x^2 - 2x factorise fully

Given:

The graph of a triangle ABC.

A line is parallel to AC and passes through the point D.

To find:

The point at which the intersection of this parallel line be with the line BC.

Solution:

From the given figure it is clear that A(1,7), B(9,7), C(9,1) and D(5,7).

Slope of AC is

[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]Slope=\dfrac{1-7}{9-1}[/tex]

[tex]Slope=\dfrac{-6}{8}[/tex]

[tex]Slope=\dfrac{-3}{4}[/tex]

Slope of parallel lines are same. So, the slope of parallel line is also [tex]-\dfrac{3}{4}[/tex].

The parallel line passes through D(5,7) with slope [tex]-\dfrac{3}{4}[/tex]. So, the equation of the line is

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-7=-\dfrac{3}{4}(x-5)[/tex]

[tex]y=-\dfrac{3}{4}(x)+\dfrac{15}{4}+7[/tex]

[tex]y=-\dfrac{3}{4}(x)+\dfrac{28+15}{4}[/tex]

[tex]y=-\dfrac{3}{4}(x)+\dfrac{43}{4}[/tex]              ...(i)

From the given graph it is clear that the line BC is a vertical line. So, the x-coordinates of all the points lie on BC are the same, i.e., 9.

Putting x=9, we get

[tex]y=-\dfrac{3}{4}(9)+\dfrac{43}{4}[/tex]

[tex]y=\dfrac{-27}{4}+\dfrac{43}{4}[/tex]

[tex]y=\dfrac{16}{4}[/tex]

[tex]y=4[/tex]

Therefore, the point at which the intersection of this parallel line be with the line BC is (9,4).

Answer:

Step-by-step explanation:

each one would be two and a half inches

Answer:

3/2x²+28x+130

Step-by-step explanation:

Area of shaded region = Area of rectangle – Area of triangle

Area of rectangle:

[tex](2x + 15)(x + 10) = \\2x {}^{2} + 35x + 150[/tex]

Area of triangle:

[tex] \frac{1}{2 } \times (x + 4)(x + 10) = \\ \frac{1}{2} x {}^{2} + 7x + 20[/tex]

then subtract

Answer:

(-1,-2)

Step-by-step explanation:

Maybe

Answer:

Step-by-step explanation:

For this question, it's C

Answer:

2

2

3x

Step-by-step explanation:

1.) we can divide both sides by three to get

(3x+6)/3=x+?

x+2= x+?

from here we can tell that ?=2

2.) Let's start by dividing both sides by negative one

(x-2)/ -1= ?-x

simplify

-x+2= ?-x

Here we get ?= 2

3.)

Let's mulitply both sides by 5 to get

15x-10= 5(?-2)

15x-10 = 5?-10

15x= 5?

3x= ?

the answer here is 3x

Answer:

The lowest common factor of 72 and 108 is 216

Answer:

See the attached document

Step-by-step explanation:

hope this is correct.......

Answer:

M = 26

Step-by-step explanation:

4m + 3m - 5 + 3 = 180 degree

7m -2 = 180 degree

7m = 180+2

7m = 182

m = 182/7

m =   26

26 x 4 - 5 = 104 - 5 = 99

26 x 3 +3 = 78+ 3 = 81

Answer:

Step-by-step explanation:

The change in y over the change in x between points is the slope. 53-29 over 3-2 is the slope. 24/1 is 24. You need the equation in y=mc+b form. b is the y intercept. (0, -19) is the point from the table containing the y int.. b=-19. Plug 24 and -19 into mc+b. To get y=24x-19

Answer:

[tex] \frac{2}{3} \bigg[ x\sqrt{ {x}} + (x - 1)\sqrt{ {(x - 1)}} \bigg] + c[/tex]

Step-by-step explanation:

[tex] \int \frac{1}{ \sqrt{x} - \sqrt{x - 1} } dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ (\sqrt{x} - \sqrt{x - 1} )( \sqrt{x} + \sqrt{x - 1} )} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ (\sqrt{x})^{2} - (\sqrt{x - 1} )^{2}} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ x - (x - 1 )} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ x - x + 1} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ 1} dx \\ \\ = \int (\sqrt{x} + \sqrt{x - 1}) dx \\ \\ = \int \sqrt{x} \: dx+ \int\sqrt{x - 1} \: dx \\ \\ = \int {x}^{ \frac{1}{2} } \: dx+ \int {(x - 1)}^{ \frac{1}{2} } \: dx \\ \\ = \frac{ {x}^{ \frac{3}{2} } }{ \frac{3}{2} } + \frac{ {(x - 1)}^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} {x}^{ \frac{3}{2} } + \frac{2}{3} {(x - 1)}^{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} \bigg[ \sqrt{ {x}^{3} } + \sqrt{ {(x - 1)}^{3} } \bigg] + c \\ \\ = \bold{\purple {\frac{2}{3} \bigg[ x\sqrt{ {x}} + (x - 1)\sqrt{ {(x - 1)}} \bigg] + c}} [/tex]

Answer:

552 eggs

Step-by-step explanation:

A dozen is equal to 12

Solve:

Multiply 46 by 12

Answer:

1

Step-by-step explanation:

Answer:    c = 14.287  approximately

==========================================================

Work Shown:

Refer to the diagram below. Note how side a is opposite angle A, and side c is opposite angle C.

tan(angle) = opposite/adjacent

tan(A) = a/c

tan(57) = 22/c

c*tan(57) = 22

c = 22/tan(57)

c = 14.2869670503452

c = 14.287

This value is approximate. Make sure your calculator is in degree mode

Answer:

big

Step-by-step explanation:

pp

Answer:

4536

Step-by-step explanation:

Hesap makinesi kulan

Answer:

2z + 5

Step-by-step explanation:

you have to combine like terms

subtract 4z - 2z and you get 2z

the number with the variable next to it goes first not the constant

2z + 5

the variable is z and the constant is 5 because it doesn't have variable next to it

hope this makes sense and helps :)

tell me if you have any questions

Step-by-step explanation:

Here as the like terms only are 4z and -2z so,

We simplify the like terms:

5 + 4z - 2z. [B.O.D.M.A.S rule] (subtraction only)

= 5 + 2z (Ans)

Answer:

ᴀ.)

Step-by-step explanation:

Hope you get it right!! :)

Answer:

They made 2 batches

Step-by-step explanation:

If the factory used ⅔, and 1 batch is ⅓, the factory made 1 batch for each 3rd they used. ⅔, 2 batches

35 rooms + 3 suites = 38 total rooms.

38 / 4 = 9.5

2 house keepers can clean 9 rooms each and 2 house keepers can clean 10 rooms each

2 Housekeepers need to clean more rooms than the other two.

Answer:

cool

Step-by-step explanation:

Answer:

LOL that's just

Step-by-step explanation:

epik uhhh wsg?

Answer:

75.27

Step-by-step explanation:

Rectangle = 20+2+2+20-11=47

quarter circle = 1/4(2)(11)(3.14)=17.27 + 11 = 28.27

47+28.27=75.27

Answer:

75.27.cm

Step-by-step explanation:

it works i got a 100 on the test

Answer:

75.36 inches

Step-by-step explanation:

C = π·d

C = 3.14(24)

C = 75.36

Answer:

What do you need though...

A basic rundown since I have no clue what you need help with

Parallelograms

(4 sided shapes that always adds up to 360 degrees if you add all the angles inside with opposite sides parallel)

Squares, rectangles (most common)

Triangles

3 sided figures with all the interior angles being added up equals to 180 degrees. The 3 sides of a triangle can be found with a^2+b^2=c^2.

The properties are 2 legs and 1 hypotenuse. To determine if its a triangle, if the 2 legs added up (two of the shortest sides) they must be greater then the hypotnuse (greatest side).

THese are the two of the most common shapes if you need an huything else just lemme know in the comments.

Answer:

1 if u cut  all of them in half

Step-by-step explanation:

Answer:

1.921

Step-by-step explanation: