How bout this 1? yaall kno it

ASSIGNMENT: Show that the correct solution to the following system of equations is (-2, 0). Upload a photo of your work or neatl

ki77a [65]

Answer:

Step-by-step explanation:

5 0

3 years ago

Triangle ABC has vertices at A(2,3),B(-4,-3) and C(2,-3) find the coordinates of each point of concurrency.

dem82 [27]

Answer:

Circumcenter =(-1,0)

Orthocenter =(2,-3)

Step-by-step explanation:

Given : Points A = (2,3), B = (-4,-3), C = (2,-3)

Formula used :

→Mid point of two points- $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

→Slope of two points - $\frac{y_2-y_1}{x_2-x_1})$

→Perpendicular of a line = $\frac{-1}{slope of line})$

Circumcenter- The point where the perpendicular bisectors of a triangle meets.

Orthocenter-The intersecting point for all the altitudes of the triangle.

To find out the circumcenter we have to solve any two bisector equations.

We solve for line AB and AC

So, mid point of AB = $(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)$

Slope of AB = $\frac{-3-3}{-4-2}=1$

Slope of the bisector is the negative reciprocal of the given slope.

So, the slope of the perpendicular bisector = -1

Equation of AB with slope -1 and the coordinates (-1,0) is,

(y – 0) = -1(x – (-1))

y+x=-1………………(1)

Similarly, for AC

Mid point of AC = $(\frac{2+2}{2},\frac{3-3}{2})=(2,0)$

Slope of AC = $\frac{-3-3}{2-2}=\frac{-6}{0}$

Slope of the bisector is the negative reciprocal of the given slope.

So, the slope of the perpendicular bisector = 0

Equation of AC with slope 0 and the coordinates (2,0) is,

(y – 0) = 0(x – 2)

y=0 ………………(2)

By solving equation (1) and (2),

put y=0 in equation (1)

y+x=-1

0+x=-1

⇒x=-1

So the circumcenter(P)= (-1,0)

To find the orthocenter we solve the intersections of altitudes.

We solve for line AB and BC

So, mid point of AB = $(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)$

Slope of AB = $\frac{-3-3}{-4-2}=1$

Slope of the bisector is the negative reciprocal of the given slope.

So, the slope of CF = -1

Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF

(y – 0) = -1(x – (-1))

y+x=-1………………(3)

Similarly, mid point of BC = $(\frac{-4+2}{2},\frac{-3-3}{2})=(-1,-3)$

Slope of AB = $\frac{-3+3}{-4-2}=0$

Slope of the bisector is the negative reciprocal of the given slope.

So, the slope of AD = 0

Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD

(y-(-3)) = 0(x – (-1))

y+3=0

y=-3………………(4)

Solve equation (3) and (4),

Put y=-3 in equation (3)

y+x=-1

-3+x=-1

x=2

Therefore, orthocenter(O)= (2,-3)

7 0

3 years ago

A tin of biscuits contains shortbread and choc-chip biscuits in the ratio 2:3 . The tin contains 80 biscuits. How many short-bre

Aleksandr [31]

Answer:

32

Step-by-step explanation:

There are 80 biscuits inside the tin.

Also, they said that those biscuits are in the ratio

Short bread : Choc - chip

2 : 3

Altogether there are 5 shares ( 2 + 3)

And now you can divide 80 by 5 to find how many biscuits contain per a share.

80 ÷ 5 = 16

In the question, they asked us to to find the number of short biscuits inside the tin.

Let us find that.

There are 2 shares for short bread biscuits.

So,

Number of short biscuits ⇒ 2 × 16

⇒ 32

Hope this helps you :-)

5 0

2 years ago

What will $110,000 grow to be in 9 years if it is invested today at 11%?

timama [110]

Answer:

218,900

Step-by-step explanation:

6 0

2 years ago

What statement best describes the function?

xxMikexx [17]

Answer:

d

Step-by-step explanation:

3 0

3 years ago