Step-by-step explanation:
Since you haven't provided any functions, I can answer this question generally as to what the function would look like.
So when a polynomial has an even degree, then the two end behaviors will go in the same direction, and when it has an odd degree, then the two end behaviors will be in opposite directions. When a polynomial has a positive leading coefficient the right side will go towards infinity, and if a polynomial has a negative leading coefficient the right side will go towards negative infinity.
So let's look at the information:
As x approaches negative infinity, y approaches positive infinity.
Just given this we can't really say anything about the polynomial since we have to relate this to the right end behavior, or as x approaches infinity, so let's look at that.
As x approaches positive infinity, y approaches negative infinity.
This means that as x increases, y decreases, so that means the leading coefficient is negative. Since we know both end behaviors, and they're opposite (one y-value goes to negative infinity, and the other positive infinity), that means the polynomial is an odd degree.
So this means the polynomial will look something like this:
[tex]ax^n+bx^{n-1}+cx^{n-2}...[/tex]
where the leading coefficient "a" is negative and the degree of the polynomial (degree of leading coefficient) will be odd.
Answer:A
Step-by-step explanation:
edge 2023
What is the slope of a line that is perpendicular to the line whose equation is ax by=c?
Answer:
b/a
Step-by-step explanation:
Perpendicular lines have slopes that are opposite sign and reciprocals (flipped over).
In the equation
ax + by = c,
the slope of the line is
-a/b
If you haven't memorized this pattern yet, you can calculate it by solving ax+by=c for y.
by = -ax +c
y = -a/b x + c/b
The slope is -a/b
So a perpendicular line would be opposite sign and flipped, b/a
for each reasons it gives you the options to choose: commutative property of addition, associative property of addition, distributive property, and combining like terms
Answer:
associative
combining
commutative
Step-by-step explanation:
1. associative property of addition since the grouping is changed
2. combining like terms since it's the addition of 4 and 6
3. commutative property of addition since it's a change of order
Mrs. Bailey has equal numbers of nickels and quarters but the value of the quarters is $1.80 more than the value of the nickels. What is the total value of all coins together in dollars and cents
Total value of all coins together is $2.7
Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
1 Nickel = $0.05 and 1 quarter = $0.25.
Let number of nickels and number of quarter be x.
According to the situation
x.(0.25) = $1.80 + x.($0.05)
x(0.25 - 0.05) = $1.80
x (0.2) = $1.80
x = $1.80/0.2
x = 9 coins
Therefore total value of the currency is 9(0.05 + $0.25) = 9 (0.3) = $2.7
Thus total value of all coins together is $2.7.
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I thought of the number that is between 104 and 140. The number is divisible by 6 and 15. What is my number?
Answer:
120
Step-by-step explanation:
Lets find the numbers multiples of 6 that are in the range from 104-140:
108, 114, 120, 126, 132, 138
Now out of these lets find which is divisible by 15
[tex]\frac{108}{15}=7.2\\\\\frac{114}{15}=7.6\\\\\frac{120}{15}=8\\\\\frac{126}{15}=8.4\\\\\frac{132}{15}=8.8\\\\\frac{138}{15}=9.2[/tex]
120 Is the only solution in this set which is also equally divisible by 15, making it the answer.
(2x² – 3x)(3x² + 2x - 1)
Answer:
6x^4-5x^3-8x^2+3x
Step-by-step explanation:
-factor it using FOIL (first outside inside last)
Find the area of the blue shape below. Use 3.14 for π
If anyone knows the answer please help!
Answer:
1413.86 ft^2.
Step-by-step explanation:
The diameter of the circle = 50 - 2(18)
= 50-36
= 14 ft.
So its radius is 7 ft.
The total area of the blue shape
= 2(35 * 18) + 3.14*7^2
= 1413.86 ft^2.
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 48.
The probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.
According to thr question.
We have to find the probability of selecting none of the correct six integers from the positive integers not exceeding 48.
Let E be the event of selecting 6 numbers from 40 and S be the sample space of all integers not exceeding 48.
Now,
The total number of ways of selecting 6 numbers from 48
[tex]= ^{48} C_{6}[/tex]
[tex]= \frac{48!}{6!\times 42!}[/tex]
[tex]= \frac{48\times 47\times46\times45\times44\times43\times42!}{6!\times\ 42!}[/tex]
= 8835488640/6!
And, the total number of ways of selecting 6 incorrect numbers from 42
= [tex]^{42} C_{6}[/tex]
[tex]= \frac{42\times41\times40\times39\times38\times37\times36!}{6!\times36!}[/tex]
= 3776965920/6!
Therefore, the probability of selecting none of the correct six integers, when the order in which they are selected does not matter is given by
[tex]= \frac{^{42C_{6} } }{^{48} C_{6} }[/tex]
[tex]= \frac{\frac{3776965920}{6!} }{\frac{8835488640}{6!} }[/tex]
= 3776965920/8835488640
= 0.427
≈ 0.43
Hence, the probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.
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Three lorries each making five trips per day transport 2500 crates from a factory to a distributor in two days .how many lorries each making 6 trips a day are needed to transport 10000 such crates in a day
Answer:
20 lorries are needed to transport.
Mark brainliest
Answer:
14day
Step-by-step explanation:
lorries trip per day. crates
3. 5 2500
? 6 10000
(6×3×10000)÷(5×2500)=14days
A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
The equation of parabola is given by
(X-h)^2 = 4p(Y-k)^2
2p = 30 - 0
p = 15
4p = 4 × 15
= 60
In this case h = 0
So, we have (h,p) = (0,15)
So we get
We have equation: x^2 = 60(y-15)
y = x^2 / 60 + 15
What is a parabola?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax. Some of the important terms below are helpful to understand the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.
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There are 6 dogs and 5 cats.
In how many different orders can these animals be placed in line if any animal can be next to any other animal?
In how many different orders can these animals be placed in line if the dogs and cats are lined up alternately?
(Hint - The first animal MUST be a dog)
In how many different orders can these animals be placed in line if the first and last animal in line must be a cat?
Using the arrangements formula, the number of orders is given as follows:
39,916,800 if no restrictions.86,400 if they are lined up alternatively.7,257,600 if the first and last must be cats.What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are no restrictions, the number of ways is:
[tex]A_{11} = 11! = 39,916,800[/tex]
When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:
[tex]A_6A_5 = 6! \times 5! = 86,400[/tex]
When the first and last are cats, we have that:
For the first and last animals, there are 5!/2! = 20 ways.For the middle 9 animals, there are 9! ways.Hence:
20 x 9! = 7,257,600.
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X – 3 = 7 so X = thank
Answer:
x=10
Step-by-step explanation:
x-3(+3)=7+3
We need to add 3 to both sides to isolate x.
x=10
Answer:
x = 10Step-by-step explanation:
x - 3 = 7
x = 7 + 3
x = 10
The area of the trapezoid is 40 square units.
A trapezoid is shown. The lengths of the bases are 6 and 10, and the height of the altitude is h.
What is the height of the trapezoid?
3 units
5 units
10 units
12 units
The altitude of the trapezoid, based on the given parameters is 5 units
How to determine the height of the trapezoid?From the question, we have the following parameters about the trapezoid
Base length 1 of the trapezoid = 6
Base length 2 of the trapezoid = 10
Area of the trapezoid = 40
Altitude of the trapezoid = h
The area of the trapezoid is calculated using
Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid
Substitute the given parameters in the above formula
40 = 0.5 * (6 + 10) * h
Evaluate the sum of 6 ad 10 (do not approximate)
40 = 0.5 * (16) * h
Evaluate the product of 0.5 and 16 (do not approximate)
40 = 8 * h
Divide both sides by 8 (do not approximate)
h = 5
Hence, the altitude of the trapezoid, based on the given parameters is 5 units
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Answer:
5 units
Step-by-step explanation:
What are the y-intercept and the asymptote of g(x) = 3x – 5? (0, –5); y = 3 (0, –2); y = 5 (0, –4); y = –5 (0, 5); y = –3
The y-intercept of the equation g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation g(x) = 3^x - 5 is y = -5
How to determine the y-intercept?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The y-intercept is a point on the graph where the value of x is 0
This is represented by x= 0 or (0, y)
This means that we substitute 0 for x in the above equation
So, we have:
g(0) = 3^0 - 5
Evaluate the exponent 3^0
g(0) = 1 - 5
Evaluate the difference of 1 and 5
g(0) = -4
Rewrite this point as
(0, -4)
This means that the y-intercept of the equation g(x) = 3^x - 5 is (0, -4)
How to determine the asymptote?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The asymptote is a point on the graph where that is parallel to the graph
In the above equation, we have:
g(x) = 3^x - 5
Express the radical as 0
y = 0 - 5
Evaluate the difference of 0 and 5
y = -5
This means that the asymptote of the equation g(x) = 3^x - 5 is y = -5
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A train to new york city leaves every 7 minutes. another train to boston leaves the station every 6 minutes. suppose it is 6:30 am right now. at what time will both trains leave the station together again if both of them left the station together at 6:30 am?
Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
What is LCM?The lowest integer that is a multiple of two or more numbers is known as the LCM. For instance, the LCM of 4 and 6 is 12, and the LCM of 10 and 15 is 30. There are numerous ways for determining the least common multiples, just as there are for computing the greatest common divisors. One approach is to divide both numbers by their primes.To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:
If a train to New York City departs every 7 minutes and another to Boston departs every 6 minutes,The two trains then depart together after a time equal to the LCM of their individual intervalsLCM (7,6) = 42As a result, if they begin at the same time, they will depart at the same time every 42 minutes.If both trains left the station at 6.30 a.m., they will leave together again 42 minutes later, at 7.12 am.
Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
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Use the equation to complete an algebraic proof that proves the answer is x = 7/6. Write your proof in your journal and upload your answer. You will be awarded 5 points for the statements and 5 points for the reasons.
I need the algebraic proofs please!!!
Using the algebraic equation, (2x + 6)/5 = 4x - 3, it has been proved that x = 7/6
Algebraic Proof for the Given Algebraic Equation
The given algebraic equation is,
(2x + 6)/5 = 4x - 3
2x + 6 = 5(4x - 3)
2x + 6 = 20x - 15
20x - 15 = 2x + 6
This algebraic equation can be written as,
20x - 2x - 15 = 6
18x = 15 + 6
18x = 21
x = 21/18
x = 7/6
Hence, using the given algebraic equation, it has been proved that the value of x is 7/6.
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please solve by BODMAS rule
Answer:
Step-by-step explanation:
1/3 + 1/3 x 1/3 / 1/3 - 1/3
= 1/3 + 1/3 x 1/1 -1/3
= 1/3 + 1/3 - 1/3
= 2/3 - 1/3
= 1/3
Answer:
5/9.
Step-by-step explanation:
1/3 + 1/3 * 1/3 / 1/3 - 1/3 * 1/3
= 1/3 + 1/3 * 1 - 1/3 * 1/3
= 1/3 + 1/3 - 1/3 * 1/3
= 2/3 - 1/9
= 5/9.
Allen wants to buy colored pencils that cost $3.50. He has 2 dollars, 5 quarters, 2 dimes, and 7 pennies. Does he have enough money to buy the colored pencils
Answer:
Yes
Step-by-step explanation:
First we need to determine how much money Allen has
2 dollars = 2.00
5 quarters = 5 * .25 = 1.25
2 dimes = 2 * .10 = .20
7 pennies = 7 * .01 = .07
Add this together
2.00 + 1.25+.20+.07 =3.52
3.52 > 3.50
This is more than 3.50 so he has enough money to buy the pencils
(06.01 mc) what is the value of the expression 9 (fraction 1 over 2)4 ⋅ 48? 12 15 17 18
The value of the given expression is 105.
What are expressions?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.To find the value of the given expression:
Given function - 9 + (fraction 1 over 2)4 ⋅ 48Let, 9 + 1/2 ⋅ 4 ⋅ 48.Follow the PEMDAS order of operations:
Multiply and divide (left to right).
1/2 ⋅ 4 ⋅ 48 = 96 9 + 1/2 ⋅ 4 ⋅ 48 = 9 + 96Add and subtract (left to right)
9 + 96 = 105Therefore, the value of the given expression is 105.
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Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°
Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°
By applying the theorem of intersecting secants, the measure of angle XYZ is equal to: A. 35°.
How to determine angle <XYZ?By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the theorem of intersecting secants.
What is the theorem of intersecting secants?The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, angle XYZ will be given by this formula:
<XYZ = ½ × (m<WZ - m<XZ)
Substituting the given parameters into the formula, we have;
<XYZ = ½ × (175 - 105)
<XYZ = ½ × 70
<XYZ = 35°.
By applying the theorem of intersecting secants, we can infer and logically deduce that the measure of angle XYZ is equal to 35°.
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Answer: 35
Step-by-step explanation:
A tailor needs meters of cloth to make a poncho. How many meters does he need to make 15 ponchos of the same size?
Answer:
15 mister of cloths are needed to make 15 m if 1 puchu is 1 miter
Answer:15 meters
step by step explanation
At a concert for the band Algal Rhythms, 75% of the tickets were sold at the full price of $30. The remaining 25% of tickets were sold at a discounted price of $10. What was the average selling price of a ticket at the Algal Rhythms concert? Express your answer in dollars, rounded to the nearest cent.
The average selling price of a ticket at the Algal Rhythms concert is $25
How to determine the average selling price of a ticket at the Algal Rhythms concert?The given parameters are:
75% of the tickets were sold for $30.
The remaining 25% were sold for $10.
The average selling price of a ticket at the Algal Rhythms concert is calculated using
Average = Sum of (Price * Percentage)
So, we have
Average = 30 * 75% + 10 * 25%
Evaluate the expression
Average = 25
Hence, the average selling price of a ticket at the Algal Rhythms concert is $25
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Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
Answer:
parallel
Step-by-step explanation:
//
Answer: these lines are parallel.
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{6x-2y=-2} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x-2y+2=0} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x+2=2y\ |:2} \atop {x=2}} \right. \\\\\left \{ {{3x+1=y} \atop {y=3x+12}} \right.\\ \\\left \{ {{y=3x+1} \atop {y=3x+12}} \right. \\So,\ these\ lines\ are\ parallel.[/tex]
What are the zeros of the polynomial function: f(x) = x^3 - x^2 – 6x ?
Answer:
x=0, x=3, x=-2
Step-by-step explanation:
factor the equation
x(x^2-x-6)
factor more
x(x-3)(x+2)
set it equal to 0
x(x-3)(x+2)=0
plug in numbers for x that would result in the answer being 0
0(0-3)(0+2)=0
3(3-3)(3+2)=0
-2(-2-3)(-2+2)=0
The graph compares shoe sizes for a group of 100 two-year-old boys and a
group of 60 three-year-old boys.
Two box and whisker plots showing shoes sizes on a number line from 2.5 to 13. The upper plot represents the group of 2 year-old boys. For this upper plot, the minimum number is 3, the maximum number is 9.5, the right side of the box is 7.5, the left side of the box is 3.5, and the bar in the box is at 6. The lower plot represents the group of 3 year-old boys. For this lower plot, the minimum number is 5, the maximum number is 11.5, the right side of the box is 9.5, the left side of the box is 6.5, and the bar in the box is at 8.
About how many more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys?
The number of two year old boys that wear a size 6 is greater than the number of three year old boys that wear a size 6 by 35.
How many more two year olds wear a size 6?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines called the whiskers and a box. The whiskers represent the minimum and maximum scores.
On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile
50% of the two year olds wear a size 6 = 50% x 100 = 50
25% of the three year olds wear a size 6 = 25% x 60 = 15
Difference in the number : 50 - 15 = 35
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7. Which of these statements is true?
A. 1-(-4)<4- (-2)
B. (-2)(3) > (-1)(-6)
C. 6÷
D.-(5-3)=-5-3
Answer:
A. because 5 < 6. 1-(-4)=5. and 4-(-2) =6
Let f (x) = x4 – 2x3 – 3x2 + 4x + 4, g of x is equal to the square root of the quantity x squared minus x minus 2 end quantity and h of x is equal to the quantity negative x squared plus 1 end quantity over the quantity x squared minus x minus 2 end quantity Part A: Use complete sentences to compare the domain and range of the polynomial function f (x) to that of the radical function g(x). (5 points) Part B: How do the breaks in the domain of h (x) relate to the zeros of f (x)? (5 points)
The domain of f(x) is all set of real values while, the domain of g(x) is x ≤ -1 or x ≥ 2 and both functions have the same range
Part A: Compare the domain and range of the function f(x) to g(x)The functions are given as:
f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4
g(x) = √(x^2 - x - 2)
Domain
The polynomial function f(x) has no restriction on its input.
So, the domain of f(x) is all set of real values
Set the radical of g(x) = √(x^2 - x - 2) greater than 0
x^2 - x - 2 ≥ 0
Factorize
(x + 1)(x - 2) ≥ 0
Solve for x
x ≥ -1 and x ≥ 2
Combine both inequalities
x ≤ -1 and x ≥ 2
So, the domain of g(x) is x ≤ -1 or x ≥ 2
Range
Using a graphical calculator, we have:
Range of f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4 ⇒ f(x) ≥ 0Range of g(x) = √(x^2 - x - 2) ⇒ g(x) ≥ 0Hence, both functions have the same range
How do the breaks in the domain of h(x) relate to the zeros of f(x)?We have:
h(x) = (-x^2 + x)/(x^2 - x - 2)
Set the denominator to 0
x^2 - x - 2 = 0
The above represents the radical of the function f(x)
This means that the breaks in the domain of h(x) and the zeros of f(x) are the same
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Complete question
Let f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4, g(x) = √(x^2 - x - 2) and h(x) = (-x^2 + x)/(x^2 - x - 2)
Part A: Use complete sentences to compare the domain and range of the polynomial function f (x) to that of the radical function g(x). (5 points)
Part B: How do the breaks in the domain of h (x) relate to the zeros of f (x)? (5 points)
Ramiro was on a two day road trip.on the first day he drove at an average speed of 40 mph.on the second day he drove at an average of 60 mph.if he drove 2 hours longer and went 20 miles farther on his first day find the total distance ramiro traveled on his road trip.
Considering the relationship between velocity, distance and time, it is found that the total distance traveled was of 380 miles.
What is the relationship between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For the first day, we have that:
v = 40, t = t + 2, d = d + 20, hence:
40 = (d + 20)/(t + 2)
For the second day, we have that:
v = 60
60 = d/t
d = 60t
Then, replacing in the first equation:
40 = (60t + 20)(t + 2)
60t + 20 = 40t + 80
20t = 60
t = 3.
Then the distances are given by:
First day: d = 60t + 20 = 60 x 3 + 20 = 200 miles.Second day: d = 60t = 60 x 3 = 180 miles.Total: 200 miles + 180 miles = 380 miles.More can be learned about the relationship between velocity, distance and time at https://brainly.com/question/28143163
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Prove that the number A= [tex]20^{8^{2014} } }+113 is composite
Cheese proof:
We can just prove that it is divisible by 3, which means that it is composite. We can use modular exponentiation, where if [tex]a \equiv b \pmod{n}[/tex] then [tex]a^x \equiv b^x \pmod{n}[/tex]. In this case, [tex]{-1}^{8^{2014}} \equiv 20^{8^{2014}} \pmod{3}[/tex]. This is much easier to calculate! Since [tex]8^{2014}[/tex] is even, [tex]-1^{8^{2014}}=1[/tex], meaning that now we only need to prove that [tex]0\equiv(1+113) \pmod{3}[/tex], which is obviously true.
(e) ABCD is an isosceles trapezium. Prove that: (1) AC=BD (2) BE=CE (3) AE=DE
Answer:
look at attached image for the step-by-step proof. thanks for reposting this lol
A cube. the top face has points a, g, e, f and the bottom face has points b, h, d, c. the diagonal from a to e is startroot 288 endroot inches and the diagonal from a to d is startroot 432 endroot inches. what is the length of ed in the given cube? round to the nearest tenth of an inch if necessary. in.
The length of the line ed according to the description of the cube is; 8.5.
What is the length of ed in the given Cube?First, since the shape is a cube, it follows that the diagonal of the top face can be used to determine the length of the sides of the top face.
Therefore , we have; length of each side of the top face;
ag = ge = ef = fa = √288/2 = 6√2.
Also, the diagonal of a to d is; √432 = 12√3.
Hence, the length of ed in the group as evident from the length of sides of the cube's top face in which case,
Consequently, the length of line ed is;√432 × 8.5.
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