Answers
The correct value of the given function is (E) g⁻¹(-3) = 3.
What are functions?A mathematical expression, rule, or law establishes the relationship between an independent variable and a dependent variable (the dependent variable). A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
So, g⁻¹(-3):
x = -1g(x) = -3Then, g(x)·x = (-1)(-3) = 3
Then, g⁻¹(-3) = 3.Therefore, the correct value of the given function is (E) g⁻¹(-3) = 3.
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Related Questions
In the answer section, give the question letter and the word TRUE or FALSE for each of the following:
Answers
a) We rewrite the right side of the expression as:
[tex](-2)^4=((-1)\cdot2)^4=(-1)^4\cdot2^4=1\cdot2^4=2^4\ne-2^4.[/tex]So we see that the expression of point a is FALSE.
b) We consider the expression:
[tex]b^x.[/tex]We take the logarithm in base b, we get:
[tex]\log_b(b^x)=x\cdot\log_b(b)=x\cdot1=x.[/tex]We see that the logarithm of a number x to a base b is just the exponent you put onto b to make the result equal x. We conclude that this expression is TRUE.
c) We know that in any base a, we have:
[tex]\log_a(0)\rightarrow-\infty.[/tex]We conclude that the expression of this item is FALSE.
d) Logarithms are defined only for numbers greater than 0. So we conclude that this expression is FALSE.
e) We consider the expression:
[tex]\log_b(b^{10})-\log_b(1)=10.[/tex]Applying the properties of logarithms, we get:
[tex]\begin{gathered} 10\cdot\log_bb-0=10, \\ 10\cdot1=10, \\ 10=10\text{ \checkmark} \end{gathered}[/tex]We see that this expression is TRUE.
Answera) FALSE
b) TRUE
c) FALSE
d) FALSE
e) TRUE
What is the product in simplest form? State any restrictions on the variable9X^2+9X+18)/(X+2) TIMES (x^2-3x-10)/(x^2+2x-24)
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So, here we have the following expression:
[tex]\frac{9x^2+9x+18}{x+2}\cdot\frac{x^2-3x-10}{x^2+2x-24}[/tex]The first thing we need to notice before simplifying, is that the denominator can't be zero.
As you can see,
[tex]\begin{gathered} x+2\ne0\to x\ne-2 \\ x^2+2x-24\ne0\to(x+6)(x-4)\ne0\to\begin{cases}x\ne-6 \\ x\ne4\end{cases} \end{gathered}[/tex]These are the restrictions on the given variable.
Now, we could start simplyfing factoring each term:
[tex]\begin{gathered} \frac{9x^2+9x+18}{x+2}\cdot\frac{x^2-3x-10}{x^2+2x-24},x\ne\mleft\lbrace2,4,-6\mright\rbrace \\ \\ \frac{9(x^2+x+2)}{x+2}\cdot\frac{(x-5)(x+2)}{(x+6)(x-4)},x\ne\lbrace2,4,-6\rbrace \end{gathered}[/tex]This is,
[tex]9(x^2+x+2)\cdot\frac{(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]So, the answer is:
[tex]\frac{9(x^2+x+2)(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]It could be also written as:
[tex]\frac{(9x^2+9x+18)(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]Round the decimal number to the nearest thousandth.
11.59978
Answers
Answer:
Step-by-step explanation:
The sum of a number and 4 times it’s reciprocal is 13/3. Find the number(s).
Answers
Let the unknown number be "x"
We will write an algebraic equation from the word problem given. Then we will solve for "x".
