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
kirza4 [7]
3 years ago
10

Fast easy question! The figures below are similar. What is the value of x

Mathematics
1 answer:
Ivahew [28]3 years ago
6 0

Answer:

12

Step-by-step explanation:

You might be interested in
A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si
Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

Area = 128

Let the dimension of the paper be x and y;

Such that:

Length = x

Width = y

So:

Area = x * y

Substitute 128 for Area

128 = x * y

Make x the subject

x = \frac{128}{y}

When 1 inch margin is at top and bottom

The length becomes:

Length = x + 1 + 1

Length = x + 2

When 2 inch margin is at both sides

The width becomes:

Width = y + 2 + 2

Width = y + 4

The New Area (A) is then calculated as:

A = (x + 2) * (y + 4)

Substitute \frac{128}{y} for x

A = (\frac{128}{y} + 2) * (y + 4)

Open Brackets

A = 128 + \frac{512}{y} + 2y + 8

Collect Like Terms

A = \frac{512}{y} + 2y + 8+128

A = \frac{512}{y} + 2y + 136

A= 512y^{-1} + 2y + 136

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

A' = -512y^{-2} + 2

Set

A' = 0

This gives:

0 = -512y^{-2} + 2

Collect Like Terms

512y^{-2} = 2

Multiply through by y^2

y^2 * 512y^{-2} = 2 * y^2

512 = 2y^2

Divide through by 2

256=y^2

Take square roots of both sides

\sqrt{256=y^2

16=y

y = 16

Recall that:

x = \frac{128}{y}

x = \frac{128}{16}

x = 8

Recall that the new dimensions are:

Length = x + 2

Width = y + 4

So:

Length = 8 + 2

Length = 10

Width = 16 + 4

Width = 20

To double-check;

Differentiate A'

A' = -512y^{-2} + 2

A" = -2 * -512y^{-3}

A" = 1024y^{-3}

A" = \frac{1024}{y^3}

The above value is:

A" = \frac{1024}{y^3} > 0

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0
3 years ago
Help I will be marking brainliest!!!
Keith_Richards [23]
<h3>Answer:  A.  18*sqrt(3)</h3>

=============================================

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer

----------------------

An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

4 0
2 years ago
Match the numerical model to the corresponding graphical and algebraic models.
nikitadnepr [17]

Answer:

I'd say d but if you worry choose to be then go with B

8 0
2 years ago
Shawn says that 3.22 is a rational number. Leah says 3.22 is a repeating decimal. Who is correct and why?
MAVERICK [17]

Answer:

Hi, There! Leah Is Correct

Step-by-step explanation:

A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all.

____________________________________________________________

-Darkspirit-

3 0
2 years ago
Read 2 more answers
Need 78 pieces of wood 29 cm long. Boards are 6 m long. How many boards are needed?
Wittaler [7]

I believe the answer is 4 because 6m/29= 20.6897 and so then you do 20.6897 x 3= 62.0691. So 3 is too small so do 20.6897x 4= <span>82.7588. 82 >78 so the answer is that you need 4 boards.
</span>

5 0
3 years ago
Other questions:
  • In one year, 144 of the people enrolled in a college went on a winning outreach during the college year. It was 4/5 of the peopl
    7·1 answer
  • All my points and BRAINLIEST!!!!<br><br> Please help
    5·2 answers
  • A sample of 5 buttons is randomly selected and the following diameters are measured in inches. Give a point estimate for the pop
    15·1 answer
  • What is <br> 2x+y=0 5x+3y=-11
    11·1 answer
  • Pls answer ill give brainliest to the best
    12·2 answers
  • Using the distributive property and expanded form to solve what is 8(a + 3b)
    13·1 answer
  • IF YOU ANSWER IN THE NEXT 3 MIN. AND GET IT RIGHT! YOU WILL BE THE BRAINIEST!!!
    6·2 answers
  • [Please, help me. I need it quickly]<br>If cosA+sinA=√2, then prove A=45°.
    12·1 answer
  • Lulu has 10 feet of ribbon. She uses 1 feet of ribbon for a project. She uses the
    8·1 answer
  • Need help on the Sin(4x) part of the question please!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!