Answers
-Variables in the exponents of the terms.
-Variables in the denominator.
- Negative exponents.
-Fractionals exponents.
-The variables cant be as radicals.
Therefore:
a) It is a polynomial (The variable is under a radical)
b) It is not a polynomial.
c) It is a polynomial.
d) It is not a polynomial. (It has a variable in the denominator).
e) It is a polynomial.
f) It is not a polynomial. (It has a variable in the denominator).
Related Questions
A punch recipe requires 4/5 of a cup of pineapple juice for every 2 1/2 cups of soda. What is the unit rate of soda to pineapple juice in the punch?
Answers
2 1/2----------> (2*2+1)/2-----------> 5/2
[unit rate of soda to pineapple juice]=[quantity of soda]/[quantity of pineapple]
[unit rate of soda to pineapple juice]=[5/2]/[4/5]----> 25/8-------> 3.125---> 3 1/8
the answer is 3.125 (3 1/8)
Olive has read 79 pages of her book. Which equation shows how many more pages she has to read?
Answers
p = t - 79
would be the equation.
Hope this helps!
The graph below shows the solution to a system of inequalities
Which of the following inequalities is modeled by the graph?
A. x + 4y ≥ 15; y ≥ 0
B.x − 4y ≥ 15; y ≥ 0
C.x + 4y ≤ 15; y ≥ 0
D.−x − 4y ≥ 15; y ≥ 0
Answers
using a graph tool
I proceed to graph each of the cases to verify the answer
see the attached figures
the solution is the option C) x + 4y ≤ 15; y ≥ 0
Write, and show on a number line, the set of all the numbers that are:
greater than (−3) and less than 3.
Answers
Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order. What is the sample space showing the possible orders of the other three runners? S = {FGI, GFI, IFG} S = {FGI, FIG, GFI, GIF} S = {FGI, FIG, GFI, GIF, IFG, IGF} S = {FGI, FIG, GFI, GIF, HFG, HGI, IFG, IGF}
Answers
F can come first then the possibilities of other 2 players are ;
FGI and FIG
G can come first then the possibilities of other 2 players are ;
GIF and GFI
Next If I comes first then the possibilities are
IGF and IFG
Therefore sample space for all the possibilities as noted above are;
S = {FGI, FIG, GFI, GIF, IFG, IGF}
The sample space or sets showing the possible orders of the other three runners is S = {FGI, FIG, GFI, GIF, IFG, IGF}.
What are Sets?Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as curly bracket {..}.
Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team.
Haley is the first runner in the relay. The other runners can run in any order.
The sample space or sets showing the possible orders of the other three runners will be
S = {FGI, FIG, GFI, GIF, IFG, IGF}
Thus, the correct option is C.
More about the sets link is given below.
https://brainly.com/question/8053622
Which model shows the correct factorization of x2 + 2x - 8
Answers
1) Write to factors, with x as the first term, this way:
(x )(x )
2) The sign to the right of the x in the first factor is the same sign of the coeficient of x in the polynomial.
That is +.
The sign to the right of the x of the second factor is the product of the sign of the coefficent of x (this is +) and the sign of the independent term (this is - ).
So that is (+).(-) + -.
Now the two factors have this form:
(x + ) (x - )
3) Now find two numbers whose product is - 8 and whose difference is +2
Those numbers are + 4 and -2.
Then the two factors are:
(x + 4) (x - 2).
So the answer if that the correct factorization is (x + 4) (x - 2)
The correct answer is D.
I just took the test.
a carpenter and helper can do a certain job in 18 days if the carpenter takes walks 1.5 times as fast as the helper how long would it take each working alone?
Answers
x-----------> time it takes the carpenter working alone
y-----------> time it takes the helper working alone
we know that
x+y=18 days------------>equation 1
x=y/1.5---------------> equation 2
I substitute 2 in 1
(y/1.5)+y=18----------> (y+1.5y)/1.5=18---------> 2.5y=18*1.5
2.5y=27-----------> y=27/2.5-----------> y=10.8 days
x+y=18--------> x=18-10.8---------> x=7.2 days
the answer is
time it takes the carpenter working alone is 7.2 days
time it takes the helper working alone is 10.8 days
Answer:
i dunno know
Step-by-step explanation:
2+2=FISH
Find the first five non-zero terms of taylor series centered at x=3x=3 for the function below. f(x)=6x−x2−−−−−−√ f(x)=6x−x2
Answers
Note, that because of simple function (parabola) almost all the members of the series are '0'.
