Question 1

Show that the points A(-1,2),B(3,-2),and C(-6,-3),are the vertices of a right triangle.

Accepted Answer

The answer of Show that the points A(-1,2),B(3,-2),and C(-6,-3),are the...

Question 2

Suppose the cost to produce 100 units of a product is $5000,and the cost to produce 125 units is $6000.If cost c is linearly related to output q,find an equation relating c and q.

Accepted Answer

The answer of Suppose the cost to produce 100 units...

Question 3

When the temperature T (in degrees Celsius)of a certain laboratory animal is reduced,its heart rate r (in beats per minute)decreases.At a temperature of 37°C,the animal had a heart rate of 200,and at a temperature of  
its heart rate was 140.If r is a linear function of T for 26 ≤ T ≤ 38,(a)determine this function and (b)determine the heart rate at a temperature of 30°C.

Accepted Answer

The answer of When the temperature T (in degrees Celsius)of...

Question 4

For the linear function f(x)= -5x + 5,find: (a)the slope and (b)the vertical axis intercept.(c)Sketch the graph of f.

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The answer of For the linear function f(x)= -5x +...

Question 5

Find the slope of the linear function f(t)=  
.

Accepted Answer

The answer of Find the slope of the linear function...

Question 6

Suppose f is a linear function with slope 5 and such that f(1)= 4.Find f(x).

Accepted Answer

The answer of Suppose f is a linear function with...

Question 7

Suppose q and p are linearly related such that p = 30 when q = 5,and p = 50 when  Find p when q = 15.
A) 100
B) 110
C) 120
D) 130
E) 140

Accepted Answer

The answer of Suppose q and p are linearly related...

Question 8

Suppose f is a linear function such that f(0)= 6 and f(3)= 4.Find f(x).

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The answer of Suppose f is a linear function such...

Question 9

Suppose f is a linear function such that f(-2)= 5 and f(5)= 2.Find f(x).

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The answer of Suppose f is a linear function such...

Question 10

Suppose that a manufacturer will place on the market 80 units of a product when the price is $10 per unit,and 100 units when the price is $12 per unit.Find the supply equation for the product assuming that price p and quantity q are linearly related.
A) p =  q + 2
B) p =  q + 10
C) p = -  q + 12
D) p = 10q + 12
E) p = 10q - 988

Accepted Answer

The answer of Suppose that a manufacturer will place on...

Question 11

Suppose that consumers will demand 800 units of a product when the price is $10 per unit,and 1000 units when the price is $8 per unit.Find the demand equation for the product assuming that price p and quantity q are linearly related.

Accepted Answer

The answer of Suppose that consumers will demand 800 units...

Question 12

Suppose f(1)= -5 and f(-2)= 4.Find f(x)if f is a linear function.
A) f(x) =  - 
B) f(x) = -  + 
C) f(x) = -3x - 2
D) f(x) = -3x + 5
E) f(x) =  +

Accepted Answer

The answer of Suppose f(1)= -5 and f(-2)= 4.Find f(x)if...

Question 13

Suppose f is a linear function with slope 2 and such that f(-3)= 8.Find f(x).

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Question 14

Suppose f(0)= 4 and f(3)= 8.Find f(12)if f is a linear function.
A) -3
B) 6
C) 13
D) 20
E) 24

Accepted Answer

Since f is a linear function, it has the form f(x) = mx + b, where m is the slope and b is the y-intercept. We are given two points on the line: (0,4) and (3,8).

Using these points, we can compute the slope:

m = (8-4)/(3-0) = 4/3

Now we can use the slope and one of the points to find the y-intercept:

4 = (4/3)(0) + b

b = 4

So the linear function is:

f(x) = (4/3)x + 4

To find f(12), we simply plug in x = 12:

f(12) = (4/3)(12) + 4 = 20

Therefore, the answer is D) 20.

Question 15

For the linear function f(x)= 2x + 1,find: (a)the slope and (b)the vertical axis intercept.(c)Sketch the graph of f.

Accepted Answer

The answer of For the linear function f(x)= 2x +...

Question 16

Suppose f is a linear function with slope -3 and f(2)= 5.Find f(x).
A) f(x) = -3x + 2
B) f(x) = -3x + 5
C) f(x) = -3x + 7
D) f(x) = -3x + 11
E) f(x) = -3x + 13

Accepted Answer

The slope-intercept form of a linear function is f(x) = mx + b. Given the slope m = -3 and the point (2, 5), substitute into the equation: 5 = -3(2) + b, which gives b = 11. Thus, f(x) = -3x + 11.

Question 17

Suppose the variables q and p are linearly related such that p = 3 when q = 20,and p = 5 when q = 15.Find p when q = 12.

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The answer of Suppose the variables q and p are...

Question 18

In a test of a diet for pigs,the average live weight w (in kilograms)of a pig was a linear function of the number d of days after the start of the diet,where 0 ≤ d ≤ 50.The weight of a pig at the beginning of a diet was 25 kg and thereafter the pig gained 5 kg every nine days.(a)Express w as a function of d.(b)Find the weight of a pig 36 days after the beginning of the diet.

Accepted Answer

The answer of In a test of a diet for...

Question 19

Suppose f is a linear function with slope 2 and f(1)= 3.Find f(2).
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

Since f is a linear function with a slope of 2, for every unit increase in the input (x), the output (f(x)) increases by 2. Given f(1) = 3, to find f(2), we add the slope (2) to f(1), resulting in 3 + 2 = 5.

Question 20

Suppose that a manufacturer will place 1000 units of a product on the market when the price is $10 per unit,and 1400 units when the price is $12 per unit.Find the supply equation for the product assuming the price p and quantity q are linearly related.

Accepted Answer

The answer of Suppose that a manufacturer will place 1000...

Quiz 4: Lines parabolas and Systems

Show that the points A(-1,2),B(3,-2),and C(-6,-3),are the vertices of a right triangle.

Suppose the cost to produce 100 units of a product is $5000,and the cost to produce 125 units is $6000.If cost c is linearly related to output q,find an equation relating c and q.

For the linear function f(x)= -5x + 5,find: (a)the slope and (b)the vertical axis intercept.(c)Sketch the graph of f.

Find the slope of the linear function f(t)= .

Suppose f is a linear function with slope 5 and such that f(1)= 4.Find f(x).

Suppose q and p are linearly related such that p = 30 when q = 5,and p = 50 when Find p when q = 15.

Suppose f is a linear function such that f(0)= 6 and f(3)= 4.Find f(x).

Suppose f is a linear function such that f(-2)= 5 and f(5)= 2.Find f(x).

Suppose that a manufacturer will place on the market 80 units of a product when the price is $10 per unit,and 100 units when the price is $12 per unit.Find the supply equation for the product assuming that price p and quantity q are linearly related.

Suppose that consumers will demand 800 units of a product when the price is $10 per unit,and 1000 units when the price is $8 per unit.Find the demand equation for the product assuming that price p and quantity q are linearly related.

Suppose f(1) = -5 and f(-2) = 4.Find f(x) if f is a linear function.

Suppose f is a linear function with slope 2 and such that f(-3)= 8.Find f(x).

Suppose f(0) = 4 and f(3) = 8.Find f(12) if f is a linear function.

For the linear function f(x)= 2x + 1,find: (a)the slope and (b)the vertical axis intercept.(c)Sketch the graph of f.

Suppose f is a linear function with slope -3 and f(2) = 5.Find f(x) .

Suppose the variables q and p are linearly related such that p = 3 when q = 20,and p = 5 when q = 15.Find p when q = 12.

Suppose f is a linear function with slope 2 and f(1) = 3.Find f(2) .

Suppose that a manufacturer will place 1000 units of a product on the market when the price is $10 per unit,and 1400 units when the price is $12 per unit.Find the supply equation for the product assuming the price p and quantity q are linearly related.