MATHEMATICS
HIGH SCHOOL

Answer:

Answer:

see explanation

Step-by-step explanation:

the ratio of the opposite interior angles = 8 : 9 = 8x : 9x

The exterior angle of a triangle = sum of the opposite interior angles, hence

8x + 9x = 119

17x = 119 ( divide both sides by 17 )

x = 7

8 parts = 8x = 8 × 7 = 56

9 parts = 9x = 9 × 7 = 63

The sum of the 3 angles in a triangle = 180°

subtract the sum of the 2 angles from 180 for third angle in triangle

180° - (56 + 63)° = 180° - 119° = 61°

The 3 angles of the triangle are 56°, 61°, 63°

HIGH SCHOOL

How to find amplitude and period from equation?

If your graph is a COS or SIN graph :

a is the Amplitude

and period is:

If your graph is a TAN graph :

A TAN graph has no amplitude as it has no Maximum or Minimum value.

To find period :

a is the Amplitude

and period is:

If your graph is a TAN graph :

A TAN graph has no amplitude as it has no Maximum or Minimum value.

To find period :

HIGH SCHOOL

If the function f is continuous for all real numbers and f(x) = (x^2-4)/(x+2) when x cannot equal -2 , then f(-2) =?

The function is continuous for all real numbers:

f ( x ) = ( x² - 4 ) / ( x + 2 ) = =

= x - 2

f ( -2 ) = - 2 - 2 = - 4

f ( x ) = ( x² - 4 ) / ( x + 2 ) = =

= x - 2

f ( -2 ) = - 2 - 2 = - 4

Answer: -4

Step-by-step explanation:

If f is continuous you know that lim x-> a f(x) = f(a)

Since the limit x-> -2 = (x-2)(x+2)/(x+2) = -4, this is done by canceling out the top term and the bottom term (x+2)

Your answer is -4

MIDDLE SCHOOL

Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. What is the solution?

Answer:

Marcos had 6 nickel coins and 9 quarter coins.

Step-by-step explanation:

We are given the following in the question:

Let x be the number of nickel coins and y be the number of quarter coins.

Marcos had 15 coins in nickels and quarters.

Thus, we can write the equation:

He had 3 more quarters than nickels. We can write he equation,

Solving the two equations, we get,

Thus, Marcos had 6 nickel coins and 9 quarter coins.

COLLEGE

Here is a test to how good your math is, In ∆ABC , A = ( 1 , 2 ) ; B = ( 5 , 5 ) and <ACB = 90° . If area of ∆ABC is to be 6.5 square units , then the possible number of points for C is ?

Answer:

There are no points for C to make this triangle

Step-by-step explanation:

We need to find the distance from point A to B

d = sqrt((x2-x1)^2 + (y2-y1)^2 )

= sqrt((5-1)^2 + (5-2)^2

= sqrt(4^2 + 3^2)

= sqrt(16+9)

= sqrt(25)

= 5

We know the hypotenuse only

We can find the base in terms of the hypotenuse using the Pythagorean theorem

c^2 = a^2 + b^2

c^2 - a^2 = b^2

Taking the square root of each side

sqrt( c^2 - a^2) = sqrt(b^2)

sqrt( c^2 - a^2) = b

c = 5

sqrt(25 - a^2)=b

The area of a triangle is

A = 1/2 b* h where b is the base and a is the height

6.5 = 1/2 (sqrt(25-a^2)) *a

Multiply each side by 2

2*6.5 = 2*1/2 (sqrt(25-a^2)) *a

13 = (sqrt(25-a^2)) *a

Divide each side by a

13/a = sqrt(25-a^2)

Square each side

169/a^2 = 25-a^2

Multiply each side by a^2

169 = 25a^2 -a^4

Subtract 169 from each side

0= -a^4 +25a^2 -169

Divide by -1

0= a^4 -25a^2 +169

Using the discriminant

b^2 -4ac

25^2 - 4 * 1 * 169

625 - 676

-51

a^2 is imaginary

There is no solution

Answer:

Zero

Step-by-step explanation:

The distance AB is ...

... √((5-1)²+(5-2)²) = √(16+9) = 5

The largest right triangle that can be constructed with AB as the hypotenuse is one with an altitude of 5/2 = 2.5 units. Its area will be ...

... (1/2)·5·2.5 = 6.25 . . . . square units

It is not possible to construct the triangle ABC described.

_____

In order to achieve the given area, ∠C would need to be 87.75° or smaller. It could not be 90°.