A client would like his logo printed on to a canvas that’s at least 70 inches. The original logo is 4.5 inches wide and 3.6 inches tall.
Which of the following dimensions will keep the logo in proportion and large enough to meet the clients requirements.

A. 45 in by 36 in

B. 87.5 in by 70 in

C. 70 in by 56 in

C. 70 x  56 is  the NEW LOGO dimension.

Step-by-step explanation:

The original dimension of the logo = 4.5 in x 3.6 in

Here, the length of the logo = 4.5 inches

The width of the logo = 3.6 inches

Now to enlarge the given logo in proportion, each dimension of the logo should be multiplied by a CONSTANT FACTOR  K.

So, the new length  of logo =  4.5 x K

And the new width  of logo = 3.6 x K

Let us consider the given options:

A. 45 in by 36 in

Here, 45  = 4. 5 x K

So, K  = 45/4.5 = 10

Also, 36 = 3.6 x K

so, K  = 36/3.6 = 10

So, in both the case K = 10.

Hence 45 X  36 can be the NEW LOGO dimension.

B.87.5 in by 70 in

Here, 87.5   = 4. 5 x K

So, K  = 87.5 /4.5 = 9.44

Also, 70 = 3.6 x K

so, K  =70/3.6 = 19.44

So, in both the case K = 19.44.

Hence 87.5 x  70 can  be the NEW LOGO dimension.

B.70 in by 56 in

Here, 70  = 4. 5 x K

So, K  = 70 /4.5 = 15.55

Also, 56 = 3.6 x K  ⇒  K  =56/3.6 = 15.55

So, in both the case K = 15.55.

Hence 70 x  56 can  be the NEW LOGO dimension.

But in all conditions, only one condition satisfies the length at least 70 inches.

So, 70 x  56 is  the NEW LOGO dimension.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions