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mrs_skeptik [129]
3 years ago
8

A triangle has vertices at points (0, 0), (a, b), and (2a, 0). Select all points that lie on the sides of the triangle. A. (a, 0

) B. (0, b) C. (–a, b) D. (a/2,b/2) E. (a/3,b/4)
Mathematics
1 answer:
RSB [31]3 years ago
4 0

Answer:

A. (a, 0)

D. (a/2,b/2)

Step-by-step explanation:

(a, 0) lies on one side of the triangle, because it is between (0,0) and (2a,0)

(0, b) doesn't lie on one side of the triangle, because only the only point with x-coordinate = 0 is (0,0)

(–a, b) doesn't lie on one side of the triangle, because only positive values are valid

Imagine the triangle with vertices (0,0), (a, 0) and (a,b). Let's call β the angle at vertex (0,0)

tan(β) = b/a

For triangle with vertices (0,0), (a/2, 0) and (a/2,b/2)

tan(β) = (b/2)/(a/2) = b/a

then, (a/2,b/2) lies on one side of the triangle

For triangle with vertices (0,0), (a/3, 0) and (a/3,b/4)

tan(β) = (b/4)/(a/3) = (3/4)*(b/a) ≠ b/a

then, (a/3,b/4) doesn't lie on one side of the triangle

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Use the properties of exponents to enter an equivalent expression with a single exponent.
Gelneren [198K]

({10}^{2} ) {}^{4}  =  {10}^{2 \times 4}  =  {10}^{8}

I hope this can help you ^_^

5 0
3 years ago
-6x-14y=16 and -2x+7y=17 solve by elimination show the work
professor190 [17]

Answer:

(- 5, 1 )

Step-by-step explanation:

- 6x - 14y = 16 → (1)

- 2x + 7y = 17 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the x- term

6x - 21y = - 51 → (3)

Add (1) and (3) term by term to eliminate x

0 - 35y = - 35

- 35y = - 35 ( divide both sides by - 35 )

y = 1

Substitute y = 1 into either of the 2 equations and solve for x

Substituting into (1)

- 6x - 14(1) = 16

- 6x - 14 = 16 ( add 14 to both sides )

- 6x = 30 ( divide both sides by - 6 )

x = - 5

solution is (- 5, 1 )

6 0
2 years ago
Can someone please help me?
makkiz [27]
Second one...................
7 0
4 years ago
Calculate the area of the shape below.
Vsevolod [243]

Answer:

24ft²

Step-by-step explanation:

divide up the shape:

big triangle:

(looking for base)

9.8²= 4² + b²

b  = 8.95ft

(finding area)

0.5*8.95*4 = 17.9ft²

small triangle:

(looking for base)

12-8.95=3.05ft

(finding area)

0.5*3.05*4 = 6.1ft²

Whole Shape:

17.9+6.1 = 24ft²

3 0
3 years ago
White and black shapes are used in a game Some of the shapes are circles All the other shapes are squares The ratio of white to
PIT_PIT [208]

Answer:

The fraction of all shapes which are square in shape is \frac{23}{32}.

Step-by-step explanation:

Given that , in a game , white and black shapes are used. Some of them are circle in shape and remains are square in shape.

The ratio of white to black shapes are 5:11.

Consider 5x= the number of shapes which are white in color.

11x= The number of shapes which are black in color.

There are (5x+11x)= 16x shapes in the game.

The  white circle and white square are in the ratio 3:7.

The number of white square is

=(\textrm{The number of white shape})\times (\frac{7}{3+7})

=(5x)\times (\frac{7}{10})

=\frac{7x}{2}

The black circles and black square are in the ratio 3:8

The number of black square is

=(\textrm{The number of black shape})\times (\frac{8}{3+8})

=(11x)\times (\frac{8}{11})

=8x

Therefore the total number of shape which are square is

=\frac{7x}{2}+8x

=\frac{7x+16x}{2}

=\frac{23x}{2}

The fraction of all shape are square is

=\frac{\textrm{shape in square}}{\textrm{Total number shape}}

=\frac{\frac{23x}{2}}{16x}

=\frac{23}{32}

5 0
3 years ago
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