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4 years ago

11

Tanya has a garden with a trench around it. The garden is a rectangle with length 2.5m. The trench and garden together make a re

ctangle with length 3.5m and width 3m.
Find the area of the trench

2 answers:

tiny-mole [99]4 years ago

6 0

Answer:

5.5m2

Step-by-step explanation:

Nadusha1986 [10]4 years ago

4 0

Answer:

5.5m2

Step-by-step explanation:

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4 years ago

What is the vertex of the function f (x) = x2 - 10x?<br>(5,-25)<br>(5.-75)<br>(-5,75)<br>(-5,25)

JulsSmile [24]

Option A

The vertex is (h, k) = (5, -25)

<em><u>Solution:</u></em>

<em><u>Given function is:</u></em>

$f(x) = x^2-10x$

<em><u>The vertex form is given as:</u></em>

$y = a(x-h)^2+k$

<h3>where (h, k) is the vertex</h3>

Rewrite the equation in vertex form

$f(x) = x^2-10x$

Complete the square for $x^2-10x$

Use the form $ax^2+bx+c$ to find the values of a, b, c

a = 1 , b = -10, c = 0

Consider the vertex form of a parabola

$a(x+d)^2+e$

Substitute the values of a and b into the following formula to find "d" :

$d = \frac{b}{2a}\\\\d = \frac{-10}{2 \times 1}\\\\d = -5$

Find the value of "e" using the formula,

$e = c - \frac{b^2}{4a}\\\\e = 0 - \frac{(-10)^2}{4 \times 1}\\\\e = -25$

Substitute the value of a, d, e into vertex form

$a(x+d)^2+e\\\\1(x-5)^2-25\\\\(x-5)^2-25$

Set y equal to above equation

$y = (x-5)^2-25$

Compare the above equation with vertex form

$y = a(x-h)^2+k$

$y = (x-5)^2-25$

We find, h = 5 and k = -25

Thus the vertex is (h, k) = (5, -25)

7 0

3 years ago