The product of the polynomials is [tex]15x^4 - 8x^3 - 6x^2 - 22x - 15.[/tex]
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
To find the product of the polynomials (3x² - 2x - 3) (5x² + 4x + 5), we can use the distributive property of multiplication to multiply each term in the first polynomial by each term in the second polynomial, and then combine like terms.
We can start by multiplying the first term in the first polynomial, 3x^2, by each term in the second polynomial:
3x² (5x² + 4x + 5)
= [tex]15x^4 + 12x^3 + 15x^2[/tex]
Next, we multiply the second term in the first polynomial, -2x, by each term in the second polynomial:
-2x(5x² + 4x + 5) = -10x³ - 8x² - 10x
Finally, we multiply the third term in the first polynomial, -3, by each term in the second polynomial:
-3(5x² + 4x + 5) = -15x² - 12x - 15
Putting these three results together, we have:
(3x² - 2x - 3) (5x² + 4x + 5)
= [tex]15x^4 + 2x^3 - 3x^2 + 12x^2 - 10x^3 - 10x - 15x^2 - 12x - 15[/tex]
Simplifying and collecting like terms, we get:
(3x² - 2x - 3)(5x² + 4x + 5)
[tex]15x^4 - 8x^3 - 6x^2 - 22x - 15[/tex]
Therefore,
The product of the polynomials is [tex]15x^4 - 8x^3 - 6x^2 - 22x - 15.[/tex]
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1+(2/3)-(-9/2)
i don't understand this and i need help
Answer:
6.167
Step-by-step explanation:
1 + 2/3 - (-9/2)
1 + 2/3 + 9/2
Taking LCM (1 x 2 x 3)
6/6 + 4/6 + 27/6
6 + 4 + 27/6
37/6
6.167 Ans
Diameter = 5 yards find the area of the circle in square feet
Answer:
6.25π or 19.625
Step-by-step explanation:
Diameter=2r
Area=πr^2
We need to find the radius (5/2=2.5)
Plug in 2.5 for the area forumla= π2.5^2
Solve = 6.25π
A web browser is open on your computer screen. The area of the browser window is 24 square inches. Find the length of the browser window x. The browser covers 3/13 of the screen. What are the dimensions of the screen?
We will see that the length of the browser window is 4.9 inches, and the screen is a square of sidelength 10.2 in
How to find the length of the browser window?
We know that the area of the browser window is 24 in^2, we will assume that the window is a perfect square, then the area is equal to the square of the length x, we have:
x^2 = 24 in^2
x = √(24 in^2) = 4.9 in
How to get the dimensions of the screen?We know that the browser covers 3/13 of the screen, so the area of the screen is 13/3 times the area of the browser:
A = (13/3)*24 in^2 = 104 in^2
Again, if the screen is square of sidelength s, we have:
s^2 = 104 in^2
s = √(104 in^2) = 10.2 in
If you want to learn more about areas, you can read:
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Find the slope of the line that passes through (3, 6) and (10, 9).
Answer:
The slope is 3/7.Step-by-step explanation:
Use the slope formula.
Slope formula:
[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{RISE}{RUN} }[/tex]
[tex]\sf{y_2=9}\\\\\sf{y_1=6}\\\\\sf{x_2=10}\\\\\sf{x_1=3}[/tex]
Solution: Rewrite it down.
[tex]\sf{\dfrac{9-6}{10-3}=\boxed{\sf{\dfrac{3}{7}}}[/tex]
Therefore, the slope is 3/7, which is the correct answer.I hope this helps! Let me know if you have any questions.
A bicycle manufacturer is studying the reliability of one of its models. the study finds that the probability of a brake defect is 4 percent and the probability of both a brake defect and a chain defect is 1 percent. if the probability of a defect with the brakes or the chain is 6 percent, what is the probability of a chain defect? 1.5 percent 2 percent 2.5 percent 3 percent
Using Venn probabilities, it is found that there is a 0.03 = 3% probability of a chain defect.