Given,
Sum of number (x) and 4 times the reciprocal is 13/3
We can convert it into an algebraic equation:
[tex]x+(4\times\frac{1}{x})=\frac{13}{3}[/tex]Now, let's solve for the unknow, x,
[tex]\begin{gathered} x+(4\times\frac{1}{x})=\frac{13}{3} \\ x+\frac{4}{x}=\frac{13}{3} \\ \frac{x^2+4}{x}=\frac{13}{3} \\ 3(x^2+4)=13\times x \\ 3x^2+12=13x \\ 3x^2-13x+12=0 \\ (x-3)(x-\frac{4}{3})=0 \\ x=3 \\ x=\frac{4}{3} \end{gathered}[/tex]The numbers are
[tex]\begin{gathered} 3 \\ \text{and} \\ \frac{4}{3} \end{gathered}[/tex]Let x equals negative 16 times pi over 3 periodPart A: Determine the reference angle of x. (4 points)Part B: Find the exact values of sin x, tan x, and sec x in simplest form. (6 points)
Answers
The reference angle of x is -60 degree. The exact values of sin x, tan x, and sec x is [tex]$\sin \left(-60^{\circ}\right)=-\frac{\sqrt{3}}{2}$[/tex], [tex]$\tan \left(-60^{\circ}\right)=-\sqrt{3}$[/tex], [tex]$\sec \left(-60^{\circ}\right)=2$[/tex]
[tex]x=-\frac{16 \times 180}{3}$$[/tex]
Multiply the numbers: [tex]$16 \times 180=2880$[/tex]
[tex]$x=-\frac{2880}{3}$[/tex]
Divide the numbers: [tex]$\frac{2880}{3}=960$[/tex]
x=-960
Or, x = 2 [tex]\times[/tex] 360 - 960
Follow the PEMDAS order of operations
Multiply and divide (left to right) 2 [tex]\times[/tex]360 : 720 =720-960
Add and subtract (left to right) 720-960: -240
x= -240
Reference angle =180-240
Reference angle= -60
Sin (-60 degree)= [tex]$\sin \left(-60^{\circ}\right)=-\frac{\sqrt{3}}{2}$[/tex]
[tex]$\tan \left(-60^{\circ}\right)=-\sqrt{3}$[/tex]
[tex]$\sec \left(-60^{\circ}\right)=2$[/tex]
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find the surface area of the triangular prism 7 6 7 9
Answers
The surface area of the triangular prism will be 217.95 cm²
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
It is given that,
Base side, a = 7 sm
Base side, b = 6 cm
Base side, c = 7 cm
Height, h = 9 cm
The surface area of a triangle prism: The formula for a triangular prism's surface area is,
A=bh+(b₁+b₂+b₃) units²
where b is the base of a triangular face, h is the height of a triangular face, b₁ is the side of the triangular base, b₂ is the side of the triangular base, and l is the prism's length.
The surface area of the triangular prism will be,
[tex]\rm A = ah + bh + ch + \dfrca{1}{2} \sqrt{-a^4 +2(ab)^2 +2(ac)^2 -b^4+2(bc)^2 -c^4}[/tex]
Substitute the given values,
[tex]\rm A = 7 \times 9 + 6 \times 9 + 7 \times 9 + \dfrac{1}{2} \times \sqrt{-7^4 + 2(7 \times 6)^2 +2 (7\times 7)^2 -6^4 + 2(6 \times 7)^2 - 7^4} \\\\ A = 217.94 \ cm^2[/tex]
Thus, the surface area of the triangular prism will be 217.95 cm².
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solve P=2M+2M for G
G=?
Answers
G=P-2M/2
Step-by-step explanation:
P=2G+2M
p - 2M = 2G
G=P - 2M/2
Circle O shown below has an are of length 47 inches subtended by an angle of 102°.Find the length of the radius, x, to the nearest tenth of an inch.
Answers
We will have the following:
[tex]\begin{gathered} 47=\frac{102}{360}\ast2\pi(x)\Rightarrow\pi(x)=\frac{1410}{17} \\ \\ \Rightarrow x=\frac{1410}{17\pi}\Rightarrow x\approx26.4 \end{gathered}[/tex]So, the radius is approximately 26.4 inches.
Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval.
Answers
We have the following integral in the discrete sum form:
[tex]\lim_{||\Delta||\to0}\sum_{i\mathop{=}1}^{\infty}(6c_i+3)\Delta x_i.[/tex]In the interval [-9, 6].
To convert to the integral form, we convert each element of the discrete sum form:
[tex]\begin{gathered} \lim_{||\Delta||\to0}\sum_{i\mathop{=}1}^{\infty}\rightarrow\int_{-9}^6 \\ 6c_i+3\rightarrow6x+3 \\ \Delta x_i\rightarrow dx \end{gathered}[/tex]Replacing these in the formula above, we get the integral form:
[tex]\int_{-9}^6(6x+3)\cdot dx.[/tex]AnswerMurray has tossed a coin 120 times. The coin landed on heads 54 times. What is the experimental probability that the coin will land on heads on the next toss?
