Which of the binomials below is a factor of this trinomial

A 96 inch stick breaks into two pieces in the ratio of 3:5. How big is each piece?

Svetlanka [38]

40 cm.

let the length of the first part be 3x, second part be 4x, third part be 5x.

where x is a positive length in cm.

why 3x,4x and 5x ?

so that the ratio of lengths of the 3 parts be 3:4:5.

total length of the stick = 3x + 4x + 5x = 12x=96cm

so x=96/12 = 8cm

therefore the largest part of the stick (5x)= 5*8 =40cm

6 0

2 years ago

Two architects bid for a small government project, both

blondinia [14]

Answer:

10 hours

Step-by-step explanation:

let x be the total number of hours

Amazing design total charge = 45x+250

super structures total charge = 60x+100

both companies charge the same amount when both equation equals

45x+250=60x+100

60x-45x=250-100

15x=150

x=10

therefore at 10 hours both companies will charge the same amount

4 0

2 years ago

If you type 20 words per minute how long did it take to type 5356 words in length Please help

Alex_Xolod [135]

Answer:

268

Step-by-step explanation:

You would take 5356 and divide it by 20

4 0

3 years ago

Read 2 more answers

How much chocolate will each person get if 3 people share a half pound equally?

SIZIF [17.4K]

Each person would get 1/6 of the half pound.

1/2 divided by 3= 1/6

7 0

3 years ago

Read 2 more answers

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

2 years ago