If a is fixed and b,c are unknowns then the equation b+c=10-a has 11-a solutions. They are pairs (b,c): (0,10-a), (1,9-a), (2,8-a), ... (10-a,0). As a runs from 0 to 10 we have total number of solutions (11-0)+(11-1)+...(11-1)=11+10+...+1=(1+11)*11/2=66.

4 0

3 years ago

You make photo props by cutting rectangles out

KATRIN_1 [288]

Answer:

I can only read the top 2 dimensions:

The one on the left is 32 ft^2, the one on the right is 31 ft^2

Step-by-step explanation:

left top: (8x5)-(2x4) = 32

right top: (8x4)-(1x1) = 31

left low: (10x?)-(4x7) = ?

right low: (8x?)-(2x6) = ?

8 0

3 years ago

A new hospital tracked the number of births during its first 6 months of operation, as shown in the table. Find a quadratic func

UNO [17]

Let x refers to the Month numbers
And y refers to Number of births

There is 5 steps to find the quadratic function that models the data.

First step ⇒ Plot the data pairs (x, y) in a coordinate plane.
 which are the blue circles in the attached figure

Second step ⇒ Draw the parabola you think best fits the data.
 Which is the red function in the attached figure.

Third step ⇒ Estimate the coordinates of three points on the
 parabola, which are (2, 108), (4, 68), and (6, 75).
 which are the black squares in the attached figure

Fourth step ⇒ Substitute the coordinates of the points into the model 
 y = ax2 + bx + c
 to obtain a system of three linear equations.

 4a + 2 b + c = 108 ---------(1)
 16a + 4 b + c = 68 ---------(2)
36a + 6 b + c = 75 ---------(3)

Fifth step ⇒ Solve the linear system.
 By using the calculator
 a = 5.875 , b = -55.25 , c = 195

So, the quadratic model for the data is ⇒ y = 5.875 x²- 55.25 x + 195
============================================
To predict the number of births for month 8
substitute with x = 8 ⇒ y = 5.875 * 8²- 55.25 * 8 + 195 = 129

3 0

3 years ago

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