If a ⊂ b, b may have more elements than a. True false

Answers

Answer 1

Answer:

That's true. If A is a subset of B, it means that every element in A is also an element in B. This means that B has, at least, as many elements as A. Nothing prevents B from having more elements though, which don't belong to A.

Consider this example:

$A = \{1,2,3,4\},\quad B=\{1,2,3,4,5,6\}$

A is a subset of B, because every element of A (1,2,3,4) is also an element of B (1,2,3,4 are in B as well).

Still, B has two more elements (5,6) which don't belong to A, so a superset can have (and typically does actually) more elements than its subset.

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PLEASEEE HELP. Solve x^3-7x^2+6x-42=0

Answers

factor by grouping

x^2(x-7) + 6(x-7) = 0 [took x^2 out of the first two and a 6 out of the last two]
(x-7)(x^2+6) = 0 [moved (x-7) out to the front]
x = -i sqrt(6) , i sqrt(6) , 7

only one real solution of x = 7

$x^(3) -7 x^(2) +6x-42=0$

$(x-7)$ is a factor since it is a factor of -42 and 7 is a solution for f(x) to equal 0.

$(x-7)(a x^(2) +bx+c)=0$

$(x-7)( x^(2) +bx+6)=0$

$-7 x^(2) +b x^(2) =-7 x^(2)$

$-7+b=-7$

$b=0$

$(x-7)( x^(2) +6)=0$

$x-7=0$

$x^(2) +6=0$

$x=7$ (only solution because you can't square root (-6))

Find the area of a triangle with base of 10 inches and altitude to the base of 16 inches. 80 in² 135 in² 160 in²

Answers

Answer:

Option 1st is correct

area of a triangle is, 80 in²

Step-by-step explanation:

Area of triangle(A) is given by:

$A = (1)/(2) b \cdot h$

where,

b is the base

h is the height or altitude of the triangle respectively.

As per the statement:

Base of a triangle(b) = 10 inches and

Height = altitude(h) = 16 inches

Substitute these in [1] we get:

$A = (1)/(2)(10) \cdot 16$

⇒ $A = 5 \cdot 16 = 80$ in²

Therefore, the area of a triangle is, 80 in²

10 × 16 = 160
160 / 2 = 80

Your answer would be 80in²

Hope that helps!

Write a unit rate that compares the quantities describe 50 hockey players on 5 teams

Answers

Answer:

Step-by-step explanation:

50 divded by 5=10

5 divided by 5=1

10/1=10

Factor the expression 5x^3 - x^2 + 5x - 1

Answers

Hello,

5x^3-x^3+5x-1=x²(5x-1)+(5x-1)=(5x-1)(x²+1)=(5x-1)(x-i)(x+i)

$5 x^(3) - x^(2) + 5x - 1$

Group like terms
$( 5x^(2) - x^(2) ) + (5x - 1)$

Find the common factor of each term and simplify
$x^(2) (5x - 1) + 1 (5x - 1)$
$( x^(2) + 1) (5x - 1)$

Additional :-
Find the roots of each of the terms:
(i) $( x^(2) + 1)$
- using the quadratic equation ( $x = \frac{-b (+ or -) \sqrt{ b^(2) - 4ac } }{2a}$ )
- $\frac{-0 + \sqrt{0^(2 - 4(1)(1)) } }{2}$ OR $\frac{-0 - \sqrt{0^(2 - 4(1)(1)) } }{2}$
- Since the discriminant is negative ( $√(-4)$ ) [a negative number cannot be rooted] then this equation has no real roots (imaginary roots)

(ii) $5x - 1$
- Simply Solve for x
5x - 1 = 0
5x = 1
x = $(1)/(5)$

Thus the only solution this has or the only root this expression has is $(1)/(5)$ OR 0.2

What is the square root of 49 multiplied by the square root of 9

Answers

First we need to find the the answer to both the square root of 49 and 9.

The "square root" is a term referring to a number, multiplied by itself (x • x) would be = to your square root.

So for example: Square root of 16 = 4 because 4*4=16

So lets get out numbers:

$√(9) =3$
$√(49)=7$

Now you multiply 3*7 (or 7*3) and you get 21.

Final answer: 21

Well, first, you need to find the square root of the two numbers. To find it, they are the numbers multiplied by each other to get a product. Example: The square root of 49 = 7. Why? Because 7 times 7 = 49. You see how we multiplied 7 by its own self, and how we DIDN'T multiply 7 by any other number BUT itself? See, that's how you find the square root. So, we know that 3 times 3 = 9, and THAT means the square root of 9 = 3. All we have to do now is solve the problem when it says to multiply both of the numbers, (7 times 3), and WHAT DO YOU GET? 21! (Get it? Like the 21 joke-trend?) :D (Laughing emote). :P
Final Answer: 21. :-)

Solve for x: ax2 - 2ax + (a + 1) = 0

Answers

Answer

x=a 1/2+i / a 1/2

Step-by-step explanation:

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