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3 years ago

Which statement is true?

Mathematics

2 answers:

REY [17]3 years ago

7 0

Choice (B) is true.

For (A): 5 is not a divisor of 14, whose only divisors are 1, 2, 7, and 14.

For (B): the factors of 10 are: 1, 2, 5, and 10. The factors of 15 are: 1, 3, 5, and 15. As we can see, the only, and greatest, common factor is 5.

For (C): 3 is not a factor of 13, which is a prime number.

For (D): again, 3 is not a factor of 14.

wariber [46]3 years ago

5 0

The correct answer is b

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3 years ago

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3 years ago

If a ship's path is mapped on a coordinate grid, it follows a straight-line path of slope 3 and passes through point (2, 5).

Ugo [173]

Part A: The equation of the ship's path is $y=3x-1$

Part B: The two ships sails perpendicular to each other.

Explanation:

Part A: It is given that $m=3$ and point (2, 5)

Substituting these in the slope intercept form, we have,

$y-y_{1}=m\left(x-x_{1}\right)$

$\begin{aligned}y-5 &=3(x-2) \\y-5 &=3 x-6 \\y &=3 x-1\end{aligned}$

Thus, the equation of the ship's path in slope intercept form is $y=3x-1$

Part B: The equation of the second ship is $x+3 y-6=0$

Let us bring the equation in the form of slope intercept form.

$\begin{aligned}3 y &=-x+6 \\y &=-\frac{1}{3} x+2\end{aligned}$

Thus, from the above equation the slope is $m=-\frac{1}{3}$

To determine the two ships sailing perpendicular to each other, we have

$m_{1} \times m_{2}=-1$

where $m_{1}=3$ and $m_{2}=-\frac{1}{3}$

$\begin{aligned}3 \times-\frac{1}{3} &=-1 \\-1 &=-1\end{aligned}$

Since, both sides of the equation are equal, these two ships sails perpendicular to each other.

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3 years ago