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
Butoxors [25]
3 years ago
13

Your school wants to take out an ad in the paper congratulating the basketball team on a successful​ season, as shown to the rig

ht. The area of the photo will be half the area of the entire ad. What is the value of​ x?
Mathematics
1 answer:
iogann1982 [59]3 years ago
3 0

Answer:

x_1 =-14.43 in, x_2 = 2.426in

Since the measurement can't be negative the correct answer for this case would be x =2.426 in

Step-by-step explanation:

Let's assume that the figure attached illustrate the situation.

For this case the we know that the original area given by:

A_i = 7 in *5 in = 35in^2

And we know that the initial area is a half of the entire area in red A_i = \frac{A_f}{2}, so then:

A_f = 2 A_ i =2*35 = 70

And we know that the area for a rectangular pieces is the length multiplied by the width so we have this:

70 = (x+7) (x+5)

We multiply both terms using algebra and the distributive property and we got:

70 =x^2 +12 x +5

And we can rewrite the expression like this:

x^2 +12 x -35 = 0

And we can solve this using the quadratic formula given by:

x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}

Where a = 1, b =12 and c=-35 if we replace we got:

x = \frac{-12 \pm \sqrt{(12)^2 -4(1)(-35)}}{2*1}

And the two possible solutions are then:

x_1 =-14.43 in, x_2 = 2.426in

Since the measurement can't be negative the correct answer for this case would be x =2.426 in

You might be interested in
Determine of which lines, if any, are parallel or perpendicular. Explain.
nalin [4]

Answer:

lines b and c are perpendicular

Step-by-step explanation:

Use slope

slope for parallel is the same

slope for perpendicular is negative reciprocal

line a slope- 1-3/-2-0 is -2/-2 or 1

line b slope- 1-4/4-6 is -3/-2 or 3/2

line c slope- 3-1/1-4 is 2/-3 or - 2/3

none are the same so none are parallel

- 2/3 is the negative reciprocal of 3/2 so lines b and c are perpendicular

8 0
3 years ago
23/5 as a whole number or mixed number in simplest form and 12/4 whole and mixed numbers and in simplest form 36/6 in whole or m
iren2701 [21]

23/5 = 4  3/5

12/4 = 3

36/6 =6

29/6 = 4 5/6

47/8 =5 7/8

5 0
3 years ago
Read 2 more answers
At a recent computer convention, Pomie Lau demonstrated new software to potential customers. She was paid $15 each for the first
saul85 [17]
Answer= $185.00

Commission=15(10)+2(17.50)
Commission=150+35.00
Commission=$185.00

6 0
3 years ago
Thank you very much anh you
Neko [114]

Hello from MrBillDoesMath!

Answer:

See discussion below

Discussion:

#4

The sum of the interior angles of a polygon of n sides is (n-2)* 180. As the polygon in #4 has 7 sides , the sum of the interior angles is (7-2)*180 = 5 * 180 = 900.

We can also compute the sum of the interior angles by adding up each of the angles (expressed in terms of x)  shown in #4. Starting at the top of the polygon and proceeding counterclockwise gives:

900 =  (8x +34) + (10x+21)+(9x+30)+(7x+45)+(5x+44)+(12x+13)+(6x+29)  =>

           (8x + 10x+9x+7x+5x+12x+6x) + (34+21+30+45+44+13+29)  =

           57x                                            + 216

This simplifies to

900 =  57x + 216                => subtract 216 from both sides

900-216 = 57x                    => 900-216= 684

684= 57x                            => divide both sides by 57

684/57  = x                         => as 684/57 = 12

x = 12

The diagram has makes repeated use of the same variable for vertices. That is, the diagram shows 4 P's, 1 Q, 2 R's, 0 S's, and 1 T making it impossible to determine the values of some angles.  For example, consider m RST -- whatever that means.

#5 uses the same ideas but the vertices are properly  labeled (I'll leave the grunt of determining the  individual angles to you but here are the main points).

Sum of interior angles = (7 -2) * 180 = 5 * 180 = 900.

900 =  (8x+62) + (7x+66)+(5x+83)+(6x+55)+(10x+42)+(8x+45)+(4x+67)  =>

900 =   (8x + 7x +5x+6x+10x+8x+4x) + (62+66+83+55+42+45+67)

900=     48x                                        +  420             =>

900 -420 = 48x                                                          =>   subtract 420

480  = 48x                                                                  =>   divide by 48

x = 480/48 = 10

Thank you,

MrB

6 0
3 years ago
Write one hundred and fourteen thousandths as a decimal number.
LiRa [457]

100.014. I think this is it

6 0
3 years ago
Other questions:
  • Find the weight of the cast iron shape shown below at 0.26 pounds per cubic inch. (round to the nearest pound). The height of th
    10·1 answer
  • What is the value of x? 6.75+3/8x=13 1/4
    5·2 answers
  • Find the missing factor.<br> 4b2 + 17b + 15 = (b + 3)(<br> )
    9·1 answer
  • Which of the following vectors are orthogonal to (1,5)? Check all that apply
    11·1 answer
  • HELP!! Just need the answer to the question in the picture, please!
    11·1 answer
  • What is 3x squared-12x=0
    15·1 answer
  • These triangles are
    13·1 answer
  • Here are some values of sequence Q. Write a recursive definition for the sequence.
    6·1 answer
  • Being an introvert is cool.
    14·2 answers
  • Change y-7=m(x-4) to standard form
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!