All potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational rots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.
The rational root theorem suggests that for a polynomial function
f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.
In the question, we are asked to find the potential rational roots of
f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3.
Comparing the given polynomial function with the standard polynomial function f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, we can say aₙ = 15, and a₀ = 3.
By rational root theorem, we know that all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.
Therefore, we can say that p = {factors of ±3} and q = {factors of ±15},
or, p = {±1, ±3}, q = {±1, ±3, ±5, ±15}.
Now, we can write all potential roots by calculating p/q.
p/q = {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}
Therefore, all potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational roots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.
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Please help! Simplify the following expression by combining like-terms.
Step-by-step explanation:
[tex] = 4x - 8y + 6 {x}^{2} + 3x - 5y[/tex]
[tex] = 6 {x}^{2} + (4x + 3x) + ( - 8y - 5y)[/tex]
[tex] = 6 {x}^{2} + 7x - 13y[/tex]
The answer is B.
Answer:
b.) 6x² + 7x - 13y
Explanation:
Given Expression
= 4x - 8y + 6x² + 3x - 5y
collect like terms
= 6x² + 4x + 3x -8y - 5y
combine similar terms
= 6x² + 7x - 13y
is 4+-x equivalent to 4-x
Answer:
Yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
4 + -x ==> 4 - x
Example
x = 3; 4 + (-3) = 4-3 =1
The table and the graph below each show a different relationship between the same two variables, x and y.
How much more would the value of y be on the graph than its value in the table when x = 12?
Answer:
240
Step-by-step explanation:
Using the straight line formula; y=mx+c, take two points, for example, (4, 80) and (5, 100)
m=change in y/change in x, so;
m=(100-80)/(5-4)= 20
Take point (4, 80)
80=20×4 + c
80-80=c=0
so y=20x
y=20×12=240
Sonam says that the 20th figure in this pattern has 400 small triangles. do you agree? explain your thinking.
Answer:
No. There should be 210 small triangles
Step-by-step explanation:
The number of small triangles in these figures forms a sequence
Fig No Small Triangles
1 1
2 3 (1+2)
3 6 (1+2+3)
So the nth figure should have 1+2+3+.....+(n-1)+ n
1+2+3+.....+(n-1)+ n = [tex]\frac{n (n-1)}{2}[/tex]
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210
Factor this expression completely 9x^2 - 72x + 8
The solution for the given equation will be x=7.8873 and x=0.112699.
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Find the Solution for
9x²−72x+8=0
using the Quadratic Formula where
a = 9, b = -72, and c = 8
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{(-72)\pm\sqrt{(-72)^2-4(9)(8)}}{2(9)}[/tex]
x= [tex]\dfrac{72\pm4896}{\sqrt{18}}[/tex]
The discriminant b2−4ac>0
so, there are two real roots. After solving for plus and then minus we will get two values as follows.
x=7.8873
x=0.112699
Therefore the solution for the given equation will be x=7.8873 and x=0.112699.
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what is
f(-1)=-3x^{2}+7x+4
Step-by-step explanation:
please mark me as brainlest
f(x)=|3x +5| +6
g(x) = 7
Find (f + g)(x).
Answer:
(f+g)(x)
= |3x+5| + 13
Step-by-step explanation:
(f+g)(x) means
f(x) + g(x)
so you add the functions together.
|3x+5| + 6 + 7
And simplify.
|3x+5| + 13
What is the value of y? 17.5ft 12.5ft 11.6ft 16.5ft
Answer:
y = 16.5 ft
Step-by-step explanation:
• in the right triangle BCD :
cos(∠BCD) = 8/14
________
• In the right triangle ABC :
cos(∠BCA) = 14/(8+y)
________
Since ∠BCD and ∠BCA are the same one
then
cos(∠BCD) = cos(∠BCA)
Therefore
[tex]\frac{8}{14} =\frac{14}{y+8}[/tex]
[tex]\Longleftrightarrow 8(y+8)=14^2[/tex]
[tex]\Longleftrightarrow 8y+64=196[/tex]
[tex]\Longleftrightarrow 8y=196-64[/tex]
[tex]\Longleftrightarrow 8y=132[/tex]
[tex]\Longleftrightarrow y=\frac{132}{8}[/tex]
[tex]\Longleftrightarrow y=16.5[/tex]
If m < 0 and b > 0, the graph of y = mx + b does not pass through which quadrant?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer: Quadrant III
Step-by-step explanation:
The slope is negative and the y-intercept is positive.
This means that it is impossible for both x and y to be negative, and thus it does not pass through Quadrant III
Solve the following equation, and check your solution. Be sure to show all work in order to receive full credit.
Solve -17 + n/5 = 33.
Answer:
n = 250
See solution and check blow.
Step-by-step explanation:
Solution:
-17 + n/5 = 33
Add 17 to both sides.
-17 + 17 + n/5 = 33 + 17
n/5 = 50
Multiply both sides by 5.
n/5 × 5 = 50 × 5
n = 250
Check:
-17 + n/5 = 33
Since we found out that n = 250, substitute 250 for n in the equation.
-17 + 250/5 = 33
Simplify the left side. Divide 250 by 5.
-17 + 50 = 33
Add on the left side.
33 = 33
Since 33 = 33 is a true statement, the solution n = 250 is correct.
Which points can be connected to draw a line of symmetry through this diamond?
Drag and drop an answer to the box to complete the statement. please answer asap!
The line is drawn at point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.
What is a line of symmetry?It is defined as the line which will make exactly two halves with similar shape and size in geometry. For a two-dimensional shape, there is a line of symmetry, and for three-dimensional shapes, there is a plane of symmetry. In other words, if we make a mirror image of the shape around the line of symmetry, we will get exactly the same half portion.
We have given a figure in the picture.
The figure is a quadrilateral(a kite)
As we know, lines of symmetry make exactly two halves with similar shapes and sizes.
IF we draw a line from Point A to Point C we will get two similar and figures in size and shape.
Thus, the line is drawn point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.
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Answer:
point C
Here is a step-by-step explanation of the statement:
1. Draw a point B and a point C on a piece of paper or a computer screen.
2. Draw a straight line that goes through both point B and point C.
3. Fold the paper along the line you just drew, so that the line is the fold line.
4. Notice that if you were to fold the paper exactly in half along the line, point B would match up with its reflection on the other side of the line, and point C would match up with its reflection on the other side of the line.
5. This means that the line you drew is a line of symmetry, because it divides the paper into two identical halves that can be folded together.
6. Therefore, the statement "A line drawn through point B and point C is a line of symmetry" is true.
Genesis is going to see a movie and is taking her 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $3 each. How much total money would Genesis have to pay for her family if she were to buy 6 snacks for everybody to share? How much would Genesis have to pay if she bought x snacks for everybody to share?
Total cost with 6 snacks:
Total cost with x snacks:.
need answer quickly as possibly!
Answer #1:
The total cost with 6 snacks is $78.
Answer #2:
The total cost with x snacks is represented by the expression 60 + 3x.
Step-by-step explanation for answer #1:
Starting off with what we know:
Genesis has 3 kids, so there are 4 people total including Genesis.Each movie ticket is $15.Each snack is $3.To answer the question of how much money Genesis would have to pay for her family if she bought 6 snacks for everybody, first consider the total cost of the movie tickets.
Multiply the total number of people by the cost of each movie ticket:
[tex]4* 15=60[/tex]
Genesis will be paying $60 total only to see the movie with her 3 kids. To find the total cost of both seeing the movie and buying 6 snacks, simply multiply the number of snacks by the cost of each snack:
[tex]6 * 3=18[/tex]
Then, add the total cost of the movie tickets by the total cost of the snacks to achieve your first answer:
[tex]60+18=78[/tex]
The total cost with 6 snacks is $78.
Step-by-step explanation for answer #2:
To find the total cost of "x" snacks (x is being used as a variable term to represent a quantity subject to change), we can create an algebraic expression.
Let "t" represent the total cost.
Since we've established that finding the total cost is just a matter of adding the total cost of movie tickets (60) and the total cost of snacks (3 multiplied by the number of snacks), let "x" represent the number of snacks in the equation to find the total cost with x snacks:
[tex]60+3x=t[/tex]
The total cost with x snacks is represented by the expression 60 + 3x.
