(27/8)-^2/3??????????/
Answer: 4/9
Step-by-step explanation:
[tex]\displaystyle\\(\frac{27}{8} )^{-\frac{2}{3}} =\\\\(\frac{3*3*3}{2*2*2})^{-\frac{2}{3}}=\\\\ (\frac{3^3}{2^3} )^{-\frac{2}{3}} =\\\\((\frac{3}{2})^3)^{-\frac{2}{3} } =\\\\(\frac{3}{2})^{-\frac{3*2}{3}} =\\\\(\frac{3}{2})^{-2}=\\\\(\frac{2}{3})^2 \\\\\frac{2^2}{3^2} =\\\\\frac{4}{9}[/tex]
Decide whether the table shows a proportional relationship between x and y.
x y
17 2 5/6
5/6 5/36
6 1/6
19 3 1/6
The table shows a proportional relationship between x and y.
In this question, we have been given a table which contains values of x and y.
We need to decide whether the table shows a proportional relationship between x and y.
x y
17 2 5/6
5/6 5/36
6 1/6
19 3 1/6
First we convert the improper fraction in the y-column to proper fraction.
2 5/6 = 17/6
and 3 1/6 = 19/6
so, given table would be,
x y
17 17/6
5/6 5/36
6 1/6
19 19/6
Consider the ratio x/y of each row:
x y x/y
17 17/6 1/6
5/6 5/36 1/6
6 1/6 1/6
19 19/6 1/6
As the ratio x/y is constant, x and y are directly proportional.
Therefore, the table shows a proportional relationship between x and y.
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find inequality : JoJo can eat no more than 25 carbs per meal. Which inequality describes JoJo's situation?
Answer:
Jojo is on a low carb diet
The graph of the function y = x^3 + ax^2 + b has a local minimum point at (4, -11). Find the coordinates of the local maximum. Answer: (0, 21)
Answer:
(0, 21)
Step-by-step explanation:
Stationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
Differentiate the given function:
[tex]\begin{aligned}y & = x^3+ax^2+b\\\implies \dfrac{\text{d}y}{\text{d}x}&=3 \cdot x^{3-1}+2 \cdot ax^{2-1}+0\\\implies \dfrac{\text{d}y}{\text{d}x}& = 3x^2+2ax\end{aligned}[/tex]
Set the differentiated function to zero:
[tex]\begin{aligned} \dfrac{\text{d}y}{\text{d}x}& =0\\ \implies 3x^2+2ax & = 0 \\ \implies x(3x+2a)&=0\end{aligned}[/tex]
Therefore the stationary points occur when:
[tex]\implies x=0[/tex]
[tex]\implies 3x+2a=0 \implies x=-\dfrac{2}{3}a[/tex]
There is a stationary point at (4, -11), therefore substitute x = 4 into the expression for x and solve for a:
[tex]\begin{aligned}x & = 4\\\implies -\dfrac{2}{3}a & = 4\\a & = -\dfrac{3}{2}(4)\\a & = -6\end{aligned}[/tex]
Substitute the found value of a and the point (4, -11) into the function and solve for b:
[tex]\begin{aligned}y & = x^3 + ax^2 + b\\\implies -11 & = (4)^3+(-6)(4)^2+b\\ -11 & = 64-96+b\\b & = -11-64+96\\ b & = 21\end{aligned}[/tex]
Therefore, the function is:
[tex]\boxed{y=x^3-6x^2+21}[/tex]
The other stationary point is when x = 0. Therefore, to find the coordinates of this point, substitute x = 0 into the function:
[tex]\begin{aligned}y & =x^3-6x^2+21\\x=0\implies y & =(0)^3-6(0)^2+21\\ y & =21 \end{aligned}[/tex]
Therefore, the coordinates of the other stationary point are (0, 21).