Finn imagines 1 more row of nines to find the total area of 9 * 9 rectangle. explain how this could help him solve 9 * 9
Answers
but i would say imagining nine rows of nine
the area would be 81.
Hope this helps :)
A hotel is in the shape of a square pyramid. Each side of the base is 183 meters long and the height is 110 meters. What is the hotel's volume? Enter your answer in the box
Answers
Answer:
1,227,930 m²
Step-by-step explanation:
We are given that,
Base of the pyramid = 183 meter
Height = 110 meter.
Since, we know,
Volume of a square pyramid = [tex]Base^2\times \frac{Height}{3}[/tex]
We have,
Volume of the square pyramid = [tex]183^2\times \frac{110}{3}[/tex]
i.e. Volume of the square pyramid = [tex]33489\times 36.667[/tex]
i.e. Volume of the square pyramid = 1,227,930 m²
Hence, the volume of the square pyramid is 1,227,930 m².
which method could be used to factor 4x^2-50
Answers
The correct factorization for [tex]\(4x^2 - 50\) is \(2(x\sqrt{2} - 5)(x\sqrt{2} + 5)\)[/tex], where [tex]\(\sqrt{2}\)[/tex] is included in each term.
The given quadratic expression [tex]\(4x^2 - 50\)[/tex] can be factored using the difference of squares method.
The difference of squares formula is[tex]\(a^2 - b^2 = (a + b)(a - b)\).[/tex]
In this case, a = 2x and [tex]\(b = \sqrt{50}\).[/tex]
1. Identify the expression as a difference of squares: [tex]\(4x^2 - 50 = (2x)^2 - (\sqrt{50})^2\).[/tex]
2. Apply the difference of squares formula:[tex]\(4x^2 - 50 = (2x + \sqrt{50})(2x - \sqrt{50})\).[/tex]
3. Further simplify by factoring out 2: [tex]\(4x^2 - 50 = 2(2x + \sqrt{50})(2x - \sqrt{50})\).[/tex]
The correct factorization for [tex]\(4x^2 - 50\) is \(2(x\sqrt{2} - 5)(x\sqrt{2} + 5)\)[/tex], where [tex]\(\sqrt{2}\)[/tex] is included in each term.
Compare the two fractions. Use >, <, or =.
1st fraction, 2/3
2nd fraction, 4/6
Answers
Multiply by 2 for both numerator and denominator
2/3 = 4/6
2nd Fraction = 4/6
Both are the same fraction, 4/6:
2/3 = 4/6
A container shape as a rectangular prism can hold 840 wooden cube blocks with edge lengths of 1/2 feet. What is the volume of the container?
Answers
volume of one wooden cube blocks=(1/2)³=1/8 ft³
volume rectangular prism=840*(1/8)=105 ft³
the answer is 105 ft³
V = L ^ 3
Where:
L: side.
We have then that the volume of a cube is:
V = (1/2) ^ 3
V = 1/8
Then, the prism volume is:
Vtotal = 840 * V
Vtotal = 840 * (1/8)
Vtotal 105 feet ^ 3
Answer:
the volume of the prism is:
Vtotal 105 feet ^ 3
How many x intercepts appear on the graph of this polynomial function? F(x)=x^4-5^2.
1 x intercept
2 x intercepts
3 x intercepts
4 x intercepts
Answers
[tex]0= x^{4}- 5^{2} \\ \\ 25= x^{4} \\ \\ [/tex]
Taking square root of both sides we get:
[tex](5) = x^{2} , \\ -5= x^{2} [/tex]
The square root of -5 will result in a complex number. So we reject this value and only consider [tex]5= x^{2} [/tex]
Taking the square root again, we get:
[tex]+- \sqrt{5}=x [/tex]
Thus the F(x) has two x-intercepts at [tex]x= \sqrt{5} [/tex] and [tex]x= -\sqrt{5} [/tex]
How to find A? help please and thanks
Answers
With similar triangles, we can compare the sides using ratios.
The equation we can use to find side A is stated below.
Side 1A / Side 1B = Side 2A / Side 2B
The number refers to the triangle, and the letter refers to the side of each triangle. Side A in both triangles must be the base of the triangle, and side B in both triangles can be either of the other sides. The only restriction is that once we pick a side B on triangle 1, we must pick that same side on triangle 2.
