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Alekssandra [29.7K]
4 years ago
5

Given the sets M = {3, 4, 5, 6, 7} and N = {4, 6, 8, 10, 12}, the set M∩N is identified by which notation below?

Mathematics
1 answer:
jasenka [17]4 years ago
4 0
The upside down u (intersection) just wants us to find what the two sets have in common....
which is 4 and 6
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In a right triangle the lengths of the legs are 8 and 8 square root 3. Find the length of the hypotenuse.
kogti [31]

Answer:

16

Step-by-step explanation:

Using pythagorean theorem, a^2+b^2=c^2, you can substitute the legs in. 8^2+8sqrt3^2=c^2. C is the hypotenuse. you get 64+64sqrt9=c^2. This simplifies to 64+64(3)=c^2. This equals 256=c^2. Sqrt of 256 is 16, which is C.

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Write each number as a logarithm with base 3.
Ksenya-84 [330]
Log3(x)=0 so 3^0=x which is 1
log3(x)=-2 so 3^-2=x which is 1/9
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8 0
3 years ago
A napkin is 37 centimeters long.How many millimeters is this?
Oxana [17]

Answer:

370 millimeters

Step-by-step explanation:

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3 0
3 years ago
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Solve this rational equation ​
tino4ka555 [31]

Answer:

<h2>x = -1</h2>

Step-by-step explanation:

\text{Domain:}\\\\x-4\neq0\ \wedge\ x-2\neq0\ \wedge\ x^2-6x+8\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x^2-4x-2x+8\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x(x-4)-2(x-4)\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ (x-4)(x-2)\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x-4\neq0\ \wedge\ x-2\neq0\\\\\boxed{D:x\neq4\ \wedge\ x\neq2}

\dfrac{1}{x-4}+\dfrac{x}{x-2}=\dfrac{2}{x^2-6x+8}\\\\\dfrac{1(x-2)}{(x-4)(x-2)}+\dfrac{x(x-4)}{(x-4)(x-2)}=\dfrac{2}{(x-4)(x-2)}\\\\\dfrac{x-2+x(x-4)}{(x-4)(x-2)}=\dfrac{2}{(x-4)(x-2)}\iff x-2+x(x-4)=2\\\\x-2+(x)(x)+(x)(-4)=2\\\\x-2+x^2-4x=2\qquad\text{subtract 2 from both sides}\\\\x^2-3x-4=0\\\\x^2-4x+x-4=0\\\\x(x-4)+1(x-4)=0\\\\(x-4)(x+1)=0\iff x-4=0\ \wedge\ x+1=0\\\\x-4=0\qquad\text{add 4 to both sides}\\x=4\notin D\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1\in D

8 0
3 years ago
if a rectangle have length of 10 inches and width of 8 inches what is the new area if each corner is cut by x^2
Natali5045456 [20]

Answer:

80 - 4x^2

Step-by-step explanation:

<u>Area of a rectangle</u>

A rectangle of width W and length L has an area of:

A = W.L

The given rectangle has a length of L=10 inches and a width of W=8 inches, thus its area is:

A = 8*10 = 80

A = 80\ in^2

If each corner is cut by a square of x*x, then the total area will be:

A' = 80 - 4x^2

The new area is \mathbf{80 - 4x^2} square inches

5 0
3 years ago
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