MATH HELP???....Please?

Question

* If f(4) = 0 and f(6) = 6 what represents f(x)?


* A boy in a fashion design contest made a shirt for himself and a proportional one for a small doll. The boy was 5 feet 5 inches tall, and the doll was 13 inches tall. If the boy's shirt sleeve was 30 inches long, how long, in inches, was teh sleeve of teh doll's shirt?

Answer 1

Based on the information you have given, f(x) could be anything. But let's assume the simplest case, f(x) = ax +b.

Then 4a + b = 0 and 6a + b = 6.

This means that 24a + 6b = 0 and 24a + 4b = 24.

Subtract the second equation from the first to give 2b = -24 or b = -12.

Now use this value of b in either equation to find a. We'll take the first equation, which gives 4a - 9 =0, so a = 3.

Check:
4 x 3 - 12 = 0 -- OK
6 x 3 - 12 = 6 -- OK

So f(x) = 3x - 12 (assuming f is of the form f(x) = ax + b)

The fashion doll problem is much easier. The boy was 65 inches tall and the doll was 13 inches tall. So if the boy's sleeve was 30 inches long, the doll's sleeve was 30 x 13/65 = 6 inches long.

Answer 2

Your first question cannot be answered. But I believe you mean this is a line function. So I'm going to give you the equation of a line that actually passes by (4,0) and (6,6). Well, all you have to do is find the slope. The slope equals (y1-y2)/(x1-x2)=(6-4)/(6-0)=2/6=1/3. We can find the p value (in the equation y=mx+p). We'll have p=y-mx ( m is the slope). You'll have: p=6-6/3=6-2=4. The equation is thus: y=x/3+ 4 or y=(x+12)/3, if you prefer.

The sleeve of your doll should be proportional to that of the boy. 5 feet 5 inches =65 inches. So we'll have x/13=30/65, so x=390/65 inches, or 78/13 or 6 inches long.

Answer 3

f(x) = x


In the shirt question, the proportion is 65 inches to 13 inches. This is a 5 to 1 ratio. So if the boys sleeve is 30, then the doll sleve will be 1/5 of that, or 6 inches.

Answer 4

Let's solve with proportions:

5 feet 5 inches tall = 65inches

Let x = doll's sleeve length

65/13 = 30/x

65x = 390

x = 6 inches
.

Answer 5

that's a ratio problem, convert all lengths to inches, and cross multiply, then divide. the doll's height multiplied by the boy's sleeve length divided by the boy's height, so 13 x 30/65= 6

the length of the doll's sleeve is 6 inches

Answer 6

For the first part, you need to know what kind of function f is... is it linear? quadratic? I'm guessing it's linear because of the second part.

So f(4) = 0 means the point (4, 0) is on the line, and f(6) = 6 means (6, 6) is on the line. Then the slope,

m = (y_2 - y_1) / (x_2 - x_1) = (6 - 0)/(6 - 4) = 6/2 = 3

and we can use the point (4, 0) in point-slope form to get

y - 0 = 3(x - 4)
or y = 3(x - 4)
or y = 3x - 12.

(it's NOT y = x as the person above said because then f(0) would be 0, not 4.)

Answer 7

Use the proportion (doll's height)/(boy's height) = (doll's sleeve length)/(boy's sleeve length).

(13 inches)/(65 inches) = (doll's sleeve length)/(30 inches)

((13 inches)(30 inches))/(65 inches) = doll's sleeve length

6 inches = doll's sleeve length

Answer 8

ans for ?2 = 6 inches
30/65 = x/13
x = 13*50/65