Answer:
Simplified: -4a²b²+18a³-2b³
3a(6a²-4ab²)+8a²b²-2b³
Multiply 3a by 6a² and-4ab²
18a³-12a²b²+8a²b²-2b³
combine like terms (-12a²b² and 8a²b²)
-4a²b²+18a³-2b³
Hope this helps
Step-by-step explanation:
Here we have to simplify the polynomial :
[tex] \\ \longrightarrow \sf \qquad3a(6a^2-4ab^2)+8a^2b^2-2b^3\\ \\[/tex]
Using Distributive property we get :
[tex]\longrightarrow \sf \qquad18a^3- {12}^{2} b^2+8a^2b^2-2b^3\\ \\[/tex]
Combining the like terms we get :
[tex]\longrightarrow \sf \qquad18a^3-4a^2b^2-2b^3\\ \\[/tex]
Therefore,
The Simplified expression is [tex] \sf 18^3-4a^2b^2-2b^3[/tex]i will give 100 points
Part A
(√6)² x (√2)²6 x 212Part B
(∛3)³ x (√12)²3 x 1236Addtional Information:
[tex]\bold{(\sqrt{x} )^2 = x}[/tex][tex]\bold{(\sqrt[3]{x} )^3 = x}[/tex]Answer:
(a) 12
(b) 36
Step-by-step explanation:
Knowledge check: [tex]\sqrt{x} =\sqrt[2]{x}[/tex]
Apply the exponent rule:
[tex](\sqrt[n]{x})^n=x\quad\textsf{if}\:n\:\textsf{is odd or}\:x\geq 0[/tex]
Question (a)
[tex](\sqrt{6})^2 \times (\sqrt{2})^2=6 \times 2=12[/tex]
Question (b)
[tex](\sqrt[3]{3})^3 \times (\sqrt{12})^2=3 \times 12=36[/tex]
The flight of javelin released 6.5 feet from the ground at an initial velocity of 68 feet per second is modeled by the function h=-16^2+6.5 where h is the height of the javelin in feet after r seconds . Determine how many seconds it will take the javelin to reach the maximum height and find the maximum height. Round to the nearest hundredth if necessary
Using the vertex of the quadratic equation, it is found that a maximum height of 78.75 feet is reached after 2.13 seconds.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the height is modeled by:
h(t) = -16t² + 68t + 6.5.
The coefficients are a = -16, b = 68, c = 6.5, and the vertex will be given by:
[tex]x_v = -\frac{b}{2a} = -\frac{68}{-32} = 2.13[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a} = -\frac{68^2 - 4(-16)(6.5)}{-64} = 78.75[/tex]
A maximum height of 78.75 feet is reached after 2.13 seconds.
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
Name two sides that appear to be intersecting, but not perpendicular
Answer:
Two distinct lines intersecting each other at 90° or a right angle are called perpendicular lines. Here, AB is perpendicular to XY because AB and XY intersect each other at 90°. The two lines are parallel and do not intersect each other. They can never be perpendicular to each other.
Step-by-step explanation:
hope it helps, God bless!
The carpet for the office you completed cost $576. If you're using the same carpet in the new client's bedroom, how much will it cost? Round up to the nearest whole dollar. (Hint: You may want to find the area of each room and the cost of the carpet per square foot.)
$360 $280 $64 $225
with explanation please
The cost of similar carpet in the client's bedroom is $225
Given Data
Cost of Carpet = $576Area of Office = 16*19.2 = 307.2 square feetArea of Bedroom = 12*10 = 120 square feetif 307.2 square feet of carpet will cost $576
the 120 square feet of carpet will cost $x
cross multiplying we have
x = 120*576/307.2
x = 69120/307.2
x = $225
Learn more about area of shapes here:
https://brainly.com/question/2607596
Val is going to plant b vegetable seeds in one garden and 3b + 10 vegetable seeds in another. How
many seeds is Val going to plant?
Val is going to plant seeds.
Answer:
The question is not showing what we are supposed to find.
b+3b+10
Work out the size of angle x.