To determine if a stationary point is minimum or maximum, differentiate the function again:
[tex]\begin{aligned}y & =x^3-6x^2+21\\\implies \dfrac{\text{d}y}{\text{d}x} & = 3x^2-12x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6x-12\\\end{aligned}[/tex]
Substitute the x-coordinate of the stationary point into the second derivative:
[tex]\begin{aligned} \dfrac{\text{d}^2y}{\text{d}x^2} & = 6x-12\\x=0 \implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6(0)-12= -12 \\\end{aligned}[/tex]
[tex]\textsf{As $\dfrac{\text{d}^2y}{\text{d}x^2} < 0$, stationary point $(0,21)$ is a maximum.}[/tex]
Differentiation Rules
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex]
22 out of 25
math students
bring their
calculators to
class how many
students would
have a
calculafors in a
group of 80
math students
HELP PLEASE
thank you so much for the help!!
The independent variable in these equations based on how they are written is x, since y is a function of x here so y depends on the value of x, while x can be changed freely.
So, for each of these questions, plug in the given value of the independent variable for x.
Independent variable equal to 10: 0.1*10 + 5 = 6
Independent variable equal to 50: 0.1*50 + 5 = 10
Independent variable equal to 120: 0.1*120 + 5 = 17
Simplify the expression
Answer:
-8
Step-by-step explanation:
2x/7 =
2(12)/-3 =
24/-3 =
-8
Answer:
-8
Explanation:
Given expression:
[tex]\rightarrow \sf \dfrac{2x}{y}[/tex]
when x = 12, y = -3
Substitute values inside expression:
[tex]\rightarrow \sf \dfrac{2(12)}{-3}[/tex]
multiply
[tex]\rightarrow \sf \dfrac{24}{-3}[/tex]
simplify
[tex]\rightarrow \sf -8[/tex]
A student does an experiment in a lab on the boiling point of water. In the 3 trials, the student gets the temperatures of 99.2, 99.5, 100.2 degrees C. Are these measurements:
Question 2 options:
Accuracy
Neither precision nor accuracy
Both precision and accuracy
Precision
The measurements are precise. Therefore, the correct option is D.
What is precision?It should be noted that precision simply means how close a test is when it's repeated.
On the other hand, it should be noted that accuracy simply means how close the results are to the standard value.
Therefore, when the student does an experiment in a lab on the boiling point of water. In the 3 trials, the student gets the temperatures of 99.2, 99.5, 100.2 degrees, they're precise.
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Simplify the expression below:
-3/7 ( y-28) - 1/21 y
please show your work and i'll give brainliest :,)
A point A (x, y) is translated 7 units to the left and 2 units up. What is the mapping to the new point A’?
(x+2, y+7)
(x-7, y+2)
(x+2, y-7)
(x+7, y+2)
Reason:
7 units to the left means x becomes x-7
2 units up means y becomes y+2
Therefore, the old preimage (x,y) translates or shifts to the new image (x-7, y+2)
Example:
[tex](\text{x},\text{y}) = (3,5)\\\\(\text{x},\text{y})\to(\text{x}-7,\text{y}+2)\\\\(3,5)\to(3-7,5+2)\\\\(3,5)\to(-4,7)\\\\[/tex]
The preimage (3,5) moves to (-4,7) after shifting 7 units left and 2 units up.
Find the average rate of change of the function f(x) = x² + 4x from x₁ = 3 to x₂ = 5.
The average rate of change of the given function is 12.
The average rate of change of function f on interval [a,b] is:
f(b) -f(a)/b-a
we have interval [x₁,x₂]
[x₁,x₂] = [3,5]
f(3) = x²₊4x
f(3) = 3²+4(3)
f(3) = 21
f(5) = x²₊4x
f(5) = 5²+4(5)
f(5) = 45
f(x₂) -f(x₁)/x₂-x₁
⇒ 45-21/5-3
= 24/2
= 12
The average rate of change of function f(x) = x²+4x on interval [3,5]
is 12.
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Solve.
⎧⎩⎨⎪⎪2x−y+2z=−6−3y+z=−22x−3z=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
The solution is (x, y, z) = (-1, 0, -2)
Given equations are:
2x−y+2z=−6 ---------------(1)
−3y+z=−2 ------------------(2)
2x−3z=4 -------------------(3)
From (2), z = -2+3y
Substitute this into (1) and (3)
(1)⇒ 2x-y+2(-2+3y) = -6
⇒ 2x+5y-4=-6
⇒2x+5y = -2
and
(3) ⇒ 2x-3(-2+3y)=4
⇒ 2x-9y+6 = 4
⇒ 2x-9y=-2
Now solve 2x+5y = -2 and 2x-9y=-2
Subtracting the equations above,
14y = 0
⇒y=0
Then from 2x-9y=-2, x = -1
From (2),z = -2+3y
⇒ z = -2
So the solution is (x, y, z) = (-1, 0, -2)
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Let f (x) = 3x2 − 2x + 4. Evaluate f (a + h) and simplify your answer as much as possible.
The expression f(x) = 3 · x² - 2 · x + 4 evaluated at x = a + h is equal to the expression f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4.
How to evaluate and simplify a quadratic equation
In this question we find a quadratic equation, which has to be evaluated at x = a + h and simplified afterwards. Then, the complete procedure is shown below:
f(x) = 3 · (a + h)² - 2 · (a + h) + 4
f(x) = 3 · (a² + 2 · a · h + h²) - 2 · a - 2 · h + 4
f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4
The expression f(x) = 3 · x² - 2 · x + 4 evaluated at x = a + h is equal to the expression f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4.
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write an expression to show the total number of songs on Iris's playlist after w weeks
120 + 4w is the expression to show the total number of songs on Iris's playlist after w weeks.
She total ahs 120 songs already
She downloads or adds 4 songs every week
An expression to show the total number of songs on Iris's playlist after w weeks is:
120 + 4w
What is an mathematical expression?An expression or mathematical expression is a limited combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.
Many authors differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical objects.
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I can’t find a way to flip the number and to swap it as well
Answer:
Reflect over the x axis and than turn 90 degrees clockwise about the origin.
the estimate closest to the length of a pen: 30cm, 160mm, or 16 mm.
Answer:
160 mm.
Step-by-step explanation:
the average pen is 149mm. the average pen is 14.9cm. 160mm is closest.
It would have to be the 160mm.
This is because store-bought pens average 130 and 140mm/ 13 – 14 cm. This is closely followed by pens in the 140 – 150mm range.
Hope this helps!
Have a great day and God bless! :)
4x + 3 = 18 - x help please
Answer:
the answer is x=3
Step-by-step explanation:
Answer:
Please mark my answer as the brainliest, it would mean a lot to me
x = 5
Step-by-step explanation:
4x + 3 = 18 - x
3x + 3 = 18
3x = 15
x = 5
The temperature at
7:00 P.M is 18°F. At
7:00 A.M. the next
day, the temperature
is -12°F. What integer
represents the change
in temperature?
Answer: -30 degrees fahrenheit
Step-by-step explanation: 18 + (-12) = -30
19 more than four times a number is equal to the difference between -86 and three times the number find the number
Answer:
the number is -15
Step-by-step explanation:
if you turn the word problem into an equation it would be
4x+19=-86-3x
with x being the unknown number
the next step is to move the -3x to the other side by adding it to the 4x
your equation should now be 7x+19=-86
next you should move the 19 to the other side by subtracting it from the -86
this leaves you with the equation
7x= -105
lastly you must divide the -105 by seven which leaves you with the answer x= -15
If f(x) = 3x2 – 2x + 4 and g(x) = 5x2 + 6x – 8, find (f +g)(x).
