According to the Rational Root Theorem, Negative two-fifths is a potential rational root of which function?
f(x) = 4x4 – 7x2 + x + 25
f(x) = 9x4 – 7x2 + x + 10
f(x) = 10x4 – 7x2 + x + 9
f(x) = 25x4 – 7x2 + x + 4
Answers
Answer:
Neither expression satisfies the given rational root.Step-by-step explanation:
To find the right answer, we just need to replace the given root in each expression and see which one gives zero.
First expression.\(f(x)=4x^{4} -7x^{2} +x+25\\f(-\frac{2}{5})= 4(-\frac{2}{5})^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+25=\frac{64}{625}-\frac{28}{25} -\frac{2}{5} +25 \approx 23.58\)
Second expression.\(f(x)=9x^{4}-7x^{2} +x+10=9(-\frac{2}{5} )^{4} -7(-\frac{2}{5} )^{2} +\frac{2}{5} +10 \approx 9.5\)
Third expression.\(f(x)=10x^{4}-7x^{2} +x+9=10(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+9 \approx 7.7\)
Fourth expression.\(f(x)=25x^{4}-7x^{2} +x+4=25(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+4 \approx 3.12\)
Therefore, neither expression satisfies the given rational root.
Answer:
D. f(x) = 25x^4 - 7x^2 + x + 4.
Step-by-step explanation:
The correct answer to your question is D.
Related Questions
Q1) (a) (i) Write x²+8x-9 in the form (x+k)² +h.
PLEASE ANSWER QUICKLY!!!!!
Answers
Answer:
(x+4)^2 -25
Step-by-step explanation:
x²+8x-9 in the form (x+k)² +h.
We need to complete the square.
x^2 +8x -9
Take the coefficient of x.
8
Divide by 2.
8/2 =4
Square it.
4^2 = 16
Add this then subtract i.
x^2 +8x+16 -16 -9
The x^2 +8x+16 becomes (x+4) ^2 and we can simplify the remaining terms.
(x+4)^2 -25
Points B and D are on the perpendicular bisector of ^ABC. The measure of
Answers
The measure of angle ABC in the figure of triangle attached is
< ABC = 46 degreesWhat are perpendicular bisectors?In geometry, a perpendicular bisector is a line or line segment that divides another line segment into two equal parts and is perpendicular to it.
From the definition of perpendicular bisector, we have that
< A = < C
and using triangle ABD
< A + < ABD = 90
< A + 28 = 90
< A = 90 - 28
< A = 62
Using triangle ABC
< A + < ABC + < C = 180
62 + < ABC + 62 = 180
< ABC = 180 - 62 - 62
< ABC = 56
OR
< ABD = < DBC = 28 degrees
and < ABC = < ABD + < DBC adjacent angles
< ABC = < ABD + < DBC
< ABC = 28 + 28
< ABC = 56 degrees
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complete question
The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees
When x > 0 and y > 0, what expression is equivalent to √180x^9y^16 in simplest form?
Answers
Answer:
\(6x^4y^8\sqrt{5x}\)
Step-by-step explanation:
\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)
\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)
\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)
\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)
\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)
\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)
\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)
\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)
\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)
\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)
\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)
\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)
\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)
\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)
\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)
\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)
\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)
\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)
\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)
\(6 \sqrt{5x}\;x^4\;y^8\)
\(\textsf{Rearrange:}\)
\(6x^4y^8\sqrt{5x}\)
\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)
\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)
I need definitions of theses now!!!!!!!!!!!!!!!!!!!!!!!!!!!!
4. Adding and Subtracting Complex Numbers
5. Multiplying Complex Numbers
6. Solving Quadratic Equations with Complex Roots
Answers
Answer: Hope this helps!
Adding and subtracting complex numbers. Just as with real numbers, we can perform arithmetic operations on complex numbers. To add or subtract complex numbers, we combine the real parts and combine the imaginary parts.
Multiplying a complex number by a real number
(x + yi) u = xu + yu i. In other words, you just multiply both parts of the complex number by the real number. For example, 2 times 3 + i is just 6 + 2i. Geometrically, when you double a complex number, just double the distance from the origin, 0.
When the roots of a quadratic equation are imaginary, they always occur in conjugate pairs. A root of an equation is a solution of that equation. If a quadratic equation with real-number coefficients has a negative discriminant, then the two solutions to the equation are complex conjugates of each other.
Answer:
5 was right
Step-by-step explanation:
In one city, 75 percent of residents report that they regularly recycle. In a second city, 90 percent of residents report that they regularly recycle. Simple random samples of 75 residents are selected from each city. Which of the following statements is correct about the approximate normality of the sampling distribution of the difference in sample proportions of residents who report that they regularly recycle?
a. The sampling distribution is approximately normal because both sample sizes are large enough.
b. The sampling distribution is not approximately normal because although the sample size for the first city is large enough, the sample size for the second city is not large enough.
c. The sampling distribution is not approximately normal because although the sample size for the second city is large enough, the sample size for the first city is not large enough.
d. The sampling distribution is not approximately normal because neither sample size is large enough.
e. There is not enough information provided to determine whether the sampling distribution is approximately normal.
Answers
can you show me a picture then maybe i can help you
Verónica Ana y Luis pintan una barda y les pagan 300 cuánto dinero debería recibir cada quien
Answers
Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.
Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).
Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.
Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.
1/4-1/8=_/8 I really need your help im confused
Answers
Answer: it think its 1/8 hope it helps
Step-by-step explanation:
D.
A
B.
A sidewalk in the shape of two triangles, a rectangle, and a square
was built around the edge of a building as shown.
108 ft²
T
6 ft
162 ft²
144 ft²
180 ft²
11
6 ft
What is the area of the sidewalk in square feet?
11
18 ft
30 ft
Answers
The area of the sidewalk is 388 square feet.
How to find the area of the sidewalkTo find the area of the sidewalk you can find the area of each individual shape and add them together.
Area of the first triangle T = (1/2) x 6 ft x 11 ft = 33 sq. ft.
Area of the second triangle = (1/2) x 6 ft x 18 ft = 54 sq. ft.
Area of the rectangle = 6 ft x 30 ft = 180 sq. ft.
Area of the square = 11 ft x 11 ft = 121 sq. ft.
Therefore, the total area of the sidewalk is:
33 sq. ft. + 54 sq. ft. + 180 sq. ft. + 121 sq. ft. = 388 sq. ft.
So, the area of the sidewalk is 388 square feet.
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Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height 5h. Use cylindrical shells to compute the volume V of a napkin ring of height 5 h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h .
Answers
Answer:
V = 1/6 π ( 5h)^3
Step-by-step explanation:
Height of napkin rings = 5h
Compute the volume V of a napkin ring
let a = 5
radius = r
express answer in terms of h
attached below is the detailed solution
zoey wants to use her computer tablet throughout a 6-hour flight. Upon takeoff, she uses the tablet for 2 hours and notices that the battery dropped by 33% from 100% to 67%. How many total hours can Zoey expect from the tablet on a full battery charge?
Answers
The number of hours expected from a full battery charge can be found
using a constant rate of change of battery level.
The number of total hours Zoey can expect from the tablet on a full battery
charge is \(\underline{\mathrm{6. \overline{06} \ hours}}\).
Reasons:
The percentage of the initial charge on the battery = 100%
The percentage drop after she uses the battery for 2 hours = 33 %
Which gives;
33% ≡ 2 hours of battery use
\(\mathrm{1\% \equiv \dfrac{2}{33} \ hours \ of \ battery \ use }\)
\(\mathrm{Full \ battery \ charge \ 100\% \equiv \dfrac{2}{33}\times 100 = 6.\overline{06} \ hours \ of \ battery \ use }\)
The number of hours Zoey can expect from full battery charge = \(\underline{\mathrm{6. \overline{06} \ hours}}\).
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-4/15x =1.44 Enter your answer as a mixed number in simplest form.
Answers
Answer:
\(\frac{ - 4}{15x} = 1.44 \\ - 4 = 15x \times 1.44 \\ 15x = \frac{1.44}{ - 4} \\ 15x = \frac{144}{ - 4 \times 100} \\ 15x = 0.36 \\ x = \frac{36}{100 \times 15 } \\ x = 0.024\)
Answer:
-5 2/5
Step-by-step explanation:
i took the test from k12
The zero of this function is 3 . What do you think "zero of a function" means?
Answers
The zeros of a function are the values of x that, when evaluated in the function, make the output of the function to be zero.
What doe the "zero of a function" means?A function is written in general form as y = f(x)
That notation says that, when we use the input "x" in a given function, that function "transforms" that input x into an output "y"
So y = f(x) is the value that the function takes for the input x.
A zero is an input of the function such that:
0 = f(x)
So the zeros are the inputs that have an output of zero, in this case you know that the function has a zero at 3, and as you can see, when x = 3, the function intercepts the x-axis, which is the axis defined by y = 0.
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Find all zeros? One zero has been given.
Answers
The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,
x = -1 and x = 1/2 respectively
What is the zeros of a function?The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
In the given problem, the zero of the function;
f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are
f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0
f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0
f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0
f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0
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Understanding Dilations and Similarity
1. Each problem shows three figures. Two of the figures in each problem are similar,
with a center of dilation at X.
Draw lines to determine which two figures are similar.
a.
b.
2. Explain how you used lines to determine which figures are similar.
Answers
From the given diagram, figure A is similar to figure C.
The dilation of two figures are given in a figure.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
From the figure given below,
a) Figure A is similar to figure C. We can see from point X the figure A is dilated to figure C.
b) Figure A is similar to figure B. We can see from point X the figure A is dilated to figure B.
Therefore, from the given diagram, figure A is similar to figure C.
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Write an explicit equation for the arithmetic sequence defined byt(n+1)= t(n)-4t(2) = 10
Answers
We need to find the explicit equation for the sequence:
\(\begin{gathered} t\mleft(n+1\mright)=t\mleft(n\mright)-4 \\ \\ t(2)=10 \end{gathered}\)First, we can complete the given table. Notice that when we subtract 4 from the n-th term, we obtain the next term (n+1).
Then, to find a previous term, we can add 4. Thus. we obtain:
n t(n)
0 14+4 = 18
1 10+4 = 14
2 10
3 10-4 = 6
4 6-4 = 2
5 2-4 = -2
Now, observing the above relations, we need to write an expression for t(n) in terms of n:
n t(n)
0 18 = 18 - 0*4
1 14 = 18 - 1*4
2 10 = 18 - 2*4
3 6 = 18 - 3*4
4 2 = 18 - 4*4
5 -2 = 18 - 5*4
...
n 18 - n*4
Therefore, an explicit equation for the sequence is:
\(t(n)=18-4n\)A piece of wood is in the shape of a rectangular prism with a length of 10 inches, a width of 4 inches, and a height of 5 inches. You cut the wood in half to form two pieces of wood, each with a length of 5 inches. What is the percent increase in the total surface area? Round your answer to the nearest hundredth, if necessary. %
Answers
Answer: 18.18%
Step-by-step explanation:
First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:
\($$SA = 2lw + 2lh + 2wh$$\)
where \(\(l\)\) is the length, \(\(l\)\) is the width, and \(\(h\)\) is the height. For the original piece of wood, \(\(l = 10\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\).
After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, \(\(l = 5\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\). The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.
The percent increase in the total surface area is given by the formula:
\($$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$\)
Let's calculate these values.
The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.
et f(t,y) be a continuously differentiable function for all values of t and y. You are told that y = 1 is a solution of the differential equation y = f(t,y). Which of the following can not also be solution? (a) y = 0. (b) y =+2 +5. (c) y = et + 2. (d) y = cos t.
Answers
As per the concept of differentiable function, the impossible solution is y = 0.
In statistics function refers the relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Here we have given that let f(t,y) be a continuously differentiable function for all values of t and y. You are told that y = 1 is a solution of the differential equation y = f(t,y).
Here we need to find in which of the following can not also be solution.
While we looking into the given question we have identified that f(t , y) be a continuously differentiable function for all values of t and y.
Which means that it will definitely gives the solution instead of zero.
And we also know that y = 1 is a solution of the differential equation y = f(t,y).
This will clarifies that 0 must not e the solution of the function.
Therefore, option (a) is correct.
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PLS HELP DUE TODAYY
Luis wants to buy a skateboard that usually sells for $79.79. All merchandise is discounted by 12%. What is
the total cost of the skateboard if Luis has to pay a state sales tax of 6.25%. Round your intermediate
calculations and answer to the nearest cent.
Step-
Answers
$75.14
Explanation:
Got this off of slader, hope it helps :)
Which graph represents 12 = 3x + 4y line a, line b, line c
Answers
Answer:
green line or "b"
Step-by-step explanation:
we can set this up into the slope intercept form
y=mx+b
where m is the slope and b is y intercept
12=3x+4y
-3x -3x
-3x+12=4y
/4. /4. /4
-3/4x+3=y
we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"
hopes this helps please mark rainliest
Find the 19th term (-1,-4,-7,-10)
Answers
Answer:
- 55Step-by-step explanation:
Given sequence:
-1,-4,-7,-10, ...The first term is -1 and the common difference is -3
19th term is:
- 1 + 18(-3) = -1 - 54 = -55a library has 67,982 books. the children's section represents 1/3 of the total books. of the remaining books, 75% are fiction. how many books are in the non-fiction section?
Answers
Answer:
11331 non fiction books
Step-by-step explanation:
Given :
Total books = 67982
Childrens section = 1/3 of total
Number of children's books :
(1/3 * 67982) = 22660 books (approximately)
Books left :
67982 - 22660 = 45,322 books
Fiction books:
75% of remaining
0.75 * 45322
33991.5
= 33991 books
If the only section left is non - fiction, then
Non - fiction books = (45322 - 33991) = 11331
The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range of the transformed function is the same as the parent function, but the domains of the functions are different. The domain of the transformed function is the same as the parent function, but the ranges of the functions are differe
Answers
Both the domain and range of the transformed function are the same as those of the parent function.
What are Range and Domain?
The collection of all potential output values that a function can generate given its domain is known as its range.
The set of all potential input values for which a function is specified is referred to as its domain.
The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.
Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.
A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.
Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.
A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well
So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.
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A rectangular lawn has a width of 3 1/2 yards. The length of the lawn is 2 yards. What is the area
Answers
Answer:
7 yards
Step-by-step explanation:
Multiply length and width wen finding the area so 3 1/2 time 2
Answer:
7 yards
Step-by-step explanation:
Area= LxW
3 1/2 x 2=7
No clue if someone can explain
Answers
Answer:
your trying to find out how much each cookie cost
from looking at this we can see that 2 cookies is 1 dollar so each cookie is 50 cents
Hope This Helps!!!
find the values of x where the graph of the function has a point of inflection given f(x)=x^4-x^3
Answers
f(x) has a point of inflection at x = 0 and x = 1/2.To find the values of x where the graph of the function\(f(x) = x^4 - x^3\) has a point of inflection, we need to find where the second derivative of the function changes sign from positive to negative or vice versa.
The first derivative of the function is:
\(f'(x) = 4x^3 - 3x^2\)
The second derivative of the function is:
\(f''(x) = 12x^2 - 6x\)
Setting f''(x) equal to zero and solving for x gives:
\(12x^2 - 6x = 0\)
6x(2x - 1) = 0
This equation has two solutions:
x = 0, or x = 1/2
To determine whether these values of x correspond to points of inflection, we need to look at the sign of the second derivative on either side of each value.
When x < 0, f''(x) is positive because both \(12x^2\) and -6x are positive. When 0 < x < 1/2, f''(x) is negative because \(12x^2\)is positive but -6x is negative. When x > 1/2, f''(x) is positive again because both \(12x^2\) and -6x are negative.
Therefore, f(x) has a point of inflection at x = 0 and x = 1/2.
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Which function represents a reflection of f(x) = 3/8 (4)^x across the y-axis?
Answers
A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:
(x, y) → (-x, y).
\(f(x) = \frac{3}{8} (4)^x\) → \(g(x) = \frac{3}{8} (4)^{-x}\)
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How to solve
(2.31*10^-6)+(3.41*10^3)
Answers
2.31 x 10^-6+3.41 x 10^3
Convert the decimal to a fraction
231/100 x 10^-6 + 3.41 x 10^3
Multiply
231/100 x 1/10^6 + 3.41 x 1000
Combine
231/100 x 1/10^6 + 3410
Calculate
231/(10^2 x 10^6) + 3410
Answer:
231/10^8 + 3410
Hope it helped :)
Which One Doesn’t Belong?
7.9x
7.9 (-10)
7.9 + x
-79
Answers
Answer:
7.9 + x because they all equal -79 except that one
What is the image of (-8,-8)(−8,−8) after a dilation by a scale factor of \frac{1}{4} 4 1 centered at the origin?
Answers
We conclude that the image of (-8, -8), after a dilation by a scale factor of 1/4, is (-2, -2).
What is the image after the dilation?
For a point (x, y), a dilation by a scale factor of k gives the point (k*x, k*y).
Now, in this case, we have the point (-8, -8) and the scale factor is k = 1/4.
Then, using the above relation, we can write the coordinates of the image after the dilation as:
(-8*(1/4), -8*(1/4)) = (-2, -2).
We conclude that the image of (-8, -8), after a dilation by a scale factor of 1/4, is (-2, -2).
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The price to go to a show is usually $16.50, but if you go on Tuesday, you will only pay $9.90.
What percent of the original price is the discounted ticket price?