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Liula [17]
3 years ago
15

What is the slope of the line represented by the data table?

Mathematics
1 answer:
djyliett [7]3 years ago
6 0
A) Slope:    (y2 - y1) / (x2 - x1)

You can use point  (-1, -6) and (0, -8)

Slope =    (-8 - -6) /(0 - -1) =   (-8+6)/(0+1) = -2/1  = -2.

Slope = -2.

b) Point (0, -8)  is the point such that  x = 0,  and y = -8, this point represents the vertical intercept  of the equation.  The point where the line cuts the y axis.

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Is a function always a relation
ziro4ka [17]

Answer:

No, to be a function a relation must fulfill two requirements: existence and unicity.

Step-by-step explanation:

  • Existence is a condition that establish that every element of te domain set must be related with some element in the range. Example: if the domain of the function is formed by the elements (1,2,3), and the range is formed by the elements (10,11), the condition is not respected if the element "3" for example, is not linked with 10 or 11 (the two elements of the range set).
  • Unicity is a condition that establish that each element of the domain of a relation must be related with <u>only one</u> element of the range. Following the previous example, if the element "1" of the domain can be linked to both the elements of the range (10,11), the relation is not a function.
3 0
2 years ago
Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p
Damm [24]

Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

Answer:

Number of t-shirts to make maximum profit = 2790 shirts

Maximum profit = $12,209

Step-by-step explanation:

From the question, we are given that the profit function is;

p(x) = -x³ + 4x² + x

For the maximum value of the profit function,

(dp/dx) = 0 and (d²p/dx²) < 0

Since, p(x) = -x³ + 4x² + x

Then,

(dp/dx) = -3x² + 8x + 1

at maximum point (dp/dx) = 0, thus;

-3x² + 8x + 1 = 0

Solving this using quadratic formula, the roots are;

x = -0.12 or 2.79

Also, (d²p/dx²) = -6x + 8

Now, let's put the roots of x into -6x + 8 and check for maximum value conditon;

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

Maximum has to be d²p/dx² < 0

So, the one that meets the condition is -8.74 < 0 at x = 2.79

Thus, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousands) = 2790

Now, the maximum profits that corresponds to this number of t-shirts of 2.79(in thousands) is obtained by putting 2.79 for x in the profit function;

So,

p(2.79) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.7176 + 31.1364 + 2.79

p(x) = 12.2088 (in thousand dollars) ≈ $12,209

6 0
2 years ago
5x + 1 = 56<br><br> Solving 2 step equations?
frutty [35]

Answer:

the x would equal to 11 ,so x=11

4 0
3 years ago
Write an expression that represents n plus 7 multiplied by 3.
diamong [38]
The <span>expression that represents n plus 7 multiplied by 3 is
(n + 7)(3)
The entire expression, (n + 7) is multiplied by 3 since it would be inconvenient to state the expression as given above if what is meant was
(n + 7x3). It would have simply been n plus 21.</span>
7 0
3 years ago
Read 2 more answers
WILL MARK U AS BRAINLIEST PLZ HELP
Radda [10]

Answer:

112 if you don't include the triangle sides as they are not necessary, but 124 if you include one triangle and 136 if you include both triangle sides

5 0
2 years ago
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