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2 years ago

Quadrilateral ABCD is a rectangle. BD = 6x - 14 and AC = 8x - 20. What is BD?

Mathematics

1 answer:

BigorU [14]2 years ago

8 0

Answer:

Step-by-step explanation:

The diagonals are equal length:

$6x - 14 = 8x - 20\\-2x = -6\\x = 3$

$BD = 6x - 14\\BD = 6 * 3 - 14\\BD = 18 - 14\\BD = 4$

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Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

Viefleur [7K]

QUESTION 1

Given that:

$f(x)=2x^2+3x-9$ ,

$g(x)=5x+11$ ,

and

$h(x)=-3x^2+1$

Then;

$f(x)-g(x)+h(x)=2x^2+3x-9-(5x+11)+(-3x^2+1)$

$f(x)-g(x)+h(x)=2x^2+3x-9-5x-11-3x^2+1$

Group similar terms;

$f(x)-g(x)+h(x)=2x^2-3x^2+3x-5x-11-9+1$

Simplify;

$f(x)-g(x)+h(x)=-x^2-2x-19$

QUESTION 2

Given that;

$f(x)=4x-7$ .

$g(x)=(x+1)^2$

and

$s(x)=f(x)+g(x)$

Substitute the functions;

$s(x)=4x-7+(x+1)^2$

Substitute x=3

$s(3)=4(3)-7+(3+1)^2$

$s(3)=12-7+(4)^2$

$s(3)=5+16$

$s(3)=21$

QUESTION 3

Given:

$f(x)=3x+2$

$g(x)=x^2-5x-1$

$f(g(x))=f(x^2-5x-1)$

This implies that;

$f(g(x))=3(x^2-5x-1)+2$

Expand the parenthesis;

$f(g(x))=3x^2-15x-3+2$

$f(g(x))=3x^2-15x-1$

QUESTION 4

The given function is;

$f(x)=3(x-6)^2+1$

Let

$y=3(x-6)^2+1$

$\Rightarrow y-1=3(x-6)^2$

$\Rightarrow \frac{y-1}{3}=(x-6)^2$

$\Rightarrow \sqrt{\frac{y-1}{3}}=x-6$

$\Rightarrow x=6+\sqrt{\frac{y-1}{3}}$

The range is:

$\frac{y-1}{3}\ge0$

$y-1\ge0$

$y\ge1$

The interval notation is;

$[1,+\infty)$

6 0

3 years ago

a rectangle of perimeter 100 units has the dimensions shown. Its area is given by the function A = w(50 - w). What is the GREATE

Anna [14]

If A=w(50-w)

A=50w-w^2

dA/dw=50-2w

d2A/dw2=-2

Since the acceleration is a constant negative, that means that when velocity, dA/dw=0, it is at an absolute maximum for A(w)...

dA/d2=0 only when 50=2w, w=25

So as the case with any rectangle, the perfect square will enclose the greatest area possible with respect to a given amount of material to enclose that area...

So the greatest area occurs when W=L=25 in this case:

A(25)=50w-w^2

Area maximum is thus:

Amax=50(25)-(25)^2=625 u^2

7 0

2 years ago

The base of a rectangle is 6cm longer than its height. The area of a rectangle is 91cm squared. What is the perimeter of the rec

r-ruslan [8.4K]

Width = 7cm

Length = 13cm

<u>Explanation:</u>

Area of rectangle = $91cm^{2}$

Let width of the rectangle = b ,

So, length = b+6

Area of rectangle = (length X width) - eqn 1

Putting the value of length and width in above equation 1,

$91cm^{2} = b (b+6)\\91 = b^{2}+6b\\b^{2} + 6b-91 = 0\\$

On solving the quadratic equation we get,

b = 7cm

So, width (b) = 7cm

and length = 7+6

l = 13cm

Hence,

Width = 7cm

Length = 13cm

6 0

3 years ago

Given f(x) = x^4 -3x^3 +10x^2 -9x +1. Is (x-2) a factor? Is x=-3 a zero? Find f(-1) show all work.

gizmo_the_mogwai [7]

Step-by-step explanation:

(x-2) is not a factor

x = -3 is not a zero

<h2>Please mark my answer as the brainliest for further answers :)</h2>

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2 years ago

Some one I need help on the ones I circled plz I just need to find the gcf of each pair of numbers

notka56 [123]

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3 0

3 years ago