What is a Venn probability?In a Venn probability, two non-independent events are related to each other, as are their probabilities.
The "or probability" is given by:
[tex]\rm P(A \cup B ) = P(A)+P(B)-P(A\cap B)[/tex]
In this problem, the events are:
Event A: Brake defect.
Event B: Chain defect.
For the probabilities, we have that:
The study finds that the probability of a brake defect is 4 percent, P(A) = 0.04.The probability of both a brake defect and a chain defect is 1 percent, P(A∩B) = 0.01.The probability of a defect with the brakes or the chain is 6 percent, P(A∪B) = 0.06.Substitute all the values in the formula
[tex]\rm P(A \cup B ) = P(A)+P(B)-P(A\cap B)\\\\0.06=0.04+P(B)-0.01\\\\P(B)=0.06-0.04+0.01\\\\ P(B)=0.03[/tex]
0.03 = 3% probability of a chain defect.
Hence, there is a 0.03 = 3% probability of a chain defect.
You can learn more about Venn probabilities at brainly.com/question/25698611
Answer:
D
Step-by-step explanation:
The first three steps in writing f(x) = 40x 5x2 in vertex form are shown. write the function in standard form. f(x) = 5x2 40x factor a out of the first two terms. f(x) = 5(x2 8x) form a perfect square trinomial. (eight-halves) squared = 16 f(x) = 5(x2 8x 16) – 5(16) what is the function written in vertex form? f(x) = 5(x 4) – 80 f(x) = 5(x 8) – 80 f(x) = 5(x 4)2 – 80 f(x) = 5(x 8)2 – 80
The function which is the vertex form of the equation whose first three steps shown in writing is f(x)=5(x +4)²- 80.
What is the vertex form of parabola?Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
The first three steps in writing the function in vertex form are shown.
[tex]f(x) = 40x +5x^2[/tex]
Write the function in standard form.
[tex]f(x) = 5x^2+ 40x[/tex]
Factor out of the first two terms by taking out the common number 5 from the equation,
[tex]f(x) = 5(x^2 +8x)[/tex]
Form a perfect square trinomial with (8/2)² = 16,
[tex]f(x) = 5(x^2 +8x+ 16) - 5(16)\\f(x) = 5(x+4)^2 - 80[/tex]
Hence, the function which is the vertex form of the equation whose first three steps shown in writing is f(x)=5(x +4)²- 80.
Learn more about the vertex form of the parabola here;
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Answer:
c
Step-by-step explanation:
can anyone help me with this I don't know the answer?
Calculate the volume of each of the following prisms.
1)
length = 35
width = 14
height = 24
2)
length = 27
width = 14
height = 21
3)
length = 21
width = 21
Height = 21
Answer:
1) 11760
2) 7938
3) 9261
Step-by-step explanation:
hope this helps
(NO LINKS PLEASE)
Wanda spun a spinner 30 times, and the results were recorded in the following tally chart.
A tally chart. Striped has 12 tally marks, solid has 9 tally marks, and dotted has 9 tally marks.
Based on the experiment, what is the probability of landing on the solid section of the spinner?
Enter your answer as a fraction, like this: 42/53
Answer:
3/10
Step-by-step explanation:
12+9+9=30
9 of those are solid
9 out of 30
simplified is 3/10
Answer: 3/10
Step-by-step explanation:
helpppppppppppp meeeeeeeeeee
Answer:
3 gallons per 4 minutes
Step-by-step explanation:
two point are given
(4 minutes, 3 gallons) and
(8 minutes, 6 gallons)
The question asks about gallons (there is an increase of 3 gallons)
per minute (there is an increase of 4 minutes)
or .75 gallons per one minute
Create a dot plot to represent the data. what can you conclude about the dot plot of the data set? select the three best answers. the range of the number line should be 0 to 7 to represent the frequency. four families said they ate out twice the previous week. one family said they ate out 5 times the previous week. the data set is symmetrical. the median best represents the data set.
The range of the dot plot can be from zero to seven because it covers the given data set. Then the correct options are A, B, and C.
What is frequency?The element which appears a number of times are called frequency.
The data set shown below represents the number of times some families went out for dinner the previous week.
The data set is given as:
4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1
Rearrange in ascending order
0, 0, 1, 1, 2, 2, 2, 2, 4, 4, 5, 6
Data Frequency
0 2
1 2
2 4
3 0
4 2
5 1
6 1
Because the median is 2, and the data points to the left and right are not symmetrical, the data set is not symmetrical.
From the given data set
4 has a frequency of 2
5 has a frequency of 1
Then the range of the dot plot can be from zero to seven because it covers the given data set.
More about the frequency link is given below.
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Sara uses ribbon to make hair bows. The length of each ribbon Sara uses is represented by the line plot shown. What is the difference, in feet, between one of the pieces of ribbon that has the longest length and one of the pieces that has the shortest length?
Answer:
1
Step-by-step explanation:
because if you do 1 1/2 - 1/2 = 1
How to solve and what is the final answer to the question
Answer:
12
Step-by-step explanation:
Differentiate the equation. It will give you -1/6x + 2 = dy/dx.
Let dy/dx = 0 (you do this because the highest point is usually the turning point. The gradient is zero at the turning point, meaning that you'd have to set dy/dx to be zero to figure out the highest point).
Then rearrage for x
-1/6x+2=0
1/6x = 2
x = 12
A box contains 6 red marbles, 4 blue marbles, and 8 yellow marbles.
13. Find P(yellow then red) if a marble is selected, and then a second marble
is selected without replacing the first marble.
Answer:
Step-by-step explanation:
The total number of marbles is 6 + 8 + 4 = 18]
If the first marble drawn is yellow, that happens with a probability of 8/18
So the important thing to note is that now there are 17 marbles,
Now a red marble is drawn. We didn't replace the yellow.
There are 6 red marbles.
So the chances of getting a red marble is 6/17
Answer. P(Y then R) = 8/18 * 6/17 = 48/306
48 / 306 reduces down to 8/51 = 0.156
I need help! will mark brainliest and add bonus points. The question is own below:
The mean age of 17 golfers is 52
The mean age of 9 of the golfers is 74
what is the mean age of the 8 golfers
Answer:
27.25 Years Old
Step-by-step explanation:
Find the total age of the 17 golfers.
52(17) = 884
Find total age of the 9 golfers.
9(74) = 666
Subtract.
884 - 666 = 218
Divide by the 8 golfers.
218/8 = 27.25
Which expressions are equivalent to
5^2
5^8
SOMEONE HELPPPP!
What is the volume of this oblique cone?
o 288TT cm
o 324T1 cm
o 14417 cm
o 432TT cm
Answer:
432 pi cm^3
Step-by-step explanation:
volume = 1/3 pi * r^2 h
= 1/3 pi (81)(16) = 432 pi cm^3
Calculate the circumstances of the shape below
Answer:
[tex]c = 2\pi r \ \\ 2 \times \pi \times 3 \\ = 6\pi[/tex]
PLEASE HELP FAST. What is the area of this right triangle?
Formula for the area of a triangle = 1/2 x base x height
Base = 24
Height = 7
Area = 1/2 x 24 x 7 = 12 x 7 = 84
Answer: 84 yd^2
Hope this helps!
Which equation is equivalent to n+4 = 11?
Answer:
n = 7
Step-by-step explanation:
n+ 4 = 11 subtract 4 from both sides of the equation
n + 4 -4 = 11-4
n = 7
Hey there!
n + 4 = 11
SUBTRACT 4 to BOTH SIDES
n + 4 - 4 = 11 - 4
CANCEL out: 4 - 4 because it give you 0
KEEP: 11 - 4 because it help solve for the n-value
NEW EQUATION: n = 11 - 4
SIMPLIFY IT!
n = 7
Therefore, your answer is: n = 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
help pls
make sure its correct
The quadratic regression equation of company X sales would have a degree of 2
The quadratic regression equation is y = -507.61x^2 +23372.94x -170697.85The profit for selling at $22.75 is $98316.63The quadratic regression equationTo determine the quadratic regression equation, we make use of a graphing calculator
From the graphing calculator,we have the following calculation summary
a = -507.61b = 23372.94c = -170697.85A quadratic regression equation is represented as:
y = ax^2 + bx + c
So, we have:
y = -507.61x^2 +23372.94x -170697.85
Hence, the quadratic regression equation is y = -507.61x^2 +23372.94x -170697.85
The profit for selling at $22.75This means that:
x = 22.75
So, we have:
y = -507.61 * 22.75^2 + 23372.94 * 22.75 -170697.85
Evaluate
y = 98316.63
Hence, the profit for selling at $22.75 is $98316.63
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Find the lowest common denominator for these fractions and then subtract and simplify.
4/9 and 1/3
1/9
2/9
3/9
Answer:
1/9
Step-by-step explanation:
20 cm
16 cm
10 cm
12 cm
V=
help quick please
Answer:
960 cm^3
Step-by-step explanation:
The volume of any object is found by multiplying the area of the base times the height. I'll use the triangular sides as the base in this case. The area of the triangle is (bh)/2, so this calculation is:
(16x12)/2 = 96
The height is 10, so Volume is 96 x 10 = 960 cm^3
Answer answer answer
Answer:
B which is b=4
Step-by-step explanation:
POSITIVE FOUR, just to be clear
Answer:
the answer is b
Step-by-step explanation:
Vertex: (-1,4) Point: (1,8)
Answer:
See below
Step-by-step explanation:
I assume you want the quadratic that has these values
Vertex form of this parabola
y = a(x- - 1)^2 + 4 insert the given point to calculate 'a'
8 = a (1 + 1)^2 + 4 shows a = 1
y = (x+1)^2 + 4 expand this vertex form to get the quadratic form
y = x^2 + 2x + 5
Put the polynomials in order from lowest degree to
highest degree
(Look at Photo)
What is the perimeter of a 5 by 12 triangale
Answer:
30 units
Step-by-step explanation:
IF it is a right triangle AND these are the LEGS then the hypotenuse = 13
5+12 + 13 = 30
The record low temp in Fargo, ND is -37*F. The record high is 109*F. What is the difference in the record high and the record low temperatures?
Answer:
109 - -37 = 146
Step-by-step explanation:
since you are subtracting a negative, the negative number and the sign cancel each other out. So all you have to do is add.
For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?
0
9
12
16
Answer:
The graph y = 18x2 + mx + 2= 12
So the answer is 12
The value of m does the graph of y = 18 x² + m x + 2 have exactly one x-intercept is 12.
What is Intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
We have Equation.
y = 18 x² + m x + 2
Now, to find exactly one intercept we will use Discriminant Method as
D = m² - 4 x 18 x 2 = 0
m² - 144 = 0
m² = 144
m = -12 or m = 12
Thus, the required value of m is 12.
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PLEASE HELP ME OUT 39 POINTS
Answer:
Option A for part (a) and Option B for part (b)
Step-by-step explanation:
Step 1: Determine the ratios in part a
First Batch --> 8 minutes / 2 customers = 4 minutes per customer
Second Batch --> 18 minutes / 6 customers = 3 minutes per customer
Third Batch --> 21 minutes / 7 customers = 3 minutes per customer
In part (a) we would choose option a which is that it does not always take the same amount of time to serve each customer.
Step 2: Determine the ratios in part b
First Batch --> 27 points / 3 dollars = 9 points per dollar
Second Batch --> 45 points / 5 dollars = 9 points per dollar
Third Batch --> 63 points / 7 dollars = 9 points per dollar
In part(b) would choose option b which is that each dollar spent appears to earn the same number of points which would give us 8 dollars for 72 points.
Answer: Option A for part (a) and Option B for part (b)