The product of [tex]-2x^{3}[/tex] + x - 5 and [tex]x^{3}[/tex] - 3x - 4 is [tex]-2x^{6}[/tex] + [tex]7x^{4}[/tex] + [tex]3x^{3}[/tex] + [tex]12x^{2}[/tex] - 4x + 20. The order of the polynomials does not affect the result; they yield the same product.
a) To find the product of [tex]-2x^{3}[/tex] + x - 5 and [tex]x^{3}[/tex] - 3x - 4, we multiply each term in the first expression by each term in the second expression and combine like terms.
[tex]-2x^{3}[/tex] * [tex]x^{3}[/tex] = -2[tex]x^{6}[/tex]
[tex]-2x^{3}[/tex] * (-3x) = 6[tex]x^{4}[/tex]
[tex]-2x^{3}[/tex] * (-4) = 8[tex]x^{3}[/tex]
x * [tex]x^{3}[/tex] = [tex]x^{4}[/tex]
x * (-3x) = -3[tex]x^{2}[/tex]
x * (-4) = -4x
-5 * [tex]x^{3}[/tex] = -5[tex]x^{3}[/tex]
-5 * (-3x) = 15[tex]x^{2}[/tex]
-5 * (-4) = 20
Combining all the terms, we have:
-2[tex]x^{6}[/tex] + 6[tex]x^{4}[/tex] + 8[tex]x^{3}[/tex] + [tex]x^{4}[/tex] - 3[tex]x^{2}[/tex] - 4x - 5[tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 20
Simplifying further:
-2[tex]x^{6}[/tex]+ 7[tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] + 12[tex]x^{2}[/tex] - 4x + 20
Therefore, the product of -2[tex]x^{3}[/tex] + x - 5 and [tex]x^{3}[/tex] - 3x - 4 is -2[tex]x^{6}[/tex] + 7[tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] + 12[tex]x^{2}[/tex] - 4x + 20.
(b) The product of two polynomials is commutative, which means that changing the order of the polynomials being multiplied does not affect the result. In other words, the product of [tex]x^{3}[/tex] - 3x - 4 and -2[tex]x^{3}[/tex] + x - 5 will be the same as the product obtained in part (a).
Therefore, the product of -2[tex]x^{3}[/tex] + x - 5 and [tex]x^{3}[/tex] - 3x - 4 is equal to the product of [tex]x^{3}[/tex] - 3x - 4 and -2[tex]x^{3}[/tex] + x - 5. The order of the polynomials being multiplied does not impact the final result, so both expressions yield the same product.
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What is the coefficient of 8b+3.2
Answer:
8
it's the prefix to the variable
Step-by-step explanation:
Answer:
Step-by-step explanation:
8
Solve the inequality x+6<7. Then graph the solutions.
What are the solutions? Select the correct choice below and fill in the answer box to complete your choice.
A.
xgreater than or equals
B.
xgreater than
C.
xless than
D.
xless than or equals
help will give brainliest
Answer:
y = 4
Step-by-step explanation:
KM / 10 = KO / 16
(4y - 1) / 10 = 6y / 16
KO = 4y-1 + 2y+1 = 6y
cross-multiply:
60y = 64y - 16
-4y = -16
y = 4
find the equation of a line passing through the point(-3,0) and (2,-3)
Answer (assuming the question allows it to be written in slope-intercept form):
[tex]y = -\frac{3}{5} x-\frac{9}{5}[/tex]
Step-by-step explanation:
1) First, find the slope of the equation. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], substitute the given points' x and y values, and simplify:
[tex]m = \frac{(-3)-(0)}{(2)-(-3)} \\m =\frac{-3-0}{2+3}\\m = -\frac{3}{5}[/tex]
Thus, the slope is [tex]-\frac{3}{5}[/tex].
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute real values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{3}{5}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line crosses, use the x and y values of any one of the given points to substitute into the formula. (Either one is fine. I chose (2,-3).) Then, isolate y to put it into slope-intercept form and find the answer:
[tex]y-(-3) = -\frac{3}{5} (x-(2))\\y + 3 = -\frac{3}{5} x + \frac{6}{5} \\y = -\frac{3}{5} x - \frac{9}{5}[/tex]
Answer:
y = -3
Step-by-step explanation:
Lana and Andrew gather data by surveying their classmates. Lana asked them about the longest time they had ever run. Andrew asked them about their favorite color.
How could Lana and Andrew represent their data?
Would they represent them in the same way?
Why or why not?
Answer:
No because Andrew aske them being different to Lana an far over.
Martina bought 4 CDs that were each the same price. Including sales tax, she paid a total of $70.40 . Each CD had a tax of $ 1.10 . What was the price of each CD before tax?
[tex]1.10 \times 4 = 4.40[/tex]
[tex]70.40 - 4.40 = 66[/tex]
[tex]66 \div 4 = 16.5[/tex]
Each CD was $16.50 before tax
Proof
[tex]total \: cost = 16.5(4) + 1.10(4)[/tex]
[tex]total \: cost = 66 + 4.40[/tex]
[tex]total \: cost = 70.40[/tex]
BCDE is a rhombus. Find the missing measures.
BC = 28 and BD = 32
CD =
FD =
EF =
EC =
Answer: CD=28
FD= 16
Step-by-step explanation:
Jennifer is four less than three times Toby's age. If Jennifer is 23, then how old is Toby? equation: solution:
Answer:
T = Toby
T=(23+4)/3
Step-by-step explanation:
If Jennifer’s age is 4 less than 3 times Toby’s age then Jennifer’s age by three,
T=(23+4)/3
and 3 times that, so we divide
T=(23+4)/3
Then Toby is 9 years of age, and shouldn’t be driving.
Line AB is definited by the equation ax+by=c where a=0, b=1, and c=-2 graph line AB
Answer:
graph shown below
Step-by-step explanation:
ax + by = c where a = 0, b = 1, and c = -2 would be 0x + 1y = -2 or y = -2.
On a graph, this would look like:
There are 6 bananas in a bunch and 4 monkeys want to share them
evenly. How many bananas does each monkey get? *
Answer:
1.5 banana each
Step-by-step explanation:
Uptown towing company charges $60 to tow a car plus $25 per day for vehicle storage. Downtown Towing company charges $75 for towing plus $20 per day for vehicle storage. Write the two equations for the companies
Answer:
Uptown towing company: 60 + 25d
Downtown towing company: 75 + 20d
Step-by-step explanation:
Uptown towing company: 60 + 25d
Downtown towing company: 75 + 20d
Where d = number of days
60 + 25d
75 + 20d
Equate both equations
60 + 25d = 75 + 20d
60 - 75 = 20d - 25d
-15 = -5d
d = -15/-5
d = 3
x^2y+y^2-30x+221=0 find the radius
Answer:
2
Step-by-step explanation
Let's complete the square. We get:
(x^2-30x)+y^2+221=0
(x^2-30x+225)+y^2+221-225=0
(x-15)^2+y^2-4=0
(x-15)^2+y^2=4
By analyzing this, we see that the radius is just :[tex]\sqrt{4}[/tex]=2
find the slope of the line y = 4/3x - 2/3
Answer:
4/3
Step-by-step explanation:
Line equations are of the format:
y = m*x + b
((m is slope; b is y-intercept))
So this line has a slope of 4/3 and a y-intercept of -2/3.
Bir sayının 2 bölü 5 'sinin 3 eksiği, bu sayının çeyreğine eşittir.
Buna göre bu sayı kaçtır?
Answer:
si cardo bahyanbayansusb
HURRYYYY FASTTT
There are 16 fluid Ounces of juice in 2 bottles of your favorite juice. How many fluid Ounces are there in 10 bottles?
80 fluid Ounces
72 fluid Ounces
160 fluid Ounces
96 fluid Ounces
Answer:
80 fluid ounces
Step-by-step explanation:
16*5=80
Answer:
80 fluid Ounces
Step-by-step explanation:
I majored in Mathematics
Can someone please help me with this ASAP
Answer:
24.84
Step-by-step explanation:
Hopefully this helps! let me know if it doesn't
Someone plz help me I will give brainliest
Answer:
2. 3/4 x 5/9 = 3x5/4x9 = 15/36 = 5/12
4. 4/7 x 1/2 = 4x1/7x2 = 4/14 = 2/7
6. 4/9 x 2/3 = 4x2/9x3=8/27
Step-by-step explanation:
Hope it helps!
Answer:
Hey again
2.- *in order* 3, 9, 15/36, 5/12
4.- *rewrite it in the same order it was in* so, 4/7 x 1/2= 5/14 simplified to=haha jk thats as simplified as it gets/ its 5/14
6.- *rewrite it as is* 4/9 x 2/3 =8/27
Step-by-step explanation:
15/36 simplified *wich you are required to have simplified* is 5/12
A steel bridge is 1000m lang at 20 degrees celsius. The bridge will expand or contract by .10m when the temperature changes by 1 degree celsius. How long would the bridge be at 24 degrees celsius? *
Answer:
1000.4m
Step-by-step explanation:
Objects usually expand when the temperature is warmer
Each degree celsius higher, the bridge expands by .10m
If the temperature goes from 20 to 24, it increases by 4 degrees which will be 0.4m
1000m+0.4m=1000.4m
determine if JK and LM parallel, perpendicular, or neither .
Answer:
3 - Perpendicular.
4 - Parallel.
Step-by-step explanation:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]JK = \frac{1-(-7)}{-4-(-10)} = \frac{8}{6} = \frac{4}{3}[/tex]
[tex]LM = \frac{-2-2}{-6-(-3)} = \frac{-4}{3}[/tex]
Perpendicular, because two lines are considered perpendicular if their slopes are opposite reciprocals.
[tex]JK = \frac{-2-(-2)}{3-11} = \frac{0}{-8} = 0[/tex]
[tex]LM = \frac{-2-(-7)}{1-1} = \frac{5}{0} = 0[/tex]
Find the slope- intercept from for the line Perpendicular to y-1/5x+5 passing through the point (3,-4)
Solve for x to the nearest tenth.
please help i’m failing
Answer:
x≈ 8.3
Step-by-step explanation:
ok first you have to find the hypotenuse of the smaller triangle
a²+b²=c²
2²+4²=c²
4+16=20
√20≈ 4.5
4.5²+7²=c²
20.25+49≈ 69.25
√69.25≈ 8.3
Answer:
x = [tex]\sqrt{69}[/tex]
Step-by-step explanation:
Pythagorean theorem: A^2 + B^2 = C^2
first, find the length of the line cutting through the shape:
let's call this line L.
plug the numbers into the theorem.
4^2 + 2^2 = L^2
16 + 4 = L^2
20 = L^2
next, plug 7 and L into the theorem again to find x
L^2 + 7^2 = x^2
20 + 49 = x^2
69 = x ^2
x = [tex]\sqrt{69}[/tex]
Hello! It would help a lot if I had assistance with this question:
Answer:
numerator
Step-by-step explanation:
Answer:
Numerator
Step-by-step explanation:
Numerator is at the top while on the bottom is the denominator.
hi anyone tell me the answer
Answer:
x= 136 degree ( being vertically opposite angle)
Answer:
x = 136
Step-by-step explanation:
x and 136 are vertical angles and congruent, then
x = 136
I NEED HELP ASAP!!!!!!!!
Answer: b
Step-by-step explanation:
Teddy is writing a proof about the figure shown on the coordinate plane below. He wants to show that quadrilateral WXYZ is a parallelogram.
Which statement proves that WXYZ is a parallelogram?
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
D. Show that segments WX and XY have slopes that are opposite reciprocals of each other.
The statements are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Teddy is writing a proof about the figure shown on the coordinate plane below. He wants to show that quadrilateral WXYZ is a parallelogram.
The statements that prove WXYZ as a parallelogram are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
Therefore, the statements are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
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Consider points a, b, and c in the graph. Determine which of these points is relative minima on the interval x = –1 and x = –2 in the graph.
Options:
1.)B
2.)A and B
3.)C
4.)A
Answer:
as we can see here point {\color{Red}a} lies on the interval (-2, -1)
so option A is correct
Step-by-step explanation:
The required minima on the graph in the interval x = -1 and x = -2 is A. Option 4) is correct.
Given that,
A Curve is shown on the graph,
In the interval of x = -1 and x = -2, relative minima is to be determined.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Since,
A minimum of the curve it that point where the slope of the curve is zero and at that point where the slope is zero the neighboring values must be greater to the point on the curve.
So point a is required minima where the slope is zero and also neighboring values are greater than a
Thus, the required minima on the graph in the interval x = -1 and x = -2 is A. Option 4) is correct.
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Help me out?!?! tysmmmm
Answer:
1 is isoscele
2 is scalene
3 is equalateral
4 is scalene
Helpppp I’m marking brainliest
Answer:
y=x+6
tell me if its right
Answer: y = x + 6
Step-by-step explanation:
Solve for x in the following figure and choose the appropriate result.
Answer:
2x is equal to 45
e is equal to x and 2
Step-by-step explanation:
Find the constant of proportionality that creates a direct proportion between x and y,
Constant of Proportionality
Answer:
y=x
Step-by-step explanation:
Something that would create a direct proportionality is y=x because both of them are in an equation which means they are directly proportional