In order to solve this IVP using Laplace transforms, we must first write f(t) in terms of the Heaviside function.
f(t)=0*(u(t)-u(t-Pi))+1*(u(t-Pi)-u(t-2Pi))+0*(u(t-2Pi))
f(t)=u(t-π)-u(t-2π)
So, the rewritten IVP is
y'' +y = u(t-π)-u(t-2π)y(0)=0, y'(0)=1
Taking the Laplace transform of both sides of the equation, we get:
s2L{y}-sy(0)-y'(0)+L{y}=(1/s)*e-πs-(1/s)*e-2πs
s2L{y}-1+L{y}=(1/s)*e-πs-(1/s)*e-2πs
(s2+1)L{y}=1+(1/s)*e-πs-(1/s)*e-2πs
L{y}=1/(s2+1)+(1/s(s2+1))e-πs-(1/s(s2+1))*e-2πs
Now, we must take the inverse transform of both sides to solve for y.
The first inverse transform is easy enough. By definition, it is sin(t).
The second two inverse transforms will be a little tougher, we will have to use partial fraction decomposition to break them down into terms that are easier to compute.
A/s+(Bs+C)/(s^2+1)=1/(s(s^2+1))
A(s^2+1)+(Bs+C)(s)=1
As^2+A+Bs^2+Cs=1
Rewriting this system in matrix form, we get:
1 1 0 A 0
0 0 1 * B = 0
1 0 0 C 1
Using row-reduction we find that A=1, B=-1, and C=0. So, our reduced inverse transforms are:
L-1{(e-πs)(1/s-s/(s2+1))}
and
L-1{(e-2πs)(1/s-s/(s2+1))}
Using the first and second shifting properties, these inverse transforms can be computed as.
L-1{(e-πs)(1/s-s/(s2+1))}=u(t-π)-cos(t-π)u(t-π)
L-1{(e-2πs)(1/s-s/(s2+1))}=u(t-2π)-cos(t-2π)u(t-2π)
Combining all of our inverses transforms, we get the solution the IVP as:
y=sin(t)+u(t-π)-cos(t-π)u(t-π)+u(t-2π)-cos(t-2π)u(t-2π)
In mathematics, the Laplace transform, named after its discoverer Pierre Simon Laplace (/ləˈplɑːs/), transforms a function of real variables (usually in the time domain) into a function of complex variables (in the time domain). is the integral transform that Complex frequency domain, also called S-area or S-plane).
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Bryan's Boutique sells shirts, skirts, shoes and hats. If Bryan sells 3 types of shirts, 6 types of skirts, 8 types of bracelets and 2 types of hats, how many different outfits can a customer put together if an outfit must include one shirt, one skirt, one bracelet and one hat?
Using the Fundamental Counting Theorem, it is found that the customer can put together 288 different outfits.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Bryan sells 3 types of shirts, 6 types of skirts, 8 types of bracelets and 2 types of hats, hence the parameters are given as follows:
[tex]n_1 = 3, n_2 = 6, n_3 = 8, n_4 = 2[/tex]
Hence the number of different outfits is given as follows:
N = 3 x 6 x 8 x 2 = 288
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Solve For x :
[tex] \color{purple}{ \pmb{ \frak{2x \: = 100 \red { \: ?}}}}[/tex]
[tex] \\ \\ \\ \\ \\ [/tex]
[tex] { \color{yellow}\bigstar}\underline{ \pmb{ \frak{Thank \: uh }} \color{purple}{ \hearts} !!\: }[/tex]
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given ,
[tex]2x = 100[/tex]
To find ,
value of x
Now ,
[tex]\longrightarrow{2x = 20}[/tex]
Dividing both sides by 2 , we get
[tex] \frac{2x}{2} = \frac{100}{2} \\ \\ \longrightarrow\boxed{ \: x = 50} [/tex]
nikal -,- xD
Answer:
[tex]\bf x=50[/tex]Step-by-step explanation:
[tex]\bf 2x=100[/tex]
Divide both sides by 2:-
[tex]\bf \cfrac{2x}{2}=\cfrac{100}{2}[/tex]
Simplify:-
[tex]\bf x=50[/tex]
___________________
In △ABC, AB = 13, AC = 20, BC = 21. Find the length of the altitude AD
The length of the altitude AD is 12 units.
How to find the height of a triangle?The height of the triangle can be found as follows:
We have to find an angle using cosine law before we can find the height.
Therefore,
20² = 13² + 21² - 2 × 21 × 13 cos B
400 = 169 + 441 - 546 cos B
400 - 610 = - 546 cos B
-210 = - 546 cos B
cos B = -210 / -546
cos B = 0.38461538461
B = cos⁻¹ 0.38461538461
B = 67.3810899783
B = 67.38°
Hence,
sin 67.38° = opposite / hypotenuse
sin 67.38° = AD / 13
cross multiply
AD = 13 sin 67.38°
AD = 11.9999882145
AD = 12 units
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Humood's house is (-5,7)
The school is (3,1)
If each unit in the graph is 50m, find the distance from Humood's house to the school.
The distance from Humood's house to the school is 500m
How to determine the distance from Humood's house to the school?The given parameters are:
Humood's house is (-5,7)
The school is (3,1)
The distance between both points is calculated using
[tex]d = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2[/tex]
Substitute the known values in the above equation
[tex]d = \sqrt{(-5 - 3)^2 + (7 - 1)^2[/tex]
Evaluate
d = 10
Each unit in the graph is 50m.
So, we have
Distance =10 * 50m
Evaluate the product
Distance = 500m
Hence, the distance from Humood's house to the school is 500m
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A bowl holds Fraction 3 over 10 cups of oil when it is Fraction 2 over 5 full. Which statement best describes the quotient of 3 over 10 division sign2 over 5?
1. The maximum amount of oil the bowl can hold is Fraction 3 over 4 cup.
2. The amount of oil that can be still poured in the bowl is Fraction 3 over 4 cup.
The statement that describes the quotient of 3 over 10 division sign2 over 5 is A. The maximum amount of oil the bowl can hold is Fraction 3 over 4 cup.
How to illustrate the fraction?From the information given, we are told that a bowl holds fraction 3 over 10 cups of oil when it is Fraction 2 over 5 full.
Therefore, the statement that best describes the quotient of 3 over 10 division sign2 over 5 will be that the maximum amount of oil the bowl can hold is fraction 3 over 4 cup.
In conclusion, the correct option is A.
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Get every whole number from 0-10 using exactly five 3's, and any arithmetic operations and parentheses
See below for the combination of the arithmetic operations and exactly five 3's
How to determine the operations?The conditions are given as:
Exactly five 3'sAny arithmetic operation or combination of operationsThere are no direct rules to this, except by trial and error.
After several trials, we have the following operations:
(3 * 3 - 3 * 3)/3 = 0
3 - 3/3 - 3/3 = 1
(3 + 3 - 3 / 3)-3 = 2
(3 * 3 - 3 + 3)/3 = 3
3 *3/3 + 3/3 = 4
3 +3/3 + 3/3= 5
3 + 3 + (3 - 3)/3 = 6
(3^3 - 3 - 3)/3 = 7
3 + 3 + (3 + 3)/3 = 8
3 + 3 + 3+ 3 -3 =9
3 + 3 + 3 + 3/3 = 10
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The number of views on a viral video can be modeled by the function p(t)=590(5)^3t . Write an equivalent function of the form p(t)=ab^t
Answer:
p(t) = 2950^3t
Step-by-step explanation:
I’m not sure if this is exactly what you wanted or not. Please let me know more info and I’ll write any more answers for this question in the comments. Have a great day!!
Verify that the intermediate value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 7x 1, [0, 9], f(c) = 19 c =
we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x + 1 . And the value of c is 2.
According to the given question.
We have a function.
f(x) = x^2 + 7x + 1
As, we know that "the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M".
Now, we will apply the theorem for the given function f(x).
So,
f(0) = 0^2 +7(0) + 1 = 1
And,
f(9)=9² + 7(9) + 1 = 81 + 63 + 1 = 145
Here, f(0) = 1< 19< 145 = f(9).
So, f is continous since it is a polynomial. Then the IVT applies, and such c exists.
To find, c,
We have to solve the quadratic equation f(c) =19.
This equation is
c² + 7c + 1 = 19.
Rearranging, c²+ 7c - 18=0.
Factor the expression to get
c² + 9c - 2c -18 = 0
⇒ c(c + 9) - 2( c + 9) = 0
⇒ (c - 2)(c + 9) = 0
⇒ c = 2 or -9
c = -9 is not possible beacuse it is not in the interval [0, 9].
So, the value of c is 2.
⇒ f(2) = 2^2 + 7(2) + 1 = 4 + 14 + 1 = 19
Hence, we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x + 1 . And the value of c is 2.
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properties of intersection of sets
The intersection of the sets has the following properties: Commutative law – A ∩ B = B∩ A. Associative law – (A ∩ B)∩ C = A ∩ (B∩ C) φ ∩ A = φ
do mark brainliest
PLEASE ITS MY LAST QUESTION
Answer:
[tex]y = - \frac{1}{4} x - 10[/tex]
Step-by-step explanation:
The negative reciprocal of 4 is -1/4.
Let's substitute in our values, to find the y-intercept:
[tex]y = - \frac{1}{4} x + c[/tex]
[tex] - 11 = - 1 + c[/tex]
[tex]c = - 10[/tex]
Finally, our full equation is:
[tex]y = - \frac{1}{4} x - 10[/tex]
PLEASE HELP IM STUCK
Answer:
23
Step-by-step explanation:
The question gives the first equation:
0.05N + 0.10D = 2.20
It can be rewritten as:
0.05$ times the number of nickels plus 0.10$ times the number of dimes is equivalent to $2.20.
Notice that 0.05$ or 5 cents is equivalent to one nickel and 0.10$ or 10 cents is equivalent to one dime.
The question asks for N+D. We know that N stands for the number of nickels Daniel has and D stands for the number of dimes Daniel has. We also know that Daniel only has dimes and nickels in his pocket. Therefore N+D most be equivalent to the total number of coins, which is given in the question to be equal to 23 coins.
Therefore...
N+D = 23
How to answer this problem
Answer:
m<C = 12.0 °
Step-by-step explanation:
Since we know that this is a non-right triangle, we must use either the law of sines or law of cosines to find m<C.
The information we now have only allows us to use the law of sines, which focuses on proportions:
[tex]\frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}[/tex]
Thus, we can use:
[tex]\frac{sin(98)}{19}=\frac{sinC}{4}\\ 4*sin(98)=19*sinC\\ \frac{4*sin(98)}{19}=sinC\\ sin^-1\frac{4*sin98}{19}=12.033=12.0[/tex]
The sin^-1 represents the sin inverse, which you must use to find angle measures.
Find the value of x.
OA. 66
OB. 122
OC. 98
O D. 76
SUBMIT
Answer:
C) 98
Step-by-step explanation:
Hope this helps! sry if I'm wrong
The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.
An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.
The given equation is
15x + 120 = 5x + 1100
Take the like terms together,
15x - 5x = 1100 - 120
10x = 980
x = [tex]\frac{980}{10}[/tex]
x = 98.
Thus, the option C is correct stating that the value of x in the given equation is 98.
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The complete question is as follows:
Find the value of x in the equation:
15x + 120 = 5x + 1100.
A. 66
B. 122
C. 98
D. 76
SUBMIT.
Find the missing length.
= √ [?]
C =
C
6
2
Pythagorean Theorem: a² + b² = c²
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{Formula: a^2 + b^2 = c^2}[/tex]
[tex]\textsf{Solving:}[/tex]
[tex]\mathsf{2^2 + 6^2 = c^2}[/tex]
[tex]\mathsf{2 \times 2 + 6 \times6 = c^2}[/tex]
[tex]\mathsf{4 + 36 = c^2}[/tex]
[tex]\mathsf{40 = c^2}[/tex]
[tex]\large\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\sqrt{40}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Approximate the area under the
function between a and b using a
left-hand sum with the given
number of intervals.
f(x) = x² + 2
a = 0
b= 6
6 intervals
Answer:
67 square units
Step-by-step explanation:
The area using the left-hand sum is the sum of products of the function value at the left side of the interval and the width of the interval.
AreaThe attachment shows a table of the x-value at the left side of each interval, and the corresponding function value there. The interval width is 1 unit in every case, so the desired area is simply the sum of the function values.
The approximate area is 67 square units.
Split up the interval [0, 6] into 6 equally spaced subintervals of length [tex]\Delta x = \frac{6-0}6 = 1[/tex]. So we have the partition
[0, 1] U [1, 2] U [2, 3] U [3, 4] U [4, 5] U [5, 6]
where the left endpoint of the [tex]i[/tex]-th interval is
[tex]\ell_i = i - 1[/tex]
with [tex]i\in\{1,2,3,4,5,6\}[/tex].
The area under [tex]f(x)=x^2+2[/tex] on the interval [0, 6] is then given by the definite integral and approximated by the Riemann sum,
[tex]\displaystyle \int_0^6 f(x) \, dx \approx \sum_{i=1}^6 f(\ell_i) \Delta x \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg((i-1)^2 + 2\bigg) \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg(i^2 - 2i + 3\bigg) \\\\ ~~~~~~~~ = \frac{6\cdot7\cdot13}6 - 6\cdot7 + 3\cdot6 = \boxed{67}[/tex]
where we use the well-known sums,
[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]
HElp meee mwa mwa mwa
Answer:
[tex]a = 1, \ - 3[/tex]
Explanation:
[tex](a-6)(a+8) = -45[/tex]
distribute
[tex]a^2 + 8a - 6a - 48 = -45[/tex]
collect terms
[tex]a^2 + 8a - 6a - 48 + 45=0[/tex]
simplify
[tex]a^2 + 2a - 3=0[/tex]
factor
[tex](a - 1)(a + 3)= 0[/tex]
set to zero
[tex]a = 1, \ - 3[/tex]
Answer:
a = 1, -3
Step-by-step explanation:
Given equation:
[tex](a-6)(a+8)=-45[/tex]
Expand the brackets:
[tex]\implies a^2+8a-6a-48=-45[/tex]
[tex]\implies a^2+2a-48=-45[/tex]
Add 45 to both sides:
[tex]\implies a^2+2a-48+45=-45+45[/tex]
[tex]\implies a^2+2a-3=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
Two numbers that multiply to -3 and sum to 2 are: 3 and -1.
Rewrite the middle term as the sum of these two numbers:
[tex]\implies a^2+3a-a-3=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies a(a+3)-1(a+3)=0[/tex]
Factor out the common term (a + 3):
[tex]\implies (a-1)(a+3)=0[/tex]
Apply the zero product property:
[tex]\implies (a-1)=0 \implies a=1[/tex]
[tex]\implies (a+3)=0 \implies a=-3[/tex]
Verify the solutions by inputting the found values of a into the original equation:
[tex]a=1 \implies (1-6)(1+8) & =-5 \cdot 9 = -45[/tex]
[tex]a=-3 \implies (-3-6)(-3+8) & =-9 \cdot 5 = -45[/tex]
Hence both found values of a are solutions of the given equation.
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Define the geometric sequence as a recursive function, if the first term is 1/5 and the common ratio is 5 .
The geometric sequence when the first term is 1/5 and the common ratio is 5 is; f(n) = f(n-1) . 5.
What is the geometric sequence described?The geometric sequence described in the task content is one whose first term is; f(1) = 1/5.
Additionally, it follows from convention that the recursive function for a geometric sequence is; a product of a previous term and the common ratio.
Hence, we have; f(n) = f(n-1) . 5.
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Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.
x + y = 3,500
x – y = 2,342
Solve the system of equations. How many contemporary titles does Jarred have?
The number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.
Simultaneous equationSimultaneous equation is an equation which involves the solving for two unknown values at the same time.
number of contemporary titles = xnumber of classic titles = yx + y = 3,500
x – y = 2,342
Add both be equation
x + x = 3,500 + 2,342
2x = 5,842
x = 5,842 ÷ 2
x = 2,921
Substitute x = 2,921 into
x – y = 2,342
2,921 - y = 2, 342
-y = 2,342 - 2,921
-y = -579
y = 579
Therefore, the number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.
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A test consists of section A and section B. Section A has 15 questions and section B has 10 questions. The number of questions in section A is ____% if the questions in the test.
Is there any number in base 10 (positive or negative) that can be written in multiple
ways in base −4? Can you prove it? If yes, provide the number and the base −4
representations, and if no, show why.
The true statement is that no number in base 10 can be written in multiple ways in base 4
How to determine the true statement?The base of the numbers are given as:
Base 10 and base 4
Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers
There is only one equivalent of each number in each base.
This means that (for instance)
357 in base 10 is 11211 in base 4
The above number does not have any other representation in base 4 and it can not be written in another way.
This is the same for other numbers in base 10
Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4
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THE FIRST PERSON TO ANSWER GETS BRAINLIEST!!! A student traveled to a foreign country on an airplane. It took 18 hours to arrive at his destination, and the plane was traveling 900 kilometers per hour. When returning home, the same trip took only 15 hours going at a speed of 1,080 kilometers per hour. If t represents time and s represents the speed of the plane, which statement is true about this relationship?
(answer choices are below)
Answer:
4
Step-by-step explanation:
the time it takes for a plane to travel a distance varies directly as the speed of the plane because ts=16,200
neeed help more more please uwu
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0[/tex]
[ Multiply both sides by 2 ]
[tex]\qquad \sf \dashrightarrow \: 2 {t}^{2} + 17t - 10[/tex]
a = 2b = 17 c = 10[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 289 - ( - 80)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 369[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209 [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4} [/tex]
[tex]\qquad \sf \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552[/tex]
3. What is the greatest common factor for the two expressions? Use ^ to mean an exponent (use Shift +6 key). For example, 3x2 would be written as 3x^2. 15v³ and 12v² Write your response on the line below. Do not use any spaces or words.
The greatest common factor of the two expressions given as in the task content is; 3v².
What is the greatest common factor of the two expressions given?It follows from the task content that the terms whose greatest common factor are to be determined are: 15v³ and 12 v².
15v³ and 12v²
= 3v²(5v) and 3v²(4)
= 3v²(5v) and (4)
Consequently, in a bid to factorise the two expressions by means of their greatest Common factor, the greatest common factor can be determined as; 3v².
The correct answer choice which therefore represents the greatest common factor as required in the task content is; 3v².
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Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
The second plan has an initial fee of $53 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?What is the cost when the two plans cost the same?
Answer:
100 miles
Cost = $63
Step-by-step explanation:
Let us assume that the distance driven for both plans when they both equal in cost is X miles
Plan 1
Cost = 48 + 0.15X
Plan2
Cost = 53 + 0.1X
If they are both equal then
48 + 0.15X = 53 + 0.10X
Collecting like terms
0.15X - 0.10X = 53 - 48
0.05X = 5
X 5/0.05 = 100 miles
Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63
Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=10
There is a maximum value of 7/6 located at (x, y) = (5/6, 7).
The function given to us is f(x, y) = xy.
The constraint given to us is 6x + y = 10.
Rearranging the constraint, we get:
6x + y = 10,
or, y = 10 - 6x.
Substituting this in the function, we get:
f(x, y) = xy,
or, f(x) = x(10 - 6x) = 10x - 6x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = 10 - 12x ... (i)
Equating to 0, we get:
10 - 12x = 0,
or, 12x = 10,
or, x = 5/6.
Differentiating (i), with respect to x again, we get:
f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.
The value of y, when x = 5/6 is,
y = 12 - 6x,
or, y = 12 - 6*(5/6) = 7.
The value of f(x, y) when (x, y) = (5/6, 7) is,
f(x, y) = xy,
or, f(x, y) = (5/6)*7 = 7/6.
Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).
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Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables.
Michael
Lemons
Cups of Water
1
4
3
12
4
16
Sondra
Lemons
Cups of Water
2
6
4
12
6
18
Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?
Three-fourths and StartFraction 6 Over 4 EndFraction
StartFraction 3 Over 12 EndFraction and StartFraction 4 Over 12 EndFraction
StartFraction 16 Over 4 EndFraction and StartFraction 18 Over 6 EndFraction
StartFraction 1 Over 12 EndFraction and StartFraction 4 Over 18 EndFraction
The two ratios in the tables shown which have a common denominator you could use to compare is; 3/12 and 4/12
RatioMachael's ratio:
lemons to water = 1:4
Equivalent ratio
= 3 : 12
= 4 : 16
Sondra's ratio:
lemons to water = 2 : 6
Equivalent ratio
= 4 : 12
= 6 : 18
Therefore, the two ratios in the tables shown which have a common denominator you could use to compare is; StartFraction 3 Over 12 EndFraction and StartFraction 4 Over 12 EndFraction
Complete question
Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables. Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?
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PLS HELP!What is the difference of
Answer:
Option 3
Step-by-step explanation:
Since the denominators are the same, you can just subtract the numerators.
Amelia has a job baby-sitting for a neighbor. she is paid $20 plus $2.50 for each hour on the job. if amelia wants to earn $40 to buy a new sweater, how many hours would she need to work? a. 16 hours b. 9 hours c. 10 hours d. 8 hours please select the best answer from the choices provided a b c d
The correct option is option (d) 8 hours.
Amelia need to work for 8 hours to buy new sweater $40.
What is an equation and its solution?When two expressions are connected with the equals sign (=) in a math equation, it expresses the equality of the two expressions. A number that may be entered for the variable to produce a true number statement is the solution to an equation.
Let the hours Amelia need to work=h
Amalia paid=$20
Payment of each hour=$2.50
So, we can make an equation with given problem
40=20+2.50h
40-20=2.5h
20=2.5h
[tex]h=\frac{20}{2.5}[/tex]
h= 8
So, Amelia need to work for 8 hours to get $40.
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Enter the correct answer in the box. jackson needs to determine the value of x in this equation. rewrite the expression as a logarithmic quotient that he could enter in his calculator.
A logarithmic equation exists as an equation that uses the logarithm of an expression containing a variable. The value of the logarithmic equation x = log 2.97/log 1.13.
What is a logarithmic equation?A logarithmic equation exists as an equation that applies the logarithm of an expression having a variable. To estimate exponential equations, first, see whether you can note both sides of the equation as powers of the same number.
Given: [tex]$1.13^x = 2.97[/tex]
Taking log on both sides, we get
log [tex]$1.13^x[/tex] = log 2.97
x log 1.13 = log 2.97
x = log 2.97/log 1.13
Therefore, the value of logarithmic equation x = log 2.97/log 1.13.
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What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?
Answer:
[tex]y=-\frac{1}{3}x+7[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is -1/3.
Substituting into point-slope form and converting to slope-intercept form,
[tex]y-5=-\frac{1}{3}(x-6) \\ \\ y-5=-\frac{1}{3}x+2 \\ \\ y=-\frac{1}{3}x+7[/tex]