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larisa [96]
2 years ago
9

Calculate each unknown side length. Round your answer to the nearest tenth.

Mathematics
1 answer:
Drupady [299]2 years ago
3 0
To answer this you need to use the Pythagorean theorem, the first part it 4^2+x^2=7^2 so the answer to the bottom x is 5.7. Your next step is to do the Pythagorean theorem for the whole triangle so your equation would be 10^2 + 5.7^2= x^2 once you solve that you will get 132.49 which you need to take the square root of. Once you will do that you will find the other x = 11.5
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Name an object around your house that consists of three or more shapes. The only answer you can't use is a bike and the object c
Len [333]

My Rectangular Shed has Four Shapes

6 0
3 years ago
What is the following quotient?
seropon [69]

Answer:  Choice B) \frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\

==========================================

Work Shown:

\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\

This shows why choice B is the answer.

---------------

Explanation:

  • In the second step, I multiplied top and bottom by (\sqrt{11}+\sqrt{3})
  • This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
  • In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is \sqrt{a}-\sqrt{b} and you want to rationalize the denominator, then you should multiply top and bottom by \sqrt{a}+\sqrt{b}. The same applies in reverse as well.

This leads to the denominator becoming (\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b

Keep in mind that a \ge 0 and b \ge 0

4 0
2 years ago
Find the number of elements in A 1 ∪ A 2 ∪ A 3 if there are 200 elements in A 1 , 1000 in A 2 , and 5, 000 in A 3 if (a) A 1 ⊆ A
lina2011 [118]

Answer:

a. 4600

b. 6200

c. 6193

Step-by-step explanation:

Let n(A) the number of elements in A.

Remember, the number of elements in A_1 \cup A_2 \cup A_3 satisfies

n(A_1 \cup A_2 \cup A_3)=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)

Then,

a) If A_1\subseteq A_2, n(A_1 \cap A_2)=n(A_1)=200, and if A_2\subseteq A_3, n(A_2\cap A_3)=n(A_2)=1000

Since A_1\subseteq A_2\; and \; A_2\subseteq A_3, \; then \; A_1\cap A_2 \cap A_3= A_1

So

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-200-200-1000-200=4600

b) Since the sets are pairwise disjoint

n(A_1 \cup A_2 \cup A_3)=\\n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\200+1000+5000-0-0-0-0=6200

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-2-2-2-1=6193

8 0
3 years ago
a rectangular park has an area of 2/3 square miles the length of the park is 2 and 2/3 the width of the park what is the Widht o
r-ruslan [8.4K]
1.33333333333 thats the answer
5 0
3 years ago
The lengths of the sides of a triangle or an extended ratio 7 8 and 9 the perimeter of the triangle is 48 cm what are the length
julsineya [31]

Answer:

14cm, 16 cm, 18 cm

Step-by-step explanation:

Note that

= a:b: c = 7:8:9

We have to find the sum of the proportion

Sum of proportion = 7 + 8 + 9

= 24

Length of side a

7/24 × 48 = 14 cm

Length of side b

8 /24 × 48 = 16cm

Length of side a

9/24 × 48 = 18 cm

What are the lengths of the sides?

The lengths of the sides of the triangle in cm are

14cm, 16 cm, 18 cm

4 0
2 years ago
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