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Dimas [21]
3 years ago
14

Given that y varies directly as x when y = 8 and x=5.

Mathematics
1 answer:
stiv31 [10]3 years ago
8 0

Answer:

(a) y = 1.6x

(b) y = 48

Step-by-step explanation:

(a) Since y varies directly as x,

  y ∝ x

  y = kx [where k = proportionality constant]

  If y = 8 and x = 5

  By substituting these values in the equation,

  8 = 5k

  k = \frac{8}{5}

  k = 1.6

  Therefore, equation will be,

   y = 1.6x

(b) If x = 30, then we have to find the value of y.

   By substituting the value of x in the equation,

   y = 1.6 × 30

   y = 48  

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phil ate three less than twice as many pancakes as sara. together they combined to eat 15 pancakes. How many pancakes did each e
Levart [38]

Answer:

Let x represents the Sara eat pancake and y represents the Phil eat the pancake.

As per the statement:

Phil ate three less than twice as many pancakes as Sara.

"Twice as many pancake as Sara" means 2x

"three less than twice as many pancakes as Sara" means 2x -3

⇒y = 2x-3         .....[1]

It is also given that together they combined to eat 15 pancakes.

⇒x+y =15      .....[2]

Substitute equation [1] into [2] we get;

x+2x-3 = 15

Combine like terms;

3x-3 =15

Add 3 to both sides we get;

3x = 18

Divide both sides by 3 we get;

x = 6

Substitute the value of x in [1] we get;

y = 2(6)-3 = 12-3 =9

y = 9

Therefore, the pancakes did each eat are;

Sara eat pancake = 6 and Phil eat pancake = 9


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3 years ago
Algebra 2 please help
kogti [31]

Answer:

Here's what I get  

Step-by-step explanation:

a) Possible degree

This  looks like the graph of a cubic equation.

ƒ(x) could be a third degree function.

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As x ⟶ ∞, ƒ(x) ⟶ ∞.

The leading coefficient must be positive.

c) Coordinates of maxima and minima

There is a local maximum at (-4, 0) and a local minimum at about (-1, -18.).

d) Coordinates of zeros

There are zeros at (-4, 0) and (1, 0).

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ƒ(x) is increasing in the intervals (-∞, -4) and (-1, ∞).

ƒ(x) is decreasing in the interval (-4, -1).

f) Negative intervals

The graph is negative in the intervals (-∞, -4) and (-4, ∞).

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A cubic equation must have three roots. This function has a root at x = 1. Another is at x = -4. That root just touches the x-axis, so it must be degenerate (occur twice).

The factored form of the equation is

ƒ(x) = (x - 1)(x + 4)(x + 4)

h) End behaviour

ƒ(x) ⟶ -∞ as x ⟶ -∞ and ƒ(x) ⟶ ∞ as x ⟶ ∞ .

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Step-by-step explanation:

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