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Zepler [3.9K]
2 years ago
12

Mariah went to the store to buy a coat. The coat originally cost $120.00. Mariah used a coupon

Mathematics
2 answers:
Reika [66]2 years ago
8 0
She is saving $24!
explanation: multiply .2 (20%) by 120.
luda_lava [24]2 years ago
8 0

Step-by-step explanation:

120 times 0.20= $24

120-24= $96

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XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3
nataly862011 [7]
<h2>Answer:</h2>

4π

<h2>Step-by-step explanation:</h2>

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = \frac{1}{2} x b x h      -------------(i)

Where;

A = 18\sqrt{3}

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

<em>Substitute these values into equation(i) and solve as follows:</em>

18\sqrt{3} =  \frac{1}{2} x b x 6

18\sqrt{3} =  3b

<em>Divide through by 3</em>

6\sqrt{3} =  b

Therefore, b = XZ = 6\sqrt{3}

<em>Now, assume that the circle is centered at O;</em>

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180°   [sum of angles in a triangle]

=>  XOZ + 30° + 30° = 180°

=>  XOZ + 60° = 180°

=>  XOZ = 180° - 60°

=>  XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}

\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}

\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}

\frac{1}{12}  = \frac{1}{2|OZ|}

\frac{1}{6} = \frac{1}{|OZ|}

|OZ| = 6

The radius of the circle is therefore 6.

<em>Now, let's calculate the length of the arc XZ</em>

The length(L) of an arc is given by;

L = θ / 360 x 2 π r          ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

5 0
2 years ago
A car is traveling at a speed of 25 meters per second what is the cars speed in kilometers per hour how many kilometers will the
Likurg_2 [28]

Answer:

  • 90 km/h
  • 180 km

Step-by-step explanation:

There are 1000 m in 1 km, and 3600 s in 1 h, so the speed conversion is ...

  \dfrac{25\,m}{s}\cdot\dfrac{1\,km}{1000\,m}\cdot\dfrac{3600\,s}{1\,h}=\dfrac{90\,km}{h}

The car's speed is 90 km/h.

__

In 2 hours, the car will travel ...

  distance = speed · time = (90 km/h)(2 h) = 180 km

7 0
3 years ago
When 3^2 – 2 + 7 is subtracted from 5^3 – 4^2 + 10, what is the difference?
xxTIMURxx [149]
The difference is 105
3^2 - 2 + 7 =
(3 x 3) - 2 + 7 =
9 - 2 + 7 = 14

5^3 - 4^2 + 10 =
( 5 x 5 x 5) - ( 4 x 4) + 10
125 - 16 + 10 = 119

119 - 14 = 105
6 0
3 years ago
It takes 3 2/6 spoons of chocolate syrup to make 3 1/2 gallons of chocolate milk. How many spoons of syrup would it take to make
Anit [1.1K]

Answer: 4 gallons require 5 5/39 spoons of syrup

Step-by-step explanation:

7 0
2 years ago
Julio says,"If you subtract 15 from my number and multiply the difference by -7,the result is -175." What is Julios number
maw [93]

Answer: 40

Step-by-step explanation:

Assume Julio's number is x.

The expression would be:

-7 * (x - 15) = -175

x - 15 = -175/-7

x = -175/-7 + 15

x = 40

7 0
2 years ago
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