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stealth61 [152]
3 years ago
10

Determine whether y varies directly with x. Find the constant of variation. Write the function rule x 5 7 9 y 6 11 16

Mathematics
1 answer:
daser333 [38]3 years ago
4 0

Answer:

  a)  y does NOT vary directly with x

  b)  y = 2.5x -6.5

Step-by-step explanation:

If variation were direct the ratios of y to x would be constant. They are not:

  6/5 ≠ 11/7

y does not vary directly with x.

__

y changes by 5 from 6 to 11 when x changes by 2 from 5 to 7. Then the slope of the linear function rule is (change in y)/(change in x) = 5/2. Using a point-slope form of the equation of a line, we can write the rule as ...

  y = m(x -h) +k . . . . . . . . for a line of slope m through point (h, k)

  y = (5/2)(x -5) +6

  y = 2.5x -6.5 . . . . . simplify

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The graphs below have the same shape. What is the equation of the blue graph?
postnew [5]

Answer:

<h2>C. G(x) = (x - 1)² - 3</h2>

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

===================================

Look at the picture.

The graph of F(x) shifted 1 unit to the right and 3 units down.

Therefore the equation of the function G(x) is

G(x)=(x-1)^2-3

4 0
3 years ago
(3x^2+3)(4+x^3) what the polynomial ?
Ludmilka [50]
<span>(3x^2+3)(4+x^3)
=</span><span>12x^2 +3x^5 + 12 + 3x^3
= </span>3x^5 + 3x^3 + 12x^2 + 12
3 0
3 years ago
11. Keng creates a painting on a rectangular canvas with a width that is four inches longer
GrogVix [38]

Part A

<h3>Answer:  h^2 + 4h</h3>

-------------------

Explanation:

We multiply the length and height to get the area

area = (length)*(height)

area = (h+4)*(h)

area = h(h+4)

area = h^2 + 4h .... apply the distributive property

The units for the area are in square inches.

===========================================================

Part B

<h3>Answer:  h^2 + 16h + 60</h3>

-------------------

Explanation:

If we add a 3 inch frame along the border, then we're adding two copies of 3 inches along the bottom side. The h+4 along the bottom updates to h+4+3+3 = h+10 along the bottom.

Similarly, along the vertical side we'd have the h go to h+3+3 = h+6

The old rectangle that was h by h+4 is now h+6 by h+10

Multiply these expressions to find the area

area = length*width

area = (h+6)(h+10)

area = x(h+10) ..... replace h+6 with x

area = xh + 10x .... distribute

area = h( x ) + 10( x )

area = h( h+6 ) + 10( h+6 ) .... plug in x = h+6

area = h^2+6h + 10h+60 .... distribute again twice more

area = h^2 + 16h + 60

You can also use the box method or the FOIL rule as alternative routes to find the area.

The units for the area are in square inches.

6 0
3 years ago
6x-1=2 (2×-3) solve for x
frozen [14]
6x - 1 = 2(-6)
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8 0
3 years ago
What is the square root of 1
almond37 [142]

Answer:

1

Step-by-step explanation

3 0
3 years ago
Read 2 more answers
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