The domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}
The domain of a function is the set of inputs that are accepted by the function. The range, also known as the codomain, is the set of all the output values of the function.
Here, we are given a relation with the following set of solutions-
{(5,-3), (2,2), (0, -3), (2,1) (5,3)}
We know that all x values will form the domain and all the y values will make up the range.
Here the x values are: 5, 2, 0, 2, 5
and the y values are: -3, 2, -3, 1, 3
Thus, the domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}
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QUESTION 5
(a) Differentiate the following
(i)
y=e²x - 3e-4x
Answer: e² - 4
Step-by-step explanation:
Differentiate of e²x - 3e-4x is e² - 4
Answer:
[tex]\dfrac{\text{d}y}{\text{d}x} = 2e^{2x}+12e^{-4x}[/tex]
Step-by-step explanation:
Given function:
[tex]y=e^{2x}-3e^{-4x}[/tex]
[tex]\boxed{\begin{minipage}{3.7cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{\text{d}}{\text{d}x} e^{2x}-\dfrac{\text{d}}{\text{d}x}3e^{-4x}\\\\& =2 \cdot e^{2x}-(-4)\cdot 3 e^{-4x} \\\\ &= 2e^{2x}+12e^{-4x}\end{aligned}[/tex]
Multiple choice: Which of the following steps below would be a good first step when solving the equation 2x+5=11
Divide both sides by 2
Add 5 to both sides of the equation
Subtract 5 from both sides of the equation
Add 11 to both sides of the equation
Answer:
easy
Step-by-step explanation:
How to solve a system of equations by elimination.
Write both equations in standard form.
Make the coefficients of one variable opposites.
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
the day of the month
a) interval
b)ordinal
c) nominal
d) ratio
?
The day of the month is nominal (option c).
What is nominal data?Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable. A nominal variable is a categorical variable that is qualitative.
A ratio scale is quantitative. A ratio scale is a variable with a true zero. An example is weight. An interval variable is a variable where each value is measured along a scale. An example of an interval variable is credit score.
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PLEASE HELP! Triangle BCD has the following side lengths: BC = 60, CD = 50
Triangle RST has the following side lengths: RS = 11x-4, ST = 70
What is the value of x? (put just the number in the first box)
What is the length of side RS? (put just the number in the second box)
The value of x is 11 units and the length of side RS = 11x-4 is 117 units.
with measurement BC = 60, CD = 50.
Triangle RST : RS = 11x-4, ST = 70
What is similarity?Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.
Given:
BC = 60 and CD = 50
RS = 11x - 4 and ST = 70
Now, considering
BC : CD = RS : ST
60 : 50 = 11x - 4 : 70
60/50 = (11x - 4)/70
50 * (11x - 4) = 70 * 60
11x - 4 = 84
11x = 88
x = 11
So, RS = 11x - 4
RS = 11 x 11 - 4
RS = 117
Hence, the value of x is 11 and the length of side RS is 117
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A dog is 9 times as heavy as a cat, a hamster is 20 times as light as a cat, and a mouse is 6 times as heavy as the hamster. How many times is the dog as heavy as a mouse?
Answer:
30
Step-by-step explanation:
Let the cat have a weight of x.
Then, the dog weighs 9x.
The hamster weighs x/20.
The mouse weighs 3x/10.
So, the dog is 9/(3/10) = 30 times as heavy.
The weight of the dog is 30 times the weight of the mouse.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Let the weight of the dog be x,
A dog is 9 times as heavy as a cat,
weight of the dog = 9x - - - - -(1)
A hamster is 20 times as light as a cat
Weight of the hamster = x /20
A mouse is 6 times as heavy as a hamster.
Weight of the mouse = 6(x /20)
m(20/6) = x
Now, put x = m(20/6) in equaiton 1,
weight of the dog = 9[m(20/6)]
weight of the dog = 30m
Thus, the weight of the dog is 30 times the weight of the mouse.
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3)
Chicken cost $7.19 per pound. You buy 0.82 pounds at the supermarket.
How much did you spend?
Answer:
$5.90
Step-by-step explanation:
(7.19)(.82) Put these numbers in your calculator and multiply them together.
5.8958 Round to the nearest cent
$5.90
When the number of miles driven equals 0, why is the cost per month not equal to 0? Why does the graph have a positive slope?
Answer:
I think it's because of the down payment and the positive slope because you are going to pay in installments by months.
Cosx-1=0[tex]Cos(x)-1=0[/tex]
The solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.
What is the solution of the given trigonometric equation as in the task content?It follows from the task content that the solution to the given trigonometric equation is to be determined.
Given;
Cos(x) - 1 = 0
Add 1 to both sides of the equation;
Cos (x) = 1
Therefore, the value of x can be determined by evaluating the cos inverse of (-1).
Hence,
x = Cos-¹(1)
x = nπ (where n is any integer real number value).
Ultimately, the solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.
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Solve the inequality and express your answer in interval notation. x^2-12x+3<0
Solution:
B.) [tex](6-\sqrt{33}, 6+\sqrt{33})[/tex]
Hope this helps! If so, please lmk! Thanks and good luck!
Can someone please explain this to me? Thank youuu:)
Answer:
B: 3x+(4x+2)=180
Step-by-step explanation:
Supplementary angles are those angles that sum up to 180 degrees. The question gives you the two angles that compose the 180 degree angle thus you get the equation:
Angle 1 + Angle 2 = Supplementary Angle
In this case we see that these two angles are Angles B and C and a supplementary angle is 180 degrees thus:
(4x+2)+3x = 180
Furthermore this also allows you to find x.
The terminal side of an angle theta in standard position passes through the point -6(-4,). Use the figure to find the following value. r
Answer is - 2 [tex]\sqrt{3}[/tex] / 13
Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position
cosθ = cos (π + d) (d is the inner angle of the tringle)
= - cos 2
= - 4 / - [tex]\sqrt{(- 6^{2} + (- 4^{2} )[/tex]
= - 4 / - [tex]\sqrt{36 + 16 }[/tex]
= - 4 / -[tex]\sqrt{52}[/tex]
= - 4 / 2[tex]\sqrt{13}[/tex]
= - 2 / [tex]\sqrt{13}[/tex]
multiply by [tex]\sqrt{13}[/tex]
we get,
= - [tex]\frac{2 \sqrt{13} }{13}[/tex]
Formulae :
Arc cosecant y = arcs(x) = csc-1(x). Another way to write x = csc(y).
Arccosine y = arcos(x) = cos-1(x). Another way to write x = cos(y).
Arc cotangent y = arcos(x) = cot-1(x). Another way to write x = cot(y).
Arc secant y = arcsec(x) = sec-1(x). Another way to write x = sec(y).
Arcsine y = arcsine(x) = sin-1(x). Another way to write x = sin(y).
Arctangent y = arctan(x) = tan-1(x). Another way to write x = tan(y).
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Stephan monthly pay stub indicates that his monthly gross income is 3800 however 800 is withheld for income and social security taxes and 200 is withheld for his health and disability insurance how much is Stephan’s Disposable income
Step-by-step explanation:
3800 is the general amount, but before he can touch it, 800 and 200 are taken away from it for the described purposes.
so, what is left is
3800 - 800 - 200 = 2800
this is then the real amount he can do something with.
All flowers need water
Some trees need water
Some flowers are trees
Valud or Invalid
valid . some trees grow flowers i belive
Suppose we want to choose 6 objects, without replacement, from 12 distinct objects. (a) If the order of the choices matters, how many ways can this be done? (b) If the order of the choices does not matter, how many ways can this be done?
(a) There are 665280 ways of selection if the order of the choices matters.
(b) There are 924 ways of selection if the order of the choices does not matters.
(a) If the order of the choices matters, then we must use the permutation formula that is
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
Here n is the total no. of objects and r is chosen objects
We have n = 12
r = 6
After we substitute the value we get
[tex]^{12}P_6 = \frac{12!}{(12 - 6)!}[/tex]
[tex]^{12}P_6 = \frac{12!}{6!}[/tex]
[tex]^{12}P_6[/tex] = 665280
Thus, there are 665280 ways of selection if the order of the choices matters
(b) If the order of the choices does not matter, then we must use the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n - r)!}[/tex]
After we substitute the value we get
[tex]^{12}C_6 = \frac{12!}{6!(12 - 6)!}[/tex]
[tex]^{12}C_6 = \frac{12!}{6! 6!}[/tex]
[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7×6! / 6!×6!
[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7/ 6!
[tex]^{12}C_6 =[/tex] 665280/ 720
[tex]^{12}C_6 =[/tex] 924
Thus, there are 924 ways of selection if the order of the choices does not matters.
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Taylor is curious to know how different types of music will impact how long it takes someone to finish their homework. She gathers a group of 12 year olds and breaks them into groups of 3. The first group listens to nothing. The 2nd group listens to classical, the 3rd listens to pop music, and the 4th listens to heavy metal. Each group needs to read 20 pages of the same book and answer the same set of 20 math questions. She times each group and compares.
a) Find the Independent Variable
b) Find the dependent variable
c) Find the Control Group
d) Find the experimental group
e) Find 3 constants
Gabby worked 30 hours in 4 days. Determine the rate for ratio of the two different quantities.
30/34 hours per day
4/30 hours per day
30/4 hours per day
4/34 hours per day
The required rate for ratio of the two different quantities i.e
Gabby worked 30/4 hours per day.
Option (c) is correct.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Gabby worked 30 hours in 4 days.
According to given question we have
The ratio of the two quantities of the different kind and in the different units is a fraction that shows how many times one quantity is of the other.
By the use of arithmetic we have,
Gabby worked 30 hours in 4 days means
4 days= 30 hours
1 days = 30/4 hours
Therefore, the required rate for ratio of the two different quantities i.e
Gabby worked 30/4 hours per day.
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Answer: 30/4 hours per day
Step-by-step explanation:
write a explicit formula 96 24 6
Answer:
[tex]a_{n}[/tex] = 96 [tex](\frac{1}{4}) ^{n-1}[/tex]
Step-by-step explanation:
there is a common ratio between consecutive terms, that is
[tex]\frac{24}{96}[/tex] = [tex]\frac{6}{24}[/tex] = [tex]\frac{1}{4}[/tex]
this indicates the sequence is geometric with explicit formula
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 96 and r = [tex]\frac{1}{4}[/tex] , then explicit formula is
[tex]a_{n}[/tex] = 96 [tex](\frac{1}{4}) ^{n-1}[/tex]
PLS HELP! 50 points!
Xin has a dimes and y nickels. She has a maximum of 18 coins worth a minimum of $1.10 combined. Solve this system of inequalities graphically and determine one possible solution.
The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value. In the graphically representation we can see the line intersect each other at point (12,6).
Given that,
The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value.
We have to create a graphic representation of this inequality system and choose a potential resolution.
x + y ≤18----->equation(1)
Amount in pennies: 5x+10y≥110------>equation(2)
solves by eq2 - 5×eq(1)
5x+10y - 5(x+y) = 120 - 5×18
5x + 10y -5x-5y = 120 - 90
5y = 30
y=6
Then x=12
Therefore, x=12, y=6 is the point where two lines converge.
In the graphically representation we can see the equation (1) line and equation (2) line intersect each other at point (12,6).
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A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of triangle extends into a straight line. The angle formed between this straight line and the edge of triangle is marked as d. The angle adjacent to w is marked as c, and the other two angles inside the triangle are marked as a and b.
Step 1: m∠a + m∠b + m∠c = 90 degrees (complementary angles)
Step 2: m∠d + m∠c = 180 degrees (supplementary angles)
Step 3: Therefore, m∠a + m∠b + m∠c = m∠d + m∠c
Step 4: So, m∠a + m∠b = m∠d
In which step did the student first make a mistake and how can it be corrected? (1 point)
a
Step 1; it should be m∠a + m∠b + m∠c = 180 degrees (corresponding angles)
b
Step 1; it should be m∠a + m∠b + m∠c = 180 degrees (sum of angles of a triangle)
c
Step 2; it should be m∠d − m∠c = 90 degrees (alternate interior angles)
d
Step 2; it should be m∠d − m∠c = 90 degrees (adjacent angles)
Answer:
B
Step-by-step explanation:
from seeing the steps listed the answer should be b would be helpful if u posted the diagram along
Please help me
Thank you
Answer: 3 gallons per hour
Step-by-step explanation: 14-(3x) =5 14-5=9 9/3=3
Prepare for Rigid Transformations Think about what you know about geometric figures and parallel lines. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.
Step-by-step explanation:
Parallel Lines are lines that do not intercept with eachother. They have the same slope yet have different y-intercepts.
Draw two lines not touching.
Example
[tex]y = 5x + 1[/tex]
[tex]y = 5x + 2[/tex]
No examples
[tex]y = 5x + 2[/tex]
[tex]y = - \frac{1}{5} x + 2[/tex]
Hope this helps!
E= 1R solve for R pls help me I don’t understand
Answer:
r = e or 2.718282
Step-by-step explanation:
a) simplify both sides of the equation
2.718282 = r
b) flip the equation
r = 2.718282
A city has a population of 210,000 people. Suppose that each year the population grows by 4.5% . What will the population be after 5 years?
The population of a city after 5 years would be 261698.
We know the the formula for the exponential growth of the population is,
P(t) = a(1+r)^t
where, a is the initial population
t is the time period
r is the rate of growth
In this question, we have a = 210000, %R = 4.5
So, r = 0.045
We need to find the population after 5 years.
t = 5
Using above formula,
P = 210000 × ( 1 + 0.045)^5
P = 210,000 × (1.045)^5
P = 210,000 × 1.25
P = 261698.2
P ≈ 261698
Therefore, the population of a city after 5 years would be 261698.
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given z (x)=15x-x^2+3
Answer:
○ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]
Step-by-step explanation:
We are told that:
[tex]z(x)= 15x - x^2 + 3[/tex],
and told to find an expression for [tex]z(x - 1)[/tex].
In order to find [tex]z(x - 1)[/tex], we have to replace [tex]x[/tex] in the definition of [tex]z(x)[/tex] with [tex](x-1)[/tex]:
[tex]z(x - 1) = 15(x -1) - (x - 1)^2 + 3[/tex]
Now we can simplify:
⇒ [tex]z(x-1) = 15x - 15 - (x - 1)^2 + 3[/tex] [Distributing 15 into the first brakets]
⇒ [tex]z(x-1) = 15x - 15 - (x^2 - 2x + 1) + 3[/tex]
⇒ [tex]z(x-1) = 15x - 15 - x^2 + 2x - 1 + 3[/tex] [Distributing the minus sign]
⇒ [tex]z(x - 1) = 17x - x^2 -13[/tex] [Combining like terms]
⇒ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]
Therefore, the first option is the correct one.
219 +485 = 348 + please
Answer: please=356
Step-by-step explanation:
219 +485 = 348 + please
704=348 + please
please=356
Assistant Manager Clyde works as a part-time assistant manager for the Barkley Coffeehouse to earn money to help pay for his college expenses. He makes $11.50 per hour. The coffeehouse sells whole bean coffee, mugs, and other coffee products. Clyde earns $0.50 for each of these items he sells. Last week he worked 30 hours and earned $364. How many coffee products did he sell last week?
The number of coffee product he sells is 38.
How to find the number of coffee products he sells?He makes $11.50 per hour.
He earns $0.50 for each of these items he sells.
Last week he worked 30 hours and earned $364.
Therefore, the number of coffee product he sells last week can be calculated as follows:
let
x = number of coffee product he sells.
364 = 11.50(30) + 0.50(x)
364 = 345 + 0.50x
364 - 345 = 0.50x
19 = 0.5x
divide both sides by 0.5
x = 19 / 0.5
x = 38
Therefore, the number of coffee product he sells is 38.
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What are the coordinates of point A?
Answer:
It's coordinates are (1,-2)
Shinya went to the salon. The cost if her haircut was $18.00. He tipped the barber 20%. What was the total cost
?
A triangle has one 30° angle, an unknown angle, and an angle with a measure that is twice the measure of the unknown angle. Find the measures of the triangle's unknown angles and explain how you found the answer.
The measures of the triangle's unknown angles will be 50° and 100°.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
A triangle has one 30° angle, an unknown angle, and an angle with a measure that is twice the measure of the unknown angle.
Let 'a' and 'b' be the unknown angles of the triangle. Then the equation will be
∠a = 2 ∠b
We know that the angle sum of the triangle is 180°. Then the equation will be
∠a + ∠b + 30° = 180°
2∠b + ∠b = 150°
3∠b = 150°
∠b = 50°
Then the measure of the angle 'a' will be
∠a = 2 ∠b
∠a = 2 x 50°
∠a = 100°
The measures of the triangle's unknown angles will be 50° and 100°.
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Michael Wittry has been investing in his Roth IRA retirement account for 21 years. Two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. What is the current value of his Roth IRA
If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.
Current valueFirst step is to calculate the value loss
Value loss=1/3× original value
Value loss= 1/3× $215,613
Value loss= $71,871
Second step is to calculate the new value
New value=$215,613-$71,871
New value= $143,742
Third step is to calculate the value gained
Value gained= 1/2× new value
Valued gained=1/2× $143,742
Valued gained=$71,871
Fourth step is to calculate the current value
Current value= $143,742+$71,871
Current value=$$215,613
Therefore If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.
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