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Andrew [12]
3 years ago
11

1.Simplify 4√3 - 24√3 A. -20√3 B. 20√3 C. -6√15 D. -64√3

Mathematics
1 answer:
Zinaida [17]3 years ago
8 0
1) 4√3 - 24√3 = -20√3

2) Multiply and simplify square root of 3 times the quantity of 4 + square root of 12:
 (√3) x 4 + √12==> (√3) x 4 + √(4 x 3)==> 4√3 + 2√3 = 6√3

3) Simplify √3 + 4√3. ===> =5√3







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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)


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Because December is really cold
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Jamal baked muffins for the school bake sale. He made 12 corn muffins and 15 blueberry muffins. What is the ratio of blueberry m
dedylja [7]
The answer is 15:27 then simplify it to 5:9
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3 0
3 years ago
The height of Liliana’s picture frame is 18 inches. The frame and blue matting take up 4.5 inches of the height. Liliana wants t
Genrish500 [490]

.Answer: C

Step-by-step explanation:

4.5+p would be the full length of 18 since it is sharing the total length.

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3 years ago
PLEASE HELPPPPP PLEASE ILL GIVE YOU BRAINLIST
schepotkina [342]

Answer:

12

Step-by-step explanation:

The number of combinations for  2 shirts 3 pants and 2 shoes can be counted from the tree.

Count the different items at the end of the tree

There are 12 different combinations

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