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Jane is saving to buy a cell phone. She is given a $100 gift to start and saves $35 a month from her allowance. So after one month, Jane has saved $135. Does it make sense to represent the relationship between the amount saved and the number of months with one constant rate? Why or why not? Explain your answer.
Jane is given a $100 gift to start and saves $35 a month from her allowance.
After 1 month, Jane has saved
After 2 months, Jane has saved
After three months, Jane has saved
and so on
In general, after x months Jane has saved
This means that it makes sense to represent the relationship between the amount saved and the number of months with one constant rate (in this case the constant rate is 35). It makes sense because the amount of money increases by $35 each month. Since the amount of increase is constant, we get constant rate. Also the initial amount is known ($100), so there is a possibility to write the equation of linear function representing this situation.
Step-by-step explanation:
What is the error in this problem
Answer:
10). m∠x = 47°
11). x = 30.96
Step-by-step explanation:
10). By applying Sine rule in the given triangle DEF,
[tex]\frac{\text{SinF}}{\text{DE}}=\frac{\text{SinD}}{\text{EF}}[/tex]
[tex]\frac{\text{Sinx}}{7}=\frac{\text{Sin110}}{9}[/tex]
Sin(x) = [tex]\frac{7\times (\text{Sin110})}{9}[/tex]
Sin(x) = 0.7309
m∠x = [tex]\text{Sin}^{-1}(0.7309)[/tex]
m∠x = 46.96°
m∠x ≈ 47°
11). By applying Sine rule in ΔRST,
[tex]\frac{\text{SinR}}{\text{ST}}=\frac{\text{SinT}}{\text{RS}}[/tex]
[tex]\frac{\text{Sin120}}{35}=\frac{\text{Sin50}}{x}[/tex]
x = [tex]\frac{35\times (\text{Sin50})}{\text{Sin120}}[/tex]
x = 30.96
Find the differential coefficient of
[tex]e^{2x}(1+Lnx)[/tex]
Answer:
[tex] \rm \displaystyle y' = 2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} [/tex]
Step-by-step explanation:
we would like to figure out the differential coefficient of [tex]e^{2x}(1+\ln(x))[/tex]
remember that,
the differential coefficient of a function y is what is now called its derivative y', therefore let,
[tex] \displaystyle y = {e}^{2x} \cdot (1 + \ln(x) )[/tex]
to do so distribute:
[tex] \displaystyle y = {e}^{2x} + \ln(x) \cdot {e}^{2x} [/tex]
take derivative in both sides which yields:
[tex] \displaystyle y' = \frac{d}{dx} ( {e}^{2x} + \ln(x) \cdot {e}^{2x} )[/tex]
by sum derivation rule we acquire:
[tex] \rm \displaystyle y' = \frac{d}{dx} {e}^{2x} + \frac{d}{dx} \ln(x) \cdot {e}^{2x} [/tex]
Part-A: differentiating $e^{2x}$
[tex] \displaystyle \frac{d}{dx} {e}^{2x} [/tex]
the rule of composite function derivation is given by:
[tex] \rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dg} f(g(x)) \times \frac{d}{dx} g(x)[/tex]
so let g(x) [2x] be u and transform it:
[tex] \displaystyle \frac{d}{du} {e}^{u} \cdot \frac{d}{dx} 2x[/tex]
differentiate:
[tex] \displaystyle {e}^{u} \cdot 2[/tex]
substitute back:
[tex] \displaystyle \boxed{2{e}^{2x} }[/tex]
Part-B: differentiating ln(x)•e^2x
Product rule of differentiating is given by:
[tex] \displaystyle \frac{d}{dx} f(x) \cdot g(x) = f'(x)g(x) + f(x)g'(x)[/tex]
let
[tex]f(x) \implies \ln(x) [/tex][tex]g(x) \implies {e}^{2x} [/tex]substitute
[tex] \rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \frac{d}{dx}( \ln(x) ) {e}^{2x} + \ln(x) \frac{d}{dx} {e}^{2x} [/tex]
differentiate:
[tex] \rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \boxed{\frac{1}{x} {e}^{2x} + 2\ln(x) {e}^{2x} }[/tex]
Final part:
substitute what we got:
[tex] \rm \displaystyle y' = \boxed{2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} }[/tex]
and we're done!
Answer:
Product Rule for Differentiation
[tex]\textsf{If }y=uv[/tex]
[tex]\dfrac{dy}{dx}=u\dfrac{dv}{dx}+v\dfrac{du}{dx}[/tex]
Given equation:
[tex]y=e^{2x}(1+\ln x)[/tex]
Define the variables:
[tex]\textsf{Let }u=e^{2x} \implies \dfrac{du}{dx}=2e^{2x}[/tex]
[tex]\textsf{Let }v=1+\ln x \implies \dfrac{dv}{dx}=\dfrac{1}{x}[/tex]
Therefore:
[tex]\begin{aligned}\dfrac{dy}{dx} & =u\dfrac{dv}{dx}+v\dfrac{du}{dx}\\\\\implies \dfrac{dy}{dx} & =e^{2x} \cdot \dfrac{1}{x}+(1+\ln x) \cdot 2e^{2x}\\\\& = \dfrac{e^{2x}}{x}+2e^{2x}(1+\ln x)\\\\ & = \dfrac{e^{2x}}{x}+2e^{2x}+2e^{2x} \ln x\\\\& = e^{2x}\left(\dfrac{1}{x}+2+2 \ln x \right)\end{aligned}[/tex]
Two numbers are in the ratio 2:3. If 3 is added to the numbers, the ratio changes to 3:4. Find the numbers.
Answer:
6:9
Step-by-step explanation:
Answer:
6 and 9
Step-by-step explanation:
according to the question, the nos. are 2x and 3x.
then, (2x+3)/(3x+3)=3/4
therefore, 4(2x+3)=3(3x+3)
8x+12=9x+9
12-9=9x-8x
3=x
therefore the nos. are 2×3=6 & 3×3=9
Answer from Gauth math
Find the degree, leading coefficient, and the constant term of the polynomial.
[tex] \LARGE{ \boxed{ \purple{ \rm{Answers;)}}}}[/tex]
☃️ Degree of the polynomial- The highest degree of any term in a polynomial. Here the highest degree is 5.
⇛ 4x⁴ + 5 + 6x⁵ - 2x(° of polynomial = 5)
☃️ Leading coefficient- The coefficient of the term having the highest degree of the polynomial. Here, the highest degree is 5 and the term is 6x⁵
⇛ 4x⁴ + 5 + 6x⁵ - 2x (Leading coeff. = 6)
☃️ Constant term- It is the term having no coefficients, only a fixed real number. This remains constant in any value of polynomial.
⇛ 4x⁴ + 5 + 6x⁵ - 2x (Constant term = 5)
━━━━━━━━━━━━━━━━━━━━
I will rate you brainliest Select the best description of what the LCM of a set of polynomials is. a.It is the quotient of all the factors of the polynomials. b.It is the common numerator of a rational expression. c. It is the product of the prime factors that are either unique to or shared by the polynomials. d. It is all the polynomials in the set.
Answer:
C. It is the product of the prime factors that are either unique to or shared by the polynomials.
Step-by-step explanation:
LCM of polynomials is:
=> Finding the factors of all the numbers and variable in the expression
=> Next, we multiply the unique numbers and the variable of the expression to find the LCM.
So, C is the correct answer.
The LCM of a set of polynomials is the product of the prime factors that are either unique to or shared by the polynomials.
What is LCM of polynomial?To find the lowest common multiple (L.C.M.) of polynomials, we first find the factors of polynomials by the method of factorization and then adopt the same process of finding L.C.M.
Example : The L.C.M. of 4a2 - 25b2 and 6a2 + 15ab.
Factorizing 4a2 - 25b2 we get,
(2a)2 - (5b)2, by using the identity a2 - b2.
= (2a + 5b) (2a - 5b)
Also, factorizing 6a2 + 15ab by taking the common factor '3a', we get
= 3a(2a + 5b)
L.C.M. is 3a(2a + 5b) (2a - 5b)
According to the question
The LCM of a set of polynomials is
is the product of the prime factors that are either unique to or shared by the polynomials.
(from above example we can see that )
Hence, It is the product of the prime factors that are either unique to or shared by the polynomials.
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Solve the equation.
In a study of academic procrastination, researchers reported that for a random sample of 41 undergraduate students preparing for a psychology exam, the mean time spent studying was 11.9 hours with a standard deviation of 4.5 hours. Compute a 95% confidence interval for μ, the mean time spent studying for the exam among all students taking this course.
Answer:
The 95% confidence interval is [tex]10.5 < \mu <13.3[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 41[/tex]
The sample mean is [tex]\= x = 11.9 \ hr[/tex]
The standard deviation is [tex]\sigma = 4.5[/tex]
For a 95% confidence interval the confidence level is 95%
Given that the confidence level is 95% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical values of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 4.5 }{ \sqrt{41} }[/tex]
[tex]E = 1.377[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x - E[/tex]
substituting values
[tex]11.9 - 1.377 < \mu <11.9 + 1.377[/tex]
[tex]10.5 < \mu <13.3[/tex]
Use the information angle 8 is congruent to angle 11 to determine which lines are parallel.
A. p || q
B. l || m
C. m || n
D. l || n
Answer:
A
Step-by-step explanation:
based on line p and q
Answer: p || q
Or A
Step-by-step explanation:
good luck
Find the value of x to the nearest tenth of a degree.
20.4
21.8
42.9
68.2
Answer:
Answer is 20.4 .........
se pueden calcular las edades de Juanita y de su madre si se sabe que:
1) actualmente la suma de sus edades es 44 años
2) dentro de 11 años la edad de juanita será la mitad de la edad de su mamá
Responder:
Juanita = 11, madre = 33
Explicación paso a paso:
Dado lo siguiente:
Suma de sus edades = 44
En 11 años, Juanita tendrá la mitad de la edad de su madre
Sea la edad de la madre = my la edad de juanita = j
m + j = 44 - - - - (1)
(j + 11) = 1/2 (m + 11)
j + 11 = 1/2 m + 5,5; j - 1/2 m = - 5,5; 2j - m = - 11
2j - m = - 11 - - - - (2)
Desde (1): m = 44 - j
Sustituyendo m = 44- j en (2)
2j - (44 - j) = - 11
2j - 44 + j = - 11
3j = - 11 + 44
3j = 33
j = 11
De 1)
m + j = 44
m + 11 = 44
m = 44 - 11
m = 33
a=5,and 5+z=14,so a+z=14
Answer:
Z=9
Step-by-step explanation:
Insert A into A+Z=14
5+z=14
Subtract 5 on both sides, to find Z.
-5 -5
z=9
find the common ratio of the geometric sequence 4,3,9/4
Answer:
3/4
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
3/4
Check with the third and second terms
9/4 ÷3
9/4 *1/3= 3/4
The common ratio is 3/4
look at the image for the question
Volume = l × b × h
Length = 7m
Breadth = 7m
Height = 9m
Volume = 7×7×9
441m³
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In the Olympic tennis event ( in which each tennis player gets eliminated from the tournament after the first defeat) there are 37 players participating. Can you − in 5 seconds − count how many matches there need to be until there is one
Answer:
approximately 19 matches for single player contest and 9 matches for double player contest
Step-by-step explanation:
However, it is important to note that a tennis match is usually between two players (one player to one) or two teams of players (two players to two players),
So, there may be approximately 19 matches for single player
([tex]\frac{37 players}{2}[/tex]) and approximately 9 matches ([tex]\frac{18.5}{2}[/tex]) for double player contest.
Explain why this quadrilateral is not a parallelogram.
Answer:
A parallelogram has two sets of parallel sides. This quadrilateral only has on set of parallel sides, so therefore it cannot be a parallelogram.
Identify the segments that are parallel, if any, if ∠ADH≅∠ECK.
A. AE || CB
B. AD|| CB
C. none of these
D. AC|| CD
9514 1404 393
Answer:
C. none of these
Step-by-step explanation:
The given information tells us ΔACD is isosceles, but gives no information about any lines that might conceivably be parallel.
A rectangular city is 3 miles long and 10 miles wide. What is the distance between opposite corners of the city? The exact distance is ______ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ______ miles.
Answer:
The exact distance is [tex]\sqrt{109}[/tex] miles.
The distance is approximately 10.4 miles.
Step-by-step explanation:
It is given that a rectangular city is 3 miles long and 10 miles wide. So,
Length = 3 miles
Width = 10 miles
We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.
Using Pythagoras theorem, the length of diagonal is
[tex]d=\sqrt{l^2+w^2}[/tex]
where, l is length and w is width.
Substitute l=3 and w=10.
[tex]d=\sqrt{(3)^2+(10)^2}[/tex]
[tex]d=\sqrt{9+100}[/tex]
[tex]d=\sqrt{109}[/tex]
The exact distance is [tex]\sqrt{109}[/tex] miles.
Now,
[tex]d=\sqrt{109}[/tex]
[tex]d=10.4403065[/tex]
[tex]d\approx 10.4[/tex]
The distance is approximately 10.4 miles.
list the domain and range of the relation {(6,8), (7,7), (0,-8), (7,1), (6,8)}
Answers:
Domain = {0, 6, 7}
Range = {-8, 1, 7, 8}
======================================================
Explanation:
The domain is the set of allowed x inputs. So we simply list the x coordinates. Toss out any duplicates. Sorting the values is optional.
The range is the set of y coordinates. Like with the domain, we'll toss out any duplicates and optionally we can sort the y values.
write two properties of Zero
Answer:
the addition properties of zero and multiplication properties of zero
zero is even, not odd not neutral.
zero is neither positive or negative.
The U.S. National Whitewater Center in Charlotte uses a pump station to provide the flow of water necessary to operate the rapids. The pump station contains 7 pumps, each with a capacity to deliver 80,000 gallons per minute (gpm). The water channels and ponds in the facility contain 13 million gallons of water. If the pump station is operating 5 pumps simultaneously, assuming ideal conditions how long will it take to completely pump the volume of the system through the pump station
Answer:
t = 32,5 minutes
Step-by-step explanation:
Volume to fill = 13000000 Gal
5 pumps delivering 80000 gal/min
5 * 80000 = 400000 gal/min
If we divide the total volume by the amount of water delivered for the 5 pumps, we get the required time to fill the volume, then
t = 13000000/ 400000
t = 32,5 minutes
Consider exponential function h.
h(x) = 3x + 4
The function is always positive.
(0,5) is the y-intercept, since the graphed line never crosses the x axis, there is no x-intercept.
The function is positive and greater than 4 for all values of x
Not sure what the actual choices are on a couple of the questions. The choices would help answering.
what is the prime factorization of 7?
As Prime factorization is a process of writing all numbers as a product of primes then The prime factorization of number 7 is 7.
What is Number system?A number system is defined as a system of writing to express numbers.
Prime factorization is a process of writing all numbers as a product of primes
The number 7 is a prime number, which means it is only divisible by 1 and itself.
Therefore, the prime factorization of 7 is simply 7 itself.
Hence, the prime factorization of number 7 is 7.
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Help please anyone. Thank You
Answer:
A) 144 yd²
Step-by-step explanation:
Base= 8x8=64
Side = 1/2*8*5=20
64+20+20+20+20=144 yd²
Answer:
168 sq yds
Step-by-step explanation:
5x8/2x2=40
8x8/2x2=64
8x8=64
40+64+64=168
At the dog show, there are 4 times as many boxers as spaniels. If there are a total of 30 dogs,how many dogs are spaniels? Plz help me
Answer:
6 spaniels
Step-by-step explanation:
Create 2 equations to represent this, where b is the number of boxers and s is the number of spaniels:
4s = b
s + b = 30
We can plug in 4s as b into the second equation, s + b = 30:
s + b = 30
s + 4s = 30
5s = 30
s = 6
So, there are 6 spaniels.
Solve 2(x - 1) + 3 = x - 3(x + 1) (make sure to type the number only)
Answer:
x = -1
Step-by-step explanation:
2(x - 1) + 3 = x - 3(x + 1)
Distribute
2x -2+3 = x -3x-3
Combine like terms
2x +1 = -2x-3
Add 2x to each side
2x+1 +2x = -2x-3+2x
4x+1 = -3
Subtract 1 from each side
4x+1-1 = -3-1
4x= -4
Divide by 4
4x/4 = -4/4
x = -1
Help me with this question plz
19. 68 because 90seconds 1hr 30 mons
please help, will give brainliest for correct answer
ain't it just 3 for each one unless i'm missing something
20,000 is 10 times as much as
Answer:
2000
Step-by-step explanation:
20,000 is 2000 times the number 10.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given numbers are 20000 and 10. The number 20000 is how many times the number 10 will be calculated by dividing the number 20000 by 10.
E = 20000 / 10 = 2000
Therefore, the number 20,000 is 2000 times the number 10.
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A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1825 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
1) 35 gallons by the first car 2) 40 gallons by the second car
Step-by-step explanation:
Suppose the first car used x gallons, when the second car used the rest- 75-x
If the first car's efficiency is 35 miles per galon, its milleage is 35*x, the second car's milleage is 15*(75-x). And the summary milleage is equal to 1825.
35x+15(75-x)=1825
35x+1125-15x= 1825
20x=700
x=35- gallons consumed by the first car,
75-35=40- gallons consumed by the second one