which of the following are polynomial functions?check all that apply
(answers in picture)
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Polynomial functions must have terms that have non-negative integer exponents. We can rewrite function B, [tex]F(x)=-x^3+5x^2+7\sqrt{x}-1[/tex] as:
[tex]F(x)=-x^3+5x^2+7x^1^/^2-1[/tex]
The exponent 1/2 is not an integer exponent.
We can also rewrite the function D, [tex]F(x)=\frac{3}{5}x^4-18x^2+5-\frac{10}{x^2}[/tex], as:
[tex]F(x)=\frac{3}{5}x^4-18x^2+5-10x^-^2[/tex]
We have a negative exponent, so this is not a polynomial.
Answer:
Step-by-step explanation: It is only c and e i just did the test.
Related Questions
If there are 15 girls and 9 boys in an art class, the ____________ of girls to boys in the class is 5:3.
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two positive integers have a sum of 17 and a product of 66
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Sum | Product
33 and 2 35 66 X
22 and 3 25 66 X
11 and 6 17 66 ←
11 and 6 have a sum of 17 and a product of 66
50 points! Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled, and the sum of their outcomes is found. Each player gets a chance to guess the correct sum, and the player that guesses the correct sum wins the game.
Dustin decides to guess a sum of six. Melanie decides to guess a sum of seven.
Which player made the better decision? ________
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Answer:
Melanie is the right answer
Step-by-step explanation:
Melanie made the better decision if Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Dustin and Melanie are playing a game, where two standards, six-sided number cubes are rolled.
If the sum is 6:
The possible outcomes are = {(3,3), (2,4), (4,2), (1,5), and (5,1)}
Total outcomes = 5
If the sum is 7:
The possible outcomes are = {(1,6), (6,1), (5,2),( 2,5), (3, 4), (4,3)}
Total outcomes = 7
Thus, Melanie made the better decision if Dustin and Melanie are playing a game, where two standards, six-sided number cubes are rolled.
Learn more about the probability here:
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What is the solution of log6x+log6(x+5)=2?
Answers
Answer:4
Step-by-step explanation:just did it on edge
To solve log6(x) + log6(x + 5) = 2, combine the logarithms, rewrite in exponential form, and solve the resulting quadratic equation. The solutions are x = -9 and x = 4, but since logarithms of negative numbers are undefined, the final answer is x = 4.
To solve this logarithmic equation, follow these steps:
Combine the logarithms: Use the property of logarithms that states logb(a) + logb(c) = logb(a × c).So, we have: log6(x) + log6(x + 5) = log6(x(x + 5)).
This simplifies to log6(x² + 5x).Set the logarithmic expression equal to 2: log6(x² + 5x) = 2.Rewrite the equation in exponential form: Using the definition of a logarithm, a logarithm logb(y) = c can be rewritten as [tex]b^{\\c[/tex] = y. Thus, we get 6² = x² + 5x.
This simplifies to 36 = x² + 5x.Solve the quadratic equation: Rewrite the quadratic equation in standard form: x² + 5x - 36 = 0.
Then, factor the quadratic: (x + 9)(x - 4) = 0.Find the solutions: Set each factor to zero and solve for x.
x + 9 = 0 → x = -9
x - 4 = 0 → x = 4.Check the solutions in the original equation: Since the logarithm of a negative number is undefined, discard x = -9.
Therefore, the solution to the equation is x = 4.
Final Answer: x = 4.
1. Suppose that the amount of algae in a pond doubles every 4 hours. If the pond initially contains 90 pounds of algae, how much algae will be in the pond after 12 hours? (1 point)
would it be 720lbs
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Rewrite the radical exponent as a radical
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Solve this easy question and get points!!!
There are two trains. Both trains are going to the same place, taking the same stops, and are going the exact same speed. But one train arrives in
80 Mins and the other train arrives in 1 Hour and 20 Mins. How is this possible?
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1 hour = 60 minutes
60 + 20 = 80 minutes
80 minutes = 80 minutes
Therefore, your answer is "yes it is possible"
hope this helps
) the length of a rectangle is 5 cm less than twice the width. if the area of the rectangle is 88 , find the dimensions of the rectangle.
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when does a rhombus have 4 congruent angles?
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Use the data to create a scatter plot.
Size (lb)
8
12
9.5
5
7
7.5
Time (h)
5
6.5
4
3.5
2
5
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The ordered pairs are:
(5, 8)
(6.5, 12)
(4, 9.5)
(3.5, 5)
(2, 7)
(5, 7.5)
Answer:
See attached image.
There seems to be an increase in weight as time passes.
How do you determine whether to draw the boundary line of the graph of a linear inequality dashed or solid?
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a/an ______ angle measures less than 90degrees°, a/an ______ angle measures 90degrees°, a/an ______ angle measures more than 90degrees° and less than 180degrees°, and a/an ______ angle measures 180degrees°.
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Right
Obtuse
Straight
Jade is painting a rectangular wall. The wall is 414 yards long and 223 yards high.The formula for the area of a rectangle is A=bh. What is the area of the wall?
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The formula for the area of the rectangle is actually A = LW. The length of the rectangular wall is 414 yards while its width is 223 yards. To compute for its area, you just have to follow the formula:
A = 414 (223)
A = 92,322 yards^2
Therefore, the area of the wall is 92,322 square yards.
Answer:
hey the answer is 11 1/3
Step-by-step explanation:
ive taken the quiz and this is the answer 100%
Describe the vertical asymptotes and holes for the graph of y=x-4/x^2+3x+2,
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Therefore:
x - 4 = 0
x = 4
x² + 3x + 2 = 0
(x + 2)(x + 1) = 0
x = -2 and x = -1
There are no points in which both numerator and denominator are equal to zero, therefore there are no holes, while x = -2 and x = -1 are vertical asymptotes.
The shorter leg of a right triangle is 1414 feet less than the other leg. find the length of the two legs if the hypotenuse is 3434 feet.
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the length will be (x+14) ft
hypotenuse is 34 ft
given that our triangle is right triangle, using Pythagorean theorem?
c^2=a^2+b^2
substituting our values in the formula we get:
34^2=x^2+(x+14)^2
1,156=x^2+x^2+28x+196
simplifying this we get
0=2x^2+28x-960
solving the quadratic equation we get:
x=16 or x=-30
therefore the width is 16 ft and the length is 16+14=30
Factor completely. x^2−3x−40
Answers
8x5 = 40 and -8 + 5 = -3.
Plug it into the binomial example I provided above and....
(x - 8)(x+5)=40
Voila! You have your factored quadratic expression, hope this helps!
To factor the quadratic expression x² -3x -40, we find that the expression factors into (x - 8)(x + 5).
The question involves factoring the quadratic expression x² -3x -40 completely. To factor this expression, we look for two numbers that multiply to -40 and add to -3. The numbers that meet these conditions are -8 and 5, since
(-8) * 5 = -40 and
(-8) + 5 = -3.
Therefore, the expression can be factored into (x - 8)(x + 5).
Ashur solves the following system of linear equations.
Which statement about the solution to this system can he say is true?
The values of a and b are both equal to –4.
The values of a and b are both equal to 4.
The value of a is equal to 4, and b is equal to –4.
The value of a is equal to –4, and b is equal to 4.
Answers
The values of a and b are both equal to –4.
The given equations that make up the systems are:
-3a+7b=-16...................(Equation 1)
-9a+5b=16...................(Equation 2)
To find the values of a and b we will have to solve the two equations. To solve the equations let us employ the method of elimination.
Let us multiply (Equation 1) by -3. This will give us:
[tex] -3\times (-3a+7b=-16)=9a-21b=48 [/tex]...........(Equation 3)
Let us now add (Equation 2) to (Equation 3) to eliminate a. This will give us:
-16b=64
[tex] \therefore b=-4 [/tex]
Plugging this value of b in any of the equations we will get the value of a. Let us plug it in (Equation 1). This gives:
[tex] -3(-4)+7b=-16 [/tex]
[tex] 12+7b=-16 [/tex]
[tex] \therefore b=\frac{-28}{7}=-4 [/tex]
Thus, out of the given options, the first option is the correct one. The values of a and b are both equal to –4.
What is the average of the first n positive even numbers?
Answers
1 + n
Solution:
we have been asked to find the average of the first n positive even numbers.
Let the firm n positive even numbers be
[tex] 2,4,6,8,10,12,.........2(n-1), 2n [/tex]
As we know that average of numbers[tex] =\frac{\text{Sum of Numbers }}{Total number of Numbers}\\ [/tex]
Required Average[tex] =\frac{2+4+6+2(n-1)+2n}{n}\\ [/tex]
Required Average[tex] =\frac{2(1+2+3+....+(n-1)+n)}{n} [/tex]
As we know the sum of first n terms[tex] =\frac{n(n+1)}{2} [/tex]
Required Average[tex] =\frac{2n(n+1)}{2n}=n+1 \\ [/tex]
In a tessellation, what must the sum of the angles be where the vertices meet?
90° 180° 360° 60°
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What is the perimeter of the triangle expressed as a polynomial? 8x-2 5x-4 9x-3
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(8x-2)+(5x-4)+(9x-3)
8x-2+5x-4+9x-3
(8x+5x+9x)+(-2-4-3)
22x-9
Answer: 22x-9
at 4:00 am,there were 800,000 gallons of water remaining at a reservoir.after 4 hours of irrigation,there were 100,000 gallons of water remaining.write an equation that describes the number of gallons of water as a function of the time the field has been irrigated
Answers
To relate those two points we are going to use the point slope formula:
[tex]m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} } [/tex]
where
[tex]x_{2}[/tex] is 8
[tex]x_{1}[/tex] is 4
[tex]y_{1}[/tex] is 800000
[tex]y_{2}[/tex] is 100000
So, [tex]m= \frac{100000-800000}{8-4} [/tex]
[tex]m= \frac{-700000}{4} [/tex]
[tex]m=-175000[/tex]
Now that we have our slope, we are going to use the point-slope formula to find our equation:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-800000=-175000(x-4)[/tex]
[tex]y-800000=-175000x+700000[/tex]
[tex]y=-175000x+1500000[/tex]
The equation that describes the number of gallons of water as a function of the time the field has been irrigated is [tex]y=-175000x+1500000[/tex]
where
[tex]y[/tex] are the remaining gallons of water in the reservoir after [tex]x[/tex] hours
[tex]x[/tex] is the time the field has been irrigated in hours
A function that can be written in the form f(x)=ax2+bx+c, where a, b & c are real numbers and a is not equal to zero.
Answers
I'm not exactly sure of what answer you are looking for, however,
f(x)=ax^2+bx+c represents a quadratic function.
Quadratic functions always have their highest exponent at 2, nothing more and nothing less.
Examples of quadratic functions are...
•x^2
•3x^2
•3x^2+2
•3x^2+2x
•3x^2+2x+1
I really hope this helps!
Best wishes:)
A quadratic function seems to be a second-order polynomial function. Another quadratic function has the following general form:
[tex]f (x) = ax^2 + bx + c[/tex]here,
a, b, and c = real numbersand,
a ≠ 0The quadratic formula is obtained by completing the square on some kind of quadratic equation instead in the standard format. Because the largest power equals two, it is indeed a 2nd-degree polynomial equation.
As a result, the aforementioned response is correct.
Learn more about quadratic equation here:
https://brainly.com/question/19942005
What is the solution of the equation 5x – 1 = 45? Round your answer to the nearest ten-thousandth
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Final answer:
The solution to the equation 5x – 1 = 45 is x = 9.2, rounded to the nearest ten-thousandth.
Explanation:
The solution of the equation 5x – 1 = 45 is x = 9.2.
To solve this equation, we can start by isolating the variable x. Add 1 to both sides of the equation to get 5x = 46. Then, divide both sides by 5 to solve for x, giving us x = 9.2.
Therefore, the solution to the equation 5x – 1 = 45 is x = 9.2, rounded to the nearest ten-thousandth.
If the measurement of a central angle is 77 degrees find the length of its intercepted arc in a circle with a radius of 15 inches.
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Answer:
20.2 inches ;)
Step-by-step explanation:
Which of the symbols correctly relates the two numbers below? Check all that apply.
55 ? 35
A.
B.
C. <
D.
E. =
F. >
The other symbols dont want to show so if its another on plz tell me or add me on fb if you guys wanna help me i need to finish this,
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55>35
The correct answer is > because 55 is larger than 35 and that is the sign for larger than
which is the directrix of parabola with equation x^2=4y
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Answer:
[tex]y=-1[/tex]
Step-by-step explanation:
We have been given an equation of parabola [tex]x^2=4y[/tex]. We are asked to find the directrix of our given parabola.
First of all, we will divide both sides of our given equation by 4.
[tex]\frac{x^2}{4}=\frac{4y}{4}[/tex]
[tex]\frac{x^2}{4}=y[/tex]
[tex]y=\frac{x^2}{4}[/tex]
Now, we will compare our equation with vertex form of parabola:
[tex]y=a(x-h)^2+k[/tex], where, (h,k) represents vertex of parabola.
We can see that the value of a is [tex]\frac{1}{4}[/tex], [tex]h=0[/tex] and [tex]k=0[/tex].
Now, we will find distance of focus from vertex of parabola using formula [tex]p=\frac{1}{4a}[/tex].
Substituting the value of a in above formula, we will get:
[tex]p=\frac{1}{4*\frac{1}{4}}[/tex]
[tex]p=\frac{1}{1}=1[/tex]
We know that directrix of parabola is [tex]y=k-p[/tex].
Substituting the value of k and p in above formula, we will get:
[tex]y=0-1[/tex]
[tex]y=-1[/tex]
Therefore, the directrix of our given parabola is [tex]y=-1[/tex].
How long would it take to travel 630 miles at the rate of 35 miles per hour? 18 h 35 h 220 h 350 h
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Answer:
18h
Step-by-step explanation:
what is the answer to f(2)=2-5(2)
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In a billiards game, Pete hits a ball that is 20in. from a wall. The ball travels 34 in. until it hits the wall and bounces to a position that is 16 in. from the wall. What proportion can be used to find the distance, x, the ball traveled after it bounces off the wall to get to the ending position? CHECK ALL THAT APPLY!
options
34/x =20/16
20/16 = 34/x
16/20 = x/34
20/16 = x/34
Answers
Using Thales, 34/x=20/16
Answer A
To find the distance the ball traveled after it bounces off the wall, we can use the proportion 34/x = 20/16, which simplifies to x = 27.2 inches.
To find the proportion that can be used to find the distance, x, the ball traveled after it bounces off the wall, we can use the equation:
34/x = 20/16
After cross multiplying, we get:
34 × 16 = 20x
Simplifying further:
544 = 20x
Dividing both sides by 20, we find:
x = 27.2
Therefore, the distance the ball traveled after it bounces off the wall is 27.2 inches.
A line includes the points (2, 10) and (1, 4). what is its equation in slope-intercept form?
Answers
This problem has two parts. First you need to find the slope, so let's do that. The equation for the slope is m = y2-y1/x2-x1
We can now plug the two given points into the equation.
m = 10-4/2-1
m = 6/1
m = 6
Now that we know the slope, and one point we can put this in slope intercept form. Slope intercept form is y=mx + b
So now we can plug in one point and the slope to find b
10 = 6(2) + b
10 = 12 + b
-2 = b
Now that we know both m and b, we can plug only those two into the equation y=mx + b, and we have the equation.
The equation is y = 6x - 2