Quadratic expressions are mathematical expressions that have the power of one of its alphabets being equal to and not more than two. The given expression in the question can be simplified as 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
Algebraic expressions are mathematical expressions that consist of given number(s) and alphabet(s). When the power (exponential) of one of the alphabets is given as two, then the expression can be classified as a quadratic expression.
Thus the given expansion of the quadratic expression can be simplified as follows:
([tex]9x^{2}[/tex] + 9x - 4)([tex]9x^{2}[/tex] + 9x - 10) - 72
But,
([tex]9x^{2}[/tex] + 9x - 4)([tex]9x^{2}[/tex] + 9x - 10) = [tex]9x^{2}[/tex]([tex]9x^{2}[/tex] + 9x - 10) + 9x([tex]9x^{2}[/tex] + 9x - 10) - 4([tex]9x^{2}[/tex] + 9x - 10)
= 81[tex]x^{4}[/tex] + 81[tex]x^{3}[/tex] - 90[tex]x^{2}[/tex] + 81[tex]x^{3}[/tex] + 81 [tex]x^{2}[/tex] - 90x - 36 [tex]x^{2}[/tex] + 36x - 40
= 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40
So that we have;
(81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40) - 72 = 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40 -72
= 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
Thus the simplification of the given expression is 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
For more clarifications on the simplification of algebraic expressions, visit: https://brainly.com/question/26581327
#SPJ1
The length of a rectangle exceeds the breadth by 8 cm. Find the area of the rectangle, if its perimeter is 180 cm
Answer:
2009cm^2
Step-by-step explanation:
Given data
let the length be L
and the width be w
so
w= x
L=x+8
P= 180cm
P= 2L+2W
180= 2(x+8)+2(x)
180= 2x+16+2x
collect like terms
180= 4x+16
180-16= 4x
164= 4x
x= 164/4
x=41
W= 41cm
L= 41+8
L= 49cm
A= L*W
A=49*41
A=2009cm^2
Hence the area is 2009cm^2
PLS HELP WILL MARK BRAINLIEST !!!!!!
Which of the following variables is most commonly graphed on a line graph?
distance
time
speed
size
Answer:
If these are answer choices, i believe the correct answer is B, time.
Step-by-step explanation:
Answer:
It's Time
Step-by-step explanation:
2(1/2z+ 4)- 0.5
what could this be re written as?
a. z-3.5
b. z+7.5
c. z+8.5
d. 2z+3.5
Answer:
B. z+7.5 is the answer I chose
In Geometry, which kind of reasoning is used in proving theorems? Inductive or Deductive Reasoning? Why?
Answer:
Inductive
Step-by-step explanation:
Because our conclusion is based on facts, the conclusions reached by deductive reasoning are correct and valid.
True or False? If one of the angles of a triangle is obtuse, then the triangle is obtuse.
Answer:
True
Step-by-step explanation:
Image result for True or False? If one of the angles of a triangle is obtuse, then the triangle is obtuse.
In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°. Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees. ... Hence, if one angle of the triangle is obtuse, then the other two angles with always be acute.
Answer:
True, as long as the other angles are acute !!
Step-by-step explanation:
I hope this helps !! :D
I need help please):
Answer:
7) x = 5
8) x = 10
Step-by-step explanation:
7) 2x-3=x+2
x=5
8) 4x=2x+20
2x=20
x=10
On a map the distance between Juneau and Fairbanks is 5 inches. The approximate distance is 625 miles. The distance between Denver and Fairbanks is 19.5 inches on the same map. What is the approximate distance from Denver to Fairbanks to the nearest mile?
Answer:
The answer for this question is 2,437.5 or rounded 2,438.
Step-by-step explanation:
5 goes into 19.5, 3.9 times to get that take 19.5÷5 to get 3.9. Then take 625×3.9 to get the total of 2,437.5 miles for your answer.
Answer:
Step-by-step explanation:
jhghgjhjgjjhgghghghgbhbjhbhvgjhgygyguygygyugglygygluyglygyggylgyugyygygygygygugyggyghjghgkygkhghgjkghhgghgghgggghghhghghghghghhgghghghghghghghgghghghghjhgjggjghghjgggghhhghggjkgkjghjjghkghjkggkghjggkhghgkhghkjghjghghjkgjhkgjhhjghgkhghgkjghjgjkhhjhhghgkjgghjj.
Simplify: 5 + p > 3
GIVING BRAINLIST!!! PLEASE HELP!
Answer:
p>3-5
p>-2
Step-by-step explanation:
step 1= 5 will pass the greaterthan sign and it will be -ve
step 2= it will be (p>3-5) 3-5= -2
answer = p> -2
Answer:
The answer is p > -2
Step-by-step explanation:
Move all terms not containing p to the right side of the inequality.
~Hoped this helped~
Find the area of the triangle... HURRRY PLZ HELP HELP HELP. ILL MARK BRAINLYIST THINGY
Answer:
38.25
Step-by-step explanation:
A = 1/2(8.5)(9)
Answer:
[tex]38.25 mm^{2}[/tex]
Step-by-step explanation:
Area of a triangle = 1/2bh
b = 8.5
h = 9
1/2(8.5)(9) = 38.25
Grace bought 3 soccer balls for $14 each and 2 pairs of goalie gloves for $9 each. Write an expression for the total cost of the supplies. Then find the total cost. (LABEL)
Answer:
3(14)+2(9) is the equation
$60 is the total cost
Tell me if im right :)
Answer:
T=60
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINALIST!!!!
AB contains points (4, 2) and (−1, −8). What is the equation of the line parallel to AB that contains point (0, 5)?
9514 1404 393
Answer:
y = 2x +5
Step-by-step explanation:
We can use the slope formula to find the slope of AB, which is the same as the slope of the parallel line. Then, we can use the point-slope equation for a line to find the desired equation.
m = (y2 -y1)/(x2 -x1)
m = (-8 -2)/(-1 -4) = -10/-5 = 2
__
y -y1 = m(x -x1) . . point-slope form of equation for a line
y -5 = 2(x -0) . . . . fill in m=2, (x1, y1) = (0, 5)
y = 2x +5 . . . . . . . rearrange to slope-intercept form
Which expression has the smallest value? ǀ 65 ǀ - ǀ -34 ǀ - ǀ 27 ǀ ǀ -17 ǀ
Answer:| -17|
Step-by-step explanation: the lines represent the absolute value which is 17 out of the rest it has the smallest value
When can we say that a function is continuous?
*WILL GIVE BRAINLIEST*
Find the surface area of the rectangular prism:
Teacher resources - Surface area of prisms and cylinders page 1
A: 120 cm2
B: 12 cm2
C: 60 cm2
D: 94 cm2
150 grams decreased by 74% ?
Answer:
39
Step-by-step explanation:
multiple 159 by 74% them subtract
Help! I’ll mark brainly! I really need help don’t have much time ! Please help<3
Tom is playing at the opposite corner of the playing field to his friend . If the playing field is 180m wide and Tom is 300m away from his friend, how long is the playing field
Answer:
240 m
Step-by-step explanation:
we can picture this as a right triangle
(180)^2 + (l)^2 = (300)^2
300 would be the diagonal of the triangle since it is at the opposite corner
180 would be the height/leg of the triangle
What is 36 divided by 1.5 in long division
Answer: 24
To calculate with long division when the divisor is a decimal, add zeroes in both the dividend and divisor. This means you get 360 ÷ 15.
From here, just do normal calculation and you get 24 as your answer.
1. Perry ran 30 miles more than DeShawn last month. Perry ran 46 miles. Write and solve an ADDITION equation to represent how many miles DeShawn ran.
2. For weeding the garden, Jacob was given $12.50. Now he has $23.00. Write and solve an ADDITION equation to represent how much money Jacob had before he was paid.
3. Mary won 80 super bouncy balls playing hoops at the county fair. At school she gave one to every student in her math class. She only has 56 remaining. Write and solve a SUBTRACTION equation to represent how many bouncy balls she gave away.
4. After paying $9.00 for a pizza, Nora has $27.10. Write and solve a SUBTRACTION equation to represent how much money she started with.
5. Seven candy bars cost $12.25. Write and solve a MULTIPLICATION equation to represent the cost of one candy bar.
6. I was driving at 70 miles per hour and traveled 437.5 miles.
Write and solve a MULTIPLICATION equation to represent how many hours I traveled.
