Consider the steps to solve the equation.
2
5
(
1
2
y + 20 ) −
4
5
=
9
20
(2y − 1)

Distribute:
1
5
y + 8 −
4
5
=
9
10
y −
9
20

What is the next step after using the distributive property?
A. Use the multiplication property of equality to isolate the variable term on one side of the equation.

B. Use the multiplication property of equality to isolate the constant on one side of the equation.

C. Combine the like terms on the right side of the equation.

D. Combine the like terms on the left side of the equation.

The formula for a function of the form [tex]y = a\cdot e^{-x} + b\cdot x[/tex] with global minimum at [tex](1, 10)[/tex] is [tex]y = 5\cdot e^{1-x}+5\cdot x[/tex].

We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:

FDT

[tex]-a\cdot e^{-x}+b = 0[/tex] (1)

[tex]b = a\cdot e^{-x}[/tex]

SDT

[tex]y''=a\cdot e^{-x}[/tex] (2)

Where [tex]y'' > 0[/tex].

If we know that [tex](x, y) = (1, 10)[/tex], then we have the following system:

[tex]10 = a\cdot e^{-1}+b[/tex] (3)

[tex]b = a\cdot e^{-1}[/tex] (4)

[tex]y'' = a\cdot e^{-1}[/tex] (5)

By (4) in (3):

[tex]10 = 2\cdot a\cdot e^{-1}[/tex]

[tex]a = \frac{10}{2\cdot e^{-1}}[/tex]

[tex]a = 5\cdot e[/tex]

By (5) we prove that [tex]y'' > 0[/tex], and we get the value of [tex]b[/tex] by (4):

[tex]b = 5[/tex]

Thus, the formula for a function of the form [tex]y = a\cdot e^{-x} + b\cdot x[/tex] with global minimum at [tex](1, 10)[/tex] is [tex]y = 5\cdot e^{1-x}+5\cdot x[/tex].

We kindly invite to check this question on first and second derivative tests:  https://brainly.com/question/6097697

Answer:

a) 5.25m^2

b) 1 can

Step-by-step explanation:

a)

area of a triangle = bh/2

=(4.2 x 4.5)/2

=18.9/2

=9.45m^2

area of a rectangle = 2(l+w)

=2 x (0.6 + 1.5)

=4.2m^2

9.45-4.2 = 5.25m^2

b) 1 can, you can't have a partial can of paint

Answer:

[tex]︎{\blue{\rule{25pt}{1pt}{\purple{\rule{30pt}{3pt}{\red{\rule{50pt}{99999pt}{\purple{\rule{30pt}{3pt}{\blue{\rule{25pt}{1pt} }}}}}}}}}}︎︎︎[/tex]

Answer:

28

Step-by-step explanation:

the ratio is written as copies/dollars.

14/4=x/8

since we can multiply 4 by 2 to get 8, multiply 14 by 2 as well.

14/4=28/8

Answer:

After reviewing the question you posted I have deduced that the correct answers are:

11) Max has $10.00. He earns $25.75 per lawn that he mows.

12) No. She is wrong. She did not group like terms correctly.

Step-by-step explanation:

11)

For 11) I first identified the independent variable of the equation, being "10".

And then the dependent variable of the equation, being "25.75". (The dependent variable of an equation will always be affected by the x)

I then looked at all the possible answers to see which one shared a independent variable of "10" and a dependent variable of "25.75".

The only possible answer that matches is Max has $10.00. He earns $25.75 per lawn that he mows.

This is because the only two possible answers that have "10" being a variable that does not change (independent variable) are:

--- "Max has $10.00. He earns $25.75 per lawn that he mows.

--- "Jon buys 10 toycars for $25.75 each"

However!

"Jon buys 10 toycars for $25.75 each" is an incorrect answer because it uses "10", although independent, as the x variable that affects the independent variable of "25.75".

12)

To find the correct answer for this question I simplified the equation from:

8t-15+3t   =   11m-15

Into:

8t+3t-15   =   11m-15

Which further simplifies into:

11t-15   =   11m-15

Which then you can notice that the two equations are similiar indeed, however they do not share like terms. One equation has "t" as their term, and the other as "m" as their term. Thus they do not share any like terms and are not equivalent.

Answer:

First is translation then dialation darlin

Step-by-step explanation:

i say this because of the size of grid

Answer:

the answer is 12.2

[tex] \frac{b}{0.52} \\ we \: know \: b = 6.344 \\ then \\ \frac{6.344}{0.52} \\ = 12.2[/tex]

Answer:

Step-by-step explanation:

After creating an equilateral triangle using 3 toothpicks, I require 3 more toothpicks to create more 3 equilateral triangles ie.4 triangles it toto.

