What's the temperature change?

If 4x is one factor of 4x^2-12x, what is the other factor?

Zepler [3.9K]

If you factor 4x²-12x, you can divide 4x from each term.

4x² ÷ 4x = x
-12x ÷ 4x = -3

Therefore, the other term becomes (x-3) because 4x(x-3) = 4x²-12x

4 0

3 years ago

The probability that Caroline wins a raffle is given by the expression

RSB [31]

Answer: $\frac{n-m}{n}$

This is the same as writing (n-m)/n

Don't forget about the parenthesis if you go with the second option.

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Explanation:

The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.

For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.

The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.

We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".

Doing a bit of algebra would have these steps

$1 - \frac{m}{n}\\\\\frac{n}{n} - \frac{m}{n}\\\\\frac{n-m}{n}\\\\$

and now the expression is one single fraction.

8 0

3 years ago

Solve for all possible values of x. square root of the quantity x plus 6 end quantity plus 5 equals 17

Georgia [21]

Answer:

$x=138$

Step-by-step explanation:

So we have the equation:

$\sqrt{x+6}+5=17$

First, let's determine the domain restrictions. Recall that the radicand cannot be negative. In other words, it must be greater than or positive than 0. Thus:

$x+6\geq 0$

Subtract 6 from both sides:

$x\geq -6$

What this means is that our solutions must be greater than or equal to -6. If not, we ignore them.

So, let's subtract 5 from both sides from the original equation:

$\sqrt{x+6}=12$

Square both sides:

$x+6=144$

Subtract 6 from both sides:

$x=138$

138 is greater than -6, so 138 is a solution and is the only solution.

And we're done!

8 0

3 years ago

A buoy oscillates in simple harmonic motion y= A cos cos as waves move past it. The buoy moves a total of 3.5 feet (vertically)

NNADVOKAT [17]

Answer:

a) $y = 1.75 ft cos (\frac{\pi}{5}t)$

b) $v(t) = -1.0995 sin (\frac{\pi}{5}t)$

Step-by-step explanation:

Part a

Since the buoy oscillates in simple harmonic motion the equation to model this is given by:

$y = A cos (wt +\theta)$

For this case from the info given we know that:

$2A = 3.5 , A = \frac{3.5}{2}= 1.75 ft$

"It returns to its high point every 10 seconds." That means period =10 $T =10s$ , and the angular frequency can be founded like this:

$w = \frac{2\pi}{10}= \frac{\pi}{5}$

Assuming that the value for the phase is $\theta =0$ our model equation is given by:

$y = 1.75 ft cos (\frac{\pi}{5}t)$

Part b

From definition we can obtain the velocity with the derivate of the position function and if w calculate the derivate we got this:

$\frac{dy}{dt}= v(t) = -1.75 ft (\frac{\pi}{5}) sin (\frac{\pi}{5}t)$

$v(t) = -1.0995 sin (\frac{\pi}{5}t)$

6 0

3 years ago

Rhombus CDEF with vertices<br> C(-5, 5), D(-1,7), E(-3, 3), and<br> F(-7, 1): 270° counterclockwise

Bogdan [553]

The required coordinates of the pre image are C'(-5, -5), D' (7, 1), E' (3, 3) and F' (1, 7)

<h3>Rotation of coordinates</h3>

Rotation is a way of changing the position of an object on an xy plane.

When a coordinate point (x, y )is rotated 270 degrees counterclockwise, the resulting coordinate point will be (y,-x)

The x-coordinate is negated and then swapped.

Given the coordinates of a Rhombus CDEF with vertices <u>C(-5, 5), D(-1,7), E(-3, 3), and F(-7, 1)</u>, the resulting coordinate points will be;

C(-5, 5) = C'(-5, -5)

D(-1,7) = D' (7, 1)

E(-3, 3) = E' (3, 3) and

F(-7, 1) = F' (1, 7)

Hence the required coordinates of the pre image are C'(-5, -5), D' (7, 1), E' (3, 3) and F' (1, 7)

Learn more on rotation here: brainly.com/question/26249005

#SPJ1

7 0

2 years ago