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2 years ago

Can the product of a whole number and a decimal number less than 1 ever be greater than a whole number

1 answer:

7 0

No. The product of a whole number and a decimal number less than 1 will be greater than the whole number multiplied into. For this theorem to be proven. Let us state the mathematical expression into numbers such that 
1. N x 0.1 = N/0.1 < N 
2. 1 x 0.5 = 0.5 
3. 2 x 0.1 = 0.2 
4. 100 x 0.55 = 55

These three examples and stances then suggest the claim that the product is not equal to the whole number used in the equation.

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Can I please have help with question 2) a and b

Ulleksa [173]

Answer:

$\frac{10\sqrt{6} }{3}$ and $\frac{11\sqrt{3} }{3}$

Step-by-step explanation:

(a)

A = $\frac{1}{2}$ × 4 $\sqrt{2}$ × $\frac{5}{\sqrt{3} }$

= 2 $\sqrt{2}$ × $\frac{5}{\sqrt{3} }$

= $\frac{10\sqrt{2} }{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ ← rationalise the denominator

= $\frac{10\sqrt{6} }{3}$ units²

(b)

Using Pythagoras' identity in the right triangle

let hypotenuse be h , then

h² = (4 $\sqrt{2}$ )² + ( $\frac{5}{\sqrt{3} }$ )²

= 32 + $\frac{25}{3}$

= $\frac{96}{3}$ + $\frac{25}{3}$

= $\frac{121}{3}$ ( take the square root of both sides )

h = $\sqrt{\frac{121}{3} }$ = $\frac{11}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ ← rationalise the denominator

h = $\frac{11\sqrt{3} }{3}$

7 0

3 years ago

The table shows the outputs y for different inputs x:

Rasek [7]

Part A: Yes, the data represent a function. The definition of a function is a relation in which no value of x will have two different values of y.
(Every time you plug in 3 as x, you will always get 4 as y; it's ok if you plug in 3 and 5 as x and get the same y, you just can't get two different y's for one x; sorry, it is pretty confusing). None of the numbers in the table repeat, so we can safely say that the relation is a function.

Part B: All we have to do is plug in 11 for x in the function given to find the answer:
$f(x)=5x-21\\f(x)=5(11)-21\\f(x)=55-21\\f(x)=34$
In the table, y = 8 when x = 11, but in the function given, y = 34 when x = 11, so the function given is greater.

Part C: To find the answer to C, just plug in 99 for f(x), as it tells you to do:
$f(x) = 5x-21\\99=5x-21\\99+21=5x-21+21\\120=5x\\120/5=5x/5\\24=x$

5 0

3 years ago

Read 2 more answers

A vehicle uses 1 gallons of gasoline to travel 13 miles. At this rate, how many mile

Brrunno [24]

1 gallon (it’s stayed in the question)

6 0

3 years ago

This is due Monday but I want to get it done today, because the teacher is still going to check it, and I have practicly nothing

Crank

You don’t have anything attached:(

7 0

3 years ago

The average of 4, 9, 16, 25 and x is 2x. What is the value of x? A) 4 B)6 A)9 C)9 D)12

Elodia [21]

The average of 4, 9, 16, 25 and x is 2x means that;
(4+9+16+25+x)/5=2x
Multiply both side by 5
5(54+x)/5=2x(5)
54+x=10x
Subtract x to both side
54+x-x=10x-x
54=9x
Divided 9 to both side
54/9=9x/9
x=6
Check:
Substitute x with 6
(4+9+16+25+x)/5=2x
(4+9+16+25+6)/5=2(6)
60/5=12
12=12; so x=6 which marks B as the correct answer. Have a nice day!

5 0

2 years ago