The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.
(a) 1/2 is not a possible zero of the function
The function is given as:
[tex]f(x) =x^3 - 5x + \frac 25[/tex]
For a function,
[tex]f(x) = px^n +......q[/tex]
The list of possible roots is:
[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5
[tex]5f(x) = 5x^3 - 25x + 2[/tex]
So, we have:
[tex]p= 5[/tex]
[tex]q = 2[/tex]
The factors are:
[tex]p =\pm 1, \pm 5[/tex]
[tex]q =\pm 1, \pm 2[/tex]
So, the possible roots are:
[tex]Roots = \pm\frac{1,2}{1,5}[/tex]
Split
[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]
Hence, 1/2 is not a possible zero of the function
Read more about rational zero test at:
https://brainly.com/question/12860313
Which of the following statements is the only
sentence that is error-free?
8) The height of a stack of CD cases is Proportional to the number of CD’s in the stack. A stack of 6 CD’s is 66mm high.* Find the unit rate**
a) How high is a stack of 10 CD’s?
b) Write an equation that relates the height (y) of a stack of CD’s and the number of CD cases(x) in the stack.
Step-by-step explanation:
well, when 6 CD cases are 66 mm high, then 1 CD case is 66/6 = 11 mm high.
a)
therefore, 10 CD cases are 11×10 = 110 mm high.
b)
y = 11x
A volunteer group picked up 3 times as many plastic bottles as cans in their community. The number of papers they picked up was 15 more than of the number
of cans. If the volunteers picked up 288 cans, how many more plastic bottles than papers did they pick up?
try 4,320 for your answer
Please please help!!
Step-by-step explanation:
get add and add on ok
19. The passing marks in an examination is 40%. If Seema gets 130 marks, she fails by ups 2 marks. Find the total marks.
Given :-
Passing marks in an exam is 40% .Seema gets 130 marks and fails by 2 marks.To find :-
The maximum marks for the exam .Solution :-
According to the Question ,
[tex]\dashrightarrow[/tex] Passing marks = 40% .
[tex]\dashrightarrow[/tex] Seema's marks = 130 .
Let us take the maximum marks be x . Then ,
[tex]\dashrightarrow[/tex] Passing marks = 130 + 2
[tex]\dashrightarrow[/tex] Passing marks = 132
And , by question ,
[tex]\dashrightarrow[/tex] 40x/100 = 132
[tex]\dashrightarrow[/tex] x = 132 * 100/40
[tex]\dashrightarrow[/tex] x = 330
Hence the maximum marks for the exam is 330.
Given :
Passing marks in the examination = 40% . Marks obtained by Seema = 130 .So, Let us assume the maximum marks as x .
Also,
Passing marks = 132 [ ∵ Seema got 130 marks and she failed by 2 marks ]
According to the question :
[tex] \\ \tt : \implies\dfrac{40x}{100} = 132 \\ \\ \tt : \implies\dfrac{4 \cancel{0}x}{10 \cancel{0}} = 132 \\ \\ \: \: \: \tt \: : \implies 4x = 132 \times 10 \\ \\ \tt : \implies \: 4x = 1320 \\ \\ \tt : \implies \: x = \frac{1320}{4} \\ \\ \tt : \implies \: x = 330 \: \: \\ [/tex]
Hence, The total marks is 330 .
please try looking at the picture :(( i’m really struggling so much!!
Answer:
4- true
5-true
6-false
7-false
8-true
9-true
Step-by-step explanation:
Follow the letters and the sign of congruence
≅
Make y the subject of the formula
5y - 4h = 18
Answer:
[tex]\displaystyle \large{y=\frac{18+4h}{5} }\\[/tex]
Alternatively, you can use [tex]\displaystyle \large{y=\frac{18}{5}+\frac{4h}{5} }\\[/tex] as an answer.
Step-by-step explanation:
To make y as the subject of equation, we have to find a way to isolate y-variable.
First, add 4h both sides of equation which we obtain:
[tex]\displaystyle \large{5y-4h+4h=18+4h} \\\displaystyle \large{5y=18+4h}[/tex]
Next, we divide both sides by 5 so we can finally have y-isolated equation and thus it becomes the new subject of equation.
