Therefore, we can classify the polynomial as a quadratic polynomial.
What is polynomial?A polynomial is a mathematical expression that consists of variables and coefficients, and involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and may contain multiple terms. Each term consists of a coefficient and a variable raised to a power. The degree of a term is the power to which the variable is raised, and the degree of a polynomial is the highest degree of any of its terms. Polynomials are used in many areas of mathematics, science, and engineering, such as algebra, calculus, geometry, and physics. They are used to model real-world phenomena, to solve equations, and to approximate complex functions.
Here,
To write the polynomial 14y² - x² - 3xy in standard form, we need to arrange the terms in descending order of degree (highest degree term first) and combine like terms.
First, let's rearrange the terms:
x² - 3xy + 14y²
Now, the polynomial is in descending order of degree. We don't need to do anything else to put it in standard form.
To classify the polynomial, we count the number of terms and the highest degree of those terms. In this case, there are three terms and the highest degree term is 14y², which has degree 2.
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Tickets numbered 4, 5, 6......48, 49 are placed in a box and mixed thoroughly. One ticket is drawn from the box. Find the probability that the number on the ticket is:
(i) an even number (ii) A number less than 16
(iii) a perfect square (iv) a prime number less than 30.
Answer:
i) The probability that the number on the ticket is even is [tex]\mathbf{\frac{1}{2}}[/tex]
ii) the probability that the number on the ticket is a number less than 16 is [tex]\mathbf{\frac{6}{23}}[/tex]
iii) The probability that the number on the ticket is a perfect square is [tex]\mathbf{\frac{5}{46} }[/tex]
iv) the probability that the number on the ticket is a prime number less than 30 is [tex]\mathbf{\frac{4}{23} }[/tex]
Step-by-step explanation:
Tickets numbers are: 4, 5, 6......48, 49
So, total tickets in box = 46
We need to find probability that the number on the ticket is:
i) an even number.
Even number in tickets are: 4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48
Total number of favourable outcomes = 23
So, the formula used is: [tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}[/tex]
Total number of outcomes = 46
Number of favourable outcomes = 23
Putting values and finding probability
[tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{23}{46}\\Probability=\frac{1}{2}[/tex]
So, the probability that the number on the ticket is an even number is [tex]\mathbf{\frac{1}{2}}[/tex]
ii) A number less than 16
Even number in tickets are: 4,5,6,7,8,9,10,11,12,13,14,15
Total number of favourable outcomes = 12
So, the formula used is: [tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}[/tex]
Total number of outcomes = 46
Number of favourable outcomes = 12
Putting values and finding probability
[tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{12}{46}\\Probability=\frac{6}{23}[/tex]
So, the probability that the number on the ticket is a number less than 16 is [tex]\mathbf{\frac{6}{23}}[/tex]
iii) a perfect square
Perfect squares are: 4,9,16,25,36
Total number of favourable outcomes = 5
So, the formula used is: [tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}[/tex]
Total number of outcomes = 46
Number of favourable outcomes = 5
Putting values and finding probability
[tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{5}{46}[/tex]
So, the probability that the number on the ticket is a perfect square is [tex]\mathbf{\frac{5}{46} }[/tex]
iv) a prime number less than 30.
Prime numbers less than 30 are: 5,7,11,13,17,19,23,29
Total number of favourable outcomes = 8
So, the formula used is: [tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}[/tex]
Total number of outcomes = 46
Number of favourable outcomes = 8
Putting values and finding probability
[tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{8}{46}\\Probability=\frac{4}{23}[/tex]
So, the probability that the number on the ticket is a prime number less than 30 is [tex]\mathbf{\frac{4}{23} }[/tex]
If Elena eats 2 servings of granola , how many calories dose she eat?
Answer:
700
Step-by-step explanation:
Please give brainliest
Divide 1750 by 5 and get 350.
350 times 2 is 700
What are the five ways we should examine characters to gain information about them?
Answer:
The five methods are physical description, action, inner thoughts, reactions, and speech.
Step-by-step explanation
Please Help me!! It’s question number 2
Answer:
if you need help with any other question i got you but i cant see like 30% of the whole problem
Help me plz . Due tonight
Answer: y= - ( x - 5) ( x + 7)
Step-by-step explanation: The x-intercepts are at -5 and 7. when you don’t have a negative symbol before the parentheses, that indicates that the parabola will be shaped like a U. when you do, it’s shaped the opposite of a U. and now look at the equation answer.
Barbara photographs a bird. The bird measures 8.6 cm tall in the photo and is actually 52.4 cm tall. Approximately how long is the bird's beak if it measures 1.1 cm in the photo?
An actual measurement represents a reading that is taken manually at the physical thickness measurement location on the equipment.
Find the solution ?actual measurement = 8.6cm(bird's height), ? (beak)
photo measurement = 52.4(birds height), 1.1 (beak)
if 52.4 = 8.6
1.1 = 1.1 x 8.6
52.4
= it is roughly 0.18cm
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Razee is filling bags with party favors for his birthday party the table to the right shows the number of bags he still needs to fill after 4, 5, 6 and seven minutes if he is working at a constant rate what was the initial number of party favor bags razee had to fill?
The initial number of party favor bags Razee had to fill were 48 bags.
Here, we will use arithmetic progression to solve this problem.
We are given that:
At 4 minutes, 36 bags were remaining.
At 5 minutes, 32 bags were remaining.
At 6 minutes, 28 bags were remaining.
At 7 minutes, 24 bags were remaining.
This can also be written as:
a₄ = a + 3d = 36
a₅ = a + 4d = 32
a₆ = a + 5d = 28
a₇ = a + 6d =24
where a is the initial number of party favor bags.
a₅ - a₄ = a + 4d - a - 3d
a + 4d - a - 3d = 32 - 36
d = -4
a + 3d = 36
a + 3(-4) = 36
a - 12 = 36
a = 36 + 12
a = 48
Therefore, the initial number of party favor bags Razee had to fill were 48 bags.
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Adjacent angles share a vertex and a ________
Ray
Line
Point
Segment
evaluate the expression 7x if x=11
A.18
B.77
C.4
D.711
A 10-foot ladder is leaning against a wall. The bottom of the ladder is 4 feet from the wall as shown in the picture.
Which of the following is the approximate distance from the top ladder base of the wall.
A) 6ft
B) 9ft
C) 11ft
D) 14ft
Answer:
9ft. (B)
Step-by-step explanation:
Pythagoras theorem( a²+ b²= c²)
=a²+4²=10²
a²+16=100
a²=100-16
a²=84
a=√84
=9.1
approx. =9
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The time it takes to fly from LA to NY varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h? Answer as a decimal only.
The time taken by the plain if it flies at a speed of 800 km/h is 6 hours 45 minutes
Given,
Time taken by plain to fly from Los Angeles to New York = 6 hours
Speed of plain = 900 km/h
We have to determine the time taken by the plain if it flies at a speed of 800 km/h
Distance cover by plain = speed x time = 900 x 6
Distance cover by plain = 5400 kilometer
New time taken by plain = Distance cover by plain / New speed of plain
New time taken by plain = 5400 / 800
New time taken by plain = 6 hours 45 minutes
That is, the time taken by the plain if it flies at a speed of 800 km/h is 6 hours 45 minutes
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Solve for all values of x in simplest form, |x - 2| - 1 = 2
Answer:
(x-2)-1=2
(x-2)-1 +1=2+1
(x-2)=3
x=3+2
x= 5
Write the steps in detail
On how to solve an angle bisector
problem, please use completé sentences.
A triangle's opposite side is split in half by an angle bisector into two segments that are proportional to the other two sides.
We can solve this problem by using the formula explained in the angle bisector theorem below.
Angle Bisector theorem :
In the below image, PS is the angle bisector of ∠P in ΔPQR.
As a result, we can state that by using the angle bisector theorem as
PQ/PR = QS/SR
or
a/b = x/y.
By this, we can solve the angle bisector theorem.
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Marco is going back-to-school shopping. he has a coupon for $10 off a purchase at kohl's. he's only focusing on shoes today, which are $25 each. what equation represents the total of his purchases (y) based on the numbers of shoes bought (x)? responses
Answer: y = 25x -10
Step-by-step explanation:
What is the slope of any line parallel to the graph of y = 8x + 20?
Answer:y=mx+b
m=slope
Step-by-step explanation:
the slope is 8
The slope of line is 8.
Given that,
Graph is y = 8x + 20We need to find the slope of line.According to the scenario, calculation of data are as follows,
Formula for slope of parallel line is as follows,
y = mx + b ( where m = slope)
So, by comparing both equations we get,
m = 8
or slope of line = 8
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The base of a rectangular crayon box is 8 centimeters long and 4 centimeters wide. Its height is 10 centimeters. What is the volume of the crayon box?
Answer:
320
Step-by-step explanation:
first we find the base of the box which is 8 x 4 = 32. then take base x height whcih is 32 x 10 = 320
which graph best represents this system of equations and its solution . 8x-4y=-16 3x+15y=-6
Answer:
B
Step-by-step explanation:
The required graph that represents the system of the equation and their solution is shown. Option D is correct.
Given that,
To determine the graph which shows the system of equation 8x-4y=-16 3x+15y=-6 and their solution,
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
The given system of equations is 8x-4y=-16 3x+15y=-6,
The solution of the above equation is given when applying methods like substitution, elimination and sublimation is (-2,0).
Plotting the graph of the system of equations it comes out to be as shown.
Thus, the required graph that represents the system of the equation and their solution is shown. Option D is correct.
