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Svetradugi [14.3K]
3 years ago
11

When Alice went to the print shop, she was confronted with many choices of sizes: 7-inch by 9-inch, 8-inch by 10-inch, and 12-in

ch by 16-inch. She's afraid that if she picks the wrong size, part of the photo will be cut off. Which size should Alice pick and why?
Mathematics
1 answer:
Alex3 years ago
5 0

Answer:

12-inch by 16-inch- it's the largest available and can be reduced to scale for smaller photos.

Step-by-step explanation:

-Given the dimensions 7-inch by 9-inch, 8-inch by 10-inch, and 12-inch by 16-inch:

#If Alice buys 7-inch by 9-inch and the photo turn's out to be a 8-inch by 10-inch or 12-inch by 16-inch then part of her photo will be cut off.

Hence, Don't buy.

#If Alice buys 8-inch by 10-inch and the photo turn's out to be a 12-inch by 16-inch then part of her photo will be cut off. However, if the photo is a 7-inch by 9-inch then it will fit.

Hence, don't buy.

#If Alice buys a  12-inch by 16-inch and the photo turns out to be smaller than expected the she can always print it out and trim or reduce the to scale excessive print paper to the desire dimensions.

Hence, buy  the 12-inch by 16-inch since it's the largest available and can be reduced to scale for smaller photos.

You might be interested in
If a + b + c.= 5 and ab + bc +ca = 10 , then prove that a3+ b3+ c3-3abc = -25
Alex Ar [27]

Start with

(a+b+c)^3=a^3+b^3+c^3+3(a^2b+a^2c+ab^2+ac^2+b^2c+bc^2)+6abc

Given that a+b+c=5, we know (a+b+c)^3=125.

Also, ab+bc+ca=10, so

a^2b+a^2c+ab^2+ac^2+b^2c+bc^2=a(ab+ac)+b(ab+bc)+c(ac+bc)

=a(10-bc)+b(10-ca)+c(10-ab)

=10(a+b+c)-3abc

=50-3abc

So we have

125=a^3+b^3+c^3+3(50-3abc)+6abc

125=a^3+b^3+c^3+150-9abc+6abc

\implies -25=a^3+b^3+c^3-3abc

QED

3 0
3 years ago
Is the point (8, -3) a solution to the linear equation 2x + 3y = 12
11111nata11111 [884]

Answer:

No, (8, -3) is not a solution.

Step-by-step explanation:

2x + 3y = 12

(substitute the variables for the point; x = 8 & y = -3)

2(8) + 3(-3) = 12

16 - 9 = 12

7 ≠ 12

5 0
4 years ago
Relations and Functions, please help with these 3 questions asap. I will give brainliest! Only answer if you know how to do this
gladu [14]
<h2>                      Question # 1</h2>

Part A) Is the relation a function? Explain.

A function relates each element of a set  with exactly one element of another set.

Important things for a relationship to be a function:

  • Every element in X is related to some element in Y.
  • A function cannot have one-to-many relationship.
  • A function must contain single valued, means it is not having one-to-many relation

Considering the points on coordinate plane

(-4, 2), (-3, 0), (-2, -1), (0, 2), (2, -3), (3, 3)

If we carefully observe, we determine that relation

  • relates each element of a set  with exactly one element of another set
  • is single-valued, means It is not giving back 2 or more results for the same input. In other words, it is not having one-to-many relation.
  • It is in fact, having many to one. For example, the pairs (0, 2) and (-4, 2) is having many- to-one relationship.

So, from the above observation, it is clear that the relationship is a function.

Part B) What is the domain of the relation?

Considering the points on coordinate plane

  • (-4, 2)
  • (-3, 0)
  • (-2, -1)
  • (0, 2)
  • (2, -3)
  • (3, 3)

Also we know that domain of the relation is the set of all the x-values of an ordered pairs.

So, the domain of the relation: {-4, -3, -2, 0, 2, 3}

Part C) What is the range of the relation?

Considering the points on coordinate plane

  • (-4, 2)
  • (-3, 0)
  • (-2, -1)
  • (0, 2)
  • (2, -3)
  • (3, 3)

As we know that the range of a relationship is the set of all the y-values of an ordered pair.

So, the range of the relationship will be: { -3, -1, 0, 2, 3}

<em>Note:</em>

  • The duplicated entries in the domain and range are written only once.
  • Also, the domain and range can be written in ascending order.

Part D) What is the value of y when x = 2? Explain

Considering the points on coordinate plane

  • (-4, 2)
  • (-3, 0)
  • (-2, -1)
  • (0, 2)
  • (2, -3)
  • (3, 3)

From the given points on the coordinate plane, it is clear that when the value of x = 2, then the value of y = -3

Therefore, the value of y is -2 when x = 2

<h2>                           Question # 2</h2>

Considering the points on coordinate plane

(-4, -1), (-2, 1), (0, -3), (2, 3), (4, -2)

If we bring a point, let say (2, 4), and graphed on the coordinate system, then the relation will no longer be function.

The reason is that the induction of the point (2, 4) would violate the definition of a relation to be a function.

Observe that (2, 4) and (2, 3) will make the relation having one-to-many relationship as (2, 4) and (2, 3) is giving 2 outputs i.e. y = 4, and y = 3 for a single input i.e. x = 2.

Therefore, the induction of the point (2, 4), when graphed, makes the relation not a function.

<h2>                       Question # 3</h2>

Part A)

f\left(x\right)\:=\:|x\:-\:3|\:-\:2; x = -5

The attached figure a shows the graph for the function

f\left(x\right)\:=\:|x\:-\:3|\:-\:2

In the attached figure a, the graph represents an absolute value relationship as the absolute value of a number is never negative.

Evaluate the function for x = -5

f\left(x\right)\:=\:|x\:-\:3|\:-\:2

|\left-5\right\:-\:3|\:-\:2....[A]

Solving

\left|-5-3\right|

\mathrm{Subtract\:the\:numbers:}\:-5-3=-8

=\left|-8\right|

\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a

\left|-8\right|=8

So,

\left|-5-3\right|=8

Equation [A] becomes

\:|-5\:-\:3|\:-\:2\:=8\:-\:2\:                   ∵   \left|-5-3\right|=8      

                        =6

Therefore,

the value of f\left(x\right)\:=\:|x\:-\:3|\:-\:2 at x = -5 will be 6.

i.e.  f(x)=6

<h2 />

Part B)

g\left(x\right)=1.5x;\:x=0.2

The attached figure b shows the graph for the function

g\left(x\right)=1.5x

In the attached figure b, the graph shows that the function represents a linear relationship as the graph is a straight line.

Evaluate the function for x = 0.2

As

g\left(x\right)=1.5x

Putting x = 0.2

g\left(x\right)=1.5\left(0.2\right)

As

1.5\left(0.2\right)=0.3

So

g\left(x\right)=0.3

So,

the value of g\left(x\right)=1.5x at x = 0.2 will be 0.3.

i.e.  g\left(x\right)=0.3

Part C)

p\left(x\right)\:=\:|7\:-\:2x|;\:x\:=\:-3

As the absolute value of a number will be never negative.

The attached figure c shows the graph for the function

p\left(x\right)\:=\:|7\:-\:2x|

In the attached figure c, the graph represents an absolute value relationship as the absolute value of a number is never negative.

Evaluate the function for x = -3

p\left(x\right)\:=\:|7\:-\:2x|

Solving

\left|7-2x\right|

\left|7-2\left(-3\right)\right|

=\left|7+6\right|

=\left|13\right|

\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0

=13

So,

\left|7-2x\right|=13

So,

the value of p\left(x\right)\:=\:|7\:-\:2x| at x = -3 will be 13.

i.e  p\left(x\right)\:=13

Keywords: function, relation

Learn more about functions from brainly.com/question/2335371

#learnwithBrainly

3 0
4 years ago
After lunch, the family has 1/8 of a pizza left. What percentage of the pizza did they eat
ira [324]

Answer:

7/8 of the pizza was eaten

5 0
2 years ago
Read 2 more answers
PLS HELP 25 POINTS!!
IRISSAK [1]

Answer:

the set of first conponent of the ordered pair is called domain

the set of second component of ordered paur is called range

7 0
3 years ago
Read 2 more answers
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