[tex]\displaystyle \large{\frac{5y}{5} =\frac{18+4h}{5} }\\\displaystyle \large{y=\frac{18+4h}{5} }[/tex]
Thus the answer is y = (18+4h)/5
Alternatively for solution, you can separate the fraction which we obtain a valid alternative solution.
[tex]\displaystyle \large{y =\frac{18}{5} +\frac{4h}{5} }\\[/tex]
Either one of these solutions work.
_______________
Let me know in the comment if you have any questions.
The table shows the ratio between the number of books ordered and their cost: Number of Books Cost (dollars) 7 14 8 16 9 18 Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid. (10 points)
14/7 = 2
16/8 = 2
18/9 = 2
This shows the cost of one book is $2
Multiply the number of books bought by 2 to get the cost:
1 x 2 = 2
2 x 2 = 4
3 x 2 = 6
Answer: (1,2) (2,4) (3,6)
Starting from the origin (0,0) for every 1 book bought ( x axis) move 2 more up than the previous total (y axis)
Using the 3 ordered pairs in the answer at x value 1 place a dot at y 2, then a dot at x2,y4 and again at x3,y6
Answer:
I'm doing the same test right now the ratios are 1 to 2 but the answers would be 1 to 2, 2 to 4, and 3 to 6 . you have to double the numbers that are shown
Step-by-step explanation:
I didn't copy the guy above it's litterallty simple multiplication hope my answer helped
HELP PLZZZZZZZ with #1
Answer:
Option A, 300 - 20w
Step-by-step explanation:
In a week, she withdraws $20
in w weeks, she will withdraw ; w × 20
= 20w
Balance = Initial amount - Amount withdrawn
= 300 - 20w
Identify the terms and like terms in the expression.3n+7−n−3
Answer:
n
Step-by-step explanation:
In algebra, like terms are terms that have the same variables and powers.
worth 10 points thankyou
Answer:
DCBA
Step-by-step explanation:
What are coordinate of (2,-3) when it is reflected over X axis.
Answer:
the asnwer is (2,3)
Step-by-step explanation:
To qualify for a scholarship, a student must score at least 90% on a written test. The test is 64 questions. Using this metric, what is the greatest number a student can miss and still qualify for the scholarship?
Answer:
6 questions
Step-by-step explanation:
First, you divide the total score of 100 by the 64 questions to get 1.5625 points per question. Next, you divide the lowest score to qualify of 90 by the 1.5625 to get 57.6 questions correct to qualify. Then, you round 57.6 questions correct up to 58 questions correct because a fraction of a question correct doesn't make sense. Finally, you subtract the total number of questions (64) by the required correct answers (58) to get 6 questions you can miss to still qualify for the scholarship.
Maggie's brother is 5 years younger than three times her
age. The sum of their ages IS 43.
How old is Maggie?
Answer:
Step-by-step explanation:
Let Maggie's age = x
The brother's age = 3x - 5
x + 3x - 5 = 43
4x - 5 = 43 Add 5 to both sides
4x - 5 + 5 = 43+5
4x = 48 Divide by 4
4x/4 = 48/4
x = 12
Maggie = 12
Brother = 3*12 - 5
Brother = 36 - 5
Brother = 31
9 13 / 16 + 10 3 / 8 =
Iqbal and Sachin have bookshelves of the same size and holding books of the same sizes. Iqbal's shelf is 7/8 full and Sachin's shelf is 12/15 full. If 351 more books of the same size are distributed among them, then they can fill their shelves completely. How many books does Sachin have now?
a)
864
b)
865
c)
800
d)
850
Answer:
540 books
Step-by-step explanation:
It is given that Iqbal's shelf is 7/8 full ..
→ That Means we can say that, iqbal's shelf is (1 - 7/8) = 1/8 is Empty .....
Similarly,
Sachin's shelf is 12/15 full.
→ That Means we can say that, sachin's shelf is (1 - 12/15) = 3/15 is Empty.....
→ Both total Empty = (1/8 + 3/15)
Taking LCM of denominator ,
→ (15+24 /120)
→ 39/120
→ 13/40 part is Empty in both .