Answers
Answer:
Explanation:
Experimental probability = number of favorable outcomes/number of total outcomes
From the information given,
number of favorable outcomes = 54
number of total outcomes = 120
The experimental probability that the coin will land on heads on the next toss = 54/120
Dividing the numerator and denominator by 6,
The experimental probability that the coin will land on heads on the next toss = 9/20
Work out the following sums and write the answers correctly.
a) £1.76 + £2.04
b) £5.62 + £2.38
Answers
Answer of a is €3.8
Answer of b is €8
Solution :
To get the answer add two decimal number
ie. the sum of first question is €1.76 + €2.04 = €3.8
the sum of second question is €5.62 + €2.38 = €8
Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined.Addends are the numbers added, and the result or the final answer we get after the process is called the sum.To learn more about Addition refer :
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Round to the nearest tenths 62.32
Answers
Answer:62.3
Step-by-step explanation:
The probability that an individual is left-handed is 12%, In a randomly selected class of 30students, what is the probability of finding exactly 4 left-handed students?
Answers
Given that:
- The probability that an individual is left-handed is 12%.
- There are 30 students in the class.
You need to use this Binomial Distribution Formula, in order to find the probability of finding exactly 4 left-handed students :
[tex]P(x)=\frac{n!}{(n-x)!x!}p^x(1-p)^{n-x}[/tex]Where "n" is the number being sampled, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.
In this case:
[tex]\begin{gathered} n=30 \\ x=4 \\ p=\frac{12}{100}=0.12 \end{gathered}[/tex]Therefore, by substituting values into the formula and evaluating, you get:
[tex]P(x=4)=\frac{30!}{(30-4)!4!}(0.12)^4(1-0.12)^{30-4}[/tex][tex]P(x=4)\approx0.2047[/tex]Hence, the answer is:
[tex]P(x=4)\approx0.2047[/tex]Alpha Industries is considering a project with an initial cost of $7.9 million. The project will produce cash inflows of $1.63 million per year for 7 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.58 percent and a cost of equity of 11.25 percent. The debt-equity ratio is .59 and the tax rate is 21 percent. What is the net present value of the project?
Answers
The net present value of the project of the company Alpha Industries is $494,918.
Given,
The initial cost of the project = $7.9 million
Cost of debt = 5.58 percent
Cost of equity = 11.25 percent
The debt-equity ratio= .59
Tax rate = 40 percent.
Let us assume
Equity be $x, then
Total = $1.59x
Respective weights = Pretax cost of debt × (1 - tax rate)
=5.58% × (1 - 0.4)
Respective weights = 3.348%
WACC = Respective costs × Respective weights
WACC = (x ÷ 1.59x × 11.25%) + (0.59x ÷ 1.59x × 3.348)
WACC = 8.318%
The present value of annuity = Annuity × (1 - (1 + interest rate)^ - time period] ÷ Rate
=1.63 × [1 - (1.08317811321)^-7]÷ 0.08317811321
= $1.63 × 5.150256501
The present value of annuity = $8,394,918.10
The net present value = The present value of cash inflows - The present value of cash outflows
= $8,394,918.10 - $7,900,000
The net present value of the the project = $494,918
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can you check to see if my work is correct?
Answers
The Solution.
[tex]P=-\frac{1}{250}T^2+2.8T-394[/tex]To obtain the maximum value of T, we differentiate with respect to x and equate to zero.
[tex]\begin{gathered} \frac{dP}{dT}=2(-\frac{1}{250}T)+2.8\text{ =0} \\ \\ -\frac{1}{125}T+2.8=0 \\ \\ -\frac{T}{125}=-2.8 \\ \text{Cross multiplying, we get} \\ T=125\times2.8=350^oF \end{gathered}[/tex]To get the maximum value of P, we shall substitute 350 for T in the given function.
[tex]\begin{gathered} P=-\frac{1}{250}(350^2)+2.8(350)-394 \\ \\ P=-490+980-394 \\ P=96\text{ percent} \end{gathered}[/tex]The correct answer is T = 350 degrees Fahrenheit , and P = 96 percent.
The length of a rectangle is 5yd less than twice the width, and the area of the rectangle is 33yd^. Find the dimensions of the rectangle.
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Let l be the length of the rectangle and w its width.
