Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function.
[tex]f(x)=\frac{1}{(x+3)}-2[/tex]STEP 2: Explain the means to use to find the required values
Since we were given a graph and can not use a caculator, we will be using the graph to get the values.
STEP 3: Plot the given function on a graph
STEP 4: Get the domain of the function
Domain: The domain is all x-values or inputs of a function. The domain of a graph consists of all the input values shown on the x-axis.
[tex]\begin{gathered} The\text{ domain from the graph is given as:} \\ x<-3\text{ or }x>-3 \\ \text{The interval notation is given as:} \\ (-\infty,-3)\cup(-3,\infty) \end{gathered}[/tex]STEP 5: Get the Range of the function
The range is all y-values or outputs of a function.
[tex]\begin{gathered} \mathrm{The\: set\: of\: values\: of\: the\: dependent\: variable\: for\: which\: a\: function\: is\: defined} \\ \text{The range of the graph is given as:} \\ f(x)<-2\text{ or }f(x)>-2 \\ \text{The interval notation is given as:} \\ (-\infty,-2)\cup(-2,\infty) \end{gathered}[/tex]STEP 6: Get the value on which the function is increasing on
[tex]\begin{gathered} \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)>0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: increasing.} \\ \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)<0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: decreasing.} \end{gathered}[/tex]STEP 7: Get the value on which the function is decreasing on
[tex]\begin{gathered} \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)<0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: decreasing.} \\ It\text{ can be s}een\text{ that the function on the graph decreases on the point betw}een\text{ negative infinity} \\ \text{and -3 and the point betw}een\text{ -3 and infinity. }\therefore This\text{ can be written as:} \\ \: \\ \mathrm{Decreasing}\colon-\infty\:STEP 8: Get the values of the asymptotes
An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.
[tex]\mathrm{Vertical}\colon\: x=-3,\: \mathrm{Horizontal}\colon\: y=-2[/tex]
Related Questions
After making your 20th payment of $524.50 on your car loan, you wanted to find out how much is left of your original 5 years loan at 6.2% compounded monthly of $27,000.00. What is the amount of the remaining balance of your car loan?
Answers
The amount of the remaining balance of the car loan is $26293.1103.
Given,
The initial loan amount, P = 27000
The rate of interest, r = 6.2%
Time period, t = 5 years
Interest is compounded monthly.
The 20th payment of the loan = $524.50
We have to find the remaining balance of the car loan.
Here,
Amount, A = P[1 + r/n]^nt
Where,
A is the total amount = principal amount + compound interest
P is the principal amount
r is the rate of interest
n is the number of times compounded
t is the time period
So,
A = P[1 + r/n]^nt
A = 27000 × [1 + 6.2/100/12]^12 × 5
A = 27000 × [12.062/12]^60
A = 27000 × [1.005166]^60
A = 27000 × 1.362
A = 36783.1103
The total amount should be paid after 60 months is $36783.1103
Now,
The 20th payment = $524.50
That is,
524.20 × 20 = 10490
$10490 is paid and the balance amount;
36783.1103 - 10490 = 26293.1103
Therefore,
The amount of the remaining balance of the car loan is $26293.1103.
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Solve for brainliest and 20 points please
Answers
Answer:
C.
Step-by-step explanation:
540
Answer:
540
Step-by-step explanation:
you can use this equation to find the sum of angles for a shape
(n-2)180 with n being the number of sides. Since a pentagon has 5,
its 5-2= 3 then times 180 is 540
A cone has a volume of 3014.4 cubic inches and a radius of 12 inches.what is the height?
Answers
h = 20inches
Explanations:The formula for calculating the volume of a cone is expressed as:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where:
r is the radius
h is the height
Given the following
r = 12 inches
V = 3014.4 cubic inches
Substitute to determine the height
[tex]\begin{gathered} 3014.4=\frac{1}{3}\times3.14\times12^2\times h \\ 3014.4\times3=452.16h \\ h=\frac{9043.2}{452.16} \\ h=20inches \end{gathered}[/tex]Hence the height of the cone will be 20inches
this. this is sucking my soul away.
Answers
Check the picture below.
let's recall that twin sides stemming from a common vertex, make twin angles at the base.
