f(0) = -3(0) + 5 = 5
f(-4) = -3(-4) + 5 = 17
f(6) = ½(6) - 4 = -1
f(9) = 2
f(2) = ½(2) - 4 = -3
Using the restraints, find which equation the f(x) function validates and plug it in.
Determine algebraically whether the function is even, odd, or neither: f(x)=3x ³ +5
If xy=3 yz=6 zx=2 find x+y+z
For the following function y = f(x) = 4x^3 - 5
I worked out this Calculus problem, but I keep getting 1/-432 for part c. Can anyone work out the problem step-by-step so I can understand what I’m doing wrong? It would be greatly appreciated.
The answer for each of the differentiation are; f'(-6) = 432; f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432
How to differentiate functions?
1) f(x) = 4x³ - 5
We will differentiate it to get;
f'(x) = df/dx = 12x²
f'(-6) = 12(-6)²
f'(-6) = 432
2) We are given the formula;
x = f⁻¹(y)
Thus;
y = 4x³ - 5
4x³ = y + 5
x³ = (y + 5)/4
x = ∛((y + 5)/4)
f⁻¹(y) = ∛((y + 5)/4)
c) f⁻¹(y) = ∛((y + 5)/4)
df⁻¹/dy = -1/12y²
At f(-6), we have;
df⁻¹/dy = 1/432
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Find BC.
plssss helpp!!!
Answer:
BC is 22.5 mi
Step-by-step explanation:
Using the pythagorean theorem formula. c² = a² + b²
BC² = AB² + AC²
BC² = 19² + 12²
BC² = 361 + 144
BC² = 505
√BC² = √505
BC = 22.5
Therefore BC is 22.5 mi
The Math Club has 23 members and needs to elect officers. They will need a President, Vice President, Secretary, and Treasurer. How many ways can a 4-member committee be formed?
Answer:
212520 different committees
Step-by-step explanation:
Candidates
For a President: 23
For a Vice President: 22
For a Secretary: 21
For a Treasurer: 20
Number of ways: (23)(22)(21)(20) = 212520
Hope this helps
Answer:
To whom it may concern the answer to this problem would be 212,520.
Step-by-step explanation:
Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...
[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]
Remember that the 19! cancel each other out. Hope this helps!
Which expression is equivalent to this polynomial?
x2+12
OA. (X +2v3i)(c – 2v3i)
OB. (x+6i)(x - 6i)
OC. (x + 2√3)²
OD. (x + 2√3)(x − 2√3)
x² + 12 is equivalent to the polynomial (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i).
What are Polynomials?Polynomials are defined as algebraic expressions consisting of constants, variables and exponents combined using operations like addition, multiplication, subtraction and division.
The given expression is x² + 12.
We have the identity (a + b) (a - b) = a² - b²
(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (2[tex]\sqrt{3}[/tex]i)²
= x² - (2² × √3² × i²)
We know that i² = -1, where i is the imaginary number in complex numbers
(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (4 × 3 × -1)
= x² + 12
Hence we get that (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) is equivalent to x² + 12.
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What is the equation of the parabola? (3 points)
A) y = -1/8x^2 +5
B) y = 1/8x^2 +5
C) y = 1/8x^2 - 5
D) y = -1/8x^2 -5
Answer:
A.
Step-by-step explanation:
The parabola opens down, so the "a" value (the number in front of x^2) must be negative. The y-intercept is (0, 5) so the constant must be positive 5.
Please answer all three questions Pleaseeeeee tysmm <3
Answer: 2 3/4 > 2.68 is correct (only)
Step-by-step explanation: 2 3/4 = 2.75, and 2.75 is greater than 2.68
The rest are incorrect. 7.895 * 10^2 (100) = 789.5, and 5.43 * 10^3 (1000) = 5430. So 789.5 > 5430 is false.
Sqrt(63) = 7.93, and 7.93 > 8.11 is false.
Absolute values ( | | ) mean that no matter if it is negative or positive, it will become positive (unless the negative sign is outside the absolute value). 1.5 > 3.2 is false, and even without the absolute value, -1.5 is still less than 3.2
The graphs below have the same shapes. What is the equation for the red graph?
The equation for the red graph is f(x) = -x².
How to depict the equation?From the information given, g(x) = 4 - x².
The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:
(x, y) = (x, y -4).
The equation of the function will be:
f(x) = g(x) - 4
f(x) = (4 - x²) - 4
f(x) = -x²
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Find and prove an inequality relating 100n and n^{3} .
An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
What is inequality?An inequality is comparison of two values, showing if one is less than, greater than, or simply not equal to another value.
Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.
Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
Induction hypothesis:
Suppose 100n ≤ k³ for some positive integer k ≥ 10.
We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.
Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100
≤ k³ + 3k² (∵ k ≥ 10 )
≤ k³ + 3k² + 3k
≤ k³ + 3k²+3k + 1
So 100( k + 1 ) ≤ ( k + 1 )³, which is true.
Hence by the principle of mathematical induction, 100n ≤ k³ for every integer k ≥ 10.
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What should be added to -2 1/9 to get 11
Answer:
u should add 118/9
Step-by-step explanation:
please mark me as brainlest
Find the equation of a line that passes through the point (-2,1) and has a gradient of -3.
Leave your answer in the form
y
=
m
x
+
c
A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.
We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is
y = mx + c...(1), where m is the gradient of the straight line and c is a constant.
Given that the gradient of the given straight line = m = -3.
Putting this value in (1), we get
y = -3x + c ...(2)
Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.
So, 1 = (-3)(-2) + c
i.e. 6 + c = 1
i.e. c = 1 - 6 = -5
(2) can be written as
y = -3x - 5
Therefore the equation of the given straight line is
y = -3x - 5
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What are the domain and range of the function f of x equals the quantity of x squared minus 3 x minus 28, all over x plus 4?
Solve for y.
frankly im confusion
a:4.53
b.4
c.7.47
c.8
Answer:
8
Step-by-step explanation:
Due to lines r & s being parallel to each other, we can apply the rule of alternate interior angles to solve for y in this problem.
Applying this, we'll be obtaining the equation that of:
[tex]116=15y-4[/tex]
We now simply solve for y.
[tex]120=15y\\y=8[/tex]
Therefore, y is equal to 8.
This can be checked by plugging it into the equation:
[tex]15(8)-4[/tex]
[tex]120-4[/tex]
[tex]116[/tex]
And look at that, we got 116 for our answer, exactly the same as the other angle.
Any questions feel free to ask :)
What is 3/4 divided by 1/2
Answer:
1 1/2
Step-by-step explanation:
Convert both fractions into decimals
⇒ 3/4 (0.75) and 1/2 (0.50)
Divide the decimals:
⇒0.75 ÷ 0.50
Find the quotient
⇒ 1.5
Convert the quotient to a fraction
⇒ 1 1/2
Terms:
Operations with fractions
If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).
A. (f + g)(x) = 5x + 11
B. (f + g)(x) = –3x + 5
C. (f + g)(x) = –5x – 11
D. (f + g)(x) = 3x – 5
Answer:
B
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= x + 8 - 4x - 3 ← collect like terms
= - 3x + 5
Answer:
[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]
Step-by-step explanation:
Given functions:f(x) = x + 8g(x) = -4x - 3Solution:Add both functions
(f + g)(x) = x + 8 + (-4x - 3)
(f + g)(x) = x + 8 - 4x - 3
(f + g)(x) = x - 4x + 8 - 3
(f + g)(x) = -3x + 5
[tex]\rule[225]{225}{2}[/tex]
Can anyone please help me with this question?
Karl receives his first mark of the year in his law course. He scores 94th percentile. What is his mark!?
Answer:
Even though only 6% of students scored higher than Karl, we cannot know his personal score based on his percentile. He could have gotten a 62, as long as everyone else [94% of the class] got an even lower score.
So, we cannot know Karl's mark, we are only able to understand Karl's score in relation to the rest of the students in his law course.
Which expression is equivalent to √48x5, if x> 0?
A. 12x³√3x
B. 4x³√3
C. 4x²√3x
D. 12x²√
Answer:
C. 4x²√(3x)
Step-by-step explanation:
if x > 0
[tex]\sqrt{48x^{5}} =\sqrt{48} \times \sqrt{x^{5}}[/tex]
[tex]=\sqrt{16\times 3} \times \sqrt{x^{4}\times x}[/tex]
[tex]=\sqrt{16} \times \sqrt{3} \times \sqrt{x^{4}} \times \sqrt{x}[/tex]
[tex]=4\times \sqrt{3} \times \sqrt{\left( x^{2}\right)^{2} } \times \sqrt{x}[/tex]
[tex]=4\times \sqrt{3} \times x^{2}\times \sqrt{x}[/tex]
[tex]=4\times x^{2} \times \sqrt{3} \times \sqrt{x}[/tex]
[tex]=4\times x^{2}\times \sqrt{3x}[/tex]
Question 9
Write the equation of the line passing through (3,-17) parallel to 8x - 7y=87
Rewriting the equation of the given line in slope-intercept form,
[tex]8x-7y=87\\\\-7y=-8x+87\\\\7y=8x-87\\\\y=\frac{8}{7}x-\frac{87}{7}[/tex]
The slope of the given line is thus 8/7, and since parallel lines have the same slope, the slope of the line we want to find is also 8/7.
Substituting into point-slope form,
[tex]y+17=\frac{8}{7}(x-3)\\\\y+17=\frac{8}{7}x-\frac{24}[7}\\\\\boxed{y=\frac{8}{7}x-\frac{143}{7}}[/tex]
The parabolas y = -x² and y= -x² - 4x + 6 are graphed below. What are the y-values of the solutions to this system of equations?
y= 1,9
y= 1,6
y= -0,6
y= -3,1
Answer:
y = 1, 9.
Step-by-step explanation:
They are the y values of the points of intersection of the 2 parabolas.
y = 1, 9.
[tex] \displaystyle \sum_{n = 1}^{ \infty } {4}^{ - n} [/tex]
evaluation of the sum above
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]
The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.
To find the first term in the series, substitute n = 1 into the expression:
[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]
The common ratio of the geometric series can be found by dividing one term by the previous term:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]
As | r | < 1 the series is convergent.
When a series is convergent, we can find its sum to infinity (the limit of the series).
Sum to infinity formula:
[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]
where:
a is the first term in the seriesr is the common ratioSubstitute the found values of a and r into the formula:
[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]
Therefore:
[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]
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What is 2(x+3) / 4(x+1)
Answer:
x² + 4x + 3
---------------
2
---- => fraction line
If the factors of quadratic function f are (x-7) and (x+3) what are the zeros of function g?
If the factors of quadratic function f are (x – 7) and (x + 3). The solution of the quadratic function f will be the negative 3 and 7.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
If the factors of quadratic function f are (x – 7) and (x + 3).
Then the zeroes of function f will be
(x – 7)(x + 3) = 0
x = 7, -3
Then the solution of the quadratic function f will be the negative 3 and 7.
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Factor the binomial 9t to second power,-4 =
Using subtraction of perfect squares, it is found that the factored expression is:
9t² - 4 = (3t - 2)(3t + 2).
What is the subtraction of perfect squares factoring?It is given as follows:
a^2 - b^2 = (a - b)(a + b)
In this problem, the binomial is given as follows:
9t² - 4.
Hence:
a² = 9t² -> a = 3t.b² = 4 -> b = 2.Hence the factored expression is:
9t² - 4 = (3t - 2)(3t + 2).
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3x+6-2 = 6x-(7/2*9/0)
[tex]3x+6-2 = 6x-( \frac{7}{2} \times \frac{9}{0} ) \\ \\ 3x + 4 = 6x - \frac{63}{0} \\ \\ 3x + 4 = 6x - 0 \\ \\ 4 + 0 = 6x - 3x \\ \\ 3x = 4 \\ \\ x = \frac{4}{3} .[/tex]
The value of x is 4/3 .
Answer: No Solution
Why?
Any number divided by 0 is not defined, but we are given 9/0 in the question. Hence we cannot solve the equation for the value of ‘x’.
A teacher asked her students how many pets they own. Here
are the results:
0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8
On a piece of paper, draw a dot plot to represent the data.
Then determine which answer choice matches the dot plot
you drew.
Step-by-step explanation:
the answer is (c)
because 0 is 3 in number,
1 is 4 in number,
2 is 3in number
3 is 2 in number,
4 is 2 in number,
no 5,6,7
8 is 1 in number
and no 9
The dot plot ( C )is solved and each dot represents one student's response
What is a dot plot?A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.
Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.
Given data ,
Let the data of the number of pets owned by student be represented as A
Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }
The frequency of 0 = 3
The frequency of 1 = 4
The frequency of 2 = 3
The frequency of 3 = 2
The frequency of 4 = 2
The frequency of 8 = 1
In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.
For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.
Hence , the dot plot is solved
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A student wants to simulate 37 birthdays, but she does not have a calculator or software program available, so she makes up 37 numbers between 1 and 365. Is it okay to conduct the simulation this way? Why or why not?
It is not okay to conduct the simulation because people generally favor some numbers.
How to illustrate the information?From the information given, the student wants to simulate 37 birthdays, but she does not have a calculator or software program available.
In this case, it's not okay to conduct the simulation because people generally favor some numbers.
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The following lots of Commodity Z were available for sale during the year. Beginning inventory 9 units at $50 First purchase 16 units at $50 Second purchase 21 units at $59 Third purchase 16 units at $62 The firm uses the periodic system, and there are 23 units of the commodity on hand at the end of the year. What is the ending inventory balance at the end of the year according to the FIFO method?
According to the FIFO method, the ending inventory balance for Commodity Z is $1,405
How much inventory is left under FIFO?FIFO means that earlier inventory is sold first and later inventory would be the last goods left.
Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:
= (16 x 62) + (7 x 59)
= 992 + 413
= $1,405
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Question 7 (2 points)
In the figure below, AABC and AADF are congruent equilateral triangles. Determine the values of x and y-
X =
B
2x+9
D
y=
A
C
6⁰
5x-12
F
2x + 9 = 5x - 12
2x - 5x = - 1- 9
- 3x = - 21
x = 21/3
x = 7
Y = 60°
La diferencia de las medidas de dos ángulos suplementarios es 20% determina el complemento del menor de dichos ángulos
Smaller angle = 50
Larger angle = 130
Let smaller angle be x degree
=> larger angle= [tex]3x - 20[/tex]
Since these angles are supplementary , So
[tex]= > x + 3x - 20 = 180\\= > 4x = 200\\= > x = 50\\= > 3x - 20\\ = > 150 - 20 = 130[/tex]
So smaller angle would be 50 deg & larger angle would be 130 deg.
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