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4 years ago

Factorise x^2-y^2-2x+6y-8

1 answer:

3 0

X^2 - y^2 - 2x + 6y - 8
= (x^2 - 2x + 1) - (y^2 - 6y + 9) - 8 - 1 + 9 
= (x - 1)^2 - (y - 3)^2 
= [(x - 1) - (y - 3) ] [(x - 1) + (y - 3)] 
= (x - 1 - y + 3) ( x - 1 + y - 3) 
= (x - y + 2) (x + y - 4)

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Let <img src="https://tex.z-dn.net/?f=K" id="TexFormula1" title="K" alt="K" align="absmiddle" class="latex-formula"> be a circle

yan [13]

The bisector of angle APQ passes through O and this is illustrated below.

<h3>How to illustrate the information?</h3>

From the information given, the center is O. and the circle passes through O and cuts at K.

In this case, it should be noted that the circles are equal according to the SAS test.

Here, AOB + APQ = 180° (Linear pair)

2AOB = 180

AOB = 90.

Therefore, the bisector of angle APQ passes through O.

Learn more about bisector on:

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2 years ago

A pendant is formed using a cylinder and cone. Once assembled, as shown below, the pendant is painted. How many square millimete

solmaris [256]

Surface area of cylinder is given by area of circle + area of the rectangle that curved around the cylinder

Area of the base of the cylinder = $\pi r^{2} = 8^{2} \pi =64 \pi$
Area of the cylinder 'wall' = width × length = $12$ × $2r \pi$ = $12$ × $16 \pi$ = $192 \pi$

Note that the wall of the cylinder is in the shape of a rectangle. The width of the rectangle is the height of the cylinder. The length of the rectangle is the circumference of the circle base.

Surface area of cone is given by $\pirl$ where $l$ is the slanted height of the cone

SA of cone = $\pi (8)(10)=80 \pi$

Hence total painted surface area is $80 \pi +192 \pi +64 \pi =336 \pi$

3 0

3 years ago

Read 2 more answers

Miss Jones attended a a southern living home party she purchased a vase which cost $34.99The shipping charge was three dollars a

jenyasd209 [6]

The answer is $41.12
(Work is below)

First add the total of the vase and shipping-
Vase: $34.99
Shipping: $ 3.00
+__________
$37.99

Then calculate sales tax by multiplying $37.99 x 0.0825 -
Above Total: $37.99
Sales Tax Rate: $ 0.0825
x__________
$ 3.1341
You round down because ^ less than five (five or above you would round up)

Sales Tax: $3.13

Then you add the sales tax to the above total

Vase: $37.99
Shipping: $ 3.13
+__________
$41.12

8 0

3 years ago

The equation y=x^2-12x+45 models the number of books y sold in a bookstore x days after an award-winning author appeared at an a

romanna [79]

Answer: The first day the author reaches 100 days is on day 16.

To solve this problem, you could use a graphing calculator to graph the given equation. Then, determine when this line crosses 100. It crosses when x = 15.539. Therefore, we would have to round up to 16 so it is at least 100.

You could use the quadratic equation to solve: 100 = x^2 -12x + 45

Either you will get 16. If you use the quadratic formula, make sure to only use the positive answer.

7 0

3 years ago

What is 19/25 as decimal

Radda [10]

Well first we need to find how we can turn 25 into 100
Well one way would be to multiply by 4
25 x 4 = 100

Since we multiplied the bottom number by 4 we should multiply the top number by 4.

So..
19 x 4 = 76

So our new fraction is..
76
-----
100

Now we can easily turn this into a decimal.
76/100 = 0.76

Answer = 0.76

Good Luck! :)

3 0

3 years ago

Read 2 more answers