Look at the figure below:If siny - and tan yo =9-what is the value of cos yº? O cos y 90cos yOcos yO cos y® - 90
Answers
The trigonometric functions tangent, sine and cosine are related by the following equation:
[tex]\tan \theta=\frac{\sin \theta}{\cos \theta}[/tex]In this case, the angle is y°, so:
[tex]\tan y\degree=\frac{\sin y\degree}{\cos y\degree}[/tex]Since we want the cosine, we can solve for it ans substitute the given tangent and sine:
[tex]\cos y\degree=\frac{\sin y\degree}{\tan y\degree}=\frac{\frac{9}{c}}{\frac{9}{d}}=\frac{9}{c}\cdot\frac{d}{9}=\frac{d}{c}[/tex]This corresponds to the third alternative.
A space shuttle is moving in a straight line and is traveling at a constant speed. It takes 3 hours to get from A to B and 1 hour to get from B to C. Relative to a suitable set of axes, A is the point (4,-1,7) and B is the point (16,-10,10). Find the coordinates of C.
Answers
We will solve as follows:
First: We will use the i, j, k vector notation to describe each point as a vector:
[tex]A=4i-j+7k[/tex][tex]B=16i-10j+10k[/tex]Now, we have that the time it takes to get from A to B is 3 hours (t1). And the time it takes from B to C is 1 hour (t2).
Second: We determine the speed from A to B:
[tex]v=\frac{B-A}{t_1}\Rightarrow v=\frac{(16-4)i+(-10+1)j+(10-7)k}{3}[/tex][tex]\Rightarrow v=\frac{12i-9j+3k}{3}\Rightarrow v=4i-3j+k[/tex]Third: We now determine the value of C:
[tex]C=B+vt_2\Rightarrow C=(16+4)i+(-10-3)j+(10+1)k[/tex][tex]\Rightarrow C=20i-13j+11k[/tex]So, we would have that the coordinates of C are:
[tex]C=(20,-13,11)[/tex]A cake of mass 550 g has three dry ingredients: flour, sugar and raisins.
There is twice as much flour as sugar and one and a half times as much
sugar as raisins. How much flour is there?
Answers
Answer:
Let flour, sugar, raisins be 3x, 1.5x, x grams respectively.
Total Mass = 550g 3x+1.5x + x = 550g
5.5x = 550 x = 100g
Flour = 3x= 3 x 100 = 300g
Hence, flour in mixture is 300g
Use the table to find the products od the two polynomials. Write your answer in descending order l.
Answers
Answer:
To use the given table to find product of the two polynomials.
Given that,
[tex](x^2+x-2)(4x^2-8x)[/tex]Explanation:
Using the table, we get it as,
we get,
[tex](x^2+x-2)(4x^2-8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x[/tex][tex]=4x^4-4x^3-16x^2+16[/tex]we get,
[tex](x^2+x-2)(4x^2-8x)=4x^4-4x^3-16x^2+16[/tex]Answer is:
[tex](x^2+x-2)(4x^2-8x)=4x^4-4x^3-16x^2+16[/tex]If the function h(x)=(x+7)9 is expressed in the form f∘g with f(x)=x9, find the function g(x).
Answers
Answer:
g(x) = x + 7
Step-by-step explanation:
f(x) = x^9
g(x) = x + 7
f(g(x)) = (x + 7)^9
Can you please also give all forms of the end behavior such as ups/downs, as_,_ , and limits #25
Answers
The given function is a rational function
We will find the zeros of the denominator
[tex]\begin{gathered} 2x+1=0 \\ 2x=-1 \\ x=\frac{-1}{2} \end{gathered}[/tex]The end behavior of the function will be as follows:
[tex]\begin{gathered} x\rightarrow(-\frac{1}{2})^-;f(x)\rightarrow\infty \\ x\rightarrow(-\frac{1}{2})^+;f(x)\rightarrow-\infty \\ x\rightarrow\infty;f(x)\rightarrow\frac{1}{2} \\ x\rightarrow-\infty;f(x)\rightarrow\frac{1}{2} \end{gathered}[/tex]The graph of the function is as follows:
Hi, can you help me answer this question please, thank you!
Answers
Given that
[tex]\begin{gathered} \mu_d=\mu_2-\mu_1=21.1 \\ s_d=14.9 \\ n=8 \end{gathered}[/tex]a) The formula for the test statistics for this sample is,
[tex]t=\frac{\mu_d}{s_d\sqrt[]{n}}[/tex]Therefore,
[tex]\begin{gathered} t=\frac{21.1}{14.9\times\sqrt[]{8}}=0.50067 \\ t=0.50067\approx0.501(3\text{ decimal places)} \\ \therefore t=0.501 \end{gathered}[/tex]Hence, the test statistic for this sample is
[tex]t=0.501[/tex]b)
Calculate the mean height of five men whose weight in kg are 60, 65, 71, 75 and 80
Answers
Answer:
Given the data set of height (inches) for 12 students, calculate the mean: 60, 64, 66, 68, 70, 71, 72, 73, 78, 71, 65, 69
What is the place value of the 6-digit in the number 205.876?
Answers
The place value of 6 in 205.876 is 6 thousandth
The probability of a student eating at the cafeteria and a student living off campus is 0.07, and the probability of a student eating at the cafeteria given that the student lives off campus is 0.20, what is the probability of a student living off campus?
Answers
The probability of a student living off campus is 0.35.
What is the probability?It should be noted that probability simply means the likelihood that something will occur.
Remember the multiplication rule for conditional probability: P(B AND A)=P(B/A)P(A)
Rearranging, we find that P(A)=P(B AND A)P(B/A)
So if we think of A= the event a student lives off campus and B = event a student eats at the cafeteria, then we can plug in the known information to find:
P(A)=0.07 / 0.20
= 0.35
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Write a function to model the geometric sequence in the table. n: (1 2 3 4 5)a: (75 15 3 3/5 3/25)a) f(n) = 75 (1/5) nb) f(n) = 75 (1/5) n-1c) f(n) = 1/5 (75) nd) f(n) = 1/5 (75) n-1
Answers
First let's find the ratio of the sequence, by dividing one term by the term before:
[tex]\begin{gathered} \text{second term: 15} \\ \text{first term: 75} \\ ratio=\frac{15}{75}=\frac{1}{5} \end{gathered}[/tex]So the ratio is 1/5 and the first term is 75.
Now, we can use the following formula for the nth term of a geometric sequence:
[tex]a_n=a_1\cdot q^{n-1}[/tex]Where q is the ratio and a1 is the first term. So we have:
[tex]a_n=75(\frac{1}{5})^{n-1}[/tex]Substituting an by the function f(n), we have:
[tex]f(n)=75(\frac{1}{5})^{n-1}[/tex]So the correct option is b)
Given: GC bisects FGH. Determine the missing measurea. m
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a. Since GC bisects FGH and the angle FGH = 122°, we know that the angle FGC = 122/2 = 61°
b. Since GC bisects FGH and the angle CGH = 42°, we know that the angle FGH = 2*42 = 84°
One weekend 5,780 people saw a new movie at (7 different theaters. Each theater sold tickets at ($7.50 a piece. If each theater received the same number of moviegoers, how much did each theater make?
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Each theater sold tickets at ($7.50 a piece, if each theater received the same number of moviegoers, each theater make $6192.85 using arithmetic operations.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or more quantities. They cover topics like the study of numbers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry. Without applying the laws of arithmetic operations, we are unable to solve the issue. The four fundamental rules of mathematics are addition, subtraction, multiplication, and division.
Let the amount of each theater get be x,
No. of theaters are = 7
Cost of each ticket = $7.50
No. of people = 5780
Then we can say,
7x = 5780 ×7.50
x = [tex]\frac{5780\times7.50}{7}[/tex]
= $6192.85
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Suppose a diver jumps from a ledge that is 115 feet above the ocean and the initial upward velocity is 8 feet per second. The vertical motion of the diver can be modeled by the function h = −t^2 + 8t + 115. How long will it take until the diver enters the water? How do you know?
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The given function of the height of the diver is
[tex]h=-t^2+8t+115[/tex]h is the height in feet
t is the time in seconds
To find the time for the whole motion equate h by 0, as when the diver inter the water his jumper height will be zero. (The surface of the water is the initial position)
[tex]0=-t^2+8t+115[/tex]Switch the 2 sides and change all signs to opposite
[tex]t^2-8t-115=0[/tex]Now, we have a quadratic equation, then we will use the calculator to find the values of t
[tex]\begin{gathered} t=15.44552314 \\ \\ t=-7.445523142 \end{gathered}[/tex]Since time can NOT be a negative value, then we will ignore the 2nd value of t
The answer should be about 15.44 seconds to the nearest 2 decimal place
Create a data set that has 4 values with a mode of 3, a median of 6, and a meanof 10
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We are to create a data set of 4
that is a, b, c, d
mode means a number that occur the most
Median means the middle number
Mean means the average number
in the set, we must have a mode of 3
3, 3,
to get a median of 6, we need a number when we add to three and divide by 2 will give us 6
the number is 9
3 + 9 / 2
12/ 2 =
3, 3 , 9, d
the last number is d and it is unknown
since means is 10
mean = summation of all the numbers in the data set / the total number
the total number is 4
mean = 10
10 = 3 + 3 + 9 + d / 4
cross multiplication
10 x 4 = 3 + 3 + 9 + d
40 = 6 + 9 + d
40 = 15 + d
isolate d
d = 40 - 15
d = 25
therefore, the data set with a mode of 3, median of 6 and a mean of 10 are
3 , 3 , 9, 25
What would be the first step when solving using the substitution method?
2x + 3y = -12
x = 3y + 3
Answers
The first step of substitution method for given system is put x = 3y +3 in place of x into the equation 2x+3y=-12 .
What is the method of substitution for system of equation in two variables ?The system of the equations in two variables x and y consists of two equation of the form a₁ x + b₁ y = c₁
and a₂ x + b₂ y = c₂
where a₁, a₂, b₁, b₂ , c₁, c₂ are constants
For substitution method, first expression of one variable is found from one equation and then put this expression in another equation to create a linear equation in second variable. Solve the linear equation in one variable for second variable and then put the value of second variable in first equation to solve for first variable
Given system of equations is :
2x + 3y = -12 .....(1)
x = 3y + 3 .....(2)
So the first step will be take expression for one variable from one equation and put it into another equation.
Take x = 3y +3 which is an expression for x from equation (2),
Then put it into equation (1)
⇒ 2 (3y +3 ) + 3 y = -12 , This is the first step of substitution method for this variable
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the store bought a bike from the factory for 90$ and sold it to Andre for 117 what percentage was the markup?
Answers
The markup percentage was
[tex]\begin{gathered} P=\frac{117-90}{90}\cdot100 \\ P=\frac{27}{90}\cdot100 \\ P=30 \end{gathered}[/tex]The markup percentage was 30%.
7TH GRADE MATH, BRAINLIEST WILL BE AWARDED
Answers
Answers:
Q1.a: 11g
Q1.b: 3m
Q1.3: [tex]-k^{2}[/tex]
Q2.a: 8x + 11y
Q2.b: 2a + b - 2c
Q3.a: 5q + 7
Q3.b: 6r + 3s + 7t
Step-by-step explanation:
Q1) simplify each of these expressions:
a. [tex]4g + 6g + g[/tex]
= g(4 + 6 + 1)
= 11g
____________
b. [tex]4m - m[/tex]
= m(4 - 1)
= 3m
____________
c. [tex]5k^{2} -4k^{2} -2k^{2}[/tex]
= [tex]k^{2} (5 - 4 - 2)\\[/tex]
= [tex]-1k^{2}[/tex]
= [tex]-k^{2}[/tex]
__________________________________
Q2) copy and complete the workings to simplify these expressions:
a. [tex]5x + 3x+6y+5y\\[/tex]
= x(5 + 3) + y(6 + 5)
= 8x + 11y
____________
b.[tex]2a+4b+6c-3b-8c[/tex]
combine terms b:
2a + b + 6c - 8c
combine terms c:
= 2a + b - 2c
__________________________________
Q3) simplify these expressions by collecting like terms:
a.[tex]9q-4q+15-8[/tex]
combine terms q:
5q + 15 - 8
combine numbers:
= 5q + 7
____________
b. [tex]8r+2s+4t-2r+s+3t[/tex]
combine terms r:
6r + 2s + 4t + s + 3t
combine terms s:
6r + 3s + 4t + 3t
combine terms t:
= 6r + 3s + 7t
Help me asp please!!
Answers
It is an ongoing function. A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
What is function?In mathematics, a function is an expression, rule, or law that defines a connection between one variable (the independent variable) and another variable (the dependent variable).A function is defined as a relationship between a set of inputs and one output for each. A function is an input-output relationship in which each input corresponds to exactly one output.Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this.To learn more about function, refer to:
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4. Find and interpret theaverage rate of change forthe interval. Show your work.1
Answers
Average rate of change = -2 celcius / hour
Interpretation: For every unit change in the time (x), there is a change of -2 celcius in the temperature
Explanations:The average rate of change is to be found for the interval:
[tex]1\text{ }\leq x\leq3[/tex]From the interval, we can deduce that:
[tex]x_1=1,x_2=3[/tex]Know the corresponding value of y for each value of x shown above:
[tex]\begin{gathered} \text{When x}_1=1,y_1=\text{ 6} \\ \text{When x}_2=3,y_2=\text{ 0} \end{gathered}[/tex]The average rate of cgange is given by the formula:
[tex]\begin{gathered} \frac{\delta y}{\delta x}=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \frac{\delta y}{\delta x}=\text{ }\frac{0-6}{3-1} \\ \frac{\delta y}{\delta x}=\frac{-6}{3} \\ \frac{\delta y}{\delta x}=-2 \end{gathered}[/tex]The rate of change for the interval is -2 celcius/hour
This can be interpreted as for every unit change in the time (x), there is a change of -2 celcius in the temperature
How many positive real zeroes does f(x) = x⁵ - 4x³ + 7x² + 3x - 5 have?
Answers
Given -
f(x) = x⁵ - 4x³ + 7x² + 3x - 5
To Find -
How many positive real zeroes does f(x) have =?
Step-by-Step Explanation -
We have
f(x) = x⁵ - 4x³ + 7x² + 3x - 5
where the signs of coefficients are:
+ - + + -
We can see there are three changes in the sign in f(x).
So, from
Descarte's rule,
there are either 3 0r 1 positive real roots
Now,
f(-x) = -x⁵ + 4x³ + 7x² - 3x - 5
Signs: - + + - -
So, here f(-x) has two sign changes.
From this we can conclude there is at least 1 real root and either 4, 2 or 0 imaginary roots.
Final Answer -
Positive real zeroes f(x) have =
Minimum = 1
Maximum = 3
Writing out and solving inequalities a number divided by three less two is at most two
Answers
The inequlaity is ;
[tex]\begin{gathered} \frac{x}{3\text{ }}\text{ - 2}\leq2 \\ \end{gathered}[/tex]
And the solution is;
[tex]x\text{ }\leq\text{ 12}[/tex]
Let the number be x
The number divided by 3
That is x/3
less two means minus 2
x/3 - 2
Is at most 2 means it is less than or equal to 2
so the inequality is;
[tex]\begin{gathered} \frac{x}{3}\text{ - 2}\leq\text{ 2} \\ \\ \text{Solving the inequality, we have} \\ \\ \frac{x}{3}\text{ }\leq\text{ 2 + 2} \\ \\ \frac{x}{3}\text{ }\leq\text{ 4} \\ \\ x\text{ }\leq\text{ 3 }\times\text{ 4 } \\ x\text{ }\leq\text{ 12} \end{gathered}[/tex]The equation y = - 50x + 2000 represents thenumber of people attending a movie where xrepresents the number of weeks since the movierelease and y represents the number of people inthe theater.In the equation, what does the y-interceptindicate?A. Two thousand people attend the theater duringthe week of a movie's release.B. Every week 50 less people attend the movietheater.C. During a movie's release week, the movietheater will make $2,000.D. Every week the movie is open, the movie theaterloses $50.
Answers
two thousand people attend the theater during the week of a movie's release (option A)
Explanation:The equation:
y = -50x + 2000
y = number of people in the theater
x = number of weeks since the movie release
2000 will be the number of people in the theater at the begining of the movie release
y-intercept of an equation represent the value of y when x is zero
The 2000 is the number of people in the theater at week zero.
Hence, y-intercept indicate two thousand people attend the theater during the week of a movie's release (option A)
what is the arc measure of ct in radians? what is the arc length in feet?
Answers
We will determine the arch lenght (In radians) as follows:
*First: We transform the measure of the angle from degrees to radians, that is:
[tex]\theta=80\cdot\frac{\pi}{180}\Rightarrow\theta=\frac{4\pi}{9}[/tex]*Second: We find the arc length:
[tex]s=r\theta\Rightarrow s=(13.2)(\frac{4\pi}{9})[/tex][tex]\Rightarrow s=\frac{88}{15}\pi[/tex]So, the arc length for CT is 88pi/15 radians.
*Third: We find its measure in feet:
[tex]s\approx18.43[/tex]So, the arch length for CT in feet is approximately 18.43 feet.
1936 divided by 8 in long division
Answers
The value of 1936 divided by 8 in long division is 242.
What is long division?Long Division is a method for dividing large numbers that divides the task into numerous phases that follow a sequence. Just like in conventional division problems, the dividend is divided by the divisor, yielding the quotient and, in some cases, a remainder.
The steps are:
Step 1: Take the first digit of the dividend from the left.
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend
Using the above step the division is 242.
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Keisha is making potato casserole for a party. she needs 3/2 of a potato per guest. how many potatoes will she need for 15 guest
Answers
Keisha needs 3/2 of potato per guest ( i.e one guest is equivalent to 3/2 potato)
Thus, for 15 guests
she needs;
[tex]\begin{gathered} 15\text{ }\times\frac{3}{2} \\ \frac{15\times3}{2}=\frac{45}{2} \\ 22\frac{1}{2} \end{gathered}[/tex]Keisha needs 45/2 potatoes for 15 guests