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]
On which interval(s) is the function f(x) = x^3+3x^2−4x−12 increasing?
The interval at which the function x³ + 3x² - 4x - 12 increases is
x ∈ (- ∞, - 2.5) ∪ (0.5, ∞).
We have,
x³ + 3x² - 4x - 12
We need to draw a graph to see at which interval the graph is increasing.
The graph is given below.
We see that the graph is increasing from x = -∞ to x = -2.5 and from x = -2.5 it decreases till x = 0.5 and again from x = 0.5 it increases to x = ∞.
So we can write the interval as:
x ∈ (- ∞, - 2.5) and x ∈ (0.5, ∞)
We can write it as one single interval as:
S = (- ∞, - 2.5) ∪ (0.5, ∞)
Thus the interval at which the function x³ + 3x² - 4x - 12 increases is
x ∈ (- ∞, - 2.5) ∪ (0.5, ∞).
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0.95x = 0.55x + 60
Step 1, 2, 3 written out
0.95X -0.55X+10-62 ... Step 1: Find Roots solution. X=-4. X = 3. Step 2: Graph ... Write the Domain and Range of the function. Positive.
branlyueer099799893
3 minutes ago
Mathematics
College
ANSWER RIGHT AWAY PLEASE!
question one: simply the exponents. (show your work)
- 21^0 = ?
- (2/3)^-2 = ?
question two: Solve the problem. (leave your answer as a base number with an exponent and show your work)
- 4^6 / 4^2 = ?
question three: Convert the number into numerical form. (show your work)
- 8.723 x 10^-10 = ?
question four: Solve the problem. (leave your answer in scientific notion and show your work)
- 5.1 x 10^8 - 2.3 x 10^3 = ?
- 6 x 10^5 x 1.1 x 10^7 = ?
PLEASE ANSWER I WILL GIVE 50 POINTS TO ANYONE WHO ANSWERS AND MARK BRAINLIEST AT LEAST ANSWER THE ONES YOU KNOW
Identify the vertices and foci of each. Then sketch the graph.
Answer:(0,4)
Step-by-step explanation:
6. A dash polynomial cannot be factored by using only integers.true or False
Solve 2|x| = 3
{-3/2, 3/2}
{-1, 1}
{-2/3, 2/3}
Answer:
{-3/2, 3/2}
Step-by-step explanation:
Let's solve your equation step-by-step.
2(|x|)=3
Step 1: Divide both sides by 2.
2(|x|)/2 = 3/2
|x|= 3/2
Step 2: Solve Absolute Value.
|x|= 3/2
We know either x= 3/2 or x=−3/2
x=3/2
(Possibility 1)
x=−3/2
(Possibility 2)
Avery is renting a car and needs to compare the prices of the two car rental companies. Hertz charges $42 per day and an additional $32 in service charges. Enterprise charges $46 per day and an additional $24 in service changes.
Part A: Write an equations for EACH company that represents the total charges for renting a car for a certain number of days. For both questions (one for Hertz and one for Enterprise), define the variable used.
Part B: Use the equations you made in Part A. Which company charges more for renting a car for 6 days? Show your work and justify your answer.
Part C: If Avery decides to rent the car for only 4 days, which company is less expensive? How much money will Avery save? Show your work and explain your reasoning.
The total cost functions are:
total charges for Hertz=32+42x
total charges for Enterprise=24+46x
What does the total rental cost of each company entails?
The total rental cost of each company consists the fixed service charges and the daily charge which can be multiplied by the total of number of days of rental to determine total charges overall.
Hertz:
total charges=32+42x
when x=6 days
total charges=32+(42*6)
total charges=$284
Enterprise:
total charges=24+46x
when x=6 days
total charges=24+(46*6)
total charges=$300
Renting for 4 days:
total charges(Hertz)=32+(42*4)
total charges(Hertz)=$200
total charges(Enterprise)=24+(46*4)
total charges(Enterprise)=$208
savings=$208-$200
savings=$8
The company that charges less when Avery decides to rent car for only 4 days is Hertz and Avery can $8 as result of choosing Hertz
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Determine if the following equation is an identity equation, a conditional equation, or an inconsistent equation.
−6x+6x−6=2−5
Answer:
(c) inconsistent equation
Step-by-step explanation:
You want to know if the equation -6x+6x-6=2-5 is an identity, conditional, or inconsistent.
SimplifiedThe simplified equation, after combining like terms, is ...
-6 = -3
This is an "inconsistent" equation, always false.
Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm. Use function notation to respond to each item below. Represent the area (in square cm) of a circle that has a radius of 3.4 cm.
The area of the given circle is 36.298 cm square.
Here, we are given that f is the function that determines the area of a circle (in square cm) that has a radius of r cm.
The area of a circle is given the the formula as follows-
area of a circle = πr^2
⇒ f(r) = πr^2
The value of π is approximately 3.14
⇒ f(r) = 3.14r^2
Now, we are given that the radius of a circle is 3.4 cm.
Thus, its area will be-
f(3.4) = 3.14 × 3.4 × 3.4
= 3.14 × 11.56
= 36.298
Thus, the area of the given circle comes out to be 36.298 cm square.
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An airline charges an extra fee
for a checked bag that weighs more than 50 pounds.
Your bag weighs 44.9 pounds. You have a 2.5-pound
hair dryer, a 1.3-pound souvenir, and a 3.6-pound pair
of boots. Which items can you add to the bag without
paying the extra fee?
The items that you can add with not breaking the weight limit are:
The hair dryer, the souvenir, the boots, the boots and the souvenir, and the hair dryer and the souvenir.
Which items can you add to the bag without paying the extra fee?
The maximum weight allowed is 50 pounds, and you already have 44.9 pounds, then the weight you can add is:
50lb - 44.9lb = 5.1lb
Now, the items that you have are:
2.5 lb hair dryer.
1.3 lb souvenir.
3.6 lb pair of boots.
The only things that you can't add together are the hair dryer and the boots, because the weight adds up to:
2.5lb + 3.6lb = 6.1lb
Which is more than the 5.1lb left that you have.
Obviuously, you can't take the 3 items.
Then you can add:
The hair dryer, the souvenir, the boots, the boots and the souvenir, and the hair dryer and the souvenir.
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How can I do this -5/8 x 10/9
Solve the equation below for p:
14p-3=25
Answer:
p=2
Step-by-step explanation:
Pete Ross read in a Wall Street Journal article that the cost of parts and labor to make an Apple iPhone 4S were as follows:
Help please
Answer: $466.
Step-by-step explanation:
Add all the numbers in the graph together, you get 194.
Now, subtract 194 from 660, you get 466. That's how much profit the company makes.
The required generated profit on iPhone 4s is given as $466.2.
What is the cost price and selling price?The cost price is defined as the is the price of producing something while the selling price is the amount that the buyer pays.
Here,
As of the mentioned data,
Cost of making an iPhone = $193.8
The selling price of the iPhone = $660
Profit is meant how much money is generated from the product besides the product cost price.
Profit = selling price - cost price
Profit= 660 - 193.9
Profit = $466.2
Thus, the required generated profit on iPhone 4s is given as $466.2.
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Donna makes $9.75 per hour at her job. Kaylee makes $4 per hour at her job, and she receives a $0.25 raise each month. Which inequality could be used to find the number of months it will take for Kaylee to earn at least as much as Donna per hour?
Jakob received a $1,000-a-year raise in January, sold stocks in March for $6,000 that were originally purchased for $4,000, and in July had a $100 monthly
increase in mortgage payments on his adjustable rate mortgage. The increased mortgage payment started in July and was in effect for the remainder of the year.
What was the total impact on Jakob's cash flow for the year?
|
A. $5,400
B. $7,600
C. $6,400
D. $1,000
The total impact on Jakob's cash flow for the year is C. $6,400.
How to calculate the value?It should be noted that Jakob received a $1,000-a-year raise in January, sold stocks in March for $6,000 that were originally purchased for $4,000.
The impact will be:
= Raise + Sale of stock - Mortgage
= 1000 + 6000 - 600
= 6400
Therefore, the correct option is C
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Tracy is training to lower her mile time. She completed 4 practice runs and lost a total of 1 minute off her personal record for her mile time. What does (−1)÷4=−0.25 represent in the context of the problem?
a.She lost 1 minute off her mile time.
b.She lost an average of 0.25 of a minute off her mile time.
c.She gained 0.25 minutes on her mile time.
d.She lost 4 minutes off her mile time.
Answer:
hi can we talk for a while I'm a little alone
Maddie's Boutique paid the members of its staff $20 per hour. Then the boutique merged with another store, and the staff members started making $24 per hour. What was the percent increase in pay?
Enter your answer to the following equation below. You must include a percent sign.
The percent increase in pay was 20%
Maddie's Boutique paid the members of its staff $20 per hour.
and, the boutique merged with another store, and the staff members started making $24 per hour.
To find the what percent increase in pay ?
Now, According to the question:
Based on the given conditions,
= (24 - 20) ÷ 20
= [tex]\frac{24-20}{20}[/tex]
= 1/5
and, Covert to percentage
= 1/5 x 100
= 20%
Hence, The percent increase in pay was 20%
What is Percentage?
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is :
(value/ total value) x 100%
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() Listen
Which expressions of the division of integers will result in a rational number?
Select all that apply.
-5/7
0/6
4/0
-2/0
Reason:
A rational number is a fraction of any two integers, as long as the denominator is nonzero. This applies to the first two answer choices.
Choices C and D are undefined because of the 0 in the denominator. You cannot divide by zero. This rules out the last two choices.
Can you please help with this
for the two given fractions 3/4 and 1/6 we have:
sum = 11/12product = 1/8quotient = 9/2How to work with fractions?Here we have two fractions, 3/4 and 1/6, and we want to find the sum, product, and quotient between them.
First let's do the sum:
3/4 + 1/6
We just need to find a common denominator, which can be 12, so we can rewrite it as:
9/12 + 2/12 = 11/12
The sum of the two fractions is 11/12
Now the product, it is, we multiply denominator with denominator and numerator with numerator, we will get:
(3/4)*(1/6) = (3*1)/(4*6) = 3/24 = 1/8
The product between the two fractions is equal to 1/8.
Finally, the quotient, this is:
The product between the first numerator and second denominator, and between the first denominator and second numerator, so the quotient becomes:
(3/4)/(1/6) = (3/4)*(6/1) = (3*6)/(4*1) = 18/4 = 9/2
Then we conclude that for the two given fractions 3/4 and 1/6 we have:
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A baseball coach spent $118.25 on 11 pizzas. Estimate ate the cost of each pizza using numbers with one nonzero digit. Then find the exact cost per pizza. Show all work
The baseball coach bought each pizza at an approximate cost of $ 10 or an exact cost of $ 10.75.
What is are the approximate and exact cost of each pizza bought by a baseball coach?
In this problem we know that a baseball coach spends a total of $ 118.25 on buying 11 pizzas. First, we need to estimate the amount of money spent per each pizza bought, which is found by means of multiplication tables and the supposition of truncation, that is, finding the maximum integer less than or equal to the real total cost.
By direct inspection we find that 10 times the 11 pizzas is equal to $ 110, which is the maximum integer less than or equal to the real total cost. Then, we estimate a cost of $ 10 per each pizza bought. Second, the exact unit cost is found by dividing the total by the number of pizzas:
c = $ 118.25 / 11
c = $ 10.75
In a nutshell, the baseball coach bought each pizza at an approximate cost of $ 10 or an exact cost of $ 10.75.
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In the 1988 football season, John Elway earned $2,543,666. If he played 15 games that season, what was his average salary per game? Round to the nearest dollar.
Answer:
169,578$
Step-by-step explanation:
If you divide 2 million 5 hundred and 43 thousand 6 hundred and 66 by 15, the answer you would get would be 169,577.733333 (digit 3 goes on and on), but the question says we would need to round it to the nearest dollar. Therefore, the answer is 169,578$!!!
10y^2+12y=7y
how do i factor this, whats the two x’s
SHOW ME HOW TO FACTOR IT
45 POINTS
The two values of y after factorizing the given quadratic equation are 0, -0.5
The given equation is quadratic as the order of the equation is 2. In a quadratic equation with a single variable, the variable will have two different values which satisfy the equation. These values of the variable can be real and different, real and equal, or imaginary.
So, there will be two values of y.
Consider the given equation,
10y^2 + 12y = 7y
10y^2 +12y - 7y = 0
10y^2 + 5y = 0
Since the coefficients of y and y^2 are both multiples of 5,
5*(2y^2 + y) = 0
2y^2 + y = 0
Taking y as a common factor,
y*(2y+1) = 0
Now, we get two cases,
y = 0 or 2y + 1 = 0 => y = -(1/2) = -0.5
Therefore, y = 0 or y = -0.5
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Evaluate
P/2 -
5 when p =14
Answer:2
Step-by-step explanation:
[tex]\frac{14}{5} -5[/tex]
Divide 14 by 2 to get 7.
7−5
Subtract 5 from 7 to get 2.
Answer=2
Alguém pode me ajudar
Answer:
x≤1
Step-by-step explanation:
Benjamin has papayas and pears in a ratio of 50:94. How many pears does he have if he has 25 papayas? On the double number line below, fill in the given values, then use multiplication or division to find the missing value. delta math
If Benjamin has 25 papayas, given the ratio of papayas to pears as 50:94, he has 47 pears.
What is the ratio?The ratio is the numerical relationship that one variable has when compared with another.
The ratio has the same meaning as proportion.
Ratios are represented in percentages, decimals, fractions, or with the ratio sign (:).
How is the number determined?Another way to calculate it is to examine the ratio against the number of papayas he has.
Benjamin has 25 papayas, which is half of 50 (25/50). This means he has half of the pears, which is 47 (94/2).
Data and Calculations:Papayas = 25
The ratio of papayas to pears = 50:94
For every 50 papayas Benjamin has, he has 94 pears.
The number of pears he has = 47 (25/50 x 94)
Thus, if Benjamin has 25 papayas, given the ratio of papayas to pears as 50:94, he has 47 pears.
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How can you use the
Product of Powers, Power of a Product, and
Power of a Power Laws to evaluate and write
equivalent numerical expressions with whole-
number exponents?
Answer:
An equivalent numerical expression with whole-
number exponent using these laws can be written as:
1) 2² × 2³ = 2^5 => using product of Powers
2) 2² × 3² = (2×3)² = 6² => using power of a Product
3) (2²)³ = 2^6 => using power of a power
Step-by-step explanation:
First of all, let us understand some terms like;
1) Exponentiation: It is the mathematical process of raising one integer to the power of another. The base is the first integer, while the exponent is the second.
2) Power: A power is a phrase that depicts the same component being multiplied repeatedly.
3) Exponent: The number of times the base is used as a factor is represented by the exponent.
Now, let us understand the 7 Laws of Exponents;
1) a^m × a^n = a^(m+n) => Product With the Same Bases
2) a^m / a^n = a^(m-n) => Quotient with Same Bases
3) (a^m)^n = a^(m×n) => Power Raised to a Power
4) a^n × b^n = (ab)^n => Product to a Power
5) a^n / b^n = (a/b)^n => Quotient to a Power
6) a^0 = 1 => Zero Power
7) a^(-m) = 1/a^m => Negative Exponent Rule
Furthermore, an equivalent numerical expression with whole-
number exponent using these laws can be written as:
1) 2² × 2³ = 2^5 => using product of Powers
2) 2² × 3² = (2×3)² = 6² => using power of a Product
3) (2²)³ = 2^6 => using power of a power
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A certain race is a distance of 24 furlongs. How far is the race in (a) miles? (b) yards?
PLEASE HELP!! 50 points
I’m confused on how to solve this for gross pay :(
Ted worked 40 hours last week and earned $1200. 40% of his pay is from commission. How much did Ted earn in commission? What is his hourly wage?
Han tiene 4 tazas de jugo de naranja para poner en frascos. Si pone ½ taza de jugo en cada frasco, ¿cuántos frascos puede llenar?
Han llenaría 8 tazas con jugo de naranja porque si tomas la mitad de 1 taza de jugo de naranja puedes hacer 2 tazas ahora haz eso 4 veces y obtendrás 8 tazas de jugo de naranja
Find the average rate of change of
g(x)=-2x^3+5 from z=-4 to x=3
The average rate of change of the function from x == -4 to x = 3 is calculated as: -26.
How to Determine the Average Rate of Change of a Function?The formula for determining the average rate of change across a given interval of a function is expressed as:
Average rate of change = g(b) - g(a)/b - a.
Given the function, g(x) = -2x³ + 5 to find the average rate of change from x = -4 to x = 3, do the following:
a = -4
g(a) = g(-4) = -2(-4)³ + 5 = -2(-64) + 5 = 128 + 5 = 133
b = 3
g(b) = g(3) = -2(3)³ + 5 = -2(27) + 5 = -54 + 5 = -49
Substitute the values into g(b) - g(a)/b - a:
Average rate of change = (-49 - 133)/(3 - (-4))
Average rate of change = -182/7
Average rate of change = -26
Thus, the average rate of change of the function from x == -4 to x = 3 is calculated as: -26.
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