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
vovangra [49]
3 years ago
8

Write a proof that shows how 45 and 4.5 have a factor of 10

Mathematics
1 answer:
vovikov84 [41]3 years ago
3 0

Answer:

When you move the decimal point one place to the left, you are moving the second by a factor of 10.

Step-by-step explanation:

You might be interested in
A savings account earns 4.5% simple interest per year. If $650 is deposited and no withdrawals are made during one year, how muc
Zinaida [17]
679.25 is the answer
5 0
3 years ago
Read 2 more answers
Given f(x) =3x+7 find f(5)
ra1l [238]

Answer:

22

Step-by-step explanation:

f (5)=3 (5)+7

f (5)=15+7

f (5)=22

8 0
3 years ago
After flying kites, mariana and reena go with their friends to the local ice cream shop. ice cream sundaes cost 2$ and banana sp
Alina [70]
I believe it is $40 in all.
8 0
3 years ago
PLEASEEEEEEE HELPPPPP
coldgirl [10]

If their perimeters are equal, we can add up all the side lengths of each triangle, and set the perimeters equal to each other to find the value of x that satisfies the equation:

x - 2 + x + 3x + 1 = 2x - 5 + x + 4 + 6x - 7

Combine like terms:

5x - 1 = 9x - 8

And finally, solve for x:

7 = 4x

x = \frac{7}{4}

Therefore, x is equal to \frac{7}{4}.

<em>Hope this helps! :)</em>

6 0
3 years ago
EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =
Taya2010 [7]

Answer:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

<em>Maximum value of f=2.41</em>

Step-by-step explanation:

<u>Lagrange Multipliers</u>

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

\bigtriangledown  f=\lambda \bigtriangledown  g

for some scalar \lambda called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

\bigtriangledown  f=\lambda \bigtriangledown  g+\mu \bigtriangledown  h

The gradient of f is

\bigtriangledown  f=

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in x,y,z,\lambda,\mu.

We have

f(x, y, z) = x + 2y + 11z\\g(x, y, z) = x - y + z -1=0\\h(x, y, z) = x^2 + y^2 -1= 0

Let's compute the partial derivatives

f_x=1\ ,f_y=2\ ,f_z=11\ \\g_x=1\ ,g_y=-1\ ,g_z=1\\h_x=2x\ ,h_y=2y\ ,h_z=0

The Lagrange condition leads to

1=\lambda (1)+\mu (2x)\\2=\lambda (-1)+\mu (2y)\\11=\lambda (1)+\mu (0)

Operating and simplifying

1=\lambda+2x\mu\\2=-\lambda +2y\mu \\\lambda=11

Replacing the value of \lambda in the two first equations, we get

1=11+2x\mu\\2=-11 +2y\mu

From the first equation

\displaystyle 2\mu=\frac{-10}{x}

Replacing into the second

\displaystyle 13=y\frac{-10}{x}

Or, equivalently

13x=-10y

Squaring

169x^2=100y^2

To solve, we use the restriction h

x^2 + y^2 = 1

Multiplying by 100

100x^2 + 100y^2 = 100

Replacing the above condition

100x^2 + 169x^2 = 100

Solving for x

\displaystyle x=\pm \frac{10}{\sqrt{269}}

We compute the values of y by solving

13x=-10y

\displaystyle y=-\frac{13x}{10}

For

\displaystyle x= \frac{10}{\sqrt{269}}

\displaystyle y= -\frac{13}{\sqrt{269}}

And for

\displaystyle x= -\frac{10}{\sqrt{269}}

\displaystyle y= \frac{13}{\sqrt{269}}

Finally, we get z using the other restriction

x - y + z = 1

Or:

z = 1-x+y

The first solution yields to

\displaystyle z = 1-\frac{10}{\sqrt{269}}-\frac{13}{\sqrt{269}}

\displaystyle z = \frac{-23\sqrt{269}+269}{269}

And the second solution gives us

\displaystyle z = 1+\frac{10}{\sqrt{269}}+\frac{13}{\sqrt{269}}

\displaystyle z = \frac{23\sqrt{269}+269}{269}

Complete first solution:

\displaystyle x= \frac{10}{\sqrt{269}}\\\\\displaystyle y= -\frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{-23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=-0.4

Complete second solution:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=2.4

The second solution maximizes f to 2.4

5 0
3 years ago
Other questions:
  • original price of a calendar: $14.50 discount: 30% find the new price for the item after the discount
    8·2 answers
  • HELP PLEASE . im in credit recovery bc i obviously suck at math im going to post a photo with the question &amp; answers .someon
    5·1 answer
  • In triangle ABC, ∠ABC=70° and ∠ACB=50°. Points M and N lie on sides AB and AC respectively such that ∠MCB=40° and ∠NBC=50°. Find
    15·1 answer
  • Can you help me with #1?​
    6·1 answer
  • Margot gave 10% of x number of dollars that she earned over the summer to an animal rescue shelter. 10% of x is about $60.00. Ch
    15·1 answer
  • A surveyor starts at the southeast corner of a lot and
    11·1 answer
  • A contest is being held at a school fair for seventh-grade
    10·2 answers
  • PLEASE HELP!!!!! thank youuuu :$
    6·1 answer
  • Answer the precalculus question from khan academy pls! I will give brainliest and 5 stars. 30 points.
    7·1 answer
  • two rectangles have the exact same area. the measurements of the first rectangle is 3k by 3.calculate the value of k​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!