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3 years ago

Are these shapes similar or congruent?

Mathematics

1 answer:

aliya0001 [1]3 years ago

4 0

Answer:

Congruent

Step-by-step explanation:

Hope this helps you!!

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Solve the radical equation. Check all proposed solutions.<br> X-V5x - 14 = 4

ladessa [460]

Answer:

5x=18

Step-by-step explanation:

3 0

2 years ago

The math question is on the image<br>find the nth term of the sequence

Rus_ich [418]

Notice how Pattern 2 is Pattern 1 with 4 balls added in the bottom row.

Pattern 3 is Pattern 2 with 5 more balls.

Pattern 4 is Pattern 3 with 6 more balls.

Generalizing the trend, we expect Pattern $n$ to be identical to Pattern $n-1$ with $n+2$ more balls.

If $b_n$ is the number of balls in the $n$ -th pattern, then we have the recursive relation

$\begin{cases} b_1 = 6 \\ b_n = b_{n-1} + n + 2 & \text{for } n>1 \end{cases}$

We can solve this recurrence by substitution. Using the definition of $b_n$ , we have

$b_{n-1} = b_{n-2} + (n-1) + 2 \\\\ \implies b_n = (b_{n-2} + (n-1) + 2) + n + 2 \\\\ \implies b_n = b_{n-2} + 2\times2 + \bigg(n + (n-1)\bigg)$

$b_{n-2} = b_{n-3} + (n-2) + 2 \\\\ \implies b_n = (b_{n-3} + (n-2) + 2) + 2\times 2 + \bigg(n + (n-1)\bigg) \\\\ \implies b_n = b_{n-3} + 3\times2 + \bigg(n + (n-1) + (n-2)\bigg)$

and so on, down to

$b_n = b_1 + (n-1)\times2 + \bigg(n + (n-1) + (n-2) + \cdots + 2\bigg)$

Recall that

$\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2$

Then we find

$\displaystyle b_n = 6 + 2(n-1) + \sum_{i=2}^n i$

$\displaystyle b_n = 2n + 4 + \left(\sum_{i=1}^n i - 1\right)$

$\displaystyle b_n = 2n + 3 + \frac{n(n+1)}2$

$\displaystyle \boxed{b_n = \frac{n^2+5n+6}2}$

8 0

2 years ago

How do I find the percent of 38% of 50

ioda

First calculate your percent as: 1-0.38=0.62. Then, multiply 0.62 by 50= 31. Your answer is 31

6 0

3 years ago

Read 2 more answers

What is 45/60 in simplest form

qwelly [4]

We are asked in the problem to determine the simplest form of the number 45/60. The greatest common factor of the two numbers is 15. Hence, we divide each number by 15, that is 45 over 15 is equal to 3 and 60 over 15 is equal to 4. Hence the answer is 3/4.

8 0

3 years ago

Cone, diameter of base 18 ft slant height 14 ft

marissa [1.9K]

Answer:

207π ft²

Step-by-step explanation:

Given in the question,

diameter of the base = 18 ft

slant height= 14 ft

radius of the base = 18/2

= 9 ft

Formula to calculate the surface area

<em>here l = slant height</em>

<em> r = radius of the base</em>

<em />

plug values in the formula

A = π(9)(14)+π9²

A = 207π ft²

7 0

3 years ago