Answer:
47
Step-by-step explanation:
because you know that a triangle is 180 degrees and you have the other two degrees, so all you have to do is add 90 (the little box in the corner means 90) +43=133 and subtract by 180 giving you 47 as your answer.
Answer:
Heya! ^^
let's first look at some terms that may help us understand the concept of the question better.
______________________________________
★ Angle sum property of triangle states that the sum of all the angles of a triangle equals 180°
______________________________________
now let's come over what the question says.
we've been given a right angled triangle with measure of one of its angle as 43°.
we've to calculate the measure of the third angle named " x "
therefore ,
[tex]by \: angle \: sum \: property \: of \: triangle \\ \\ 90\degree + 43\degree + x = 180\degree \\ \\ 133\degree + x = 180\degree \\ \\ x = 180\degree - 133\degree \\ \\ x = 47\degree[/tex]
thus the measure of x is 47°.
hope helpful :D
Find the unknown angle measurement
Answer:
65
Step-by-step explanation:
115 + x = 180
x = 180 - 115
x = 65
Answer:
65°
Step-by-step explanation:
A right-angle equals 90°. Two right angles would be a line like shown in the picture.
So, 90 + 90 = 180.
Since we know the whole amount of the 2 angles combined is 180, all we have to do is subtract 115 from 180 to find the missing value.
180 - 115 = 65
Therefore, 65° equals x.
-kiniwih426
The floor of the cafeteria storage room is being tiled. The room is shaped like a parallelogram. The
parallelogram has a base of 19.5 feet and a height of 8 feet. Each package of tile will cover 4 square feet.
How many packages of tile will be needed to tile the floor?
Answer: 39
Step-by-step explanation: formula is bh. 19.5 times 8 is 156. divide by 4 because a package will cover 4 sq ft.
Answer:
39
Step-by-step explanation:
parallelogram area is base x height
A = b x h
A = 19.5 x 8 = 156 ft^2 or square feet
156 divided by 4 = 39
Suppose that a classmate asked you why (2x + 112 is not (4x² + 1). What is your response to this classmate?
O A. An expression such as (2x + 1)2 is called the square of a monornial. The expression (2x + 1)2 is equal to (22• 2xX1. 1), thus it is not equivalent to
(4x2 +1)
B. The classmate is correct. An expression such as (2x + 1)2 is called the square of a binomial. The expression (2x + 1)2 is equal to (2)?(x} = (132, thus it is
equivalent to (4x + 1)
OC. An expression such as (2x + 1)2 is called the square of a binomial. The expression (2x + 1)2 is equal to (2x+ 1x2x + 1), thus it is not equivalent to
(4x + 1)
OD. An expression such as (2x + 1)2 is called the product of the sum and difference of two terms. The expression (2x + 1)2 is equal to (2x+ 1(2x - 1), thus it is
not equivalent to (4x2 + 1)
+
The given expression is the square of a binomial, such that:
(2x + 1)^2 = 4x^2 + 4x + 1
Then the correct option is C.
Are the expressions equivalent?We want to see if:
(2x + 1)^2
Is equivalent to (4x^2 + 1).
First, this is false, let's prove that.
We have the square of a binomial (2x + 1)^2. Remember the general formula:
(a + b)^2 = a^2 + 2ab + b^2
So if we apply this to our expression we get:
(2x + 1)^2 = (2x)^2 + 2*2x*1 + 1^2 = 4x^2 + 4x + 1
Then, the correct option is C.
If you want to learn more about binomials, you can read:
https://brainly.com/question/15246027
1. Which quadratic equation has 5 and - 4 as its solutions?
Answer:
x²-x-20
Step-by-step explanation:
Using Vieta's formula
x²-(sum of roots)x+(product of roots)=0
x²-(5+-4)x+(5×-4)=0
x²-x-20=0
Write down the reciprocal of:5by8
to find the reciprocal just switch the numerator and the denominator.
= 8/5 ( 8 by 5 )
A weather reporter in your area said that the speed of sound in air today is about
1,100 feet per second.
What is that speed in scientific notation?
