Answers
The inverse function of g(x) is:
[tex]f(x) = -\frac{3}{x + 4}[/tex]
So the correct option is D.
How to get the inverse of g(x)?
Here we have the function:
[tex]g(x) = -\frac{3}{x} - 4[/tex]
Remember that two functions f(x) and g(x) are inverses if:
[tex]f(g(x)) = x\\g(f(x)) = x[/tex]
Then we must have:
[tex]g(f(x)) = -\frac{3}{f(x)} - 4 = x[/tex]
Solving for f(x), we get:
[tex]-\frac{3}{f(x)} - 4 = x\\\\ \frac{3}{f(x)} +4 = -x[/tex]
[tex]\frac{3}{f(x)} = -x - 4\\\\3 = (-x - 4)*f(x)\\\\\frac{3}{-x - 4} = f(x) = -\frac{3}{x + 4}[/tex]
Then the correct option is D.
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Related Questions
The equation represents an ellipse. which point is the center of the ellipse? (−9, 5) (−5, 9) (5, −9) (9, −5)
Answers
The point which is the center of the ellipse whose equation is; (y+5)²/121+(x-9)²/49=1 s in the task content is; (-5, 9).
Which point represents the center of the ellipse whose equation is given as; (y+5)²/121+(x-9)²/49=1?It follows from convention that the equation of an ellipse usually takes the form;
(y-h)²/a²+(x-k)²/b²=1 in which case, the center of the ellipse is given by the point; (h, k).
On this note, By comparison of the actual equation and the standard equation, it follows that;
+5 = -h and consequently, h = -5,
-9 = -k and consequently, k = 9.
Ultimately, the point which is the center of the
ellipse is; (-5, 9).
Remark: The equation of the ellipse which is missing in the task content is; (y+5)²/121+(x-9)²/49=1
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Answer: D. (9, −5)
Not (-5, 9)
Step-by-step explanation:
find the values of A and B
PLEASE HELP GIVING BRAINLIEST
Answers
Factoring the roots, the values of A and B are given as follows:
A = 3z.B = 2.What are the values of A and B?The expression is:
[tex]\sqrt{\frac{45\alpha z^3}{40y}} = \frac{A\sqrt{\alpha z}}{B\sqrt{2y}}[/tex]
We have that:
[tex]\frac{45}{40} = \frac{9}{8}[/tex]
Hence:
[tex]\sqrt{\frac{45\alpha z^3}{40y}} = \sqrt{\frac{9\alpha z^3}{8}} = \sqrt{\frac{9\alpha z^2 \times z}{4 \times 2}} = \frac{A\sqrt{\alpha z}}{B\sqrt{2y}}[/tex]
Hence, comparing the last two equalities:
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What is the simplified form of √100x³6?
O 10x¹8
O 10x6
50x18
O 50x6
Answers
100x^3
50x6
Is the answer for this one
Which of the following sets of ordered pairs represents a function
A.{-8,14) , (-7,-12) , (-6,-10) ,( -5,-8)}
B. {(-4,-14) , (-9,-12) , (-6,-10), (-9,-8)}
C {(8,-2) , (9,-1),(10,2),(8,-10)}
D. { (-8,-6) , (-5,-3) , (-2,0),(-2,3)}
Answers
Answer: A
Step-by-step explanation:
Each value of x maps onto only one value of y.
Find the indicated term of the geometric sequence.