From this, we have:
I) w - l = 5
II) l*w = 33
From I, we have w = 5 + l
Applying this to equation II, we have: l(5+l) = 33
l^2 + 5l - 33 = 0
The positive root of this equation is l = [sqrt(157) - 5]/2 = 3.8 yd (rounded to the nearest tenth)
Applying this to equation I, we have: w - 3.8 = 5, which implies w = 5 + 3.8 = 8.8 yd
Please helpp..Use the simple interest formula to determine the missing value.
p=$951.63, r= 6.5%, t= ?, i = $123.71
t=years
Answers
Using the simple interest formula, the value of time (t) is 103 years.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest. Ordinary simple interest and exact simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest. The simple interest calculation formula is the same for both approaches.So, the simple interest rate formula:
A = P (1 + rt)We need to find the value of time (t), then the formula will become:
t = (1/r)(A/P - 1)Insert the values as follows:
t = (1/6.5)(951.63/123.71) - 1)t = 102.96Rounding off: t = 103 years
Therefore, using the simple interest formula, the value of time (t) is 103 years.
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How many solutions does the system have? 2x + 3y = -6 3a - 4y = -12 no solutions O exactly one solution O infinitely many solutions
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Therefore, it has exactly one solution.
use this figure for questions 1 through 4 1. are angles 1 and 2 a linear pair?2. are angles 4 and 5 a linear pair ?3.are angles 1 and 4 vertical angles?4. are angles 3 and 5 vertical angles ?
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Linear pair angles form a straight line, so, both angles add up to 180°.
1 and 2 are not a linear pair.
4 and 5 are a linear pair.
Vertical angles are opposite angles, that are equal.
1 and 4 are vertical angles
3 and 5 are NOT vertical angles-
Translate PreImage coordinates left 9 units and down 1 unit.
Answers
Given
A(11,9)
B(11,3)
C(5,3)
D(5,9)
In the coordinate system (x,y), x determines the horizontal position, and y determines the vertical position. Having a translation of 9 units left, and 1 unit down, means that each coordinate system will be translated as (x-9 , y-1).
[tex]\begin{gathered} (x,y)\Longrightarrow(x-9,y-1) \\ \\ A(11,9)\Longrightarrow A^{\prime}(11-9,9-1)\Rightarrow A^{\prime}(2,8) \\ B(11,3)\operatorname{\Longrightarrow}B^{\prime}(11-9,3-1)\operatorname{\Rightarrow}B^{\prime}(2,2) \\ C(5,3)\operatorname{\Longrightarrow}C^{\prime}(5-9,3-1)\operatorname{\Rightarrow}C^{\prime}(-4,2) \\ D(5,9)\operatorname{\Longrightarrow}D^{\prime}(5-9,9-1)\operatorname{\Rightarrow}D^{\prime}(-4,8) \end{gathered}[/tex]Therefore, the coordinates of the post image are A'(2,8), B'(2,2), C'(-4,2), D'(-4,8).
find slope -1,4 3,15
Answers
Answer:11/4
Step-by-step explanation: First you put the points in m=x1-x2/y1-y2
m=15-4/3+1=15
6. Takao scores a 90, an 84, and an 89 on three out of four math tests. Whatmust Takao score on the fourth test to have an 87 average (mean)?a. 87b. 88c. 85d. 84e. 86
Answers
Consider x as Takao's fourth score.
Then, to achieve an 87 average, we have:
[tex]\begin{gathered} 87=\frac{90+84+89+x}{4} \\ x+263=4\cdot87 \\ x=348-263 \\ x=85 \end{gathered}[/tex]Answer:
c. 85
A money market account offers 1.25% interest compounded monthly. If you want to save $500 in two years, how much money would you need to save per month?
Answers
If you want to save $500 in two years, you need to save $20.58 per month with a 1.25% interest compounded monthly.
How is the periodic saving determined?The monthly savings can be determined using an online finance calculator as follows:
N (# of periods) = 24 months (2 x 12)
I/Y (Interest per year) = 1.25%
PV (Present Value) = $0
FV (Future Value) = $500
Results:
Monthly Savings = $20.58
Sum of all periodic savings = $494.04
Total Interest = $5.96
Thus, the investor needs to save $500 in two years to save $20.58 monthly.
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whats an inequality to compare the numbers
11 and -9
Answers
The inequality comparison
What is Inequality?
Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.
Given, numbers are
11 and -9
an inequality to show all numbers: from (11) to (–9) inclusive
-9 ≤ x ≤ 11
Hence, inequality to compare the numbers
11 and -9 is -9 ≤ x ≤ 11
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Two people start walking at the same time in the same direction. One person walks at 2 mph and the other person walks at 6 mph. In how many hours will they be 2 mile(s) apart?
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Let's define the following variable:
t = number of hours for them to be 2 miles apart
Distance covered by Person A after "t"hours would be 2t or 2 miles times "t" hours.
Distance covered by Person B after "t" hours would be 6t or 6 miles times "t" hours.
If the distance of Person A and B is 2 miles apart after "t" hours, we can say that:
[tex]\begin{gathered} \text{Person B}-PersonA=2miles \\ 6t-2t=2miles\text{ } \end{gathered}[/tex]From that equation, we can solve for t.
[tex]\begin{gathered} 6t-2t=2miles\text{ } \\ 4t=2miles\text{ } \\ \text{Divide both sides by 4.} \\ t=0.5hrs \end{gathered}[/tex]Therefore, at t = 0.5 hours or 30 minutes, the two persons 2 miles apart.
At 0.5 hours, Person A will
Finding the vertex focus directrix and axis of symmetry of a parabola
Answers
Equation:
[tex](y+1)^2=6(x-5)[/tex]The vertex is given by the following formula:
[tex](y-k)^2=4p(x-h)[/tex]where the vertex is (h, k). Thus, in our equation k = -1 and h = 5, and the vertex
is (5, -1).
Additionally, the focus is given by (h+p, k). In our case:
[tex]p=\frac{6}{4}=\frac{3}{2}[/tex]Then, the focus is:
[tex](5+\frac{3}{2},-1)[/tex]Simplifying:
[tex](\frac{13}{2},-1)[/tex]The directrix is x = h - p:
[tex]x=5-\frac{3}{2}=\frac{7}{2}[/tex]Finally, the axis of symmetry is y = -1.
How can I solve this equation if x = -2 and y = -3? 3y (x + x² - y) I've also included a picture of the equation.
Answers
In order to calculate the value of the equation, let's first use the values of x = -2 and y = -3 in the equation and then calculate every operation:
[tex]\begin{gathered} 3y(x+x^2-y) \\ =3\cdot(-3)\cdot(-2+(-2)^2-(-3)) \\ =-9(-2+4+3) \\ =-9\cdot5 \\ =-45 \end{gathered}[/tex]Therefore the final result is -45.
-5 ( -10-2(-3)) to the 2nd power . numerical exponents
Answers
The value of -5 ( -10-2(-3)) to the 2nd power is -6480.
What is an exponent?It should be noted that an exponent simply means the number through which another number can be multiplied by itself.
Based on the information given, it should be noted that PEDMAS will be used. This implies:
P = parentheses
E = Exponents
D = division
M = multiplication
A = addition
S = subtraction
-5 ( -10-2(-3)² will be illustrated thus:
It's important to calculate the value in the parentheses first according to PEDMAS.
= -5 [(-12(-3)]²
= -5 (36)²
= -5 × 1296
= -6480
The value is -6480.
In this case, the concept of PEDMAS is used to get the value.
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Simplify 2f+ 6f help me pls
Answers
Answer:
[tex]{ \tt{ = 2f + 6f}}[/tex]
- Factorise out f as the common factor;
[tex]{ \tt{ = f(2 + 6)}} \\ = 8f[/tex]
graph the line with slope 1/3 passing through the point (4,2)
Answers
To graph a line we need two points, to find a second one we need the equation of the line. The equation of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values given we have:
[tex]\begin{gathered} y-2=\frac{1}{3}(x-4) \\ y-2=\frac{1}{3}x-\frac{4}{3} \\ y=\frac{1}{3}x-\frac{4}{3}+2 \\ y=\frac{1}{3}x+\frac{2}{3} \end{gathered}[/tex]Once we know the equation of a line we find a second point on the line, to do this we give a value to x and use the equation to find y. If x=1, then:
[tex]\begin{gathered} y=\frac{1}{3}\cdot1+\frac{2}{3} \\ y=\frac{1}{3}+\frac{2}{3} \\ y=\frac{3}{3} \\ y=1 \end{gathered}[/tex]Then we have the point (1,1).
Now that we have two points of the line we plot them on the plane and join them with a straight line. Therefore the graph of the line is:
