1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lesya [120]
2 years ago
8

Lori bought some cookies for $2 each and muffins for $3 each. She bought twice as

Mathematics
2 answers:
Lubov Fominskaja [6]2 years ago
7 0

Answer:

2 cookies

Step-by-step explanation:

let c represent cookies, m represent muffins. set up a system of equations:

2c+3m=16

m=2c

(the top equation shows that cookies are $2 each, and muffins are $3, and that the total cost is $16. the bottom equation shows that Lori bought twice as many muffins as cookies).

then solve the system of equations by substitution, substituting 2c for m in the top equation:

2c+3(2c)=16

2c+6c=16

8c=16

c=2

this means that lori bought 2 cookies.

Alecsey [184]2 years ago
6 0

Answer:

2 cookies

Step-by-step explanation:

let c = no. of cookies

2c = no. of muffins

The cost for c cookies is 2c since each cookie was $2

and the cost of 2c muffins is 3(2c) = 6c since each muffing was $3

The total cost = 2c + 6c = 16

                                 8c  = 16

                                   c = 2

So, she bought 2 cookies and 4 muffins

You might be interested in
1) Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given
neonofarm [45]

Answer:

Check below, please

Step-by-step explanation:

Hello!

1) In the Newton Method, we'll stop our approximations till the value gets repeated. Like this

x_{1}=2\\x_{2}=2-\frac{f(2)}{f'(2)}=2.5\\x_{3}=2.5-\frac{f(2.5)}{f'(2.5)}\approx 2.4166\\x_{4}=2.4166-\frac{f(2.4166)}{f'(2.4166)}\approx 2.41421\\x_{5}=2.41421-\frac{f(2.41421)}{f'(2.41421)}\approx \mathbf{2.41421}

2)  Looking at the graph, let's pick -1.2 and 3.2 as our approximations since it is a quadratic function. Passing through theses points -1.2 and 3.2 there are tangent lines that can be traced, which are the starting point to get to the roots.

We can rewrite it as: x^2-2x-4=0

x_{1}=-1.1\\x_{2}=-1.1-\frac{f(-1.1)}{f'(-1.1)}=-1.24047\\x_{3}=-1.24047-\frac{f(1.24047)}{f'(1.24047)}\approx -1.23607\\x_{4}=-1.23607-\frac{f(-1.23607)}{f'(-1.23607)}\approx -1.23606\\x_{5}=-1.23606-\frac{f(-1.23606)}{f'(-1.23606)}\approx \mathbf{-1.23606}

As for

x_{1}=3.2\\x_{2}=3.2-\frac{f(3.2)}{f'(3.2)}=3.23636\\x_{3}=3.23636-\frac{f(3.23636)}{f'(3.23636)}\approx 3.23606\\x_{4}=3.23606-\frac{f(3.23606)}{f'(3.23606)}\approx \mathbf{3.23606}\\

3) Rewriting and calculating its derivative. Remember to do it, in radians.

5\cos(x)-x-1=0 \:and f'(x)=-5\sin(x)-1

x_{1}=1\\x_{2}=1-\frac{f(1)}{f'(1)}=1.13471\\x_{3}=1.13471-\frac{f(1.13471)}{f'(1.13471)}\approx 1.13060\\x_{4}=1.13060-\frac{f(1.13060)}{f'(1.13060)}\approx 1.13059\\x_{5}= 1.13059-\frac{f( 1.13059)}{f'( 1.13059)}\approx \mathbf{ 1.13059}

For the second root, let's try -1.5

x_{1}=-1.5\\x_{2}=-1.5-\frac{f(-1.5)}{f'(-1.5)}=-1.71409\\x_{3}=-1.71409-\frac{f(-1.71409)}{f'(-1.71409)}\approx -1.71410\\x_{4}=-1.71410-\frac{f(-1.71410)}{f'(-1.71410)}\approx \mathbf{-1.71410}\\

For x=-3.9, last root.

x_{1}=-3.9\\x_{2}=-3.9-\frac{f(-3.9)}{f'(-3.9)}=-4.06438\\x_{3}=-4.06438-\frac{f(-4.06438)}{f'(-4.06438)}\approx -4.05507\\x_{4}=-4.05507-\frac{f(-4.05507)}{f'(-4.05507)}\approx \mathbf{-4.05507}\\

5) In this case, let's make a little adjustment on the Newton formula to find critical numbers. Remember their relation with 1st and 2nd derivatives.