A / 7 = 3 / 2
Then we can solve for the length of side A.
A = 7*3/2 = 21/2 = (E) None of These
Find the 5th partial sum of the arithmetic sequence an=2n–3.
Answers
The figures shows the show the dimension of a tennis court and a basketball court given in term of the width x in feet.
Answers
Formula
------------------------------------------------------------------------------
Perimeter = 2(Length + Width)
------------------------------------------------------------------------------
Perimeter of the Tennis Court
------------------------------------------------------------------------------
Perimeter of the Tennis Court = 2(Length + Width)
Perimeter of the Tennis Court = 2 (2x + 6 + x)
Perimeter of the Tennis Court = 2 (3x + 6)
Perimeter of the Tennis Court = 6x + 12
------------------------------------------------------------------------------
Perimeter of the Basketball Court
------------------------------------------------------------------------------
Perimeter of the Basketball Court = 2(Length + Width)
Perimeter of the Basketball Court = [tex]2(3x -14 + \dfrac{1}{2}x + 32)[/tex]
Perimeter of the Basketball Court = [tex]2( 3\dfrac{1}{2}x+ 18)[/tex]
Perimeter of the Basketball Court = [tex]7x + 36[/tex]
------------------------------------------------------------------------------
Answer: Tennis Court = 6x + 12 ; Basketball Court = 7x + 36
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Difference in the two perimeter
------------------------------------------------------------------------------
(7x + 36) - (6x + 12)
= 7x + 36 - 6x - 12
= x + 24
------------------------------------------------------------------------------
Answer: Basketball Court is (x + 24) unit greater than Tennis Court
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Tennis Court is 36 feet wide. Find dimension
------------------------------------------------------------------------------
Width of Tennis Court = x = 36 ft
Length of Tennis Court = 2x + 6 = 2(36) + 6 = 78 ft
Perimeter of Tennis Court = 6x + 12 = 6(36) + 12 = 228 ft
Width of Basketball Court = 1/2x + 32 = 1/2(36) + 32 = 50 ft
Length of Basketball Court = 3x - 14 = 3(36) - 14 = 94 ft
Perimeter of Basketball Court = 7x + 36 = 7(36) + 36 = 288 ft
------------------------------------------------------------------------------
Answer:
Tennis Court is 36 ft by78 ft and its perimeter is 228 ft.
Basketball Court is 50 ft by 94 ft and its perimeter is 288 ft
------------------------------------------------------------------------------
Please help with this question!
Ari has been paying attention to the number of calories she burns while exercising. One day she spent 3 hours hiking, and 4 canoeing, and she calculated that she burned 2338 calories. The next day, she hiked for 7 hours and canoed for one hour, and she calculated that she burned 3322 calories. How many calories per hour does Ari burn doing each exercise?
Answers
Let the calories / hour for canoeing = c
3h + 4 c = 2338
7h + c = 3322 Multiply this by 4
28h + 4c = 13288 Write the first equation underneath this one.
3h + 4c = 2338 Subtract
==================
25h = 10950 Divide by 25
h = 10950 / 25
h = 438 calories for each hour hiking.
7h + c = 3322
7*438 + c = 3322
3066 + c = 3322
c = 3322 - 3066
c = 256 calories / hour canoeing.
By setting up a system of equations, we find that Ari burns 438 calories per hour hiking and 256 calories per hour canoeing.
To determine the number of calories Ari burns per hour doing each exercise, we need to set up a system of equations based on the given information. Let x represent the number of calories burned per hour hiking, and y represent the number of calories burned per hour canoeing.
We are given two situations:
3 hours of hiking and 4 hours of canoeing burn 2338 calories: 3x + 4y = 2338.
7 hours of hiking and 1 hour of canoeing burn 3322 calories: 7x + y = 3322.
We have the following system of equations:
3x + 4y = 2338
7x + y = 3322
To solve the system, we can first multiply the second equation by 4 to eliminate y:
4(7x + y) = 4(3322)
28x + 4y = 13288
Now, subtract the first equation from this result:
(28x + 4y) - (3x + 4y) = 13288 - 2338
25x = 10950
x = 10950 / 25
x = 438
Ari burns 438 calories per hour hiking.
To find y, substitute x = 438 into the first equation:
3(438) + 4y = 2338
1314 + 4y = 2338
4y = 2338 - 1314
4y = 1024
y = 256
Ari burns 256 calories per hour canoeing.
Thus, the results reveal that Ari burns 438 calories per hour hiking and 256 calories per hour canoeing.
Each term in a binomial expansion has degree n; therefore, the product of the exponents of each term is n.
true
or
false
Answers
(a+b)^n = a^n b^0 + a^(n-1) b^1 + ......
Answer:
False
Step-by-step explanation:
In any binomial expansion of the form
[tex](x+a)^n = \Sigma_0^n nCr x^{n-r} a^{r}[/tex]
We find that each term has decreasing powers of x by 1 and increasing powers of a by 1, such that the sum of exponents is always n
Hence product of exponents of each term cannot be n.
The given statement is false.
Only the sum of the exponents of each term in a binomial expansion has degree n
Find the distance from the point p(4, −1, 1) to the line x = 1 + 2t, y = 3t, z5 − 7t
Answers
Using the tables found in the textbook, determine the difference between the monthly payments on a $120,000 home at 6½% and at 8% for 25 years.
Answers
Answer:115.20
Step-by-step explanation:
Analyze the key features of the graphs of the functions below. Select all of the quadratic functions that open down, have a vertex that is a maximum and a positive y-intercept.
The Choices are
F(x)=2x^2-4x-3
G(x)= -x^2+x+1
H(x)= -2x^2+3x-1
M(x)=x^2-9
N(x)= -3x^2+7
Answers
The only thing you need to do is look at the leading coefficient for each choice to decide which ones open down and have a maximum. If the leading coefficient is negative, then they open down and have a maximum.
F(x) is out of our choices because the leading coefficient is positive.
G(x) and H(x) are still options.
M(x) is gone for the same reason we won't choose F(x).
N(x) is still an option.
Now our choices are between G(x), H(x), and H(x). To decide which ones have a positive y-intercept, look at the constant term. If it's negative, then it has a negative y-intercept and it's out of our choices.
G(x) and H(x) remain our only options and since the question can have multiple answers, G(x) and H(x) are the answers!
I really hope this helps!
Best wishes:)
Out of the options provided, only G(x) = -x^2 + x + 1 fits the conditions asked in the question. It is a quadratic function that opens downward, has a vertex that is a maximum, and a positive y-intercept.
Explanation:The key features of a quadratic function are determined by its equation: f(x) = ax2 + bx + c. The sign of 'a' determines whether the function opens up or down. If 'a' is positive, the graph opens up, and if 'a' is negative, it opens down. The vertex of a quadratic function is given by the formula (-b/2a , f(-b/2a)). If 'a' is negative, this vertex will be a maximum. The y-intercept of the function is the value of 'c' in the quadratic equation. According to the conditions provided, we can classify the given functions.
f(x) = 2x2 - 4x - 3 opens upward and has a negative y-intercept; it’s not in the selection.G(x) = -x2 + x + 1 opens downward, has a maximum vertex, and a positive y-intercept. It fits the conditions.H(x) = -2x2 + 3x - 1 opens downward and has a maximum vertex, but has a negative y-intercept, so it’s not in the selection.M(x) = x2 - 9 opens upward and has a negative y-intercept; it’s not in the classification.N(x) = -3x2 +7 opens downward and has a maximum vertex, but it does not mention whether there is a positive y-intercept; so it’s unclear.
Learn more about Quadratic Functions here:
https://brainly.com/question/35505962
#SPJ6
select all expressions thr equal 3.15/0.45
Answers
let's analyze case by case
case A) 3.15*0.45---------> is not (3.15/0.45)
case B) 3.15/0.45-----------> is correct
case C) 3.15*(1/0.45)=(3.15*1)/0.45--------> 3.15/0.45----------> is correct
case D) 3.15/(45/100)=3.15*100/45=315/45-------------> is not (3.15/0.45)
case E) 0.45/3.15------------> is not (3.15/0.45)
the answers are
case B) 3.15/0.45-----------> is correct
case C) 3.15*(1/0.45)=(3.15*1)/0.45--------> 3.15/0.45----------> is correct
Which logarithmic equation is equivalent to 3^2 = 9?
Answers
㏒ₓᵃ =n and a=x^n
we have ㏒₃ 9=2
3 is the base
Answer:
[tex]log_3(9)=2[/tex]
Step-by-step explanation:
[tex]3^2 = 9[/tex]
Logarithmic form is the reverse of exponential form
To convert exponential form in to log form we use a rule
[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]
WE apply the same rule in our exponential equation to convert it into log form
[tex]3^2 = 9[/tex]
The base of exponent is the base of log
[tex]log_3(9)=2[/tex]
what is community property and associative property
Answers
Associative property (again, of multiplication and addition) means that it doesn't matter how you solve an expression if the same operand is used and some numbers are grouped. For eg. 3 * (5 * 4) = (3 * 5) * 4.
Final answer:
The associative property in mathematics states that the way in which numbers are grouped or associated does not affect the result of the operation. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership.
Explanation:
The associative property is a property in mathematics that states that the way in which numbers are grouped or associated does not affect the result of the operation. For example, for addition, the associative property states that (a + b) + c = a + (b + c). This property holds true for addition and multiplication, but not for subtraction and division.
Community property, on the other hand, is a concept in the field of law, specifically property law. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership. It is most commonly associated with community property states in the United States.
Click on ALL the values for n that make this inequality true. There maybe more than one answer.
[tex]120 \geq 10n + 20[/tex]
Possible Answers:
Answers
You can divide by 10 and subtract 2.
12 ≥ n + 2 . . . . . . divide by 10
10 ≥ n . . . . . . . . . subtract 2
The values that will make the inequality true are those that are 10 or less, including 0 and all negative numbers.
help please...........
Answers
Given the volume of Wesley's cube = 8 cubic centimeters.
We know the formula for volume of cube is given as follows :-
Volume of cube = (side) x (side) x (side)
8 = (side)³
side = [tex]\sqrt[3]{8} =\sqrt[3]{2*2*2} =2[/tex]
Hence, Wesley's cube dimensions are 2 centimeters.
The square must have side length as 2 centimeters.
If smallest square G represents 1 centimeters, then clearly it is H = 2 centimeters.
So, square H is the final answer.
margaret purchased a doormat measuring 1/2 yard by 2/3 yard for her back door step. If the step is 1/4 square yard, will the mat fit? explain
Answers
[the area of a doormat]=(1/2)*(2/3)---------> 2/6 --------> 0.33 yd²
[the area of the step]= 1/4 --------> 0.25 yd²
[the area of a doormat] > [the area of the step]
0.33 yd² is > 0.25 yd²
therefore
the doormat will not fit because it is too large
the answer is
the doormat will not fit
Final answer:
The doormat measuring 1/2 yard by 2/3 yard will not fit on a step that is 1/4 square yard because the doormat's area, 1/3 square yard, is larger than the step's area.
Explanation:
The question "Will a doormat measuring 1/2 yard by 2/3 yard fit on a step that is 1/4 square yard?" involves understanding of measuring areas in yards and comparing the area of the doormat with that of the step. First, we calculate the area of the doormat by multiplying its length and width (1/2 yard * 2/3 yard = 1/3 square yard).
Next, we compare the area of the doormat, which is 1/3 square yard, to the area of the step, which is 1/4 square yard. Since 1/3 square yard is larger than 1/4 square yard, the doormat will not fit perfectly on the step as it is too big.
A circle is divided into parts. Which sum could represent the angle measures that make up the circle?
Answers
A circle is always going to be 360°.
Use the zero product property to find the solutions to the equation 6x^2-5x=56
Answers
6x² -5x -56 = 0 . . . . . subtract the constant
(3x +8)(2x -7) = 0 . . . .factor*
The zero product property says the product will be zero only when one (or both) of the factors is zero.
First Factor
... 3x +8 = 0
... x + 8/3 = 0 . . . . divide by the coefficient of x
... x = -8/3 . . . . . . subtract 8/3
Second Factor
... 2x -7 = 0 . . . . . . set the factor to zero
... x -7/2 = 0 . . . . . divide by the coefficient of x
... x = 7/2 . . . . . . . add 7/2
_____
*Comment on factoring
There are various ways to do this. In basic terms, we want to find numbers that are factors of the product 6·(-56) whose sum is -5. We found those numbers to be -21 and 16. Then we can rewrite the -5x term using these numbers and factor by grouping.
... 6x² -5x -56 = (6x² -21x) +(16x -56) = 3x(2x -7) +8(2x -7) = (3x +8)(2x -7)
Answer:
B. x = -8/3, or x= 7/2
Step-by-step explanation: