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3 years ago

Two quantities are related, as shown in the table:

1 answer:

3 0

Calculate the slope:
m = y2-y1 / x2-x1
m = 4-3 / 4-2
m = 1/2

Now, y-y1 = m(x- x1)
y - 3 = 1/2(x - 2)
y - 3 = 1/2x - 1
y = 1/2x + 2

In short, Your Answer would be: Option A

Hope this helps!

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Through: (3,5), slope=5\3

ANEK [815]

So slope intercpet form
y=mx+b

m=slope
b=y intercpet

slope=5/3
in (x,y) form

x=3
y=5 is one point

subsitute and solve for b
y=mx+b
5=5/3 times 3+b
5=3/3 times 5+b
5=1 times 5+b
5=5+b
subtract 5 from both sides
0=b

equation is
y=5/3x+0 or
y=5/3x

3 0

3 years ago

Find the average value of f over the region D. f(x, y) = 3xy, D is the triangle with vertices (0, 0), (1, 0), and (1, 9)

MakcuM [25]

The average value of f over the region D is 243/4

To answer the question, we need to know what the average value of a function is

<h3>What is the average value of a function?</h3>

The average value of a function f(x) over an interval [a,b] is given by

$\frac{1}{b - a} \int\limits^b_a {f(x)} \, dx$

Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).

x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9

So, $\frac{1}{b - a} \int\limits^b_a {f(x,y)} \, dA = \frac{1}{1 - 0} \int\limits^1_0 \int\limits^9_0 {3xy} \, dxdy \\= \frac{3}{1} \int\limits^1_0 {x} \,dx\int\limits^9_0 {y} \,dy\\ = \frac{3}{1} [\frac{x^{2} }{2} ]^{1}_{0}[\frac{y^{2} }{2} ]^{9}_{0} \\= 3[\frac{1^{2} }{2} - \frac{0^{2}}{2} ] [\frac{9^{2} }{2} - \frac{0^{2}}{2} ] \\= 3[\frac{1}{2} - 0 ][\frac{81}{2} - 0 ]\\= \frac{81}{2} X3 X \frac{1}{2} \\= \frac{243}{4}$

So, the average value of f over the region D is 243/4

Learn more about average value of a function here:

brainly.com/question/15870615

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8 0

2 years ago

Translate the following verbal expression into an algebraic expression.

poizon [28]

Answer:

3 * (x + 7)

Step-by-step explanation:

Mark number as x

Then the sum of a number and seven is x + 7

Three times x + 7 can be written as

3 * (x + 7)

Parentheses mean that we first add x and 7 and then multiply their sum by 3

Alternatively you can write it as 3x + 21, since

3 * (x + 7) = 3 * x + 3 * 7 = 3x + 21

5 0

3 years ago

Pls helppppppppppppp

ira [324]

Answer:

see explanation

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation of the graph of f(x)

• If c > 0 then vertical shift up of c units

• If c < 0 then vertical shift down of c units

f(x) + 3 → vertical shift up of 3 units

Thus the point (- 3, 0 ) → (- 3, 0 + 3 ) → (- 3, 3)

f(x) - 5 → vertical shift down of 5 units

Thus point (4, - 2 ) → (4, - 2 - 5 ) → (4, - 7 )

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Given f(x) then f(x + a) represents a horizontal translation of the graph of f(x)

• If a > 0 then horizontal shift to the left of a units

• If a < 0 then a horizontal shift to the right of a units

f(x - 10) → horizontal shift to the right of 10 units

Thus point (3, 3 ) → (3 + 10, 3 ) → (13, 3 )

f(x + 4) + 5 → shift to the left of 4 units and shift up of 5 units

Thus point (6, 1 ) → (6 - 4, 1 + 5 ) → (2, 6 )

3 0

3 years ago

Find the slope for (4,5)and (2,3)

Igoryamba

Answer:

Step-by-step explanation:

7 0

2 years ago