Given :
The parent tangent function is horizontally compressed by a factor of 1/2 and reflected over the x-axis.
Explanation :
To find the equation of g.
The tangent function is
[tex]f(x)=\tan x[/tex]It is horizontally compressed by a factor of 1/2.
Then the function becomes
[tex]g(x)=\tan (\frac{1}{2}x)[/tex]After that it is reflected over x-axis.
[tex]g(x)=-\tan (\frac{1}{2}x)[/tex]Answer :
Hence the result of the transformation is
[tex]g(x)=-\tan (\frac{1}{2}x)[/tex]The correct option is D.
values for relation g are given in the table. which pair is in g inverse
Given
Values for relation g
Find
Which pair is in g inverse.
Explanation
In the inverse function , it satisfies when y = f(x)
[tex]x=f^{-1}(y)[/tex]so , in the inverse of g
since g(4) = 9 , so
[tex]4=g^{-1}(9)[/tex]g(5) = 13 , so
[tex]13=g^{-1}(5)[/tex]g(3) = 5 , so
[tex]5=g^{-1}(3)[/tex]g(2) = 2 , so
[tex]2=g^{-1}(2)[/tex]so , (13 , 5) would be found in the inverse of g
Final Answer
Hence , the correct option is (13 , 5)
HELP)1-47.Which of the relationships below are functions? If a relationship is not a function, give a reason to support yourconclusion. Homework Helpb.input (a) output (y)&-3195191900-37input (2)- 2074c.d.output (y)1001030**INSERT PICTURES OF YOUR WORK HERE.
According to the given data, from the relationship seen in the image, the ones that are functions are the following:
b. This is a function becuase there is exactly one output for every input.
Picture of work:
Input output
-3 __________ 19
5 __________ 19
19 __________ 0
0 __________ -3
c. This is a function becuase there is exactly one output for every input.
Input output
7 __________ 10
-2 __________ 0
0 __________ 10
7 __________ 3
4_____________ 0
A rectangular paperboard measuring 33 in long and 21 in wide has a semicircle cut out of it as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.)
Explanation
The question wants us to obtain the perimeter of the paperboard that remains after the semicircle has been removed
To do so, we will follow the steps below:
Step1: Find the Perimeter of the rectangle
The perimeter of a rectangle is simply the sum of all its sides
So in our case, we will have to sum sides A as given below
[tex]Perimeter\text{ of rectangle= 21 +33+33= 87 inches}[/tex]Step 2: Find the perimeter of the semi-circle
The perimeter of a semi-circle is given by:
[tex]\begin{gathered} \frac{\pi D}{2} \\ where \\ \pi=3.14 \\ D=diameter\text{ of the semicircle =21 inches} \end{gathered}[/tex]Simplifying
[tex]Perimeter\text{ of semicircle=}\frac{3.14\times21}{2}=32.97\text{ inches}[/tex]Step 3: Find the sum of the perimeters of the rectangle and semicircle
Therefore, the perimeter of the paperboard that remains after the semicircle is removed will be
[tex]\begin{gathered} perimeter\text{ }of\text{ }the\text{ }rectangle+\text{ perimeters of the semicircle =87inches + 32.97 inches} \\ perimeter\text{ }of\text{ }the\text{ }rectangle-\text{ perimeters of the semicircle =119.97 inches} \end{gathered}[/tex]Hence, the perimeter of the paperboard that remains after the semicircle is removed will be 119.97 in
find the slope (-10,8) (5,-3)
The slope can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, you have the following points:
[tex]undefined[/tex]find each measure 113° 23°x=?
We have that a vertex outside a circle is just the half of the difference of the angles:
Then, in this case:
[tex]x=\frac{113-23}{2}=\frac{90}{2}=45[/tex]Answer: x = 45º
Given: CD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC.Prove: a2=b2+c2−2bccosAFigure shows triangle A B C. Segment A B is the base and contains point D. Segment C D is shown forming a right angle. Segment C D is labeled h. Segment A B is labeled c. Segment B C is labeled a. Segment A C is labeled b. Segment A D is labeled x. Segment D B is labeled c minus x. Select from the drop-down menus to correctly complete the proof.Statement ReasonCD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC. Given△ACD and △BCD are right triangles. Definition of right trianglea2=(c−x)2+h2a2=c2−2cx+x2+h2Square the binomial.b2=x2+h2cosA=xbbcosA=xMultiplication Property of Equalitya2=c2−2c(bcosA)+b2a2=b2+c2−2bccosA Commutative Properties of Addition and Multiplication
Solution:
The equation below is given as
[tex]a^2=(c-x)^2+h^2[/tex]This represents the
PYTHAGOREAN THEOREM
The second equation is given below as
[tex]b^2=x^2+h^2[/tex]This represents the
PYTHAGOREAN THEOREM
The third expression is given below as
[tex]\cos A=\frac{x}{b}[/tex]This represents
Definition of cosine
The fourth expression is given below as
[tex]a^2=c^2-2c(bcosA)+b^2[/tex]This represents
Substitution property of equality
i have to use interval notation and i’m stuck on it
Given two sets of real numbers:
[tex]\begin{gathered} D=\mleft\lbrace w\mright|w\ge4\} \\ E=\mleft\lbrace w\mright|w<8\} \end{gathered}[/tex]we will write the given sets as intervals
so,
[tex]\begin{gathered} D=\lbrack4,\infty) \\ E=(-\infty,8) \end{gathered}[/tex]The intersections and the union of the sets will be as follows:
[tex]\begin{gathered} D\cap E=\lbrack4,8) \\ \\ D\cup E=(-\infty,\infty) \end{gathered}[/tex]please i need your help i will appreciate it
The value of c is 5/2 that satisfy the conclusions of the mean value theorem.
Given Function:
f(x) = x^2-3x+3 on interval [1,4].
The Mean Value Theorem states that for a continuous and differentiable function f(x)=x^2-3x+3 on the interval [1,4] there exists such number c from the interval [1,4] that [tex]f'(c)=\frac{f(4)-f(1)}{4-1}[/tex].
f(4) = 4^2-3*4+3
= 16-12+3
= 4+3
= 7
f(1)=1^2-3*1+3
= 1-3+3
= 1
f'(c) = 2c -3
2c-3 = 7 - 1 / 4 - 1
2c - 3 = 6/3
2c -3 = 2
2c = 5
c = 5/2
Therefore the value of c = 5/2 that satisfy the conclusions of the mean value theorem.
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build build a machine that can automatically clean a coffee mug Bill wants the machine to be able to do an amount of work represented by the inequality x + y greater than or equal to 2 while using battery power that remains at level represented by the inequalities for x + y greater than or equal to -1 where X and Y both represent the number of minutes spent on cleaning different parts of the tank at the machine Spence 5 in three minutes on X & Y respectively does he meet those requirements?
We have to meet these restrictions:
Amount of work:
[tex]x+y\ge2[/tex]Battery power:
[tex]x+y\ge-1[/tex]If the values of x and y are x=5 and y=3, then we have to evaluate each restriction:
[tex]\begin{gathered} x+y=5+3=8\ge2\longrightarrow\text{true} \\ x+y=5+3=8>-1\longrightarrow true \end{gathered}[/tex]Answer: Yes, they meet the requirements.
The governor of state A earns $48,430 more than the governor of state B . If the total of their salaries is $279,100, find the salaries of each
For the first part, we can write
[tex]B+48430=A[/tex]where A is the salary for governor A and B is the salary for governor B.
From the second part, we can write
[tex]A+B=279100[/tex]Then, we have 2 equations in 2 unknows.
Solving by substitution method.
If we substitute the firs equation into the second one ,we get
[tex](B+48430)+B=279100[/tex]which gives
[tex]2B+48430=279100[/tex]If we move 48430 to the right hand side as -48430, we have
[tex]\begin{gathered} 2B=279100-48430 \\ 2B=230670 \end{gathered}[/tex]then, B is equal to
[tex]\begin{gathered} B=\frac{230670}{2} \\ B=115335 \end{gathered}[/tex]Finally, by substituting this result into our first equation, we obtain
[tex]\begin{gathered} A+115335=279100 \\ A=279100-115335 \\ A=163765 \end{gathered}[/tex]This means that governo A earns $163,765 and gobernor B earns $115,335
3. The Hill family rented a car for the weekend. The rental agency charged a weekend fee of $35.00 and $0.12 per mile. Their final bill was $44,36, Which equation could be used to discover how many miles the family drove (A) 44.36 - 12y = 35 (B) 12x + 35 = 44.36 (C) 35 +0.12% = 44.36 (D) 44.36 + 35 = 0.127
ANSWER:
C)
[tex]35+0.12x=44.36[/tex]STEP-BY-STEP EXPLANATION:
With the help of the statement, we can conclude that the equation is the following because the value of 0.12 must go together with the x, and that the total value must be 44.36
[tex]\begin{gathered} 35+0.12x=44.36 \\ \text{where x is the number of miles the familly drove} \end{gathered}[/tex]You deposit $ 1,821 in an account earning 3 % interest compounded monthly. How much will you have in the account in 1 years?$__________ (Give your answer accurate to 2 decimal places)
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = $1821
r = Interest rate = 3% = 0.03
n = Number of times interest is compounded per year = 12
t = Time = 1
So:
[tex]\begin{gathered} A=1821(1+\frac{0.03}{12})^{12\cdot1} \\ A\approx1876.39 \end{gathered}[/tex]Answer:
$1876.39
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the variance of the waiting time is 9. Find the probability that a person will wait for between 10 and 12 minutes. Round your answer to four decimal places.
The probability that a person will wait for between 10 and 12 minutes is 0.069.
What is meant by z score?z-score is defined as the number of standard deviations by which the value of a raw score is above or below the mean value of what is being measured or observed. It tells where the score lies on a normal distribution curve. It is a numerical measurement that describes a values relationship to the mean of a group of values.
z = (raw score - mean) / standard deviation
Given,
The mean waiting time is 6 minutes and variance waiting time is 9 minutes.
Standard deviation = √variance = √9 = 3minutes
For between 10 and 12 minutes, the probability is
z = (10- 6)/3 = 1.333 and z=(12-6)/3=2
p(z≤1.3333)=0.982
p(z≤2)=0.9772
Probability that a person will wait for between 10 and 12 minutes is,
|0.9082-0.9772|= 0.069
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what is the value of 6n-2whenn=3
To find the value of an expression we only need to plug the value of the variable in said expression.
In this case we have:
[tex]6n-2[/tex]If, n=3, then:
[tex]6(3)-2=18-2=16[/tex]Therefore, the value of the expression when n=3 is 16.
K
There are 48 runners in a race. How many ways can the runners finish first, second, and third?
There are different ways that the runners can finish first through third.
(Type a whole number.)
The number of different ways that the runners can finish first through third. is 103776
There are 48 runners in a race
The number of options for the first place is 48, as only one can be in 1st postion and there are a total of 48 persons
The number of options for the second place is 47, as the person who became first cannot be in the second position
The number of options for the third place is 46, as the person who became first and second cannot be in the third position
There are different ways that the runners can finish first through third. is
48 x 47 x 46 = 103776
Therefore, the number of different ways that the runners can finish first through third. is 103776
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can you help me with my work
1. the initial value of A is 50 and B is 25 so a is bigger so A>B
2. A hits the grond on 6.53 and B on 10.477 so A is less , so A
3. A grows to 2.5 and B to 5 so A
4. the maximum of a is 2.5 and B is 5 so A
5. the maximum height of A is 81.25 and B 150 so A>B
Find the minimum or maximum value of the function f(x)=10x^2+x−5. Give your answer as a fraction.
In order to find the minimum or maximum value of the function f(x),
[tex]f\mleft(x\mright)=10x^2+x-5[/tex]First, we have to find out at which value of x the function takes it. For example:
In order to find the value of x when it takes the maximum of minimum, we are going to analyze the derivative of the function. Then we are going to be following the next step-by-step:
STEP 1: finding the derivative of the function
STEP 2: analysis of the derivative of the function.
STEP 3: minimum or maximum value of the function
STEP 1: finding the derivative of the functionWe have that the derivative of the function is given by f'(x):
[tex]\begin{gathered} f\mleft(x\mright)=10x^2+x^1-5 \\ \downarrow \\ f^{\prime}(x)=2\cdot10x^{2-1}+1\cdot x^{1-1} \\ f^{\prime}(x)=20x^{2-1}+1\cdot x^0 \\ f^{\prime}(x)=20x^1+1\cdot1 \\ f^{\prime}(x)=20x^{}+1 \end{gathered}[/tex]Then, the derivative of f(x) is:
f'(x) = 20x + 1
STEP 2: analysis of the derivative of the function.We have that the function has a maximum or a minimum when its derivative takes a value of 0:
[tex]\begin{gathered} f^{\prime}\mleft(x\mright)=0 \\ 0=20x+1 \end{gathered}[/tex]when this happens, then, x has a value of:
[tex]\begin{gathered} 0=20x+1 \\ \downarrow\text{ taking -1 and 20 to the left side} \\ -1=20x \\ -\frac{1}{20}=x \end{gathered}[/tex]When x=-1/20, the function takes its minimum or maximum
STEP 3: minimum or maximum value of the functionNow, we can replace in the equation of f(x), to see what is the value of the function when x= -1/20:
[tex]\begin{gathered} f\mleft(x\mright)=10x^2+x-5 \\ \downarrow\text{ when x=}-\frac{1}{20} \\ f(-\frac{1}{20})=10(-\frac{1}{20})^2+(-\frac{1}{20})-5 \end{gathered}[/tex]Solving f(-1/20):
[tex]\begin{gathered} f(-\frac{1}{20})=10(-\frac{1}{20})^2+(-\frac{1}{20})-5 \\ \downarrow\sin ce(-\frac{1}{20})^2=\frac{1}{400} \\ =10(\frac{1}{400})-\frac{1}{20}-5 \\ =-\frac{201}{40} \end{gathered}[/tex]Then, the minimum value of the function is
[tex]f\mleft(x\mright)=\frac{-201}{40}[/tex]Answer: -201/4010x the nunber adds to 5 is the same as 9 times the number is what
Answer:
-5
Step-by-step explanation:
5+10x=9x
clt
5=9x-10x
5=-x
x=-5
Liam wants to find the average of the following numbers. 53, 46, 57, 52, 49 He estimates the average as 50 and then finds the average. Which describes how close Liam is to his estimate?
You find the average by adding all of the numers and then divide by the ammount of numbers that were added:
[tex]A=\frac{53+46+57+52+49}{5}\Rightarrow A=51.4[/tex]So the average is 51.4 and therefore Liam was off by 1.4 units.
Each vertical cross-section of the triangular prism shown below is an isosceles triangle.4What is the slant height, s, of the triangular prism?Round your answer to the nearest tenth.The slant height isunits
The length of the diagonal of a cube can be calculated by the formula
[tex]\begin{gathered} d=a\sqrt[]{3} \\ \text{where a is one side of the cube} \\ a=60 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} d=60\sqrt[]{3}\text{ units} \\ d=103.92\text{ units (2 decimal place)} \end{gathered}[/tex]Do not round ant intermediate computations, and round your final answers to the nearest cent
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
PART ONE;
a) Find the interest that will be owed after 78 days:
[tex]Simple\text{ Interest = }\frac{Principal\text{ x Rate x Time}}{100}[/tex][tex]Simple\text{ Interest =}\frac{15,600\text{ x 3. 6 x }\frac{78}{365}}{100}=\text{ \$ 120.01}[/tex]PART TWO:
Assume that she doesn't make any payment, the amount owed after 78 days:
[tex]\begin{gathered} Amount\text{ = Principal + Simple Interest} \\ Amount\text{ = \$15600 + \$ 120.01} \\ Amount\text{ = \$ 15,720.01} \end{gathered}[/tex]evaluate this expression using the quotient rule 9^7 divided by 9^2
Using the method of Quotient rule:
[tex]\begin{gathered} \text{Which says} \\ \frac{x^{n^{}}}{x^m}=x^{n-m} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{9^7}{9^2}=9^{7-2}=9^5 \\ \\ 9^5=\text{ 9}\times9\times9\times9\times9 \\ 9^5=\text{ 59049} \\ \text{The answer is 59049} \end{gathered}[/tex]Hence the answer is 59,049.
Find the angle between the vectors (-9, -8) and (-9,5). Carry your intermediate computations to at least 4 decimalplaces. Round your final answer to the nearest degree.| 。x 6 ?
The vector for (-9,-8) is,
[tex]u=-9\hat{i}-8\hat{j}[/tex]The vector for (-9,5) is,
[tex]v=-9\hat{i}+5\hat{j}[/tex]The formula for the angle between vector u and vector v is,
[tex]\cos \theta=\frac{u\cdot v}{|u\mleft\Vert v\mright|}[/tex]Determine the angle between vectors.
[tex]\begin{gathered} \cos \theta=\frac{(-9\hat{i}-8\hat{j)}\cdot(-9\hat{i}+5\hat{j})}{\sqrt[]{(-9)^2+(-8)^2}\cdot\sqrt[]{(-9)^2+(5)^2}} \\ =\frac{81-40}{\sqrt[]{145}\cdot\sqrt[]{106}} \\ =\frac{41}{\sqrt[]{15370}} \\ \theta=\cos ^{-1}(0.3307) \\ =70.688 \\ \approx71 \end{gathered}[/tex]So angle between the vector is 71 degree.
Math sequence 1,2,4,7,__
Maths sequence :
1+1 = 2
2+2 =4
4+3 =7
7+4 =11
11+5 = 16
16 +6 = 22
22+7 = 29......
rule : add the answer with the next number to .
sequence is that the pattern rule.
use the distributive property to write an equivalent expression for 88 plus 55
We are asked to use the distributive property to write an equivalent expression for 88 plus 55.
Let us first understand what is distributive property?
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]The above property means that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
But we have only two numbers 88 and 55 so how are we going to apply this property?
We need to break these numbers.
Let us find out the GCF (greatest common factor) of these two numbers.
11 is the greatest common factor of numbers 88 and 55
So, we can break the numbers as
[tex]\begin{gathered} 88=11\cdot8 \\ 55=11\cdot5 \end{gathered}[/tex]Now we have three numbers so let us apply the distributive property.
[tex]\begin{gathered} a\cdot(b+c)=a\cdot b+a\cdot c \\ 11\cdot(8+5)=11\cdot8+11\cdot5 \end{gathered}[/tex]Therefore, the equivalent expression for 88 plus 55 is
[tex]88+55=11\cdot(8+5)_{}[/tex]Select three points: one above the line, one below it, and one on it. Substitute each into the inequality and show the results.Select the words from the drop-down lists to correctly complete the sentences.The point (−5, 5) is on, below, above the line and is, is not a solution to the inequality. The point (0, 10) is on, below, above the line and is, is not a solution to the inequality. The point (0, 0) is on, below, above the line and is not, is a solution to the inequality.(0, 0) is on, below, above the line and is now, is a solution to the inequality.
EXPLANATION
Since we have the given graph, the points that we can use are the following:
The points (-5,5) is above the line and is not a solution to the inequality.
The point (0,10) is on the line and is not a solution to the inequality.
The point (0,0) is below the line and is a solution to the inequality.
solve x 9/× = x/4 what is x
Fallington Fair charges an entrance fee of $10 and $1.00 per ticket for the rides. Levittown Fair charges $5 entrance fee and $2 per ticket. Write an equation/inequality to show when Fallington Fair and Levittown Fair will cost the same.
Information given
Fallington Fair charges an entrance fee of $10 and $1.00 per ticket for the rides. Levittown Fair charges $5 entrance fee and $2 per ticket. Write an equation/inequality to show when Fallington Fair and Levittown Fair will cost the same.
Solution
Let's put some notation for this case, let x the number of rides and we can set up the following equation:
[tex]\text{Fallington}=\text{Levitown}[/tex][tex]10+x=5+2x[/tex]And now we can solve for x on the following way:
10-5= 2x-x
5=x
So then Fallington Fair and Levittown Fair will cost the same at 5 rides
denominator of a fraction is 2 more than the numerator . if both numerator and denominator are increased by 10 , a simplified result is 9/10. Find the original fraction. Do not simplify
Let the numerator = x
The denominator of a fraction is 2 more than the numerator
So, the denominator = x + 2
if both numerator and denominator are increased by 10, a simplified result is 9/10.
So,
[tex]\frac{x+10}{(x+2)+10}=\frac{9}{10}[/tex]Solve for x:
[tex]\begin{gathered} \frac{x+10}{x+12}=\frac{9}{10} \\ \\ 10(x+10)=9(x+12) \\ 10x+100=9x+108 \\ 10x-9x=108-100 \\ x=8 \end{gathered}[/tex]so, the original fraction will be = 8/10
So, the answer will be = 8/10
The model shows the expression 21 + 9. Which expression is equivalent to this sum? O 317+3) 0 31+ 3 0 3+7+3 O 763+3)
Given data:
The given expression is (21+9).
The given expression can be written as,
[tex](21+9)=3(7+3)[/tex]Thus, the first option is correct.