Scott and seven of his friends went out to eat.
7. They split the bill evenly. Each person paid $17.82. Write and solve a DIVISION equation to represent the total bill.
8. Kathryn and her best friend found some money under the couch. They split the money evenly, each getting $24.18. Write and solve a DIVISION equation to represent the amount of money found under the couch.
Answer:
30+46=76
Step-by-step explanation:
so you want to draw out a model and write the two numbers and add them.
How many points does a student need to score 70% on a 80 point test?
Answer: 56
Step-by-step explanation:
70÷100×80=56
Answer:
56
Step-by-step explanation:
Another way to write this question is "What percent of 80 is 70%."
So we would write a percent proportion:
x/80=70/100
To find x, we will do (80*70)/100 which is 5600/100 which is 56.
You could also use benchmark fractions:
10% of 80 is 8
10% * 7 = 70% so 8 * 7 also equals 70%
8 * 7 = 56
Hope this helped, let me know if you have any questions.
The Smith Family and the Jones family went to a buffet dinner at a restaurant. The restaurant charges one price for adults and another price for children. The Smith family has two adults and three children, their bill was $40.50. The Jones family has three adults and one child, and their bill was $38.00. Determine the price of one adult and one child ticket.
8Answer:
5
Step-by-step explanation:
Question 6
Solve for x
4x = 10
A
X= 40
B
x = 2.5
С
x=4
D
x = 40
Answer:
B
Step-by-step explanation:
4x = 10
x = 10 / 4 = 2.5
=. Diego and Priya are each saving money. Diego starts with $80 in his savings account and adds $5
per week. Priya starts with $30 in her savings account and adds $15 each week.
After three weeks, who has more money in their savings account? Explain how you know.
a.
Answer:
diego. 80+(5x3)= 95
it isn't priya because 30+(5x3)=45
2x2– 21x = 11 what would the x be
Answer:
x = -1/3
Step-by-step explanation:
math help please (question 2)
The area of a triangle A is given as A =1/2 bh, where b is the base an h = height. (a) find h if A =30 and b=10
Answer:
h = 6
Step-by-step explanation:
Substitute the given to its corresponding places.
30 = [tex]\frac{1(10)h}{2}[/tex]
30 = 10h/2
Multiply both sides by two to remove the denominator.
2 [30 = 10h/2] 2
60 = 10h
Divide both sides by 10 to isolate h.
h = 6
To check, substitute everything to the original equation:
A = [tex]\frac{1(10)(6)}{2}[/tex]
A = 30 !
Determine the y-intercept of the line from the graph 3 2 1 -3 -2 -1 1 2 3 4 -2 <<
Answer:
Y-intercept is 0
Step-by-step explanation:
The line crosses at 0,0
x intercept is 0
Y intercept is 0
solve this linear equation with HOW you did it please.
9k-5k=-32
PLEASE ITS DUE IN 5 MINUTES I WILL MARK BRAINLIEST!
Answer: A. the first one wouldn't graph with the x^2 but with it I would say A. Hope this helps
which of the following equations uses the commutative property of addition to rewrite 1/4 + 2/5?
a) 1/4 + 2/5= 5/20 + 8/20
b) 2/5 + 1/4= 13/20
c) 13/20 - 2/5= 1/4
d) 2/4 + 1/5= 14/20
Answer:
B)
Step-by-step explanation:
Hope that helps!
The equation in option (b), 2/5 + 1/4 = 13/20, uses the commutative property of addition to rewriting 1/4 +2/5.
What is the commutative property of addition?The sum of two or more integers remains the same regardless of how they are grouped, according to the commutative property of addition.
The given expression is 1/4 + 2/5.
Simplify the expression as follows:
1/4 + 2/5
= (5 + 8)/20
= 13/20
Hence, it follows 1/4 + 2/5 = 13/20.
Now, using the commutative property of addition, the equation can be written as:
2/5 + 1/4 = 13/20
Hence, the equation in option (b), 2/5 + 1/4 = 13/20, uses the commutative property of addition to rewriting 1/4 +2/5.
Learn more about the commutative property of addition:
https://brainly.com/question/778086
#SPJ5