Step-by-step explanation:
The base form (or root) of a verb is the form listed in the dictionary. It is the version of the verb without any endings (endings such as -s, -ing, and ed). The base form is the same as the infinitive (e.g., to walk, to paint, to think) but without the to.
find the 19th term in each sequence. 11, 33, 99, 279
Answer:
Step-by-step explanation:
hello : note 297 no 279
297 =3×99
99 = 3 ×33
33=3×11
this the geometric sequence. ( comon : 3)
the nth term is : An = A1 × r^n when : r = 3 and A1 =11
if n = 19 A19 = 11×3^19
Which of the following tables does NOT show a proportional relationship?
A
B
C
D
Answer:
A
Step-by-step explanation:
Hey there!
In this question, it is asking us what table doesn't have a proportional relationship
In table A, there is no seen relation ship between the numbers, columns, or rows
In all of the other tables, the numbers in each column is increasing by a number again and again meaning A is the incorrect table.
Answer:
A i believe
Step-by-step explanation:
Its not B because it is proportional by 0.6666666
Its not C because it is proportional by 3
It not D because its proportional by 1.33333333
Please mark as brainliest
Please help I will give brainliest.
Answer:
The weight, in pounds, of one bag of beans.
Step-by-step explanation:
Since we know that there are 15 bags of beans, we can eliminate the first option and anything about something other than th e beans. Also, we know that we are not given the information on how heavy the bag of beans are, so with process of elimination, the 3rd one is the answer.
I hope this helped!
It would be greatly appreciated if you marked this answer as brainliest!
Aashna thinks that the largest place value that 82.3 and 11.45 have in common is the tens place. Jake thinks that the largest place value they have in common is the tenths place.
Answer the following questions with complete sentences:
Who is correct, Aashna or Jake?
Write how you would explain your answer to the person who answered incorrectly.
Answer:
Aashna is correct
Step-by-step explanation:
I would explain it that the tens places are 8 and 1, which are about 7 apart
The tens places however are 3 and 4 which is closer.
3 A packet contains 1.5 kg of oats.
oats
OO
1.5kg
Every day Maria uses 50 g of oats to make porridge.
How many days does the packet of oats last?
Answer:
30 days
Step-by-step explanation:
1.5 Kg = 1500 g
Using 50 g a day
Number of days
= 1500 / 50
= 30 days.
A six-sided number cube has sides labeled 1, 1, 2, 2, 3, and 3. What is known about the probability model for this situation? Select all correct answers.
The probability model for this situation is uniform.
The probability model for this situation is non-uniform
. The probabilities of the individual outcomes are the same.
The probabilities of the individual outcomes are not the same.
Answer:
The probabilities of the individual outcomes are the same.
The probability model for this situation is uniform.
Step-by-step explanation:
There is 2 of each number so there is an equal chance. when there is an equal chance that is uniform.
Answer:
i hope this helped :)
Step-by-step explanation:
[30 PTS!!] Using mathematically precise language, explain in detail how you would multiply the complex number [tex]z_1=r_1(cos[/tex]θ[tex]_1+i sin[/tex]θ[tex]_1)[/tex] with the complex number [tex]z_2=r_2(cos[/tex]θ[tex]_2+isin[/tex]θ[tex]_2)[/tex].
Multiplying z₁ and z₂ involves calculating their products
The product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
How to multiply the complex numbers?The numbers are given as:
z₁ = r₁(cosΘ₁ + isinΘ₁)
z₂ = r₂(cosΘ₂ + isinΘ₂)
The product is represented as:
z₁ * z₂ = r₁(cosΘ₁ + isinΘ₁) * r₂(cosΘ₂ + isinΘ₂)
This gives
z₁ * z₂ = r₁r₂(cosΘ₁ + isinΘ₁) (cosΘ₂ + isinΘ₂)
Expand
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ + i²sinΘ₁sinΘ₂ )
In complex numbers,
i² = -1.
So, we have:
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ - sinΘ₁sinΘ₂ )
Rewrite as:
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ - sinΘ₁sinΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ )
Apply sine and cosine ratios
z₁ * z₂ = r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
Hence, the product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
Read more about complex numbers at:
https://brainly.com/question/10662770
. The difference between the length and width of a rectangle is
7 cm. The perimeter of the rectangle is 22 cm. Find the length
and the width. (Remember, P= 21 + 2w.)
Answer:
Rectangle
Solve for length
l=4cm
w Width
7
cm
P Perimeter
22
cm
Using the formula
P=2(l+w)
Solving forl
l=P
2﹣w=22
2﹣7=4cm
C is a circle with centre (0,0)
L is a straight line with negative gradient.
The circle C and the line L intersect at the points A and B.
The coordinates of A are (-9,2)
The x coordinate of B is 7
Find an equation of L.
Answer:
Step-by-step explanation:
find the equation of the line drawn in the coordinate system below
Answer:
y=-2/1+4
or y=-2+4
Step-by-step explanation:
to find the slope, you count from one point of intersection to the next and the way it works is y/x so the line from one point to the next goes down 2 (making it negative also) and over 1, so -2/1 is your slope, and for the b part.. its just where the line intersects on the y axis (the line that goes up and down) so it would be 4
a cube has a volume of 1 cubic unit. what is the perimeter of one of its face
Answer: One face of a cube has a perimeter of a+a+a+a=4a.
The required perimeter of one of the faces of the cube is 4 units.
Given that,
A cube has a volume of 1 cubic unit. what is the perimeter of one of its faces is to be determined.
Perimeter is the measure of the figure on its circumference.
A cube is defined is a regular 3-dimensional structure whose dimension at every section is identical.
Here,
According to the question,
Area of the square = 1 cubic unit
a² = 1
a = 1
Now,
The perimeter of the square = 4a
= 4 (1) = 4 units
Thus, the required perimeter of one of the faces of the cube is 4 units.
Learn more about perimeter here:
brainly.com/question/6465134
#SPJ2
Please help with this problem.
Answer:
whats the problem it doesnt say anything
HELP PLEASE!!!! Posting a lot of these for a lot of points!
Answer:
Step-by-step explanation:
Area of figure I = length *width
= 4 * 5
= 20 m²
Figure II is a trapzium.
a and b are the parallel sides. a = 21 m
b = 20 - 5 = 15 m
h = 3 + 4 = 7 m
[tex]\text{area of figure 2 = $\dfrac{(a + b)*h}{2}$}[/tex]
[tex]=\dfrac{(21+15)*7}{2}\\\\\\=\dfrac{36*7}{2}\\\\\\= 18*7\\\\= 126 \ m^{2}[/tex]
Area of the figure = 20 + 126
= 146 m²
Answer:
146 m²
Step-by-step explanation:
Formulae
Area of a rectangle = width x length
Area of a triangle = 1/2 x base x height
Divide the figure into 2 rectangles and a triangle (see attachment).
Area of Rectangle 1 = 4 x 5 = 20 m²
Area of Rectangle 2 = (3 + 4) x (20 - 5) = 105 m²
Area of triangle 3 = 1/2 x (21 + 5 - 20) x (3 + 4) = 21 m²
Total area = 20 + 105 + 21 = 146 m²
Over 5 days, Penelope practices the kazoo for 4 hours. She also plays video games every day. If she spent a total of 13 hours doing both, how many hours a day does she play video games?
A. 1.6 hours
B. 1.8 hours
C. 2 hours
D. 1.4 hours
Answer:
B : 1.8 hours a day.
Step-by-step explanation:
For 5 days she practices for 4 hours.
Subtract the 4 hours by the combined 13 hours.
Divide the remainding 9 hours of video game time by the 5 days.
Factor x^2−2x. Is this a special product?
Answer:
x(x-2)
Step-by-step explanation:
x^2−2x
Factor out an x
x(x-2)
This is not a special product
What is the area of this figure? 4 cm 5 cm 5 cm
Answer:
100
Step-by-step explanation:
5*5*4=100
2.56x+0.14-187x
How to solve pls and answer
Which expressions are polynomials?
Select each correct answer.
Answer:
b and d option are correct
Answer:
B, D
Step-by-step explanation:
B, D
x cannot be in a root. (A)
x cannot be in the denominator. (C)
