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3 years ago

In △ABC, G is the centroid. If CG=12 find CD.

Mathematics

1 answer:

VladimirAG [237]3 years ago

5 0

Answer:

CD = 24

Step-by-step explanation:

If G is the centroid, then CG = GD. (12 = 12)

Since CD is CG and GD combined, we would just add these two numbers to find the total length of CD.

CG + GD = CD

12 + 12 = 24

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The length of a rectangle is 2 times the width. If the perimeter is to be less than 96 meters. What are the possible

tiny-mole [99]

Answer:

W>16

Step-by-step explanation:

The formula for calculating the perimeter of a rectangle:

P = 2L+2W

L is the length of the rectangle

W is the width of the rectangle:

Given

P = 96m

If the length of a rectangle is 2 times the width, then L = 2W

Substitute into the formula:

Since the perimeter is less than 96m

96 < 2(2W)+2W

96 < 4W+2W

96 < 6W

Divide both sides by 6:

96/6 < 6W/6

16 < W

W>16

Hence the possible values of the width are all values greater than 16.

7 0

3 years ago

the equation C = 5 9 (F - 32) is used to convert between Fahrenheit temperatures and Celsius temperatures. The temperature in Au

Anuta_ua [19.1K]

The answer is 91 Fahrenheit.

6 0

4 years ago

Read 2 more answers

An=5-6n fifth term and sum of first three terms

Korolek [52]

Answer:

5th term is -25

and sum of first three terms is -21

Step-by-step explanation:

We are given the sequence:

$\displaystyle \large{a_n = 5 - 6n}$

To find 5th term, substitute n = 5.

$\displaystyle \large{a_5 = 5 - 6(5)} \\ \displaystyle \large{a_5 = 5 - 30} \\ \displaystyle \large{a_5 = - 25}$

Therefore, fifth term is 25.

Next, to find the sum of first three terms, we will introduce sigma.

$\displaystyle \large{a_1 + a_2 + a_3 + ... + a_n = \sum_{k = 1}^{n} a_k}$

Our ak is 5-6k

Since we want to find sum of first three terms:-

$\displaystyle \large{ \sum_{k = 1}^{3}( 5 - 6k)}$

Expand Sigma in.

$\displaystyle \large{ \sum_{k = 1}^{3} 5 + \sum_{k = 1}^{3}- 6k}$

Property of Summation

$\displaystyle \large{ \sum_{k = 1}^{n} m = m \times n \: \: \: \sf{(m \: \: is \: \: constant})} \\ \displaystyle \large{\sum_{k = 1}^{n}(a_k + b_k) = \sum_{k = 1}^{n}a_k + \sum_{k = 1}^{n}b_k} \\ \displaystyle \large{\sum_{k = 1}^{n}ma_k =m\sum_{k = 1}^{n} a_k \: \: \: \sf{(m \: \: is \: \: constant})}$

Therefore:-

$\displaystyle \large{ \sum_{k = 1}^{3} 5 + \sum_{k = 1}^{3}- 6k} \\ \displaystyle \large{ (5 \times 3) - 6\sum_{k = 1}^{3}k} \\ \displaystyle \large{ 15 - 6\sum_{k = 1}^{3}k}$

Summation Formula

$\displaystyle \large{ \sum_{k = 1}^{n}k = \frac{1}{2} n(n + 1) }$

Thus:-

$\displaystyle \large{ 15 - 6\sum_{k = 1}^{3}k} \\ \displaystyle \large{ 15 - 6( \frac{1}{2}(3)(3 + 1) } \\ \displaystyle \large{ 15 - 6( \frac{1}{2}(3)(4)) } \\\displaystyle \large{ 15 - 6(3)(2 )} \\\displaystyle \large{ 15 - 6(6)} \\ \displaystyle \large{ 15 -36 = - 21 }$

7 0

3 years ago

Which expression represents the volume, in cubic units, of the composite figure?

Kipish [7]

The missing figure is attached

The expression represents the volume in cubic units of the composite figure is (Four-third)π(10)³ + π(10)²(28) ⇒ 1st answer

Step-by-step explanation:

The figure consists of

Two hemispheres
A cylinder

The volume of the hemisphere = $\frac{2}{3}\pi r^{3}$ , where r is its radius

The volume of the cylinder = πr²h, where r is its radius and h is its height

∵ The diameter of the hemisphere s and the cylinder is 20 units

∵ The radius = $\frac{1}{2}$ diameter

∴ The radius = $\frac{1}{2}$ × 20 = 10 units

∵ The volume of a hemisphere = $\frac{2}{3}$ πr³

∵ r = 10

- Substitute r by 10 in the rule

∴ The volume of a hemisphere = $\frac{2}{3}$ π(10)³

∵ The volume of the cylinder = πr²h

∵ h = 28 and r = 10

- Substitute h by 28 and r by 10 in the rule

∴ The volume of the cylinder = π(10)²(28)

∵ The volume of the figure = 2(volume of a hemisphere) +

volume of the cylinder

∴ The volume of the figure = 2( $\frac{2}{3}$ )π(10)³ + π(10)²(28)

∵ 2 × $\frac{2}{3}$ = $\frac{4}{3}$

∴ The volume of the figure = $\frac{4}{3}$ π(10)³ + π(10)²(28)

The expression represents the volume in cubic units of the composite figure is (Four-third)π(10)³ + π(10)²(28)

Learn more:

You can learn more about the volume of figures in brainly.com/question/12497249

#LearnwithBrainly

7 0

3 years ago

Read 2 more answers

The median size of a new single family home grew from 2063ft^2 in 1996 to 2523ft^2 in 2007. What is the percent of increase?

Lynna [10]

The answer is 22.30%

(1) Calculate the percentage of the initial value:
2063 ft2 is 100x%. 2523 ft2 is x%
2063 : 100% x = 2523 : x
x = 2523 * 100% : 2063
x = 122.30%

(2) Calculate the percent of increase:
x - 100% = 122.30% - 100% = 22.30%

7 0

3 years ago