5th term of 1,
1 /4,1/16,…
Answers
Answer:
[tex]\frac{1}{256}[/tex]
Step-by-step explanation:
So generally a geometric sequence can be defined as: [tex]a_n=a_1(r)^{n-1}[/tex] which is the explicit form. The r, is what each previous term is being multiplied by to get the next value which is evident in the recursive form: [tex]a_n = r(a_{n-1})\\[/tex]. Knowing this we can take two values which are "next" to each other to find what r is. In this case I'll just is 1 and 1/4, given these two values we know that: [tex]\frac{1}{4} = 1 * r[/tex], 1*r is just r... so what each term is being multiplied by is 1/4. So let's plug the values into the explicit formula: [tex]a_n=(\frac{1}{4})^{n-1}[/tex] (I didn't put an a_1 value in front, since it's just 1... so it's a bit redundant). Anyways using this formula we simply plug in 5 as n into the equation to find the 5th term: [tex]a_5 = (\frac{1}{4})^{5-1} = (\frac{1}{4})^4 = \frac{1^4}{4^4} = \frac{1}{256}[/tex]
PLEASE BELP IM ACTUALLY REALLY STUCK
Answers
Answer: 4
Step-by-step explanation:
Slope is rise over run (up over sideways) from two points.
The two points shown are (0,4) and (-2,-4).
By counting, you can find the slope, which is 8/2 = 4.
52 = -5x - 3 i need help with a math test and this one question i do not understand
Answers
Answer:
x=-52/5-i3/5Step-by-step explanation:
[tex]52 = - 5x - 3i...given \: expression \\ - 5x - 3i = 52...switch \: sides \\ - 5x - 3i + 3i = 52 + 3i...add \: 3i \: to \: both \: sides \\ - 5x = 52 + 3i...simplify \\ \frac{ - 5x}{ - 5} = \frac{52}{ - 5} + \frac{3i}{ - 5} ...divide \: both \: sides \: by \: - 5 \\ x = \frac{ - 52}{5} - i \frac{3}{5} ...simplified[/tex]
Suppose the expression a(b)n models the approximate number of people who registered for a dance program every day since the registration started, where a is the initial number of people who registered, b is the rate of increase in the number of people who registered every day, and n is the number of days since the registration started.
If the expression below models the registration for a particular dance program, what is the correct interpretation of the second factor?
Answers
There were 2.07 times as much people that applied in the fourth month than in the first month.
What is an exponential function?An exponential function is one that grows or decreases in an exponential manner. Thus, for any exponential function we can write; f(x) = ax^±n. The term a is the initial value x is the rate of change while n is the time elapsed. The positive sign is used for an exponential increase while the negative sign is used for an exponential decrease.
Thus we have;
f(x) = 27(1.2)^4
This shows us that the time elapsed is four months and f(x) = 2.07.
Therefore, there were 2.07 times as much people that applied in the fourth month than in the first month.
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Six cards with the numbers 1 to 6 are randomly placed face down on a table. what is the probability that a card with a 4 is chosen?
Answers
Answer:
P(draw 4) = 1/6
Step-by-step explanation:
Six cards means: n(s) = 6
The cost of a flight is related to the distance traveled:
Miles 225 1,100 1,375 1,675 1,950 2,250
Cost ($) 50.3 111 143 187 214 196
Find the linear regression equation that models this data.
Answers
The linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:
C(m) = 0.08316m + 31.36331
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (x,y) are given as follows:
(225, 50.3), (1100, 111), (1375, 143), (1675, 187), (1950, 214), (2250, 196).
Hence, inserting these points in the calculator, the linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:
C(m) = 0.08316m + 31.36331
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The Venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet. Enter your answers in the boxes to complete the two-way table based on the given data.
Answers
The complete table is
Dog Not Dog Total
Cat 31 10 41
Not cat 24 7 31
Total 55 17 72
Given a venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet as shown in figure which is attached below.
In the figure cat and dog are overlapping which means 31 people like both.
The people that like only dog but not cat are 24 and the people that like only car but not dog is 10.
The people that like not cat not dog is 31-24=7.
The total people that like cats are 31+10=41 and the total people that dont like cat is 24+7=31
The total people that like dogs are 31+24=55 and the people that didn't like dogs are 31+10-24=17 and the total people that like both dog and not dog and also like cat and not cat is 55+17=41+31=72.
Hence, the complete table is shown in attached figure for the given venn diagram.
