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3 years ago

Find the missing segment.

Mathematics

1 answer:

Bond [772]3 years ago

3 0

Answer:

? = 7.

Step-by-step explanation:

The two triangles are similar because of the AA Theorem.

The larger triangle's side that is equal to 9 + 3 corresponds to the smaller triangle's side length of 9, while the larger triangle's 21 + ? side corresponds to the smaller triangle's 21 side. Now, we can set up a proportion!

$\frac{9}{9+3} =\frac{21}{21 + ?}$

$\frac{9}{12} =\frac{21}{? + 21}$

$\frac{3}{4} =\frac{21}{? + 21}$

$\frac{1}{4} =\frac{7}{? + 21}$

? + 21 = 7 * 4

? + 21 = 28

? = 28 - 21

? = 7

Hope this helps!

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WILL MARK BRAINLIEST!!! 40 POINTS!! ACTUAL ANSWERS, PLZZZ

steposvetlana [31]

Answer:

Part A:

$\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807$

Part B:

The closure property describes cases when mathematical operations are CLOSED. It means that if you apply certain mathematical operations in a polynomial it will still be a polynomial. Polynomials are closed for sum, subtraction, and multiplication.

It means:

$\text{Sum of polynomials } \Rightarrow \text{ It will always be a polynomial}$

$\text{Subtraction of polynomials } \Rightarrow \text{ It will always be a polynomial}$

$\text{Multiplication of polynomials } \Rightarrow \text{ It will always be a polynomial}$

But when it is about division:

$\text{Division of polynomials } \Rightarrow \text{ It will not always/sometimes be a polynomial}$

Example of subtraction of polynomials:

$(2x^2+2x+3) - (x^2+5x+2)$

$x^2-3x+1$

Step-by-step explanation:

First, it is very important to define what is a polynomial in standard form:

It is when the terms are ordered from the highest degree to the lowest degree.

Therefore I can give:

$x^5-5x^4+3x^3-3x^2+7x+20$

but,

$x^5+3x^3-3x^2+7x+20-5x^4$ is not in standard form.

For this question, I can simply give the answer: $x^5-5x^4+3x^3-3x^2+7x+20$ and it is correct.

But I will create a fifth-degree polynomial using this formula

$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$

Also, note that

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

For $a=x \text{ and } b=7$

$\left(x + 7\right)^{5}=\sum_{k=0}^{5} \binom{5}{k} \left(x\right)^{5-k} \left(7\right)^k$

$\text{Solving for } k \text{ values: } 0, 1, 2, 3, 4 \text{ and } 5$

Sorry but I will not type every step for each value of $k$

The first one is enough.

For $k=0$

$\binom{5}{0} \left(x\right)^{5-0} \left(7\right)^{0}=\frac{5!}{(5-0)! 0!}\left(x\right)^{5} \left(7\right)^{0}=\frac{5!}{5!} \cdot x^5= x^{5}$

Doing that for $k$ values:

$\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807$

8 0

3 years ago

I need help with these two problems

____ [38]

Answer:

#4. in a decimal its 0.5

before simplfied its 6\12

after simplfied its 1\2

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8 0

3 years ago

One bag of marbles contains 2 black , 3 red , and 5 white marbles . A second bag contains 3 white and 2 black marbles . What is

BaLLatris [955]

Answer:

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Step-by-step explanation:

Bag 1 : 8 non-black out of 10

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Bag 2: 3 non-black out of 10

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Probability of both independent events happening can be calculated using the multiplication rule

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Interpretating not both black meaning at most one black, then

we calculate the probability of both are black,

P(1) = 2/10

P(2) = 2/5

Probability that both balls are black can be calculated using the multiplication rule

P(1) and P(2) = 2/10 * 2/5 = 2/25

Probability that NOT BOTH BLACK = 1-2/25 = 23/25, i.e. at most one black

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Answer:

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Answer:

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