Answer:
[tex](f+g)(x)=8x^{2} +4x-4[/tex]
Step-by-step explanation:
[tex](f+g)(x)=3x^{2} +5x^{2} -2x+6x+4-8=8x^{2} +4x-4[/tex]
Hope this helps
The quadrilaterals ABCD and JKLM are similar.
Find the length x of MJ.
Answer:
x = 4.8
Step-by-step explanation:
since the quadrilaterals are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{MJ}{DA}[/tex] = [tex]\frac{LM}{CD}[/tex] ( substitute values )
[tex]\frac{x}{6}[/tex] = [tex]\frac{2.4}{3}[/tex] ( cross- multiply )
3x = 6 × 2.4 = 14.4 ( divide both sides by 3 )
x = 4.8
a bricklayers assistant starts building a wall laying 50 bricks per hour. Two hours later the master bricklayer joins the assistant and both lay bricks. The master bricklayer lays 80 bricks per hour. write an equation stating that the assistant and the master have laid the same number of bricks. how long has each one worked when they have laid the same number?
Answer:
80t = 50(t+2)master: 3 1/3 hoursassistant: 5 1/3 hoursStep-by-step explanation:
Given an assistant bricklayer laying 50 bricks an hour has worked 2 hours longer than a master bricklayer laying 80 bricks an hour, you want an equation stating they have laid the same number of bricks. You also want to know how long each has worked.
Rate and outputThe output of each bricklayer is the product of the rate at which they lay bricks and the time for which they do it. If t is the time spent by the master bricklayer, their output will be 80t. The time spent by the assistant will be (t+2) hours, and their output will be 50(t+2).
Here is the equation that says their output is the same:
80t = 50(t+2)
TimeSolving the equation for t, we have ...
80t = 50t +100
30t = 100 . . . . . . . . . subtract 50t
t = 3 1/3 . . . . . . . divide by 30
The master bricklayer has worked 3 1/3 hours when they have laid the same number of bricks.
The assistant bricklayer has worked 5 1/3 hours at that time.
__
Additional comment
Each will have laid (80)(3 1/3) = 266 2/3 bricks.
i am sooooo confused please help
The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
f(x) = (x² - 4x + 4) / (x² - 4)
Simplify the equation, then we have
f(x) = (x² - 4x + 4) / (x² - 4)
f(x) = (x - 2)² / [(x - 2)(x + 2)]
f(x) = (x - 2) / (x + 2)
The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).
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nate works at a grocery store. he has 7 1/2 pounds of rasins. heis splitting them into 1/8 pound packages. how many packages can he make
Answer:
Nate can make 60 packages.
Step-by-step explanation:
7 1/2 is equivalent to 7 4/8, or 60/8
Divide 60/8 by 1/8 and you get 60.
Classify the system and identify the number of solutions.
3x + 5y + 4z = −11
2x − 4y − z = −11
4x + 3y − 2z = 11
Answer:
Hello,
Step-by-step explanation:
Only one solution: x=-2, y=3,z=-5
Answer:
consistent, independent; one
Step-by-step explanation:
The solution is (−2, 3, −5). Because the system has one solution, it is consistent and independent.
Write
4/11
as a decimal.
O 0.36
0.36
0.036
0.36
Answer:
0.36
Step-by-step explanation:
2. Select the polynomial functions for which (x+3) is a factor. Select all that apply. (2
f(x)=x²-12x³ +54x² - 108x+81
f(x)=x²-3x³-x+3
f(x)=x+2x¹-23x³-60x²
f(x)= x³ +5x²-3x³-29x²+2x+24
The polynomial functions for which (x+3) is a factor
A polynomial of degree n is a function of the form
f(x) = anx
n + an−1x
n−1 + . . . + a2x
2 + a1x + a0
where the a is a real number (sometimes called the coefficients of the polynomial). Although
this general formula might look quite complicated, particular examples are much simpler. For
example,
f(x) = 4x
3 − 3x
2 + 2
is a polynomial of degree 3, as 3 is the highest power of x in the formula. This is called a cubic
polynomial, or just cubic.
Theorem Polynomial Division: Suppose d(x) and p(x) are nonzero polynomials were
the degree of p is greater than or equal to the degree of d. There exist two unique polynomials,
q(x) and r(x), such that p(x) = d(x) q(x) + r(x), where either r(x) = 0 or the degree of r is
strictly less than the degree of d.
so, if we put x=-3 then f(x) must be equal to zero
here no function satisfies of none of the option is correct for [x+3] factor
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(x +3) is a factor of the function f(x)= x³ +5x²-3x³-10x²+2x-3.
Here, we are given 4 functions. If (x+3) is a factor of any of these equations, then x = -3 and y = 0 must be a solution. Let us check each function one by one-
1. f(x) = x²-12x³ +54x² - 108x+81
putting x = -3, we get-
f(-3) = -3²-12(-3)³ +54(-3)² - 108(-3)+81
= 9+324+486+324+81
= 1,224
Thus, (x +3) is not a factor.
2. f(x)=x²-3x³-x+3
putting x = -3, we get-
f(-3) = -3²-3(-3)³-(-3)+3
= 9+81+9+3
= 102
Thus, (x +3) is not a factor.
3. f(x)=x+2x¹-23x³-60x²
putting x = -3, we get-
f(-3) = -3+2(-3)¹-23(-3)³-60(-3)²
= -3-6+621+540
= 1,152
Thus, (x +3) is not a factor.
4. f(x)= x³ +5x²-3x³-10x²+2x-3
putting x = -3, we get-
f(-3) = -3³ +5(-3)²-3(-3)³-10(-3)²+2(-3)-3
= -27+45+81-90-6-3
= 0
Thus, (x +3) is a factor of the function f(x)= x³ +5x²-3x³-10x²+2x-3.
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Name a point non-coplanar to plane K
W is the point which is non coplanar to plane k .
WHAT IS A COPLANAR/NON-COPLANAR POINT ?A group of points that are in the same plane are said to be coplanar. A coplanar line connects any two or three points. It's possible that four or more points are coplanar.
The coplanar points A, B, C, and D are displayed on the left side of the above figure. Additionally, there are other sets of coplanar points in the box to the right. For instance, the left side of the box's left side is the plane that contains the coplanar points P, Q, X, and W. There are four coplanar points on each of the box's six faces, however they are not the only coplanar point groups. Points Q, X, S, and Z, for instance, are coplanar despite the fact that the plane containing them isn't depicted.
Non-coplanar points are a collection of points that are not all located on the same plane.
Points P, Q, X, and Y in the previous figure are not coplanar. Q, X, and Y are located on the box's top, and P, Q, and X are located on the box's left side, however no flat surface has all four points.
CALCULATIONsince from the figure we can find out that except two points W , Y all the points are on the plane K .
so according to question and given figure we conclude that one of the point which in non coplanar to K is W.
points highlighted in the figure is non coplanar to point k .
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another question i need quickly:
what do you do if the median is 0 and 1?
What if the median is zero?
A variable that can in principle be only zero or positive can only have mean zero if all values in practice are zero. On the other hand, such a variable can and will have median zero if more than half of the values are zero.
Can you have a median of one number?
Median of one number = the number itself.
Find the nth term, the fifth term, and the 100th term, of the arithmetic sequence determined by a = 2 and d = 3
Answer: an=3n-1 a₅=14 a₁₀₀=299
Step-by-step explanation:
a=2 d=3
[tex]\boxed {a_n=a_1+d(n-1)}\\\\a_n=2+3(n-1)\\\\a_n=2+3n-3\\\\a_n=3n-1\\\\a_{100}=3(100)-1\\\\a_{100}=300-1\\\\a_{100}=299\\\\a_5=3(5)-1\\\\a_5=15-1\\\\a_5=14[/tex]