MATHEMATICS HIGH SCHOOL

Compute without using a calculator.
sin (9π/4)tan(7π/3)

Answers

Answer 1
Answer: sin\left((9\pi)/(4)\right)tan\left((7\pi)/(3)\right)=sin\left(2(1)/(4)\pi\right)tan\left(2(1)/(3)\pi\right)=sin\left(2\pi+(1)/(4)\pi\right)tan\left(2\pi+(1)/(3)\pi\right)\n\n=sin(1)/(4)\pi tan(1)/(3)\pi=(\sqrt2)/(2)\cdot\sqrt3=(\sqrt6)/(2)

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The museum charges $12.50 for youth admission and $17.50 for adults.  One day the museum collected $1535 from a total of 110 youths  and adults.  How many admissions of each type were sold?

Answers

x - young
y - adult

12.50x+17.50y=1535\n x+y=110\n\n 12.50x+17.50y=1535\n x=110-y\n\n 12.50(110-y)+17.50y=1535\n 1375-12.50y+17.50y=1535\n 5y=160\n y=32\n\n x=110-32\n x=78

Richelle drew a hexagon KLMNOP at the right. She thinks the hexagon has six congruent angles. How can she show that the angles are congruent without using a protractor to measure them?

Answers

By using a ruler? If all six sides are the exact same size, they have all same angles.

Hope you get it!

O is the center of the circle. Assume that lines that appear to be tangent are tangent. What is the value of x?

Answers

Answer:

\boxed{\boxed{x^(\circ)=78^(\circ)}}

Step-by-step explanation:

Given that, O is the center of the circle and PQ is a tangent to the circle at point Q. OQ is a radius of the circle.

We know that, a tangent to a circle is a line which just touches the circle. And the angle between the tangent and radius is 90°.

Hence, ΔOQP is a right angle triangle. We know that the sum of the measurements of all the 3 angles of a triangle leads to 180°. So,

\Rightarrow m\angle O+m\angle Q+m\angle P=180^(\circ)

\Rightarrow x^(\circ)+90^(\circ)+12^(\circ)=180^(\circ)

\Rightarrow x^(\circ)=180^(\circ)-90^(\circ)-12^(\circ)=78^(\circ)
Angle q is right angle so you would first do 12+90=102 then you would do 180-102=78 so x=78

For two weeks, Mario recorded the color of the traffic light at the intersection of Main Street and North Avenue as his bus approached the intersection. He created this frequency table. What data did he collect to create this frequency table? A. green, red, red, red, red, red, green, red, red, yellow
B. red, red, red, yellow, red, red, green, red, red, yellow
C.red, red, red, red, red, red, green, red, red, yellow
D.red, red, green, red, red, red, green, red, red, yellow

frequency table:
Red: 7
Green: 2
Yellow: 1
Total: 10

Answers

A. Because the data in the frequency table matches the data in A.
A because that's the only one with matching data.

Find the slope of the line that contains these two points.
(2, -5) and (7, -10)

Answers

\sf Slope= (y_2-y_1)/(x_2-x_1)

Where \sf (x_1,y_1), (x_2,y_2) are the two points.

So

\sf Slope = ( -10-(-5))/(7-2)=(-10+5)/(7-2)=(-5)/(5)=-1

So the slope of (2,-5) and (7,-10) was \boxed{ -1}
m=(y1-y2)/(x1-x2)=(-5-(-10))/(2-7)=(5)/(-5) =-1
 Answer: slope is -1

The area of the triangle is 48cm. Then find the length of corresponding altitudes

Answers

Area of triangle = 1/2 × base × height 
Base of the triangle = (2 Area)/height 
Height of the triangle = (2 Area)/base 

Given:
A = 48 cm^2
Base of the triangle = (2 x 48 )/height
Height of the triangle = (2 x 48)/base
 Let the triangle be isosceles :
So,
base = height

Therefore,
Base of the triangle = (2 x 48 )/Base
(Base)^2 = 96
Base = √96
Base = √(2*2*2*2*6)
Base = 4√6
height = 4√6
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