A woman bought a stove for $2800. After using it for 2 years she decided to trade in the stove. The company estimated a depreciation of 15% for the first year of its use and a further 15% on its reduced value, for the second year.
i.) Calculate the value of the stove after two years.
ii.) Express the value of the stove after two years as a percentage of the original value. (5mks)

Answer:

Slope of f(x) is greater than slope of g(x)

g(x) has a greater y intercept

Step-by-step explanation:

Given

f(x) table

[tex]g(x) = 2x + 6[/tex]

Solving (a):

First, we determine the slope of f(x).

From the table, we take any two corresponding values of x and f(x).

Represent f(x) with y

[tex](x_1,y_1) = (-1.-12)[/tex]

[tex](x_2,y_2) = (0.-6)[/tex]

The slope (m) is calculated as thus

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{-6 - (-12)}{0 - (-1)}[/tex]

[tex]m = \frac{-6 +12}{0 +1}[/tex]

[tex]m = \frac{6}{1}[/tex]

[tex]m = 6[/tex]

Represent this with m1

[tex]m_1 = 6[/tex]

Calculating the slope of g(x).

The general form of an equation is [tex]y = mx + b[/tex]

Where m represents the slope.

We have that:

[tex]g(x) = 2x + 6[/tex]

By comparing  [tex]g(x) = 2x + 6[/tex] with [tex]y = mx + b[/tex]

[tex]m = 2[/tex]

Represent this with m2

[tex]m_2 = 2[/tex]

Comparing both slope, we can say that:

f(x) has a greater than slope of g(x)

Another comparison is that:

Slope of f(x) is 3 times the slope of g(x)

Solving (b): Function with greater y intercept.

The general form of an equation is [tex]y = mx + b[/tex]

Where b represents the y intercept.

First, we need to determine the equation of f(x) using:

[tex]y - y_1 = m(x - x_1)[/tex]

Recall that, from the table of f(x):

[tex](x_1,y_1) = (-1.-12)[/tex]

[tex](x_2,y_2) = (0.-6)[/tex]

[tex]m_1 = 6[/tex]

So:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]y - (-12) = 6(x - (-1))[/tex]

[tex]y + 12 = 6(x +1)[/tex]

[tex]y + 12 = 6x +6[/tex]

Solve for y

[tex]y = 6x + 6 - 12[/tex]

[tex]y = 6x - 6[/tex]

By comparing this with [tex]y = mx + b[/tex], the y intercept of f(x) is -6

For g(x), we have:

[tex]g(x) = 2x + 6[/tex]

By comparing this with [tex]y = mx + b[/tex], the y intercept of g(x) is 6

Comparing the y intercepts of both functions, g(x) has a greater y intercept because [tex]6 > -6[/tex]

Answer:

45:40

27:24

Step-by-step explanation:

45:40 c=5

27:24 c=3

Answer:

Greater than 10 but less than 100.

Step-by-step explanation:

Answer: x = 3 when  h(x) = 7.

Step-by-step explanation:

h(x) = 4x -5      To solve for x when h(x) = 7,  you will set the expression 4x -5 equals 7 to solve for x.

4x -5 = 7    Add 5 to both sides

   +5   +5

4x = 12       Divide both sides by 4.

x= 3

Answer:

scalene right

Step-by-step explanation:

no side congruent and right

Answer:

(x + 5)(x + 4)

Step-by-step explanation:

[tex]x^{2} +9x+20=(x+5)(x+4)[/tex]

Answer:

Step-by-step explanation:

x^2+9x+20

(x+4)(x+5)

Answer:

17

Step-by-step explanation:

22 is a multiple of 11 and 22-5 is 17

Answer:

x=-2/3,2

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

2 (3x - 2) - 4x + 1 = 9

Distribute the 2 to 3x and -2

6x - 4 - 4x + 1 = 9

Combine like terms

2x - 3 = 9

Add three to both sides

2x = 12

Divide by 2

x = 6

Answer:

9

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$1.15

Step-by-step explanation:

1*15=15

15/100=.15

1+.15=1.15

Answer:

DEMOS LOS

Step-by-step explanation:

Answer:

∠ACB = 72

Step-by-step explanation:

OAD is straight line.

∠DAB +  ∠OAB  = 180

142 + ∠OAB  = 180

          ∠OAB = 180 - 142

          ∠OAB =  38

ΔAOB is isosceles triangle. OA = OB = radius

∠OAB = ∠OBA = 38   {angles opposite to equal sides or equal}

In ΔAOB ,

∠OAB + ∠OBA + ∠AOB = 180   {Anlge sum property of triangle}

   38 + 38 + ∠AOB = 180

               76 + ∠AOB = 180

                       ∠AOB = 180 - 76

                       ∠AOB = 104

THe angle subtended by an arc of a circle at the center is double the angle subtended by it at any point on the remaining part of the circle

∠AOB =  2*∠ACB

∠ACB = ∠AOB/2

         = 104/2

∠ACB = 72

Answer:

Step-by-step explanation:

2 dimes and 5 nickels

Dimes: 10 × 2 = 20

Nickels: 5 × 5 = 25

Answer:

5 nickel and two dimes

Step-by-step explanation:

let let X be the number of Nickels

number of X is equals to 7 - x

5x+ 10*(7-x)= 45

X= 5

thus nickel is 5 and dimes is 2

Answer:

12.8 m

Step-by-step explanation:

From the diagram :

Height PR = 19m

Using Pythagoras :

From triangle PQR:

QR = x

Tan θ = opposite / Adjacent

Tan 22° = x / 19

x = tan 22° * 19

x = 0.4040262 * 19

x = 7.6764982 m

From triangle PRS:

SR = y

Tan θ = opposite / Adjacent

Tan 15° = y / 19

y = tan 15° * 19

y = 0.2679491 * 19

y = 5.0910346

Height of entire screen :

(7.6764982 + 5.0910346) m

= 12.7675328 m

= 12.8 m

Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the y-intercept is -2 and the slope is up 3 left two which is -3/2

Answer:

the answer is 16 im pretty sure

Step-by-step explanation: hope this helps :)

Answer:

3

Step-by-step explanation:

4×2.5=10

2×7.5=15

10+15=25

34-25=9

9÷3=3

Answer:

3

Step-by-step explanation:

4(2.50)=10

2(7.50)=15

15+10=25

34-25=9

3(3)=9

25+9=34

Answer:

here you go

Step-by-step explanation:

Answer: a big rock

Step-by-step explanation: i am just dumb and lazy

Answer:

71.0

Step-by-step explanation:

x = -24

Step-by-step explanation:

i hope this helps :)

Answer:A

Step-by-step explanation:

Answer:

Done!

Step-by-step explanation:

-6 - 7(4 + 3x)

Distribute;

-6 - 28 - 21x

-34 - 21x