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3 years ago

Which triangles are similar? c d a b If someone replies really fast to this I would amazingly appreciate it

Mathematics

1 answer:

nalin [4]3 years ago

7 0

Answer:

b and d

Step-by-step explanation:

b and d from the picture

same angle of 25 between sides with 1:2 side to base ratio

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At the start of the week a bookshop had science and art books in the ratio 2:5. By the end of the week, 20% of each type of book

Anastaziya [24]

Let there be 2x science and 5x art books
science books sold = 2x × 0.2 = 0.4x 
science books unsold = 2x – 0.4x = 1.6x 

art books sold = 5x × 0.2 = x 
art books unsold = 5x – x = 4x 

total books unsold = 1.6x + 4x = 5.6x 
5.6x = 2240 
x = 400 

2x science = 800 
and 5x art books = 2000

5 0

4 years ago

3x+2y=3y-2 line 1 x+y=10 line 2 solve for x/y

GrogVix [38]

Answer:

x/y=1/4

Step-by-step explanation:

3x+2y=3y-2

3x=3y-2y-2

3x=y-2

y=3x+2

x+y=10

x+3x+2=10

4x+2=10

4x=10-2

4x=8

x=8/4

x=2

2+y=10

y=10-2

y=8

x/y=2/8=1/4

3 0

4 years ago

Prove that if a and b are positive integers whose sum is a prime p, their greatest common divisor is 1.

Tasya [4]

Proof by contadiction.

Let assume there exist such positive integers $a$ and $b$ whose sum is a prime number $p$ , that their greatest common divisor is greater than 1.

$a,b\in\mathbb{Z^+}\\d=\text{gcd}(a,b)>1\\\\a=de\\b=df\\e,f\in\mathbb{Z^+}\\\\a+b=p\\de+df=p\\d(e+f)=p\\$

Since $p$ is a prime number and $d>1$ , then $d=p \wedge e+f=1$ , but we assumed earlier that $e,f\in\mathbb{Z^+}$ , and there are no two positive integers that sum up to 1.

q.e.d.

7 0

3 years ago

The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).

lesantik [10]

Answer:

(a).

$S_{n} = \frac{n}{2} (4n + 20) \\ \\S _{n - 1} = \frac{(n - 1)}{2} (4n - 4 + 20) \\ \\ S _{n - 1} = \frac{(n - 1)}{2} (4n + 16) \\ \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2} \\ \\ { \boxed{S _{n - 1} = {2 {n}^{2} + 6n - 8}}} \\$

(b).

from general equation:

$S _{n - 1} = \frac{(n - 1)}{2} (4n + 16)$

first term is 4n

common difference:

$16 = \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d = \frac{16}{n - 2}$

8 0

3 years ago

Emilio owns a bakery. The number of boxes of cookies he has left on a Monday is represented by the function x + y = 42, where y

Katarina [22]

Answer:

y=42-x

x=42-y

Step-by-step explanation:

x=42-y

Subtract y from both sides of the equation

y=42-x

Subtract x from both sides of the equation

3 0

3 years ago