
5y+1/5y-25*1/25=0
Answers
Answer:
y = [tex]\frac{5}{26}[/tex]
Step-by-step explanation:
[tex]5y + \frac{1}{5}y - 25 * \frac{1}{25} = 0[/tex]
Simplify, remember the order of operarions;
1. Parentehsis
2. Exponents
3. Multiplication/division
4. Addition/subtraction
[tex]5y + \frac{1}{5}y - 25 * \frac{1}{25} = 0[/tex]
[tex]5y + \frac{1}{5}y - 1 = 0[/tex]
[tex]5y +0.2y - 1 = 0[/tex]
[tex]5.2y -1 =0[/tex]
Inverse operations;
[tex]5.2y -1 =0[/tex]
+1 +1
5.2y = 1
/5.2 /5.2
y = [tex]\frac{5}{26}[/tex]
Find the 19th term (-1,-4,-7,-10)
Answers
Answer:
- 55Step-by-step explanation:
Given sequence:
-1,-4,-7,-10, ...The first term is -1 and the common difference is -3
19th term is:
- 1 + 18(-3) = -1 - 54 = -55Pls Answer the Question in the Photo
Answers
5 plus 5 euqals what number help
Answers
Answer:
10
Step-by-step explanation:
lol
...its 10
Step-by-step explanation:
1+1+1+1+1= 5
1+1+1+1+1= 5
5+5=10
Write the equation of a line that is parallel to Y =3x-2 that passes through (4,1)
Answers
Answer:
The equation of the line is y = 3x - 11.
Step-by-step explanation:
We are given the equation of a line:
[tex]\bullet \ \ \ y = 3x -2[/tex]
We are also given a point at which the line passes through.
[tex]\bullet \ \ \ (4, 1)[/tex]
With parallel lines, it is important to note:
Parallel lines have the same slope.Parallel lines must have a different y-intercept.We can use the point-slope equation to find the equation of the line:
[tex]\displaystyle y-y_1 =m(x-x_1)\\\\y - 1 = 3(x - 4)\\\\y - 1 = 3x - 12\\\\y - 1 + 1 = 3x - 12 + 1\\\\y = 3x - 11[/tex]
Therefore, the line that is parallel to y = 3x - 2 and passes through the point (4, 1) is y = 3x - 11.
What is 0.000435 in scientific notation?
A. 4.35 • 10/6
B; 4.35 • 10/4
C; 4.35 • 10/6
D; 4.35 • 10/4
Answers
Answer:B; 4.35 • 10/4
Step-by-step explanation:
Mike and Breanna like to run after swim practice each day. Usually they run the same distance, x miles. Today, however, they ran different
distances.
• Mike ran at 7 miles per hour and ran 2 more miles than usual.
• Breanna ran at 6 miles per hour and ran 1 more mile than usual.
Complete the table to show each person's distance and rate, which could be used to create rational equation relating their distance, rate, and
time
Distance
Rate
Mike
Breanna
Answers
Answer:
Step-by-step explanation: i got it right :) hopefully you get it in time!
How do you calculate run time and speed?
32 min * 8 min per mi = 4 miles How to calculate run time. Multiply your pace by your distance; If the pace is 9.5 minutes per mile and you run 3 miles: 9.5 min per mi × 3 mi = 28.5 minutes = 28 minutes, 30 seconds How to calculate running speed. Divide your run distance by your run time.
What do you do to calculate average speed?
choose one point on the line.choose another point on the line.find the time difference between the points.find the distance differences between the points.divide the differences in the distance by the difference in time.Learn more about average speed here https://brainly.com/question/5147964
#SPJ2
The measure of an exterior angle of a polygon is 10 degrees. How many sides does the
polygon have?
Answers
There are three modes of transporting material from Ontario to Florida, namely, by land, sea, or air. Also land transportation may be by rail or highway. About half of the materials are transported by land, 30% by sea, and the rest by air. Also, 40% of all land transportation is by highway and the rest by rail shipments. The percentages of damaged cargo are, respectively, 10% by highway, 5% by rail, 6% by sea, and 2% by air. (1) What percentage of all cargoes may be expected to be damaged? (2) If a damaged cargo is received, what is the probability that it was shipped by land? By sea? By air?
Answers
Answer:
0.057
0.6140
0.3158
0.0701
Step-by-step explanation:
Given that:
Let :
P(L) = Number transported by land = half = 50% = 0.5
P(S) = number transported by sea = 30% = 0.3
P(A) = Number transported by air = (100 - (50 + 30))% = 20% = 0.2
P(H) = highway transport = 40% of land transport = 0.4 * 0.5 = 0.2
P(R) = Rail shipment =(100- 40)% = 60% of land transport = 0.6 * 0.5 = 0.3
Percentage of damaged cargo :
Let probability of damage = P(d)
P(d | H) = 0.1
P(d | R) = 0.05
P(d | S) = 0.06
P(d | A) = 0.02
1) What percentage of all cargoes may be expected to be damaged
[P(d | H)*p(H)] + [P(d | R)*p(R)] + [P(d | S)*p(S)] + [P(d | A)*p(A)]
(0.1*0.2) + (0.05*0.3) + (0.06*0.3) + (0.02*0.2) = 0.057
(2) If a damaged cargo is received, what is the probability that it was shipped by ;
land?
([P(d | H)*p(H)] + [P(d | R)*p(R)]) / [P(d | H)*p(H)] + [P(d | R)*p(R)] + [P(d | S)*p(S)] + [P(d | A)*p(A)]
((0.1*0.2) + (0.05*0.3)) / (0.1*0.2) + (0.05*0.3) + (0.06*0.3) + (0.02*0.2)
= 0.035 / 0.057
= 0.6140
By sea?
[P(d | S)*p(S)] / [P(d | H)*p(H)] + [P(d | R)*p(R)] + [P(d | S)*p(S)] + [P(d | A)*p(A)]
(0.06 * 0.3) / 0.057
= 0.3158
By air?
[P(d | A)*p(A)] / [P(d | H)*p(H)] + [P(d | R)*p(R)] + [P(d | S)*p(S)] + [P(d | A)*p(A)]
(0.02 * 0.2) / 0.057
= 0.0701
Can u choose if it is primary or secondary please and get it right.
Answers
Answer:
secondary
Step-by-step explanation:
The ratio of apples to oranges in the fruit bowl is 1: 9 in the small bowl. If the extra large bowl has 40 fruit in total. How many are oranges?
Answers
vary hard 6th grade work
Answers
Answer:
A image was not attached
Step-by-step explanation:
Select the correct answer.
Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6-9)?
OA. x= -9
OB. x=-6
Oc. y=9
OD. y= -4
Answers
Answer:
B. x = -6
Step-by-step explanation:
A line with the equation, y = ¼, is a horizontal line. Therefore, the line that is perpendicular to it would be a vertical line, which can be represented by the equation, x = a. Where, a is the x-value or the point where the vertical line intersects the x-axis. This x-coordinate remains the same for every point on the vertical line.
Thus, since the perpendicular line passes through (-6, -9), therefore, the value of a = -6.
Thus, the equation of the perpendicular line would be:
x = -6
Delta math helpppp!!!!!!!!!
Answers
Hope this helps! :D
The radius of a cylindrical tank is 3’ and the height is 8’. What is the volume
Answers
Answer:
Given :-Radius of tank = 3 m Height of tank = 8 m To Find :-It's volume
Formula :-Volume = πr²h
Solution :-[tex] \tt \: volume = \dfrac{22}{7} \times 3 {}^{2} \times 8[/tex]
[tex] \tt volume \: = \frac{22}{7} \times 9 \times 8[/tex]
[tex] \tt \: volume = \dfrac{22}{7} \times 72[/tex]
[tex] \tt \: volume \approx \: 226.194[/tex]
Answer:
given. require. solution
r=3. v=? v=πr²h
h=8. v=3.14×3²×8
3.14×9×8
=226.08
need answer thx in advanace!
Answers
Answer:
13
Step-by-step explanation:
The term is in an arithmetic progression.
That means there is 6 between each term and the next one.
Givens
a = -30
d = 6
last term an = 42
Formula
L = a + (n - 1)*d
Solution
42 = -30 + (n -1 )*6 Add 30 to both sides
42+30 = (n - 1) * 6 Combine the terms on the left.
72 = (n - 1)*6 Divide both sides by 6
72/6 = n - 1
12 = n - 1 Add 1 to both sides
12 + 1 = n
n = 13
Ella finished a bike race in 37.6 minutes. Miranda finished the race 9 1/10 minutes sooner than Ella finished it. How many minutes did it take Miranda to finish the race?
Answers
Answer:
56.7
Step-by-step explanation:
Just Add all numbers
SOMEONE PLEASE HELP ME ASAP!!!!!!!!!!!!!
Answers
answer is 10
if not then im srry
I need help i dont understand any of this
Answers
Step-by-step explanation:
multiply all the fractions together in your calculator :)
Kai wrote the number 85 on the board. Is 85 a prime or composite?
Answers
Hello there!
85 is composite.
There are 3 ways of determining whether a number is prime or composite.
Check if the number is even. If it is, it's 100% compositeIf the number is odd, then look at its last digit. If it's 2, 4, 6, 8, 0 or 5, then it is composite.If the last digit is not 2, 4, 6, 8, 0 or 5, look at the factors of the given number. If it has 2 factors, then it's prime. If it has more than 2 factors, it's composite.Hope this helps!
[tex]GraceRosalia[/tex]
Triangle MNO is congruent to Triangle PQR. What is the measure of
Answers
Answe
Step-by-step explanation:
Answer: C :79.5
Step-by-step explanation:
Since both triangles are congruent the angles are also congruent. P the measure we are trying to find is congruent to M since they’re equal it should look like this
5x-19 = 3x+20.4
5x = 3x+ 39.4
2x = 39.4
X= 19.7
to find the measure of angle P plug in X to its equation so
3x + 20.4
3 (19.7) + 20.4
= 79.5
w/6 = 6/9 Im failing mathhhh helpppp
Answers
Answer:
W = 4
Step-by-step explanation:
4/6 = 6/9
2/3 = 2/3
multiple 2/3 by 2 and you get 4/6
4/6 = 6/9
w= 4
A truck can carry up to 2,000 pounds. The truck is carrying 1,600 pounds divided equally among 8 crates.
What is the weight of each crate?A truck can carry up to 2,000 pounds. The truck is carrying 1,600 pounds divided equally among 8 crates.
What is the weight of each crate?
Answers
Answer:
200 pounds per crate
Step-by-step explanation:
because if you divide 1600 by 8 than you get 200 pounds. then that is you unit rate
Answer:
250
2000 divided by 8
Step-by-step explanation:
which of the values satisfy the following inequality
|x-7.5| ≤ 17
select all that apply.
a. x = 27
b. x = -9
c. x = -10
d. x = 20
Answers
Answer:
So first look at the symbol. It must be less than or equal to 17.
By elimination A is 20.5 which is wrong
B is -16.5 by abs =16.5
C is -17.5 by abs = 17.5
D is 12.5
So B and D are possible solutions..
A premature infant weighing 3lbs is ordered to 1 milligram per gram of a drug. How many milligrams should you administer to the patient?
Answers
Answer:
1360.78 mg
Step-by-step explanation:
3 pounds in grams is 1360.78 grams.
so, 1 mg per gram would mean the baby should recieve 1360.78 mg of the drug.
a number s is at least -2 or less than -6 (how will it be graphed on a number line?)
Answers
Answer:
subtract 2-6 and the just put a - in front of 4 so -4
Step-by-step explanation:
Answer:
-2 will be 2 times to the left of zero and -6 would be 6 spaces to the left of zero.
Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement.
[tex]( - 5 {x}^{2} - 2x + 4) + (8 {x}^{2} - x - 1) - (x + 2)(x - 5)[/tex]
The polynomial simplifies to an expression that is a____
A.quadratic
B.liner
C.constany
______
A.trinomial
B.binomial
C.monomial
with a degree of____
A.1
B.2
C.0
Answers
Answer:
The polynomial simplifies to a quadratic with a degree of 2
Step-by-step explanation:
Expand and simplify everything
-5x²-2x+4+8x²-x-1-x²+5x-2x+10
-5x²+8x²-x²-2x-x+5x-2x+4-1+10
2x²+13
If d stands for the diameter of a circle and r stands for the radius of a circle, then:
A d = 2r
B = 2d
O c d = 3. 141
D. = 3.140
O E. d= 72
PLEASE HURRY!
Answers
Solve the following logarithmic equation.
Answers
I suppose this is the correct answer.
If average of 3 quantities is 15 , sum of quantities is....?
Answers
Answer:
45
Step-by-step explanation:
Let the three quantities be x, y and z.
[tex] \because \: average = \frac{sum \: of \: quantities}{no \: of \: quantities} \\ \\ \therefore \: 15 = \frac{x + y + z}{3} \\ \\ 15 \times 3 = x + y + z \\ \\ \huge \purple{ 45 = x + y + z}[/tex]