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The function f has the property that, for all x, 5(f)x=f(5x). If f(20)=40, what is the value of f(4)?
Answers
Using the given property, we conclude that:
f(4) = 8
What is the value of f(4)?
We know that our function has the property:
5*f(x) = f(5*x)
Now, we also know that:
f(20) = 40
Notice that we can rewrite:
f(20) = f(5*4)
Using the above property, we know that:
f(20) = f(5*4) = 5*f(4) = 40
Using the last part:
5*f(4) = 40
f(4) = 40/5 = 8
f(4) = 8
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Which system of inequalities is shown?
O A. y
y< 4
) B. y>x
y > 4
O C. y>x
y < 4
y > 4
Answers
Answer:
y < x
y < 4
Step-by-step explanation:
Dotted line means < or >, and since the shaded region is below the lines y = 4 and y = x, the answer is A.
Divide the following polynomials. Then place the answer in the proper location on the grid. Write the quotient and remainder as a sum in this format: quotient, remainder/ divisor. Do not include parentheses in your answer. 8y square- 4y+1 over 2y-1
Answers
For the division of the given polynomials, quotient = 4y and remainder =1
What is a polynomial?Algebraic expressions called polynomials include constants and indeterminates.
A specific kind of expression is a polynomial. A mathematical statement without the equals symbol (=) is called an expression.
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Constants and variables are components of a polynomial.
A polynomial is written in its standard form when its descending power of the variable is used.
[tex]\frac{8y^{2}-4y+1 }{2y-1}[/tex]
Quotient = 4y
Remainder = 1
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A submarine model starts at 8 m above the bottom of the pool. It gradually goes down at a rate of 1\2 m\s
a) Graph the relation on the grid provided. Label the axes.
b) Write an equation to represent the relation.
Pleasee
Answers
The equation that represents the relation is y = 8 - 0.5x
How to graph the relation?The given parameters are:
Start = 8m
Rate = 1/2 m/s
The linear equation that represents the submarine movement is:
y = Start - Rate * x
This gives
y = 8 - 1/2 * x
Evaluate
y = 8 - 0.5x
Hence, the equation that represents the relation is y = 8 - 0.5x
See attachment for the graph
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If the probability that a chef likes carrots is 0.13, the probability of those who like broccoli is 0.72, and the probability of those who like neither is 0.22, what is the probability of those who like both
Answers
Taking into account definition of probability, the probability of those who like both is 0.07 or 7%.
Definition of ProbabitityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Events and probability in this caseIn first place, let's define the following events:
C: The event that a chef likes carrots.B: The event that a a chef likes broccoli.Then you know:
P(C)= 0.13P(B)= 0.72In this case, considering the definition of union of events, the probability that a chef likes carrots and broccoli is calculated from:
P(C∪B)= P(C) + P(B) -P(C∩B)
Then, the probability that a chef likes carrots and broccoli is calculated as:
P(C∩B)= P(C) + P(B) -P(C∪B)
In this case, considering the definition of the complementary event and its probability, the probability that a chef likes NEITHER of carrots and broccoli is calculated as:
P [(C∪B)']= 1- P(C∪B)
In this case, the probability of those who like neither is 0.22
0.22= 1 - P(C∪B)
Solving
0.22 - 1= - P(C∪B)
-0.78= - P(C∪B)
- (-0.78)= P(C∪B)
0.78= P(C∪B)
Now, remembering that P(C∩B)= P(C) + P(B) -P(C∪B), you get:
P(C∩B)= 0.13 + 0.72 -0.78
Solving:
P(C∩B)= 0.07= 7%
Finally, the probability of those who like both is 0.07 or 7%.
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Quick please!!
What’s the distance between the following points?
Answers
Answer:
answer is 6^2 × 6^2 = squate root 72
distance equals 8.485
Answer:
6[tex]\sqrt{2}[/tex] ≈ 8.49 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = ( 8, - 9 )
d = [tex]\sqrt{(8-2)^2+(-9-(-3))^2}[/tex]
= [tex]\sqrt{6^2+(-9+3)^2}[/tex]
= [tex]\sqrt{36+(-6)^2}[/tex]
= [tex]\sqrt{36+36}[/tex]
= [tex]\sqrt{72}[/tex]
= [tex]\sqrt{36(2)}[/tex]
= [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex]
= 6[tex]\sqrt{2}[/tex] units ← exact length
≈ 8.49 units ( to 2 dec. places )
Find 8. Round to the nearest degree.
OA. 68°
OB. 69°
OC. 22°
OD. 21°
Answers
Answer:
A
Step-by-step explanation:
[tex]\cos \theta=\frac{3}{8} \\ \\ \theta=\cos^{-1} \left(\frac{3}{8} \right) \\ \\ \theta \approx 68^{\circ}[/tex]
Use the grouping method to factor this polynomial completely. 3x^3+12x^2x+8
Answers
Answer:171x+8
Step-by-step explanation:
3x^3+12x^2x+8
=27x+144x+8
=171x+8
Analyze the diagram below and complete the instructions that follow. (7x - 3) (12x -7) Solve for x.
Answers
Answer:
Step-by-step explanation:
(7x-3)(12x-7)
we are solving for x and we are multiplying.
we start with the x's 7x*12x= 84x
-3*-7=21
so now we have
84x+21=0
the 0 is a placer for answering the question
we minus 21 to both sides
84x=-21
now we divide
84/-21= -4
x=-4
can someone please help me
Answers
The trigonometric values are:
[tex]cos(\frac{3\pi}{4})=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=\frac{1}{\sqrt{2} }[/tex]
Values of trigonometric identities:The given trigonometric identities are:
[tex]cos(\frac{3\pi}{4} )\\\\sin(\frac{3\pi}{4})[/tex]
Note that:
[tex]\pi=180^o\\\\\frac{3\pi}{4}=135^0[/tex]
Therefore, using the calculator for the given expressions:
[tex]cos(\frac{3\pi}{4})=cos135^0=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=sin135^0=\frac{1}{\sqrt{2} }[/tex]
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WILL MAKE BRAINLIEST!! Solve for x.
Answers
[tex]3x + 2 = 47 \\ 3x = 47 - 2 \\ 3x = 45 \\ x = \frac{45}{3} = 15[/tex]
WILL MAKE BRAINLIEST!!
Solve for x.
Answers
Answer:
8
Step-by-step explanation:
51 + 4x + 7 = 90 - combine like terms
58 + 4x = 90 - subtract 58 from each side
4x = 32 - divide both sides by 4
x = 8
Answer:
x = 8
Step-by-step explanation:
The red square indicates that there is a right triangle. All right triangles have angles equal to 90°. Therefore, we can find the value of "x" by setting the sum of both the interior angles to 90°.
(4x + 7) + 51° = 90° <----- Sum of both angles is 90°
4x + 58 = 90° <----- Combine 58 and 7
4x = 32 <----- Subtract 58 from both sides
x = 8 <----- Divide both sides by 4
Given f(x) =
8x+1
2x-9
what is the end behavior of the function?
ONA
LR
OAS X→∞, f(x) → 9; as x→ ∞, f(x) → 9.
-
OAS X→∞, f(x) →-9; as x, f(x) → -9.
OAS X →∞, f(x) → -4; as x → ∞, f(x) → -4.
As
OAS X-∞, f(x)→ 4; as x→ ∞, f(x)→ 4.
O
BASSENG
D
se
Answers
The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is [tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex].
The last option is correct.
What is the range of the function?The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.
The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.
From the information given:
[tex]\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}[/tex]
Inverse of [tex]\mathbf{\dfrac{8x +1}{2x -9 }}[/tex] becomes [tex]\mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}[/tex]
The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:
[tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex]
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Write the following Arithmetic Sequence using an Explicit Formula: a1 = 14 ,an = an-1 – 6 A.) an = 6 – 14(n – 1)
B.) an = 14 – 6(n – 1)
C.) an = 6 + 14(n – 1)
D.) an = 14 + 6(n – 1)
Answers
The explicit formula for the sequence is an = 14-6(n-1)
Arithmetic sequenceThis are sequence that has. a common difference that is the difference between the preceding and sthe explicit formula for the sequence is an = 14-6(n-1) is equal.
Given the following
a1 = 14
an = an-1 - 6
The nth term of the sequence is expressed as:
An = a+(n-1)d
an = 14+(n-1)(-6)
an = 14 -6n + 6
an = 14-6(n-1)
Hence the explicit formula for the sequence is an = 14-6(n-1)
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f(x) = x^2 + 4x + 20 find the real roots. take your time if you want :)
Answers
Answer:
No real roots
[tex]x = -2 + 4i, x = -2 - 4i[/tex]
Step-by-step explanation:
Hello!
We can solve the quadratic by using the Quadratic Formula.
Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Quadratic Equation: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Given our Equation: [tex]f(x) = x^2 + 4x + 20[/tex]
a = 1b = 4c = 20Set the equation to 0 and solve using the formula.
Solve[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-4\pm\sqrt{4^2 - 4(1)(20)}}{2(1)}[/tex][tex]x = \frac{-4\pm\sqrt{16 - 80}}{2}[/tex][tex]x = \frac{-4\pm\sqrt{-64}}{2}[/tex][tex]x = \frac{-4\pm8i}{2}[/tex][tex]x = -2 + 4i, x = -2 - 4i[/tex]There are no real roots to the quadratic.
Joni and Lori began running from the same point. Joni ran 5 miles west while Lori ran 7 miles north. How far apart were they when they finished
Answers
The distance they finishes is 8.6 miles
Given that miles run by Joni is 5 miles and the miles ran by Lori is 7 miles
We need to find the distance they finished
To calculate the total distance along the diagonal line, the Distance Formula first squares the differences between the two x coordinates and the two y coordinates, then adds those squares, and finally calculates their square root.
We know that
According to the Distance formula
= [tex]\sqrt{(5)2+(7)^2}[/tex]
= [tex]\sqrt{25+49}[/tex]
= [tex]\sqrt{74}[/tex]
= 8.6 miles
Therefore the distance finished is 8.6 miles
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I thought of a number,double it,then decreased it by 17. Then I divided the results by 3 I got 15. What was my number
Answers
Answer:
31.
Step-by-step explanation:
We have the equation:
(2x - 17) / 3 = 15 where x is the number to be found.
Multiply both sides by 3:
2x - 17 = 45
2x = 45 + 17 = 62
x = 31.
Tony types at a rate of 30 words per minute. how many words does he type in 3 minutes?
Answers
Answer:
He can type 90 words in 3 minutes.
Step-by-step explanation:
We know how many words he can type per minute already. So now, to find how many words he can type in 30 minutes, simply multiply 3 by 30.
[tex]3 \times 30=90[/tex]
So 90 is our answer.
What is the value of the discriminant for the quadratic equation zero equals 2x^2+x-3
Answers
Discriminant for the quadratic equation [tex]2x^2+x-3=0[/tex] is [tex]d=25[/tex]
How to find the d Discriminant of the quadratic equation ?
We know that the standard quadratic equation
[tex]ax^2+bx+c=0[/tex]
Discriminant of the equation is [tex]d=b^2-4ac[/tex]
Equation given in the question is
[tex]2x^2+x-3=0[/tex]
So we can find the values of [tex]a,b,c[/tex]
[tex]a=2\\b=1\\c=-3[/tex]
Substitute the values
[tex]d=1^2-4*2*(-3)\\d=1+24\\d=25[/tex]
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