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4 years ago

Point P has coordinates (2 , 3) point Q is symmetric to point P with respect to the line x=4 what are the coordinates of point Q

Mathematics

1 answer:

Ierofanga [76]4 years ago

8 0

Answer:

Q is (6, 3).

Step-by-step explanation:

The line x = 4 is a vertical line on the coordinate grid which passes through the x-axis at the point where x = 4.

So the x coordinate of Q will be the same distance after x = 4 as P is before it. That is where x = 4+2 = 6. The y coordinate will be the same as that of P.

(Imagine that the line x = 4 is a mirror, then Q is the image of P).

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evablogger [386]

Answer:

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3 years ago

To celebrate her birthday, Whitney wants to take her friends adventuring in a 4WD vehicle from All Terrain Tours.

IgorC [24]

Answer:

Whitney can bring 6 friends.

Step-by-step explanation:

The reason why is this:

Whitney is bringing 400 pounds of things plus her own body weight!

400 + 165 = 565 pounds

Now we add on Whitneys freinds which is 165 (their body weight) + the 10 pounds of gear which equals 175 pounds. So each friend would be 175 pounds total weight.

175 x 6 = 1,050 pounds

If we add on Whitneys total weight thats:

565 + 1,050 = 1,615

Adding on another friend would be 1,790 pounds which would be over the weight limit for the vehicle.

Hence, Whitney can bring along 6 friends for her birthday.

Hope this helped! :)

4 0

3 years ago

Slope = -2/3, passes through (6, -2)

sladkih [1.3K]

Y-(-2)= -2/3(x-6)
3y+6= -2x +12
2x +3y +6=0

3 0

3 years ago

One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the

Kipish [7]

Let's call the two numbers $s$ and $l$ .

Given these variables, we can say: $s = l - 14$ , based on the first sentence in the problem.

Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

$\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}$

To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

Set up

$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

$\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}$

Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

$24l - 280 = l^2 - 14l$

Simplify

$l^2 - 38l + 280 = 0$

Subtract $24l - 280$ from both sides of the equation

$(l - 10)(l - 28) = 0$

Factor left side of the equation

$l = 10, 28$

Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This likely means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

$s = 10 - 14 = -4$ ,