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gtnhenbr [62]
3 years ago
14

What is the length of QR?

Mathematics
1 answer:
Elena L [17]3 years ago
7 0

Answer:

C

Step-by-step explanation:

Since the triangle is right with hypotenuse QR

Use Pythagoras' identity to solve for QR

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

QR² = 8² + (8\sqrt{3} )²

       = 64 + 192

       = 256 ( take the square root of both sides )

QR = \sqrt{256} = 16

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The parallelogram shown below has an area of 60 units^2
denpristay [2]

Answer:

b = 5.5

Step-by-step explanation:

In a paralelogram

A = bh

Just plug in the numbers

they said A = 60

and the number 11 is the height

60 = 11b

Divide

b = 60/11

b = 5.454545454

6 0
3 years ago
What is the ratio unknown amount (x) invested in company A to the know amount ($24) invested in company B? Write the answer as a
lara [203]

Answer:

X/24

Step-by-step explanation:

he ratio of the unknown amount (x) invested in company A to the known amount ($24) invested in company B is X/24

7 0
3 years ago
A cone of radius 10 cm and height 16 cm is divided into two parts by a plane through the midpoint of its
bazaltina [42]

Answer:

The ratio of their volumes (the top to bottom half) is 1/7

Step-by-step explanation:

The given parameters are;

The radius, r, of the cone = 10 cm

The height of the cone = 16 cm

The point at which the cone is divided = The midpoint of the its axis and parallel to its base

The ratio of the of the volume of the two parts is given as follows;

The volume, V of the entire cone = 1/3 × Base area (π·r²) × Height, h

Therefore;

V = 1/3 × π × 10² × 16 =1600·π/3 =  1675.52 cm³

The height at which the cone is divided = 16/2 = 8 cm

The height, h₁ of the uppermost divided cone = 8 cm

The ratio of the radius to the height of the cone = 10/16 = 5/8

The radius r₁, of the uppermost divided cone = The height of the uppermost divided cone × The ratio of the radius to the height of the cone

∴ r₁ = 8 × 5/8 = 5 cm

The volume, V₁, of the uppermost divided cone = 1/3 × (π·r₁²) × h₁

∴ V₁ = 1/3 × π × 5² × 8 = 200·π/3 = 209.44 cm³

Which gives;

The volume of the lower cone, V₂ =  V - V₁

V₂ =  1675.52 cm³ - 209.44 cm³ = 1400·π/3 = 1466.1 cm³

The ratio of their volumes V₁ : V₂ = V₁/V₂ = (200·π/3)/(1400·π/3) = 209.44/1466.1 = 1/7.

7 0
3 years ago
A rectangle has a length of 14 yards less than 9 times its width. If the area of the rectangle is 6183 square yards, find the le
Jlenok [28]

Answer:

 l=238\ yards

Step-by-step explanation:

From the question we are told that:

Area of Rectangle A=6183

Equation of Length

 l=9w-14

Where

w=width\ of\ triangle

Generally the equation for Area of Rectangle is mathematically given by

 A=(9w-14)w

 A=9w^2-14w

 6183=9w^2-14w

 9w^2-14w-6183=0

 w=28

Therefore

 l=9(28)-14

 l=238\ yards

4 0
3 years ago
on monday, roger drove to work in 20 minutes. on tuesday, he averaged 15 miles per hour more, and it took him 6 minutes less to
ch4aika [34]
Let the distance to his office be x, then
On monday, speed = x/20 miles per minutes = 3x miles per hour
On tuesday, speed = (3x + 15) miles per hour
Time = distance / speed
(20 - 6)/60 hours = x/(3x + 15) hours
7/30 = x/(3x + 15)
7(3x + 15) = 30x
21x + 105 = 30x
30x - 21x = 105
9x = 105
x = 105/9 = 11.7 miles

Therfore he travels an average of 11.7 miles to work.
7 0
3 years ago
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