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Lemur [1.5K]
3 years ago
11

Can you help me with this, please? ​

Mathematics
1 answer:
Aloiza [94]3 years ago
3 0

Answer:

y =x-12

Step-by-step explanation:

(x_1, y_1) = (16, 4) \ \ \ and \ \ \ (x_2, y_2) = (17, 5)

Equation of straight line is

y-y_1 =\frac{y_2-y_1}{x_2-x_1}  (x-x_1)

y-4 =\frac{5-4}{17-16}  (x-16)

y =(x-16)+4

y =x-12

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Problem page the length of a rectangle is four times its width. if the perimeter of the rectangle is 70 cm , find its area.
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One factor of the function f(x) = x3 − 8x2 + 17x − 10 is (x − 5). Describe how to find the x-intercepts and the y-intercept of t
kozerog [31]

Answer:

x-intercepts: (1,0), (2,0), (5,0)

y-intercepts: (0,-10)

Step-by-step explanation:

One factor of the function f(x) = x^3-8x^2 + 17x-10 is (x-5).

Factor the polynomial in the following way:

x^3-8x^2 + 17x-10\\ \\=x^3-5x^2-3x^2+15x+2x-10\\ \\=x^2(x-5)-3x(x-5)+2(x-5)\\ \\=(x-5)(x^2-3x+2)

Now factor the quadratic in brackets:

x^2-3x+2\\ \\=x^2-2x-x+2\\ \\=x(x-2)-(x-2)\\ \\=(x-2)(x-1)

Hence,

f(x)=(x-5)(x-2)(x-1)

The x-intercepts are points at which y = 0, so

(x-5)(x-2)(x-1)=0\\ \\x-5=0\ \text{or}\ x-2=0\ \text{or}\ x-1=0\\ \\x=5\ \text{or}\ x=2\ \text{or}\ x=1

The y-intercepts are points at which x = 0, so

y=0^3-8\cdot 0^2+17\cdot 0-10=-10

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