Answers
Given:
[tex]f(x)=h(2x)[/tex]And the values in the table.
Required:
The equation of a normal line to f at x=3.
Explanation:
The equation of the line that passes through from point (x,y) and has slope m
is given by the formula
[tex]y-y_1=m(x-x_1)[/tex]From the table at x=3, f(x)=h(2x)
that is f(3)= h(6)=9
And the slope from the table at x=3 is 1/2.
Now the equation of the line is:
[tex]\begin{gathered} y-9=\frac{1}{2}(x-3) \\ 2(y-9)=(x-3) \\ 2y-18=x-3 \\ x-2y=-15 \end{gathered}[/tex]Final answer:
Thus the equation of the normal line is
[tex]x-2y+15=0[/tex]Related Questions
An error has been made in subtracting the polynomials as shown in the student work. What error has the student made, (Ignore the response I wrote and write a new one).
Answers
In carrying out the subtraction:
[tex](6x^2-4x-5)-(3x^2-7x+2)[/tex]We observe that:
[tex]\begin{gathered} 6x^2-3x^2=3x^2 \\ -4x-(-7x)=3x\text{ and }-4x+(-7x)=-11x \\ -5-(2)=-7\text{ and }-5+(2)=-3 \\ \end{gathered}[/tex]We observe that the student added two of the terms instead of subtracting. This was the error in the students' work.
Suppose that there are 150,000,000 people in Yourtown. And, suppose that Yourtown uses 310 × 109cubic meters of water per year. What is the amount of water (in cubic meters) used per person each year in Yourtown?
Answers
Given:
The number of people = 150,000,000.
The amount of water used in town = 310 × 109 cubic meters.
Required:
We need to find the amount of water (in cubic meters) used per person each year.
Explanation:
[tex]The\text{ amount of water used per person =}\frac{The\text{ amount of water used}}{The\text{ number of people}}[/tex]Substitute the number of people = 150,000,000 and the amount of water used in town = 310 × 109 cubic meters in the equation.
[tex]The\text{ amount of water used per person =}\frac{310\times109}{150000000}[/tex][tex]The\text{ amount of water used per person =}\frac{33790}{150000000}[/tex][tex]The\text{ amount of water used per person =}\frac{3379}{15000000}[/tex][tex]The\text{ amount of water used per person =}0.000225267\text{ cubic meters}[/tex]Final answer:
[tex]The\text{ amount of water used per person =}0.000225267\text{ cubic meters}[/tex]13. Nick is five years older than Will. The sum of their ages is 21. How old is Nick? Solve algebraically.
Answers
Answer:
Nick = 13 years old.
Step-by-step explanation:
Define the variables:
Let n = the age of Nick (in years).Let w = the age of Will (in years).Given:
Nick is 5 years older than Will.The sum of their ages is 21.Create a system of equations with the given information and defined variables:
[tex]\begin{cases} w=n-5\\n+w=21\end{cases}[/tex]
Substitute the first equation into the second equation and solve for n:
[tex]\implies n+(n-5)=21[/tex]
[tex]\implies 2n-5=21[/tex]
[tex]\implies 2n-5+5=21+5[/tex]
[tex]\implies 2n=26[/tex]
[tex]\implies 2n \div 2=26 \div 2[/tex]
[tex]\implies n=13[/tex]
Therefore, Nick is 13 years old.
To find the age of Will, simply substitute the found value of n into the first equation and solve for w:
[tex]\implies w=13-5[/tex]
[tex]\implies w=8[/tex]
Therefore, Will is 8 years old.
Suppose you deposit $10,000 in an account for 8 years at the annual interest rate 3%.
a. What would be the ending account balance if the interest is compounded by monthly?
b. What would be the ending account balance if the interest is compounded daily?
c. What would be the ending account balance if the interest is continuously compounded?
d. What are the graphs of (a), (b) and (c)?
e. Are these three answers similar? Why or not why?
Answers
For the ending account balances, these are the solution
a. The ending account if it is compounded monthly is $12,708.68
b. If it is compounded daily = $12712.374
c. If it is continuous = $12712.49
d. The graphs are in the attachment
e. The answers are not similar
How to solve for the ending account balancesThis is the data that we can use to solve the problem
Principal = $10000
Time = 8 years
Rate = 3 percent
The ending balance when compounded monthly
= number of months n
= 12
A = P (1 + r/n)^nt
= 10000 (1 + 0.03/12)⁸*¹²
= 10000 (1.0025)⁹⁶
= 100000 X 1.270868
= 12,708.68
The amount that would be the ending account if it is compounded monthly is $12,708.68
b. If it is compounded daily
total number of days in a year n = 365
10000 (1 + 0.03/365)⁸*³⁶⁵
10000 x 1.2712374
= $12712.374
c. The endind account if the interest is compounding continuously
[tex]A = Pe^r^t\\\\A = 10000 *e ^0^.^0^3^*^8[/tex]
= $12712.49
e. The answers are not similar here due to the fact that all of the accounting periods that we used are not the same for the problems that we have here.
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Tim needs to be at work at 8:00 A.M. It takes him 30 minutes to get ready in the morningand 15 minutes to drive to work. What is the latest time Tim can get up in the morningwithout being late for work?
Answers
The given information is:
- Tim needs to be at work at 8:00 A.M.
- He needs 30 minutes to get ready in the morning
- It takes him 15 minutes to drive to the work
The total time Tim needs to get ready and drive to work is:
[tex]30min+15min=45min[/tex]So, he needs at least 45 minutes to be on time at work. So, the latest time Tim can get up in the morning is 45 minutes earlier than 8:00 A.M., and it is equal to:
[tex]\begin{gathered} 8:00\text{ is equal to 7 hours and 60 min, so:} \\ 60min-45min=15min \\ \\ The\text{ latest time is: }7:15A.M. \end{gathered}[/tex]The answer is 7:15 A.M.
three more than eight times a number is equal to 19. find the number.
Answers
Let that number be variable x
MATHEMATICALLY THE STATEMENT IS SAYING
[tex]8x + 3 = 19 \\ 8x = 19 - 3 \\ 8x = 16 \\ \frac{8x}{8} = \frac{16}{8} \\ x = 2 [/tex]
That number is 2ATTACHED IS THE SOLUTION
Use the drawing tools to form the correct answer on the graph.
Draw a point that belongs to the solution region of this system of inequalities.
y > 1.5x + 4
y < 2/3x + 4
Answers
A point that belongs to the solution region of this system of inequalities is (0, 4).
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).What is a graph?A graph refers a type of chart that's generally used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In this scenario, a graph which represent the solution to the given system of inequalities is shown in the image attached below.
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Find the derivative of each function. Simplify each derivative and express all exponents as positive values.
Answers
Answer:
[tex]\boxed{f^{\prime}(x)=x^2^{}-\frac{1}{2}}[/tex]Explanation:
Step 1. The function we have is:
[tex]f(x)=\frac{x^3}{3}-\frac{x}{2}[/tex]And we are asked to find the derivative of the function. The rule to find the derivative for this type of function is:
[tex]\begin{gathered} \text{for a function }of\text{ the form} \\ f(x)=ax^n \\ \text{The derivative is:} \\ f^{\prime}(x)=a(n)x^{n-1} \end{gathered}[/tex]Step 2. Before we apply the derivative rule, remember the following:
[tex]\begin{gathered} \text{for a function } \\ f(x)=g(x)+h(x) \\ \text{The derivative is:} \\ f^{\prime}(x)=g^{\prime}(x)+h^{\prime}(x) \end{gathered}[/tex]This means that we need to derivate each part or term of the function and combine them for the total derivative.
Step 3. Apply the derivative rule from step 1 to the given function.
First we rewrite the function as follows:
[tex]\begin{gathered} f(x)=\frac{x^3}{3}-\frac{x}{2} \\ \downarrow \\ f(x)=\frac{1}{3}x^3-\frac{1}{2}x^1 \end{gathered}[/tex]Apply the derivative rule:
[tex]f^{\prime}(x)=\frac{1}{3}(3)x^{3-1}-\frac{1}{2}(1)x^{1-1}[/tex]Step 4. The last step is to simplify the expression:
[tex]\begin{gathered} f^{\prime}(x)=\frac{1}{3}(3)x^{3-1}-\frac{1}{2}(1)x^{1-1} \\ \downarrow \\ f^{\prime}(x)=\frac{1}{3}(3)x^2-\frac{1}{2}(1)x^0 \\ f^{\prime}(x)=x^2-\frac{1}{2}x^{^0} \\ \sin ce^{} \\ x^0=1 \\ \downarrow\text{ The result is }\downarrow \\ f^{\prime}(x)=x^2-\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]\boxed{f^{\prime}(x)=x^2^{}-\frac{1}{2}}[/tex]y = x ^ 2 + 2x - 24 i need to know the points at the x-intercept ( , ) and ( , ) points at the y intercept: ( , )and i’d it’s a min or max
Answers
Question : the function in the question is given below as
[tex]y=x^2+2x-24[/tex]Step 1: Calculate the x-intercept
The x-intercept for any curve is the value of the x coordinate of the point where the graph cuts the x-axis, or we can say that the x-intercept is the value of the x coordinate of a point where the value of the y coordinate is equal to zero.
Equating the equation above to zero (0)
[tex]\begin{gathered} y=x^2+2x-24 \\ x^2+2x-24=0 \end{gathered}[/tex]Solving using the quadratic formula below,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The general formula of a quadratic equation is given below
[tex]ax^2+bx+c=0[/tex]By comparing the coefficient, we will have the values to be
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-24 \end{gathered}[/tex]Step 2: Substitute the values into the quadratic formula to get the values of x
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{2^2-(4\times1\times-24)}}{2\times1} \\ x=\frac{-2\pm\sqrt[]{4^{}+96}}{2} \\ x=\frac{-2\pm\sqrt[]{100}}{2} \\ x=\frac{-2\pm10}{2} \\ x=\frac{-2+10}{2}\text{ or }x=\frac{-2-10}{2} \\ x=\frac{8}{2}\text{ or x=}\frac{\text{-12}}{2} \\ x=4\text{ or x=-6} \end{gathered}[/tex]Hence,
The x-intercepts are
[tex](-6,0)\text{ and }(4,0)[/tex]x-intercepts are (-6,0) and (4,0)
Step 3: Calculate the coordinate of the y-intercept
The point where a line or curve crosses the y-axis of a graph.
In other words: find the value when x equals 0
[tex]\begin{gathered} y=x^2+2x-24 \\ y=(0)^2+2(0)-24 \\ y=0+0-24 \\ y=-24 \end{gathered}[/tex]Hence,
The y-intercept is
[tex](0,-24)[/tex]The y-intercept is (0,-24)
Below is the graph of the function on the question with its x-intercepts and y-intercepts
Step 4: Determine if the graph is minimum or maximum
The first step is to determine whether your equation gives a maximum or minimum. This can be done by looking at the x^2 term. If this term is positive, the vertex point will be a minimum; if it is negative, the vertex will be a maximum.
The coefficient of the x^2 term is a positive 1
Hence,
The equation
[tex]y=x^2+2x-24\text{ }[/tex]is a minimum quadratic graph
Complete the following statement.a0
Answers
ANSWER
x = 10
EXPLANATION
We want to find the missing box in the statement given.
Let the box be represented by x:
[tex]x\text{ + (-7) = 3}[/tex]To solve this, move (-7) to the other side, the sign changes:
[tex]\begin{gathered} x\text{ = 3 + (+7)} \\ x\text{ = 3 + 7} \\ x\text{ = 10} \end{gathered}[/tex]The box is 10.
I'll give brainliest!
Answers
The numbers written in correct scientific notation format are-
7 x 10⁻⁹
3 x 10⁻⁶
0.1 x 10⁻⁸
What is Scientific Notation?Scientific notation is a techniques of writing a large number or small number in a simple form. It involves expressing a number by the multiplication of 10 raise to the specific exponent.
Given are the set of numbers.
In order to classify the given numbers based on the correct syntax of scientific notation, it is necessary to understand the rules for writing the correct syntax.
The base to which exponent is raised should always be 10.The exponent should be a non-zero integer. (It can be both positive or negative integer)The absolute value of the coefficient is greater than or equal to 1 but it should be less than 10Based on the above rules, we can classify the correct scientific notation as -
7 x 10⁻⁹
3 x 10⁻⁶
0.1 x 10⁻⁸
Therefore, the numbers written in correct scientific notation format are-
7 x 10⁻⁹
3 x 10⁻⁶
0.1 x 10⁻⁸
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What was the most common button length? Write your answer on the line below.Answer inches
Answers
Answer:
3/4 inches
Explanation:
The most number of cross symbols (vertical line) is on the length 6/8 inches, that is, 3/4 inches.
So, the most common button is of length 3/4 inches.
6 more than a number is the same as the
number times 4.
Answers
Answer:
2
Step-by-step explanation:
AlgebraName1. If f(x) = 2x - 4, find each valdea)(3)b) f(x) = 9
Answers
Answer:
Step-by-step explanation:
Comment
The question is since f(x) really means y, then when y = 9 what's x?
Solution
y = 2x - 4
y = 9
9 = 2x - 4 Add 4 to both sides
9+4 = 2x Combine
13 = 2x Divide both sides by 2
13/2 = 2x/2
6.5 = x
Do you mean what is f(X) when x is 3. f(3) = 2x - 4. So what is y when x = 3
y = 2x - 4 Substitute 3 for x
y = 2*3 - 4 Combine
y = 6 - 4
y = 2
r-s for r=63 and s=9
Answers
54
Explanation
to figure out this, just replace the given values and evaluate
Step 1
[tex]r-s[/tex]let
r=63
s=9
now, replace
[tex]\begin{gathered} r-s \\ 63-9 \\ 54 \end{gathered}[/tex]so, the answer is 54
how long will it take $600 to earn $72 at the rate of 0.03 percent annual?
Answers
It takes 400 years for $600 to earn $72 at the rate of 0.03 percent annual
What is Simple Interest?"Simple" interest refers to the straightforward crediting of cash flows associated with some investment or deposit.
The formula for calculating Simple interest
I=PRT
Where I is the Interest
P=Principle amount
I is interest Amount
R is rate of interest per year as a percent
T is time period involved
P=600
I=72
r=0.03%
t=?
I=PRT
Plug in the values P, R and I
72=600×(0.03%)×T
72=600×0.0003×T
72=0.18×T
400=T
Hence it takes 400 years, for amount $600 to earn $72 at the rate of 0.03 percent annual.
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Determine whether the relation defines a function, and give the domain and range.{(-8, 7),(4.7).(-9, 1);
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define when a relation defines a function
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
The domain is the set of all first elements of the ordered pairs. The range on the other hand is the set of all second elements of the ordered pairs.
Since every x-values of the given relation is associated with only one y-value, therefore it defines a function.
The domain is given as:
[tex]\lbrace-8,4,-9\rbrace[/tex]The range is given as:
[tex]\lbrace7,7,1\rbrace[/tex]given the Venn diagram below what is the probability that both event A and B will occur
Answers
the probability of both is the one they share
[tex]0.2[/tex]Which of the following systems of equations can be used to find a, the number of adults attending, and s, the number of students attending the game?
Answers
The problem can be expressed in the following system of linear equations:
A total of 120 adults (a) and students (s) attended a school:
a + s = 120
Each adult paid $2.50, mathematically, that is 2.5a
Each student paid $1, mathematically, that is 1s
and the total paid by adults and students attending the game was $189
then, we have:
2.5a + 1s = 189
then, we can conclude that the problem can be expressed as follows:
a + s = 120
2.5a + 1s = 189
or equivalently:
a + s = 120
2.5a + s = 189
so, the correct answer is D.
What is the y-value when the x-value is 18?
Answers
Answer: -11
Step-by-step explanation:
Determine the values of m and n in the polynomial 2x* + mx -x + n such that the binomial (x - 1) is a factor and that the remainder when divided by (x + 2) is -18.
Answers
The remainder theorem of polynomials states: if a polynomial p(x) is divided by a binomial (x - a), the remainder obtained is p(a).
In this case, the polynomial is:
[tex]p(x)=2x^4+mx^3-x^2+n[/tex]Applying the remainder theorem p(-2) = -18, that is:
[tex]\begin{gathered} p(-2)=2\cdot(-2)^4+m\cdot(-2)^3-(-2)^2+n \\ -18=2\cdot16+m\cdot(-8)-4+n \\ -18=32-8m-4+n \\ -18-32+4=-8m+n \\ -46=-8m+n\text{ (eq. 1)} \end{gathered}[/tex]Given that (x - 1) is a factor, then p(1) = 0, that is:
[tex]\begin{gathered} p(1)=2\cdot1^4+m\cdot1^3-1^2+n \\ 0=2+m-1+n \\ -2+1=m+n \\ -1=m+n\text{ (eq. 2)} \end{gathered}[/tex]Now, we have a system of 2 equations and 2 variables: m and n. Subtracting equation 2 to equation 1, we get:
-8m + n = -46
-
m + n = -1
------------------------
-9m = -45
m = (-45)/(-9)
m = 5
Substituting this result into equation 2, we get:
5 + n = -1
n = -1 - 5
n = -6
select the correct answer what is the simplified form of 45
Answers
The solution is option C.
Which of the following order satisfies a set of number
Answers
N (natural numbers) are a subset of Z (integers) which are a subset of Q (fractions) which are a subset of R (real numbers)
An architect is standing 250 feet from the base of a building and would like to know the height of the building. If he measures the angle of elevation to be 55°, what is the approximate height of the building? Round any intermediate calculations if needed to know less than six decimal places and round the final answer to the nearest 10th of a foot
Answers
see the figure below to better understand the problem
we have that
[tex]\begin{gathered} tan55^o=\frac{h}{250}---->\text{ by TOA} \\ \\ solve\text{ for h} \\ h=250*tan55^o \\ h=357.0\text{ ft} \end{gathered}[/tex]The answer is 357.0 feet????????????????????
Answers
we have
m=-2
point (1,2)
step 1
find the equation of the line in point slope form
y-3=-2(x-1)
convert to slope intercept form
y-3=-2x+2
y=-2x+2+3
y=-2x+5
To graph the line we need two points
Find the y-intercept (value of y when the value of x is equal to zero)
For x=0
y=5
so
the y-intercept is (0,5)
Find the x-intercept
Value of x when the value of y is equal to zero
For y=0
0=-2x+5
2x=5
x=2.5
the xintercept is (2.5,0)
Plot the points (0,5) and (2.5,0), join them and graph the line
using a graphing tool
see the attached figure
please wait a minute
Use the order of operations to simplify - +4(4.50 – 1.50).O A. 122/2B. 24/1/2c. 23/1/D. 11/1/SUBMIT
Answers
SOLUTION
This becomes
[tex]\begin{gathered} -\frac{1}{2}+4(4.5-1.50) \\ opening\text{ the bracket we have } \\ -\frac{1}{2}+(4\times4.5)+(4\times(-1.50) \\ -\frac{1}{2}+18-6 \\ -\frac{1}{2}+12 \\ 12-\frac{1}{2} \\ =11\frac{1}{2} \end{gathered}[/tex]Hence the answer is option D
What’s the correct answer answer asap for brainlist
Answers
Answer: Europe quit buying crops which left the united states with a surplus of crops
hope i helped
Step-by-step explanation:
In this figure, lines a and B are intersected by Line T. Which of these statements proves that lines A and B are parallel
Answers
Correct answer is C, For the given figure, ∠2 = ∠3, as they are corresponding angles of parallel lines.
What are corresponding angles?The angles created when a transversal intersects two parallel lines are known as corresponding angles.
Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.
Two congruent or identical triangles' corresponding angles are those of a congruent pair of their sides in a triangle. As a result, these angles are equivalent or have the same value.
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Complete Question -
In the figure, lines a and b are intersected by line t. Which of these statements proves that lines a and
b are parallel?
∠1 and ∠2 are supplementary∠1 and ∠3 are supplementary∠2 = ∠3∠1 = ∠2Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money, AAA, in dollars, that he receives from the first donor given that he walks ddd kilometers is given by the formula A(d)=10dA(d)=10dA, left parenthesis, d, right parenthesis, equals, 10, d. The money, BBB, in dollars, that he receives from the second donor given that he walks ddd kilometers is given by the formula B(d)=2d+d^2B(d)=2d+d
2
B, left parenthesis, d, right parenthesis, equals, 2, d, plus, d, squared.
Let TTT be the total money that Onur raises from those donors by walking ddd kilometers in the walkathon.
Write a formula for T(d)T(d)T, left parenthesis, d, right parenthesis in terms of A(d)A(d)A, left parenthesis, d, right parenthesis and B(d)B(d)B, left parenthesis, d, right parenthesis.
Answers
The function of the total money raised from both donors after walking d kilometers is T(d) = 12d + d^2
How to determine the composite function of the total amount?From the question, the given parameters are:
First donor at d kilometers, A(d)=10dSecond donor at d kilometers, B(d) = 2d + d^2Also, from the question, T is the total money raised from both donors at d kilometers
This means that the equation of the total money can be represented a
T(d) = A(d) + B(d)
Substitute the known values in the above equation
So, we have the following equation
So, we have
T(d) = 10d + 2d + d^2
Evaluate the like terms in the above equation
T(d) = 12d + d^2
The equation cannot be further simplified
Hence, the composite function is T(d) = 12d + d^2
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Complete question
Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money, A, in dollars, that he receives from the first donor given that he walks d kilometers is given by the formula A(d)=10d
The money, B, in dollars, that he receives from the second donor given that he walks d kilometers is given by the formula B(d)=2d+d^2
Let T be the total money that Onur raises from those donors by walking d kilometers in the walkathon.
Write a formula for T(d) in terms of A(d) and B(d)
During revision, you should _____.A set your first draft aside for awhileB work from typed or printed textC write down additional thoughtsD All of the above
Answers
You should jot down any new ideas you have while you revise.
Revision is the process of rearrangement, addition, or deletion of paragraphs, sentences, or words in writing. Writers are free to edit their work both during and after the writing process. Many of the techniques associated with editing are used in revision, but it can also require more significant changes to the goal, target audience, and content.
To ensure proper memorization, revise by reading or writing the material again. A must-do before each exam is revision. Additionally, it allows you to check for errors and reorganize your work.
During revision, you should write down additional thoughts.
The correct option is (c).
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