First place 3 toothpicks end to end on a Horizontal plane to create an equilateral triangle.

THEN erect 3 toothpicks on each corner of the triangles making other ends joined up together in space above the Horizontal plane so as to create another same THREE equilateral triangles. (I am unable to provide a pictorial presentation due to inadequacy of signs & symbols on the keyboard. )

I suppose, you must have visualised the superstructure.

Thanks.

Answer:

x = -4 and y = -15

Hope This Helps!!!

Answer:

ax + by

Step-by-step explanation:

i hope its correct

if its wrong then im sorry :)

Answer:

AB=12

Hope this helps!

Answer:

Volume is the amount of space taken up by an object

Answer:

y = -2x +4

Step by step explanation:

y = -2x +4

Hello, hope you are having a splendid day.

First, we should calculate the slope of the line (Rise/Run)

The rise is how many units we move up or down; the run is how many units we move left or right.

Here, we move down 2 and over 1, so the slope is -2

Now, the y-intercept is where the graph touches the y-axis.

Here, the y-intercept is 4.

Our equation looks lke so:

y=-2x+4

Hope it helps. Ask me if you have any queries.

~An emotional teen who helps others on Brainly :)

[tex]MagicalNature[/tex]

Good luck.

Answer:

[tex]m = -\frac{11}{6}[/tex]

Step-by-step explanation:

Slope is rise over run.

[tex]\frac{15-4}{4- 10}=\frac{11}{-6} = \boxed{-\frac{11}{6}}[/tex]

Hope this helps.

Answer:

x = 17/5

Step-by-step explanation:

17+2+6x = x-15 +5x

19+6x =16x -15

19+15 = 16x-6x

34 = 10x

34/10= 10x/10

17/5 = x

x = 17/5 or 3 2/3

Answer:

240$

Step-by-step explanation:

juanita has saved 20% of the money that she needs to buy a new bicycle. if she has saved $48, how much does the bicycle cost?

48 : 20 * 100 = 240

Answer:

10) x=9

11) x=25

Step-by-step explanation:

a triangle is 180º total

10)   2x+8x+90=180

10x=90

x=9

11) 3x+1+2x+2+2x+2=180

7x+5=180

7x=175

x=25

Answer:

  -1

Step-by-step explanation:

The average rate of change of function f(x) on the interval [a, b] is ...

  m = (f(b) -f(a))/(b -a)

We have ...

  f(-1) = (-1)^5 -2(-1) +3 = -1 +2 +3 = 4

  f(1) = (1)^5 -2(1) +3 = 1 -2 +3 = 2

Then the average rate of change is ...

  m = (2 -4)/(1 -(-1)) = -2/2 = -1

The average rate of change on the given interval is -1.

Answer:

2

Step-by-step explanation:

2021/7 leaves a remainder of 5 so add 2 and that's the answer

Answer:

5

Step-by-step explanation:

set up point slope form

y + 8 = 2(x-1)

set y to zero

0+8=2(x-1)

8=2x-2

10= 2x

x = 5

Answer:

3

2

Step-by-step explanation:

Answer:

With discount : $37.76

With tax : $56.38

With both : $40.19

Step-by-step explanation:

Hope this helps

Answer:

4

Step-by-step explanation:

[tex]slope = \frac{y - 7}{ - 4 - 5} = \frac{1}{3} [/tex]

y-7=-3, then y=4

Using the vertex, it is found that the maximum height of the punt is of 27.7 feet.

The height of the punt, after x seconds, is given by:

[tex]f(x) = -0.0152x^2 + 1.25x + 2[/tex]

It is a quadratic equation with coefficients [tex]a = -0.0152, b = 1.25, c = 2[/tex].

The maximum value is the value of the function at the vertex, hence:

[tex]f_V = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]

Applying the coefficients:

[tex]f_V = -\frac{b^2 - 4ac}{4a} = -\frac{(1.25)^2 - 4(-0.0152)(2)}{4(-0.0152)} = 27.7[/tex]

The maximum height of the punt is of 27.7 feet.

A similar problem is given at https://brainly.com/question/16858635

Answer:

Percentage Calculator: 100. is what percent of 500.? = 20.

Step-by-step explanation:

Answer:250

Step-by-step explanation:

a square had 4 sides, the perimeter is 1,000. 1,000/4+250 :)

Answer:

D. $7.20

Step-by-step explanation:

9/1.25 = $7.20

Answer:

864 inches

12*3=36

36*24=864

Step-by-step explanation:

Hope this helps:)

Answer:

12*3=36

36*24=864

Step-by-step explanation: