MATHEMATICS HIGH SCHOOL

If two angles are supplementary, they must __________.add up to
add up to
be adjacent
be congruent

Answers

Answer 1
Answer: supplementary angles add up to 180
Answer 2
Answer: If two angles are supplementary, their sum is 180º and they can be expressed as x and 180-x. If they are congruent ,then the two angles are equal: 
x=180-x 
2x=180 
x=90º and 180-x=90º 
 The 2 angles have to add to 180 degrees

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Yvette is trying to calculate the distance between point C(1, 2) and point D(7, 10). Which of the following expressions will she use?

Answers

For the answer to the question above, this can be solve using the distance formula: D = sqrt [ (x2 – x1)^2 + (y2 – y1)^2] So the expression she should use is: D = sqrt [ (7 – 1)^2 + (10 – 2)^2] Then the answer would be: D = sqrt [ (6)^2 + (8)^2] D = 10 I hope my answer helped you.

8ducks for 23.60 blank per duck

Answers

Step-by-step explanation:

23.60÷8= 2.95

Each duck will be 2.95

(3 pt) Which shows the dimensions of two rectangular prisms that have volumes of 320 mm3 but different surface areas? A. 16 mm by 5 mm by 4 mm; 5 mm by 4 mm by 16 mm B. 10 mm by 4 mm by 6 mm; 6 mm by 10 mm by 4 mm C. 8 mm by 10 mm by 4 mm; 10 mm by 8 mm by 4 mm D. 8 mm by 10 mm by 4 mm; 20 mm by 8 mm by 2 mm

Answers

D. 8 mm by 10 mm by 4 mm
    20 mm by 8 mm by 2 mm

8 x 10 x 4 = 320 mm
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Models sells right handed and left Handed baseball gloves in one month 12 gloves for a total revenue 528. Right gloves cost 48 and left handed cost 36 how many right handed gloves were sold.

Answers

Answer:

8 Right handed gloves and 4 left handed gloves.

Step-by-step explanation:

Assumed the number of right handed gloves sold was x and the number of left handed gloves sold was y.

Given that 12 gloves were sold:

x + y = 12

x = 12 - y

Given that the total revenue made was 528:

48x + 36y = 528

Substitute x = 12 - y into 48x + 36y = 528:

48(12 - y) + 36y = 528

576 - 48y + 36y = 528

-12y = -48

y = 4

Substitute y = 4 into x = 12 - y:

x = 12 - 4 = 8

8 Right handed gloves and 4 left handed gloves.
11 were sold. You do revenue 528 divided by cost of that glove (48) equals 11.

If the height of a right circular cone of volume 96 pie cm sq is 18cm, then what is the radius of the base of the right circular cone?OPTIONS-
A) 4cm
B) 6cm
C) 8cm
D) 9cm

Answers

The radius of the base of this right circular cone is equal to: A) 4cm

Given the following data:

  • Volume of right circular cone = 96\pi \;cm^2
  • Height of right circular cone = 18 cm

To determine the radius of the base of the right circular cone:

Mathematically, the volume of a right circular cone is given this formula:

V = \pi r^2(h)/(3)

Where:

  • V is the volume of a cone.
  • r is the radius of a cone.
  • h is the height of a cone.

Making r the subject of formula, we have:

r = \sqrt{(3V)/(\pi h) }

Substituting the given parameters into the formula, we have;

r = \sqrt{(3 * 96\pi)/(\pi * 18) }\n\nr = \sqrt{(3 * 96)/( 18) }\n\nr=√(16)

Radius, r = 4 centimeters

Read more on volume of a cone here: brainly.com/question/13677400
Via equation:
96pi=1/3 pi * r^2 * 18
16/3 pi=1/3 pi r^2
16 pi = pi r^2
16 = r^2
r = 4

Equation:cosθ= -12/13 for π <θ<3π /2
prompt:
find sin 2θ, cos 2θ, and tan 2θ

Answers

Cosθ = -12/13.   
For π <θ<3π /2 means  180° <θ< 270°. That is the third quadrant.

Let us just have the positive value of Cosθ = 12/13

Cosθ = Adjacent / Hypotenuse = 12 / 13

So we imagine a right angled triangle with adjacent side = 12, and Hypotenuse = 13.

To get the opposite side we apply Pythagoras' Theorem. Let the opposite side be x.

x² + 12² = 13²
x² + 144 = 169
x²  = 169 - 144
x² = 25
x = √25
x = 5.

Sinθ = Opposite / Hypotenuse = 5 / 13

Tanθ = Opposite / Adjacent = 5 / 12


Recall the angle is in the third quadrant, and in the third quadrant, only Tangent is positive, Cosine and Sine are both negative.

Therefore 
Cosθ = -12/13  Sinθ = -5/13  Tanθ = 5/12

Solving:

i) Sin2θ = 2SinθCosθ.            By Trigonometric Identity.
 
            =  2*(-5/13)*(-12/13)

            = 120/169


ii) Cos2θ = 2Cos²θ - 1

              = 2*(-12/13)(-12/13) - 1

              = 288/169 - 1

              = (288 - 169) / 288

              =  119/288


Tan2θ = 2Tanθ /(1 - Tan²θ)

         = 2*(5/12) / ( 1- (5/12)²)

         =   (5/6) / ( 1 - 25/144)

         = (5/6) / ( (144 -25)/144)

         = (5/6) / (169/25)

         = (5/6) * (25/169)

         = 125/1014    

I hope this helps.
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