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Write an equation in slope intercept form of the line that passes through the points (12, 15) and (9, 6). Show all work!!
PlSSSS HELPPPPP WORTH 60 POINTSS!
Answer:
2/5
Step-by-step explanation:
Answer:
y = 3x -21
Slope intercept form: y = mx + b
m (slope) = 3
B = - 21
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what is -0.66666666666 as a fraction
Answer:
-2/3
Uhh I need 20 characters so here
-2/3, if -1/3 is 0.333333333333333333333, double that, -0.666666666666, would have to be -2/3
2. Here are some equations that are related to `x-0.1x+2.70=56.70`. Each equation is a result of performing one or more moves on that original equation. Each can also be interpreted in terms of Noah's purchase.
Question isn't complete so we assume you wish to solve the equation above
`x-0.1x+2.70=56.70
Answer:
Step-by-step explanation:
To solve this equation
x-0.1x+2.70=56.70
We first find like terms and then subtract both sides of the equation
x-0.1x+2.70=56.70= 1x-0.1x+2.70=56.70
Add like terms
0.9x+2.70=56.70
Subtract both sides of equation
0.9x=56.70-2.70
Divide both sides
0.9x=54
x=54/0.9
x= 60
pls tell me the answer to the question ASAP i'll give brainliest lol
oof whats that
Step-by-step explanation:
Which table shows a proportional relationship
9514 1404 393
Answer:
see below
Step-by-step explanation:
In a proportional relationship, the ratio of y to x is the same for all values of x and y. Here, you can determine if that is the case by looking at the first two table entries in each table.
A. -4/1 = -12/3 . . . proportional
B. -5/1 ≠ -13/3 . . . not proportional
C. -4/1 ≠ -16/3 . . . not proportional
D. -8/1 ≠ -20/3 . . . not proportional
Solve for all values of a in simplest form. 24 = (a + 2]
Answer:
a = 22
switch the sides (a + 2) = 24
a + 2 = 24
subtract 2 from both sides
a = 22
What is this line called on a ruler and what is it used for?
Answer:
A hash mark.
Step-by-step explanation:
The marks or intervals on a ruler are called hash marks. That particular hash mark measures 0 millimeters. Hash marks are used for telling the measurement of an object.
Write the equation of the line that passes through the point (-6, 1) and has a slope of 1/2.
Which is equivalent to 2163?
3
6
36
7
Answer:
Numbers 3 and 7
Step-by-step explanation:
2163÷3= 721
2163÷6= 360.5
2163÷36= 60.08
2163÷7= 309
The answer is number 3 and 7 since both can be divided by 2163 without having remainders like number 6 and 36
Answer: 3
Step-by-step explanation:
Hello I NEED help! Pls help in 10 min
what is 5/3 divided by 7
Answer:
Step-by-step Turn 7 into a fraction
3/5 ÷ 7/1
Use the recipricle and multiply
3/5 x 1/7
Multiply across
3/35
And that's it! :)
Answer:
5/21
Step-by-step explanation:
Here is a strategy I want you to remember: Keep, Change, Flip. What do I mean by that? Well...
Keep the first fraction. Change the division sign into a multiplication sign. Make the numerator of the second fraction become the denominator--and make the denominator of the second fraction become the numerator.
The denominator of any whole number is always 1. So, 7 equals to 7/1. Time to find the reciprocal of 7/1! What does reciprocal mean?
Reciprocal - Flip the fraction in terms of the numerator and denominator; Multiplicative Inverse
1/7 is the reciprocal of 7/1, for this mathematical problem. Makes sense, right?
Now, 5 times 1 equals 5 (that is the numerator). Secondly, 3 times 7 equals 21 (that is the denominator).
[tex]\frac{5}{3} * \frac{1}{7} = \frac{5}{21}[/tex]
GIVING BRAINIEST
The time it takes to travel a fixed distance varies inversely with the speed traveled. If it takes Pam 1.5 hours to bike to her fishing spot at 9 miles per hour (how long will it take her if she rides at 12 miles per hour?
Answer:
Takes her 2 hours
Step-by-step explanation:
Write the following as an algebraic expression. Then
simplify.
The perimeter of the iscosceles triangle with
base length x - 10 and legs of length x.
The answer is
☐ (Simplify your answer.)
An algebraic expression to represent the perimeter of the isosceles triangle with base length x - 10 and legs of length x is equal to y = 3x -10.
As given,
In isosceles triangle
Base length=x - 10
Length of the legs=x
Let y be perimeter of the triangle
Algebraic expression is
Perimeter of isosceles triangle =sum of all the legs length
⇒y=x - 10 +x + x
⇒y=3x -10
Therefore, an algebraic expression to represent the perimeter of the isosceles triangle with base length x - 10 and legs of length x is equal to
y = 3x -10.
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