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Nitella [24]
1 year ago
6

Consider a function that goes through the two points (0, 5) and (1, 20). Find the formula for the function if(a) the function is

linear (of the formf(x) =mx b)
Mathematics
1 answer:
EastWind [94]1 year ago
7 0

The formula for the linear function which is passing the points (0, 5) and (1, 20) is f(x) = 15x + 5.

According to the given question.

The linear form of the function is

f(x) = mx + b

Also, the function is passing through the points (0, 5) and (1, 20).

So, the given points (0, 5) and (1, 20) must satisfy f(x) = mx + b.

Now,

At (0, 5)

f(0) = m(0) + b

⇒ 5 = 0 + b

⇒ b = 5 ..(i)

Also,

at (1, 20)

f(1) = m(1) + b

⇒ 20 = m + 5     (from i)

⇒ m = 20 - 5

⇒ m = 15

Therefore, the formula for the linear function which is passing the points (0, 5) and (1, 20) is given by

f(x) = 15(x) + 5   (on substituting the vale of m and b in f(x) = mx + b).

⇒ f(x) = 15x + 5

Hemce, the formula of the function is f(x) = 15x + 5.

Find out more information about function here:

brainly.com/question/21107621

#SPJ4

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Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now?
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Helen is 16 and Jane is 8
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34 in.
Troyanec [42]

Answer:

Step-by-step explanation:

Lateral surface area of the triangular prism = Perimeter of the triangular base × Height

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

(34)² = (16)² + BC²

BC = \sqrt{1156-256}

     = \sqrt{900}

     = 30 in.

Perimeter of the triangular base = AB + BC + AC

                                                      = 16 + 30 + 34

                                                      = 80 in

Lateral surface area = 80 × 22

                                  = 1760 in²

Total Surface area = Lateral surface area + 2(Surface area of the triangular base)

Surface area of the triangular base = \frac{1}{2}(\text{Base})(\text{Height})

                                                           = \frac{1}{2}(30)(16)

                                                           = 240 in²

Total surface area = 1760 + 2(240)

                               = 1760 + 480

                               = 2240 in²

Volume = Area of the triangular base × Height

             = 240 × 20

             = 4800 in³

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We were given the slope formula;

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