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2 years ago

Factor completely. 4x^3 + 12x^2 + 3x + 9

Mathematics

1 answer:

Sergio039 [100]2 years ago

5 0

Answer:

(4x^2 + 3)(x + 3)

Step-by-step explanation:

Split the equation in the middle so you can factor it out:

4x^3 + 12x^2 | + 3x + 9

Then factor out:

4x^2(x + 3) | 3(x + 3)

Congrats, you completed your equation:

(4x^2 + 3)(x + 3)

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Which is the pair of congruent right angles?

Alex73 [517]

The little squares at corner-B and corner-E were drawn there
to show that those are right angles.

8 0

2 years ago

Read 2 more answers

Jake drove 300 miles from his house to a soccer tournament. This graph shows the distance Jake had traveled (m) and the time tha

Bad White [126]

Part A. The trip starts at 8am which corresponds to 0 hrs, point (0hr, 0mi)

2hrs later it's 10am. .point (2hr, 140mi)

The average speed is the slope between 0 and 2 hrs. Remember the slope formula m = Δy/Δx

m = (140 - 0) / (2 - 0)

m = 70 mph

Part B. Average speed from 11am - 2pm

11am is point (3hr, 140mi)

2pm is point (6hr, 300mi)

As you can see from the graph, the speed or slope changes at 1pm (5,260). You Can just use the start and end points.

m = (300-140) / (6-3)

m = 160/3

53.3 mph

* It comes out the same solution as if you average the two different slopes. 2hrs at 60mph + 1 hr at 40mph = (120 + 40)/3 = 160/3

Part C. Total average speed = total distance / total time driving

He went 70 mph for 2 hrs

stopped for an hour (slope is zero, no speed)

60 mph for 2hrs

40mph for 1 hr

300mi /5hr = 60mph

Part D. No Question....

7 0

2 years ago

For an outdoor concert by the city orchestra, concert organizers estimate that 19 comma 000 people will attend if it is not rai

My name is Ann [436]

<h2>Answer:</h2><h2>The expected number of people who will attend this concert = 2260</h2>

Step-by-step explanation:

The concert organizers estimate people will attend if it is not raining = 19000

If its raining people will attend = 4000

On the day of the concert, meteorologists predict a 90% chance of rain.

This means 10 % chance of not raining

The expected number of people = 90% (4000) + 10% (19000)

= 360 + 1900

= 2260

The expected number of people who will attend this concert = 2260

4 0

2 years ago

Find the value of x in each figure

sergey [27]

I believe x is 43.

3x+17+x-9=180 It is 180 because a straight line is 180 degrees
4x+8=180
-8 -8 subtraction property of equality
---------------
4/4x=172/4 division property of equality
x=43 solution

4 0

2 years ago

NO LINKS!!!

aleksandr82 [10.1K]

Answer:

The 6 names to circle are:

Laverna
Alfonso
Autumn
Ignacio
Kathyrn
Lawrence

The underlined letters from those circled names are:

The letters form the phrase $\underline{\text{WR}}\ \underline{\text{ON}} \ \underline{\text{G}} \ \ \ \ \ \ \underline{\text{TU}} \ \underline{\text{RN}}$ or "wrong turn". The spacing is done like that in the first version to show the various subgroups of letters.

Unfortunately the mentioned riddle at the bottom is cut off, so I don't know what the riddle is.

======================================================

Explanation:

Laverna is correct because a translation is applied. "Translation" in geometry settings means "shifting up/down/left/right". In this case, triangle JKL is shifted 5 units right and 3 units up.
Alfonso is correct. If a figure is labeled ABCD going in clockwise orientation, then a translation will preserve said orientation. The orientation only flips when a reflection occurs.
Autumn is correct. Why? Because reflections are isometries, meaning they preserve distances and lengths and angles. In other words, the two triangles are twin clones of each other.
Willa is not correct. The prime notations go on the image and NOT the preimage. In other words, the prime notations go for the "after" and not the "before". Example: triangle JKL in Laverna's diagram is the preimage, while J'K'L' is the image. JKL is "before", and J'K'L' is "after".
Ignacio is correct. The figure enlarges or shrinks (depending on the scale factor if its larger than 1, or smaller than 1). The orientation stays the same. Refer to Alfonso's scenario where I mentioned the orientation flipping only when a reflection happens.
Napoleon is incorrect. A reflection ALWAYS changes the orientation. Consider a triangle ABC where the motions from A to B to C goes clockwise. A reflection will flip the orientation to make A to B to C go counterclockwise. Example: Reflections over non-horizontal lines swap the positions of left vs right, which is another way to see why the orientation swaps as well.
Kathyrn is correct assuming no reflection operations are done.
Titus is not correct. A rotation is not the same as a reflection. Though I should point out that two reflections simplify to a rotation. The mirror lines must intersect in some way. Parallel mirror lines will have two reflections lead to a translation.
Lawrence is correct. The order P,Q,R is clockwise, and so is the order P', Q', R'. A rotation preserves orientation. In this case, a 180 degree rotation has been done. The rule for that is any (x,y) point turns into (-x,-y).

Here's a summary table:

$\begin{array}{|c|c|} \cline{1-2}\text{Student} & \text{Are They Correct?}\\\cline{1-2}\text{Laverna} & \textbf{Yes}\\\cline{1-2}\text{Alfonso} & \textbf{Yes}\\\cline{1-2}\text{Autumn} & \textbf{Yes}\\\cline{1-2}\text{Willa} & \text{No}\\\cline{1-2}\text{Ignacio} & \textbf{Yes}\\\cline{1-2}\text{Napoleon} & \text{No}\\\cline{1-2}\text{Kathyrn} & \textbf{Yes}\\\cline{1-2}\text{Titus} & \text{No}\\\cline{1-2}\text{Lawrence} & \textbf{Yes}\\\cline{1-2}\end{array}$

Put another way, here are the people to circle (i.e. the people who made true statements):

Laverna
Alfonso
Autumn
Ignacio
Kathyrn
Lawrence

In the order presented above, the letters underlined are:

Through a bit of trial and error, the letters make the phrase of:

$\underline{\text{WR}}\ \underline{\text{ON}} \ \underline{\text{G}} \ \ \ \ \ \ \underline{\text{TU}} \ \underline{\text{RN}}$

I'm not sure what to do with the extra "RN". It might be a typo, or it might be the case your teacher wants you to ignore repeats like this.

3 0

1 year ago