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3 years ago

Tree diagram to find the prime factors of 18

Mathematics

1 answer:

Lorico [155]3 years ago

6 0

18
/\
6 X 3
/\
3 X 2
prime factorization equals= 2X3X3

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At the school election there were three candidates. Isabella got 40 votes, Amelia got 60 votes and Mason got ⅓ of the votes. How

notsponge [240]

Answer: 150 people voted in the election.

Step-by-step explanation:

Let x = Total number of votes.

Mason got $\dfrac{x}{3}$ votes.

Isabella got 40 votes, Amelia got 60 votes.

Then,

Combined votes = $40+60+\dfrac{x}{3}=x$

$100=x-\dfrac{x}{3}\\\\100=\dfrac23x\\\\ x=100\times\dfrac32\\\\ x=50\times3\\\\ x=150$

Hence, 150 people voted in the election.

3 0

2 years ago

the value of c guaranteed to exist by the Mean Value Theorem for V(x) = x² in the interval [0, 3] is...? a) 1 b) 2 c) 3/2 d) 1/2

lilavasa [31]

Answer: c) $\dfrac{3}{2}$ .

Step-by-step explanation:

Mean value theorem : If f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that

$\begin{displaymath}f'(c) = \frac{f(b) - f(a)}{b-a} \cdot\end{displaymath}$

Given function : $f(x) = x^2$

Interval : [0,3]

Then, by the mean value theorem, there is at least one number c in the interval (0,3) such that

$f'(c)=\dfrac{f(3)-f(0)}{3-0}\\\\=\dfrac{3^2-0^2}{3}=\dfrac{9}{3}\\\\=3$

$\Rightarrow\ f'(c)=3\ \ \ ...(i)$

Since $f'(x)=2x$

then, at x=c, $f'(c)=2c\ \ \ ...(ii)$

From (i) and (ii), we have

$2c=3\\\\\Rightarrow\ c=\dfrac{3}{2}$

Hence, the correct option is c) $\dfrac{3}{2}$ .

4 0

3 years ago

The equation y = 35.25x + 40 gives the labor cost y of repairing a car if takes x hours to repair the car.

Lady_Fox [76]

Y = 32.25 x + 40
If it takes 6 hours to repair a car:
y = 32.25 * 6 + 40 = 193.5 + 40 = $233.50
The closest are $251.50 and $211.50.
$251.50 - $233.50 = $18
$233.50 - $211.50 = $22
$18 < $22
Answer:
The closest estimate is A ) $251.50

3 0

2 years ago

Read 2 more answers

*7. A family going on vacation rents a van for $160 plus $75 per day. The total bill was $760. How many days was the van rented?

Lina20 [59]

The answer is 7 days

3 0

2 years ago

If the zeros are 8 and 1/2, what are the factors?

timurjin [86]

Answer:

Step-by-step explanation:

Factors : (x - 8) (x- 1/2) or

(x - 8 ) (2x - 1)

Equation: (x - 8)(2x - 1) = x*2x + x*(-1) -8*2x -8*(-1)

= 2x² -x -16x + 8

=2x² -17x + 8

5 0

3 years ago