Translate this sentence into an equation.

1 answer:

8 0

To get this answer, you would want to start by dividing 96 by 6 to find matts score. (Answer 16) then just fill in the equation accordingly! m * 6 = 96

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What is the minimum value of C = 7x + 8y, given the constraints: 2x + y ≥ 8, x + y ≥ 6, x ≥ 0, y ≥ 0. A. 32 B. 42 C. 46 D. 64

marshall27 [118]

Answer: The minimum value of C is 46.

Step-by-step explanation:

Since, Here, We have to find out Min C = 7x+8y

Given the constraints are $2x+y\geq 8$ -------(1)

$x+y \geq 6$ ------------- (2)

$x \geq 0$ , $y \geq 0$ -------- (3)

Since, For equation 1) x-intercept, (4, 0) and y-intercept (0,8)

And, $2\times 0+0\geq 8$ ⇒ $0\geq 8$ ( false)

Therefore the area of line 1) does not contain the origin.

For equation 2) x-intercept, (6, 0) and y-intercept (0,6)

And, $0+0\geq 6$ ⇒ $0\geq 6$ ( false)

Therefore the area of line 2) does not contain the origin.

Thus after plotting the constraints 1) 2) and 3) we get Open Shaded feasible region AEB ( Shown in below graph)

At A≡(0,8) , C= 64

At E≡(2,4), C= 46

At B≡(6,0), C= 42

Thus at B, C is minimum, And its minimum value = 42

5 0

3 years ago

Read 2 more answers

A straight line, L, is perpendicular to the straight line y=2x-1 and passes through the point (8,1). Find an equation of L

luda_lava [24]

Let's call that other line with the eqn. y=2x-1 line M.
This line is in slope-intercept form, which means that it is written in the form y=mx+b where m is the slope and b is the y-intercept.
This means that the slope of line M is 2.

Perpendicular lines have slopes which are opposite reciprocals.
(that is to say, if you flipped the fraction and changed the sign)

Of course, 2 isn't a fraction, but it's implied as 2/1.
The opposite reciprocal would then be -1/2.
Let's plug this into our slope-intercept form equation for line L.

y = mx + b
y = -1/2x + b

Of course, we still need to find that y-intercept. (y when x = 0)
To do this, we need to interpret the slope.
Slopes are rise over run, so m = -1/2 means a change of -1 in y = 2 in x.
Let's take a point we know is in our line, (8, 1).
To find that y-intercept, we want x to be 0.
To do this, we'd have to subtract 8 from x.
And according to our slope, this means adding 4 to y.
Our y-intercept is at (0, 5), with the value b that we use being just 5.

$\boxed{y=-\frac{1}2x+5}$