Now, it has been said that, when 351 more books are distributed among them , both shelves filled completely .
So, we can say that :----
→ 13/40 part ---------------- 351
→ 1 part ---------------------- 351*40/13 = 1080 = Total Books in Both Selves .
__________________
Now, since bookshelves of the same size and holding books of the same sizes ,,
→ Both have Books in Each = 1080/2 = 540 books .
From his eye, which stands 1.61 meters above the ground, Jacob measures the angle
of elevation to the top of a prominent skyscraper to be 25°. If he is standing at a
horizontal distance of 281 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.
Step-by-step explanation:
we have a right-angled triangle, that is "hovering" 1.61 m above the ground.
the Hypotenuse (the side opposite of the 90 degree angle) is the line of sight from the eye to the top of the skyscraper.
one leg is the height of the skyscraper (minus the 1.61 m).
the other leg is the ground distance from Jacob to the skyscraper (281 m).
we know already 2 angles : the 90° angle between the ground distance and the skyscraper height. and the 25° between the ground distance and the line of sight.
and as we know that the sum of all angles in a triangle is always 180°, we know that the third angle (between the line of sight and the skyscraper height) is
180 - 90 - 25 = 65°
now we can use the law of sines
a/sin(A) = b/sin(B) = c/sin(C)
(the ratio between a side and its opposing angle)
to get all missing side lengths.
the 25° angle is opposite of the skyscraper height, and the 65° angle is opposite of the ground distance (the only side length we know so far).
so,
height/sin(25) = 281/sin(65)
height = 281 × sin(25)/sin(65) = 131.0324519... m
to get the full height of the skyscraper, we need to add the 1.61 m that the described triangle was "hovering" above ground.
therefore, the height of the skyscraper is
131.0324519... + 1.61 = 132.6424519... ≈ 132.6 m
Perform the operation. (-4x^2-2x-6)-(-7x^2-2x-2)
Answer:
3x²-4
Step-by-step explanation:
1 distribute
(-4x²-2x-6)+7x²+2x+2
2 eliminate redudant parentheses
-4x² -2x - 6+7x² +2x+2
3 Add the numbers
-4x²-2x-4+7x²+2x
4 Combine like terms
3x²-2x-4+2x
5 Combine like terms
3x²-4
Answer:
[tex]3x^{2} -4[/tex]
Step-by-step explanation:
Before solving this you have to know that,
( - ) × ( - ) = ( + )
( + ) × ( + ) = ( + )
( - ) × ( + ) = ( - )
Let us solve now.
[tex](-4x^2-2x-6)-(-7x^2-2x-2)[/tex]
[tex](-4x^2-2x-6)+7x^{2} +2x+2[/tex]
[tex]-4x^2-2x-6+7x^{2} +2x+2[/tex]
Now combine like terms
[tex]-4x^{2}+7x^{2} -2x+2x-6+2[/tex]
[tex]3x^{2} -4[/tex]
Hope this helps you .
Let me know if you have any other questions :-)
Can someone please help me with this question.
How can you tell whether two sets of data, ordered pairs, vary directly?
Answer:
graph them
Step-by-step explanation:
you can tell if you graph them
4200 in the scientific notation.
Answer:
4.2*10^3
Hope This Helps!!!
Answer:
The answer is 4.2×10^3
Step-by-step explanation:
To convert 4200 into scientific notation, follow these steps:
- Move the decimal 3 times to left in the number so that the resulting number, m = 4.2, is greater than or equal to 1 but less than 10
- Since we moved the decimal to the left the exponent n is positive
n = 3
- Write in the scientific notation form, m × 10^n
= 4.2 × 10^3
Therefore, the decimal number 4200 written in scientific notation is 4.2 × 10^3 and it has 2 significant figures.
You are going to a private apple orchard to pick apples. There is a one-time entry fee that everyone pays, and you also pay a certain amount per pound of apples you pick. It costs $46 to buy 5 pounds of apples, and it costs $58 to buy 7 pounds of apples.
The one-time entry fee is $6 and the price per pound is $4.
In order to determine the one time entry fee and the cost to pick an apple per pound, two equations would be formed from the question:
x + 5y = 46 equation 1
x + 7y = 58 equation 2
Where:
x = one-time entry fee
y = price per pound
In order to determine the value of y, subtract equation 1 from 2
2y = 12
y = 12 / 2 = 6
In order to determine the value of x, substitute for y in equation 1:
x + 5(6) = 46
x + 30 = 46
x = 40 - 36
x = 4
For more information, please check: https://brainly.com/question/25802822
Please help I don’t understand this
Answer:
d. √(1/(x+1))
Step-by-step explanation:
Just as operations can be performed on numbers and variables, so can operations be performed on functions. Here, you're asked to simplify the ratio of two functions.
[tex]\displaystyle\left(\frac{g}{f}\right)(x)=\frac{g(x)}{f(x)}=\frac{\sqrt{x-1}}{\sqrt{x^2-1}}=\sqrt{\frac{x-1}{x^2-1}}[/tex]
At this point, you're supposed to know the factoring of the difference of squares:
[tex]\displaystyle=\sqrt{\frac{x-1}{(x-1)(x+1)}}=\boxed{\sqrt{\frac{1}{x+1}}}[/tex]
3-6
5. United States senators serve
year
teims. A senator serving 4 terms
would serve for how many total
years?
Answer:
16
Step-by-step explanation:
1 term is 4 years; and 4 terms times 4 years is 16 years
Name all points collinear with point E.
Answer:
n,c,b
Step-by-step explanation:
Which of the following is an equation of a line perpendicular to the equation
y - 3x +1?
O A = - 3x + 5
B. y --3x+5
O C. y -3x5
O D. y = x+5
Answer:
There is something wrong in the answer options. Please check the equations and formatting.
Step-by-step explanation:
Assuming the referenced equation is y = 3x + 1 (and not y - 3x + 1), we can say the following.
This is written in the form of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
The slope, as I've written it, is 3. Parallel lines will have the same slope (but a different b). Perpendicular lines will have a slope that is the negative inverse of the slope of the reference line. In this case, it would have a slope of -(1/3).
None of the answer options come close to this. So something is wrong in the question, unless "NONE" is an option.
Consider the numbers 54.162 and 5,416.2. Which statements accurately reflect the relationship between the "6" in each number?
Select two (2) that apply.
The 6 in 54.162 has a greater value than the 6 in 5,416.2
The 6 in 54.162 has a smaller value than the 6 in 5,416.2.
a
The value of the 6 in 5,416.2 is 10 times greater than the value of the 6 in 54.162.
The value of the 6 in 54.162 is 10 times greater than the value of the 6 in 5, 416.2.
The value of the 6 in 5,416.2 is 100 times greater than the value of the 6 in 54.162.
The value of the 6 in 54.162 is 100 times greater than the value of the 6 in 5,416.2.
Answer:
1) The value of the 6 in 5,416.2 is 100 times greater than the value of the 6 in 54.162.
2) The 6 in 54.162 has a smaller value than the 6 in 5,416.2.
Step-by-step explanation:
1) 0.06 times 100 equals 6
2) 0.06 < 6
how to find the nth term
Answer:
Write full question
I cannot understand
Step-by-step explanation:
The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.
Y+1=1/5(x-10)
Solve for y
Answer:
y = (x-10 / 5) - 1
Step-by-step explanation:
Hope this helps :)
Answer:
y=1/5x-3
Step-by-step explanation:
y+1=1/5(x-10)
y=-1 +1/5(x-10)
y= -1 +1/5x-2
y=1/5x-3
Solve: x ÷ 0.6 = 8.9
5.34
9.5
8.3
0.07
Answer:
5.34
Step-by-step explanation:
x = 8.9 X 0.6
x = 5.34
Your welcome :)
what is the equation of the line that passes through the point (-6,6) and has a slope of -5/3?
Answer: The equation of the line that passes through the point (-6,6) and has a slope of -5/3 is y = -5/3x + -3.96.
Explanation:
y = 6, x = -6
By putting above values in equation (i)
6 = approximately -1.66 (-6) + b
6 = approximately 9.96 + b
approximately -3.96 = b
b = approximately -3.96
y = -5/3x + -3.96