Based on the given data, the total cost of 6 snacks: $78. total cost with x snacks: $60 + (3x).
Use the concept of multiplication defined as:
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that,
Genesis is going to see a movie with her 3 kids.
Each movie ticket costs $15.
There are snacks available for purchase at $3 each.
Genesis wants to buy 6 snacks for everybody to share.
To calculate the total cost for Genesis and her 3 kids,
Consider the movie tickets and the snacks.
The cost of the movie tickets can be calculated by multiplying the number of people (4 in this case) by the cost of each ticket ($15).
So, Genesis would have to pay 4 x $15 = $60 for the movie tickets.
Now, let's calculate the total cost if Genesis were to buy 6 snacks for everybody to share.
Each snack costs $3, so 6 snacks would cost 6 x $3 = $18.
Therefore, the total cost for Genesis would be,
$60 (movie tickets) + $18 (snacks) = $78.
If we consider x snacks for everybody to share,
The total cost for snacks would be x $3.
So, the final cost would be $60 (movie tickets) + (3x) (snacks).
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What is the measure of \angle x∠xangle, x?
Angles are not necessarily drawn to scale.
Answer:
Step-by-step explanation:
Comment
x and 133 sit on the the same straight line with MO in common. Therefore they are supplementary which means that the add to 180o.
Equation
x + 133 = 180
Solution
Subtract 133 from both sides
x + 133 = 180
x + 133 - 133 = 180 - 133
x = 47 degrees.
Answer
x = 47
0.33632287 to 3sf please
Answer:
.
Step-by-step explanation:
State true or false. (i) Cube of any odd number is even. F (ii) A perfect cube does not end with two zeros.T (iii) If square of a number ends with 5, then its cube ends with 25. F (iv) There is no perfect cube which ends with 8. F (v) The cube of a two digit number may be a three digit number. F (vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. T
Give reasons why
i. Cube of any odd number is even. False
ii. A perfect cube does not end with two zeros. True
iii. If square of a number ends with 5, then its cube ends with 25. False
iv. There is no perfect cube which ends with 8. False
v. The cube of a two digit number may be a three digit number. False
vi. The cube of a two digit number may have seven or more digits. False
vii. The cube of a single digit number may be a single digit number. True
Reasons
i. Cube of any odd number is even. This statement is false because the cube of odd numbers are also odd
ii. A perfect cube does not end with two zeros. This statement is True because the cube of a two digit number cannot be a 3 digit number and therefore cannot end with two zeros.
iii. If square of a number ends with 5, then its cube ends with 25. This statement is False
Using the illustration
35^2 = 35 x 35= 1225 , its square ends with 5
35^3= 35 x 35 x 35= 42875 which ends with 75
iv. There is no perfect cube which ends with 8. This statement is False.
Using the illustration, the cube of 2 is given thus
2 * 2 * 2 = 8
The cube of 2 ends with 8
v. The cube of a two digit number may be a three digit number. This statement is False.
Using the illustration, 10 is a two digit number
10 * 10 * 10 = 1000
The cube of 10 which is a two digit number is not a three digit number and same applies to all two digit numbers
vi The cube of a two digit number may have seven or more digits. This statement is False because the cube of a two digit number can only be a four digit number.
vii. The cube of a single digit number may be a single digit number. This statement is True because the cube of a single digit number can be a single, two or three digit number.
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write √a^8a^3 as an algebraic expression using a rational exponent
Answer:
A
Step-by-step explanation:
I assume that the whole expression a⁸a³ is under the square root.
then remember 2 things :
1. when multiplying the same base variable (or constant) the result is that single base variable (or constant) to the power of the sum of the exponents.
e.g. x³x² = x⁵ because
x×x×x × x×x = x×x×x×x×x = x⁵
2. a square root as exponent is 1/2.
a cubic root is 1/3 and so on.
therefore
sqrt(a⁸a³) = sqrt(a¹¹) = a^11/2
Find the value of the lettered angle b
Answer:
60°Step-by-step explanation:
30 is an opposite angle (2 angles of 30°)
sum of all angles = 360°
360 - 90 -30 - 150 - 30 = 60°
check
60 + 30 + 150 + 30 + 90 = 360°
the answer is good
Answer:
b = 60
Step-by-step explanation:
A straight line is 180 degrees
30+90+b = 180
Combine like terms
120 +b = 180
b =180-120
b = 60
A table of data is given.
x f(x)
-2 71
-1 13
0 3
1 0.6
2 0.1
Which exponential model best represents the data?
Of(x) = 3(1.2)^x
Of(x) = 2(0.3)^x
Of(x) = 2(3)^x
Of(x)=3(0.2)^x
Answer:
The choice D.
[tex]f(x) = 3 {(0.2)}^{x} [/tex]
Answer:
D
Step-by-step explanation:
Order of elimination:
1. the graph is going down exponentially. This means that the base is less than 1.
A and C are eliminated.
2. When x is equal to 0, f(x) = 3.
Substitute x for 0, and you'll find out that the only one possible is D.
Of the students at milton middle school, 132 are girls. if 55% of the students are girls, how many total students are there at milton middle school?
Answer:
There are 240 students in the school
Step-by-step explanation:
Givens
55% of the total number of students in a school are girls.
Equation
55/100 * x = 132
Solution
Multiply both sides of the equation by 100
55/100x * 100 = 132 * 100
55x = 13200 Divide by 55
55x/55 = 13200/55
x = 240
f(x) = x + 6 , find the ordered pair when x = -2.
(-2,4)
(2,-4)
(-2,-4)
(2,4)
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option A, (-2, 4)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{f(x) = x + 6}[/tex]
Find: [tex]\textsf{f(-2)}[/tex]
Solution: We need to plug in the value -2 into every variable x that we have in the expression and simplify to get the solution.
Plug in the values
[tex]\textsf{f(x) = x + 6}[/tex][tex]\textsf{f(-2) = -2 + 6}[/tex]Simplify
[tex]\textsf{f(-2) = -2 + 6}[/tex][tex]\textsf{f(-2) = 4}[/tex]Therefore, the ordered pair that would match would have a x-coordinate of -2 and a y-coordinate of 4 producing (-2, 4) which matches option A.
which one is it? I will give you twenty points, if you will answer
Answer:
A fraction equivalent to [tex]\frac{1}{2}[/tex] on the number line is [tex]\frac{3}{6}[/tex].
Drag the dot to [tex]\frac{3}{6}[/tex] on the number line.
Step-by-step explanation:
3 is half of 6. To check if this is correct multiply [tex]\frac{1}{2}[/tex] and 3.
[tex]\frac{1}{2}*3=\frac{3}{6}[/tex]
Hope this helps!
If not, I am sorry.
A local mechanic on average services 14 cars a week. How many cars does he service in 4 years
Find the solution:
3x + 2y = 12
-2x + 3y = 5
Answer:
x = 3
y = 2
Step-by-step explanation:
3x + 2y = 12
-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2
2 * 3x + 2y = 12
6x + 4y = 24
3 * -2x + 3y = 5
-6x + 9y = 15 now find the sum of both equation:
6x + 4y -6x + 9y = 24 + 15 add like terms
13y = 39 divide both sides by 13
y = 3 now that we found the value of y we can use this to calculate the value of x
3x + 2y = 12 replace y with 3
3x + 2*2 = 12
3x + 4 = 12 subtract 4 from both sides
3x = 9 divide both sides by 3
x = 3
All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? m e = startfraction z times s over startroot n endroot endfraction.
Simplify each expression
3+8b+4+7b-3
Answer:
9. 15b + 4
10. 4y + 6
11. 15r+72
12. 130n + 20
Step-by-step explanation:
9. Combine Like terms
10. Combine Like terms
11. Distribute the 8 into (r + 9) then combine like terms
12. Distribute 10 into (3n + 2 + 10n) then combine like terms
Answer:
[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]
Step-by-step explanation:
[tex]\textsf {Question 9}[/tex]
[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]
[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]
[tex]\mathsf {15b + 4}[/tex]
[tex]\textsf {Question 10}[/tex]
[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]
[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]
[tex]\mathsf {4y + 6}[/tex]
[tex]\textsf {Question 11}[/tex]
[tex]\mathsf {8(r + 9) + 7r}[/tex]
[tex]\mathsf {8r + 8(9) + 7r}[/tex]
[tex]\mathsf {8r + 7r + 72}[/tex]
[tex]\mathsf {15r + 72}[/tex]
[tex]\textsf {Question 12}[/tex]
[tex]\mathsf {10(3n + 2 + 10n)}[/tex]
[tex]\mathsf {10(13n + 2)}[/tex]
[tex]\mathsf {10(13n) + 10(2)}[/tex]
[tex]\mathsf {130n + 20}[/tex]
What value of n makes the equation true?
-1/5n+7=2
n=
[tex] \frac{ - n}{5} + 7 = 2 \\ \\ \frac{ - n + 35}{5} = 2 \\ \\ - n + 35 = 10 \\ \\ - n = 10 - 35 \\ \\ - n = - 25[/tex]
cancel (-) sign both sides ,
[tex]n = 25.[/tex]
A website sells a dress at £20 and shoes at £25. The website has an offer: Buy a dress and shoes together and get 1 3 off the price. There is also a shipping and handling charge of £4 added at the end, after any discount. If Ruth buys both a dress and shoes, how much will she actually pay?
£36
20+25=45 Take away 13 and it's 32. 32+4 (the shipping charge) is 36. So Ruth pays 36 pounds.
The product of 2 more than 3 times a number and 6 less than 4 times the number (z)
Answer:
[tex]12z^{2} -10z -12[/tex]
Step-by-step explanation:
Let the number be z
2 more than 3 times z ==> 3z + 2
6 less than 4 times z ==> 4z - 6
Product of the above two is
[tex](3z + 2) (4z - 6) \\= (3z)(4z) + (3z)(-6) + (4z)(2) + (2)(-6)\\= 12z^{2} -18z + 8z - 12\\= 12z^{2} -10z -12[/tex]
b) Another sequence is defined using this term-to-term rule, Un+1 = kun + r where k and rare constants. Given that u₁ = 37, U₂= 188 and u3 = 943, find the value of k and the value of r. b ) Another sequence is defined using this term - to - term rule , Un + 1 = kun + r where k and rare constants . Given that u₁ = 37 , U₂ = 188 and u3 = 943 , find the value of k and the value of r .
The values of k and r are given by 5 and 3 respectively.
Here in this problem it is given that,
General formula for the sequence is given by,
[tex]U_{n+1}=kU_n+r[/tex]
First term of the sequence, [tex]U_1=37[/tex]
Second term,
[tex]U_2=188[/tex]
[tex]U_{1+1}=188[/tex], rearranging
[tex]kU_1+r=188[/tex], applying general formula
[tex]37k+r=188[/tex]..........(1)
Third term,
[tex]U_3=943[/tex]
[tex]U_{2+1}=943[/tex], rearranging
[tex]kU_2+r=943[/tex], applying general formula
[tex]188k+r=943[/tex]..........(2)
Now (2) - (1) we get,
188k+r-37k-r = 943-188
151k = 755
k = 755/151 = 5
Hence the value of k is 5.
Substituting the value of k in (1) we get,
37*5+r = 188
185+r = 188
r = 188-185 = 3
Thus the value of r is 3.
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a 48 gram sample of a substance that’s used for drug research has a k value of 0.1325
Using an exponential function, it is found that the half-life of the substance is of 5.23 units of time.
What is the exponential function for the amount of a substance?The function is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which:
A(0) is the initial value.k is the exponential decay rate.The parameters are given by:
A(0) = 48, k = 0.1325.
Hence the equation is:
[tex]A(t) = 48e^{-0.1325t}[/tex]
The half-life is the amount of time for which A(t) = 0.5A(0) = 24, hence:
[tex]A(t) = 48e^{-0.1325t}[/tex]
[tex]24 = 48e^{-0.1325t}[/tex]
[tex]e^{-0.1325t} = 0.5[/tex]
[tex]\ln{e^{-0.1325t}} = \ln{0.5}[/tex]
[tex]0.1325t = -\ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.1325}[/tex]
t = 5.23.
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