x_{n+1}=x_{n}-\frac{f'(n)}{f''(n)}

f(x)=x^6-x^4+3x^3-2x

\mathbf{f'(x)=6x^5-4x^3+9x^2-2}

\mathbf{f''(x)=30x^4-12x^2+18x}

For -1.2

x_{1}=-1.2\\x_{2}=-1.2-\frac{f'(-1.2)}{f''(-1.2)}=-1.32611\\x_{3}=-1.32611-\frac{f'(-1.32611)}{f''(-1.32611)}\approx -1.29575\\x_{4}=-1.29575-\frac{f'(-1.29575)}{f''(-4.05507)}\approx -1.29325\\x_{5}= -1.29325-\frac{f'( -1.29325)}{f''( -1.29325)}\approx  -1.29322\\x_{6}= -1.29322-\frac{f'( -1.29322)}{f''( -1.29322)}\approx  \mathbf{-1.29322}\\

For x=0.4

x_{1}=0.4\\x_{2}=0.4\frac{f'(0.4)}{f''(0.4)}=0.52476\\x_{3}=0.52476-\frac{f'(0.52476)}{f''(0.52476)}\approx 0.50823\\x_{4}=0.50823-\frac{f'(0.50823)}{f''(0.50823)}\approx 0.50785\\x_{5}= 0.50785-\frac{f'(0.50785)}{f''(0.50785)}\approx  \mathbf{0.50785}\\

and for x=-0.4

x_{1}=-0.4\\x_{2}=-0.4\frac{f'(-0.4)}{f''(-0.4)}=-0.44375\\x_{3}=-0.44375-\frac{f'(-0.44375)}{f''(-0.44375)}\approx -0.44173\\x_{4}=-0.44173-\frac{f'(-0.44173)}{f''(-0.44173)}\approx \mathbf{-0.44173}\\

These roots (in bold) are the critical numbers

3 0
3 years ago
1. Jada made 14 cups of blueberry jam and divided the jam equally among
marissa [1.9K]

Answer:1 1/14

Step-by-step explanation:

5 0
2 years ago
What does "n" equal in N+2n+20-4=12+3n?
stira [4]
N+2n+20-4=12+3n
3n+20-4-12=12-12+3n
3n+4=3n
3n/3 + 4= 3n/3
n+4=n
n+4-4=n-4
n=n-4

theres no further simplification, unless i messed up ...
8 0
3 years ago
The opposite of negitive thirty-six
dexar [7]
The opposite of -36 is equal to 36
8 0
3 years ago
Read 2 more answers
How many natural numbers N have the property among 1,2,..........,N exactly 30% are divisible by 3?
k0ka [10]

Answer:

The answer is B. 2.

Step-by-step explanation:

We know that for N = 1 and N = 2, none of them are divisible by 3.

For N = 3, 33.33% are divisible by 3.  For N = 4, 25% (which is already less than 30%), so N = 5 would also be less.

At N = 6, we're back up to 33.33%.  N = 7 is already less than 30%.

At N = 9, you guessed it, 33.33%.  N = 10 is 30% (3, 6, and 9).  So we have one case.

Moving along, at N = 18, 33.33%.  N = 20 is again 30% (3, 6, 9, 12, 15, and 18).  Two cases now.

Finally, at N = 21, again 33.33%.  N = 22 and N = 23 are both greater than 30%.  As we continue this, for any N after 20, we will always be greater than 30%.

4 0
3 years ago
Other questions:
  • Consider the function arctan(x/6)arctan⁡(x/6). write a partial sum for the power series which represents this function consistin
    10·1 answer
  • I have another Brainliest
    6·2 answers
  • Solve the linear equation: 3.4 + 2(9.7 – 4.8x) = 61.2 What are the possible steps involved in solving this equation? Check all t
    14·2 answers
  • What is the approximate area of the circle? Use A. 17.6 square inches B. 24.6 square inches C. 35.2 square inches D. 98.5 square
    6·1 answer
  • 3.1 4.2 4.3 1.51 5.4 9.2 what is the answer adding it up
    12·2 answers
  • Matt works at a job where he makes a
    13·1 answer
  • The ratio of quarters to dimes in a coin collection is 5:3. You add the same number of new quarters as dimes
    6·1 answer
  • David, Stephen and June share £96 in a ratio 2:3:3. How much money does each person get
    13·2 answers
  • HELP URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!
    9·1 answer
  • One of the slowest fish is the blenny
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!