A stove can be bought on hire purchase by making a deposit of $650 and 12 monthly instalments of $195 each. Calculate the hire purchase price of the stove.

Answers:

a = 2 and b = -4

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

Explanation:

Let's define the three helper functions

which are drawn from the piecewise function. The g(x) function will change depending on what the input is.

Since we want g(x) to be continuous at x = 1, this must mean the three functions f(x), h(x), j(x) must have the same output value when the input is x = 1.

Because h(x) = 6 is a constant function, the output is always 6 regardless of the input. Therefore, we want f(x) and j(x) to have 6 as their output when x = 1. Or else, the pieces won't connect.

Plug x = 1 into the f(x) function to get

f(x) = ax^2 - b

f(1) = a(1)^2 - b

f(1) = a - b

Set this equal to the desired output of 6 and we end up with the equation a-b = 6. Solving for 'a' leads to a = b+6.

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

We'll use the same idea for j(x)

j(x) = 5ax + b

j(1) = 5a(1) + b

j(1) = 5a + b

5a+b = 6

5(b+6) + b = 6 ... plug in a = b+6; solve for b

5b+30+b = 6

6b+30 = 6

6b = 6-30

6b = -24

b = -24/6

b = -4

Which then leads to,

a = b+6

a = -4+6

a = 2

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

Since a = 2 and b = -4, we go from this

[tex]g(x) = \begin{cases}ax^2-b, \ \ x < 1\\6, \ \ x = 1\\5ax+b, \ \ x > 1\end{cases}[/tex]

to this

[tex]g(x) = \begin{cases}2x^2+4, \ \ x < 1\\6, \ \ x = 1\\10x-4, \ \ x > 1\end{cases}[/tex]

Meaning

f(x) = 2x^2+4 and j(x) = 10x-4

You should find that plugging x = 1 into each of those two functions leads to 6 as the output.

The graph is shown below. Note the red graph f(x) is only drawn when x < 1. Similarly, j(x) is only drawn when x > 1. The orange point represents h(x) which only happens when x = 1. So as the name implies, the piecewise function g(x) is composed of pieces of the three functions f(x), h(x), j(x).

Answer:

54

Step-by-step explanation:

I think it's 54

Answer:

0,33

Step-by-step explanation:

x = 36,87

y = 73,74

tan(x/2)

= tan(36,87/2)

= tan (18,44)

= 0,33

Answer:

multiply both side by 2 which gives u tan x 2 is equal to X

multiply it and it will give u the answer But make sure your calculator is in degree mode

Answer:

21484.952 ft^3

Step-by-step explanation:

a cube has the same edges so its basically

27.8^3

Answer:

6

Step-by-step explanation:

7.5-1.5

=6

that is easy

Answer:

7) [tex]x \to x - 3[/tex].

8) [tex]y \to y + 2[/tex]

9) The entire quadratic equation did not get reflected.

Step-by-step explanation:

7) A horizontal translation to the right is of the form:

[tex]x \to x - a[/tex]

Let [tex]y = -(x-3)^{2} + 2[/tex], then the horizontal translation is represented by [tex]x \to x - 3[/tex].

8) A vertical translation upwards is of the form:

[tex]y \to y + a[/tex]

Let [tex]y = -(x-3)^{2} + 2[/tex] , then the vertical translation is represented by:

[tex]y \to y + 2[/tex]

9) The only component of the quadratic equation that was reflected was the part [tex](x-3) ^{2}[/tex] along the x-axis. We can create the entire function by applying the following steps:

(i) [tex]f(x) = x^{2}[/tex] (Original function)

(ii) [tex]f(x) = (x-3)^{2}[/tex] (Horizontal translation)

(iii) [tex]f(x) = - (x-3)^{2}[/tex] (Reflection)

(iv) [tex]f(x) = -(x-3)^{2} + 2[/tex] (Vertical translation)

The entire quadratic equation did not get reflected.

Answer:

each cd is 14.60

Step-by-step explanation:

45.30-1.50= 43.80

43.80÷3=14.60

Answer:14.30

Step-by-step explanation:

$14.30 per CD and .50 tax per Cd

Given:

A synthetic division problem.

To find:

The missing number it in the given synthetic division problem.

Solution:

The given synthetic division problem is:

[tex]3|\overline{3\quad -2\quad 2\quad 4}\\[/tex]

           [tex]\quad 6\quad 8\quad 20\\[/tex]

     [tex]\overline{3\quad 4\quad ?\quad 24}[/tex]

In synthetic division, we need to add first and second row to get the bottom row.

[tex]3+0=3[/tex]

[tex]-2+6=4[/tex]

[tex]4+20=24[/tex]

Similarly,

[tex]2+8=10[/tex]

Therefore, the missing value in the given synthetic problem is 10. Hence, the correct option is C.

Answer:

-1/24

Step-by-step explanation:

To find the reciprocal, you swap the numerator and the denominator. In this case, the numerator is 24 and the denominator is 1. Therefore, it would be 1/24. Now all we have to do is make this number negative. This would make it -1/24. Therefore, the reciprocal of 24 is -1/24.

If this helps please mark as brainliest

Answer:

I think it's D

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

They are anxious to get their results

Answer:

Its option D :)

---

28° + y + 36° = 180°

x = 50

Step-by-step explanation:

the two angles at the bottom would he the same. Since the interior angles of a triangle must add up to 180 the you just subtract that from 180. 180-(65+65)=50

Answer:

x = 50

Step-by-step explanation:

Since the 2 sides are equal to each other, so are the angles. This is an isoceles triangle, by the way. All triangle interior angles add up to 180.

So, the equation is:

x + 65 + 65 = 180

x + 130 = 180

x = 180 - 130

x = 50

Answer:

Step-by-step explanation:

take angle B as reference angle

using cosec rule

cosec B=hypotenuse/opposite

cosec B=13/12

cosec B=1.08

B=cosec 67

B=67 degree

for ratio,

cosec B=13/12

Answer:

the 30% off is better because 30% of 55 is 16.5 and the coupon is for 15 so the 30% off is better.

Step-by-step explanation:

Answer:

10 x 4 = 40, 40 x 2 = 80

5 x 10 = 50, 50 x 2 = 100

5 x 4 = 20, 20 x 2 = 40

100 + 80 + 40 = 220 ft2

Answer:

12x - 3y

Step-by-step explanation:

Combine Like Terms

10x + 2x = 12x

Answer:

100,000

Step-by-step explanation:

Because the 9 thousand is more than 5.

Answer:

Step-by-step explanation:

its (-1,-6)

this is your answer

Answer:

the length of its altitude is 34.64 cm

Step-by-step explanation:

Given;

length of a side of the equilateral triangle, L = 40 cm

All the sides of an equilateral triangle are equal

To get the altitude of the triangle, draw a perpendicular line from one of the vertices to intersect the opposite side.

Let the altitude = h

half of the opposite side intersected by the altitude = 20 cm

Apply Pythagoras theorem to determine the altitude 'h'

h² = 40²  -  20²

h² = 1200

h = √1200

h = 34.64 cm

Therefore, the length of its altitude is 34.64 cm

Answer:

60

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

D. 3(d + 8) and (d + 8) + (d + 8) + (d + 8)

II. 2.235

Step-by-step explanation:

Given the following data;

3 packages at $8 each = 3 * 8 = $24

3 pair of shoes at $d each = $3d

I. To find the total amount of money Cory spent;

Total = 3d + 24

Factorizing, we have;

Total = 3(d + 8)

II. To find the value of the expression;

Your expression isn't explicitly written but I'll assume it's this;

(14.72 - 10.25)/2 =

4.47/2 = 2.235

Answer:

EF = 25 cm and FG = 35 cm

Step-by-step explanation:

After finding each scale factor for each of the 4 answers, only the last option is relatable. Every other option resulted in different numbers of EF and FG.

Answer:

D

Step-by-step explanation:

Answer:

dpr,rpd

Step-by-step explanation:

thats the answers at least i think thats for first.

Answer:

1) ∠P, ∠DPR, ∠KPR, ∠RPD

2) x = 111°

3) x = 5

4) m∠3 = 72°

Step-by-step explanation:

1) All of the angles display ∠P, you will noticed this if you go from the first letter point and it goes to ∠P and to the last letter point with only including ∠P.

2) I already solved this one in a different post of yours. Subtract all known values from 180° to get your answer.

3) Use the same principle knowing that all sides of a triangle add up to 180°. Add all of the angles together, set the equation to 180 and solve for x.

4) By the Alternate Exterior Angles Theorem, If a transversal intersects two parallel lines, then alternate exterior angles are congruent. Therfore, m∠6 ≡ m∠2, and we know m∠2. Solve by subtracting 108° from 180° because angles on the same line add up to 180°.

Answer:

C)

Step-by-step explanation:

5 times 2 equals 10

add 3

the total comes up to 13.