Use proportional reasoning to solve problems involving ratios. (Activity Sheet #4 & 5)

The size of a television is the length of the diagonal of its screen in inches. The

aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of

newer wide-screen televisions is 16:9. Find the width and height of an older 20-

inch television whose screen has an aspect ratio of 4:3. Show all work to receive

credit.

Answer:

4

Step-by-step explanation:

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

y-7=-3, then y=4

Answer:

AB=12

Hope this helps!

Answer:

x = -4 and y = -15

Hope This Helps!!!

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.

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:

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

Step-by-step explanation:

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:

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:

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:

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:

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:

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:

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

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:

[tex]\frac{12}{23} + (9 \frac{6}{8} - 3 \frac{1}{4})[/tex]

Exact Form:

[tex]\frac{323}{46}[/tex]

Decimal Form:

7.02173913  

Mixed Number Form:

7 [tex]\frac{1}{46}[/tex]

Step-by-step explanation:

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:

2

Step-by-step explanation:

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

Answer:

First is translation then dialation darlin

Step-by-step explanation:

i say this because of the size of grid

Answer:

ax + by

Step-by-step explanation:

i hope its correct

if its wrong then im sorry :)

Answer:

the info they gave us is to suppose that angle 6 is = 126°

step 1:

We know that angle 8 = angle 6 = 126°

Why? — when a circle (360°) is split by 2 lines that intersect, there will be 2 equal pairs of angles formed

step 2:

angle 2 = angle 8 = 126°

Why? — they’re alternate angles

step 3:

angle 4 = angle 2

Why? — when a circle (360°) is split by 2 lines that intersect, there will be 2 equal pairs of angles formed

step 4:

angle 1 = 180-126 (angle 4) = 54°

Why? — total angles in a straight line = 180°

Key Term:

Alternate angles:

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Answer: True

Step-by-step explanation: Because the solutions can not land on the dotted lines.

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:

D. $7.20

Step-by-step explanation:

9/1.25 = $7.20