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3 years ago

Find EH , given that line HF is the perpendicular bisector of EG

Mathematics

1 answer:

Fed [463]3 years ago

8 0

Answer:

EH = 5

Step-by-step explanation:

HF is the perpendicular bisector of EG , then

EH = HG = 5

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A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

Recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

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

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

At,

n = 1

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

which is true.

At,

n = 2

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

At,

n = 3

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

At,

n = 4

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

Therefore, the recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

3 0

3 years ago

HELP! Look at the stem-and-leaf plot. What is the mode of the numbers?

puteri [66]

The answer is 100
since the number 100 is the number that appears to be the most frequent

7 0

3 years ago

Find the degree measure of each angle in the triangle

Karo-lina-s [1.5K]

Answer:

∠L = 43°

∠M = 121°

∠N = 16°

Step-by-step explanation:

Start by setting all sides equal to 180

3x - 5 + 7x + 9 + x = 180

Add like terms

11x + 4 = 180

Solve for x

11x + 4 = 180

- 4 - 4

11x = 176

/ 11 /11

x = 16

Now, plug in 16 for all instances of x on the triangle and solve.

∠L = 43°

∠M = 121°

∠N = 16°

4 0

3 years ago

Find x if x + y = 16, x * 3 is even, x is a factor of y, and 2x+y= 20.

ozzi

Answer:

x = 0

Step-by-step explanation:

7 0

3 years ago

What type of arc lies between the two sides of a central angle and measures less than 180?

Tanzania [10]

Answer:

minor arc

Step-by-step explanation:

apex

8 0

4 years ago