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sveticcg [70]
2 years ago
15

Are the triangles similar?

Mathematics
1 answer:
Liono4ka [1.6K]2 years ago
5 0
Yes the triangles are similar
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Use the principle of inclusion and exclusion to find the number of positive integers less than 1,000,000 that are not divisable
wel
This is a simple problem based on combinatorics which can be easily tackled by using inclusion-exclusion principle.
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.

∴N(c₁) = \frac{999,999}{6} = 166666
N(c₂) = \frac{999,999}{4} = 250000
∴N(c₁c₂) = \frac{999,999}{24} = 41667
∴ Number of positive integers that are not divisible by 4 or 6,

N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4
8 0
3 years ago
Solve the following equation for X. Round your answer to four decimal places.
strojnjashka [21]

ANSWER

x = 1.2226

EXPLANATION

To solve this equation we have to apply the property of the logarithm of the base,

\log _bb=1

Thus, we can apply the natural logarithm - whose base is e, to both sides of the equation,

\ln e^{4x}=\ln 133

Now we apply the property of the logarithm of a power,

\log a^b=b\log a

In our equation,

\begin{gathered} 4x\ln e^{}=\ln 133 \\ 4x^{}=\ln 133 \end{gathered}

Then divide both sides by 4 and solve,

\begin{gathered} \frac{4x^{}}{4}=\frac{\ln 133}{4} \\ x\approx1.2226 \end{gathered}

The solution to this equation is x = 1.2226, rounded to four decimal places.

4 0
1 year ago
Which expression would be easier to simplify if you used the associative
Fynjy0 [20]

Answer:

I believe its A.

Step-by-step explanation:

3 0
3 years ago
The perimeter of a rectangle is 28 cm and<br>its length is 8 cm. Find its breadth.​
Yakvenalex [24]
Answer:
The width of the rectangle is 6cm.

Explanation:
Perimeter=2(length+width)
28=2(8+w)
Distribute 2 into the parentheses
28=16+2w
Combine like terms
28-16=2w
12=2w
Divide both sides by 2
6=w

I hope this helps! Please comment if you have any questions.
7 0
3 years ago
What is the x-coordinate of the vertex of the parabola whose equation is y = 3x^2 + 12x + 5?
Genrish500 [490]

Answer:

(-2,-7)

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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