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3 years ago

14

Dominic puts his cars in 6 rows with 5 in each row. His sister changes them into 3 rows with the same number in each row. How ma

ny cars did she put in each row?

1 answer:

miv72 [106K]3 years ago

8 0

10 cars in each row

5 cars x 6 rows = 30

30 divided by 3 = 10 cars in each row

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Find the polynomial of minimum degree, with real coefficients, zeros at

drek231 [11]

Answer:

$\huge\boxed{p(x)=4x^3-20x^2+4x+300}$

Step-by-step explanation:

$\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)$

$\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300$

7 0

3 years ago

Question 5^ Need help ... ASAP ... your help is really appreciated ...

goblinko [34]

Answer:

See below

Step-by-step explanation:

I think we had a question similar to this before. Again, let's figure out the vertical and horizontal distances figured out. The distance from C at x=8 to D at x=-5 is 13 units while the distance from C at y=-2 to D at y=9 is 11 units. (8+5=13 and 2+9=11, even though some numbers are negative, we're looking at their value in those calculations)

Next, we have to divide each distance by 4 so we can apply it to the ratio. 13/4= $\frac{13}{4}$ and 11/4= $\frac{11}{4}$ . Next, we need to read the question carefully. It's asking us to place the point in the ratio <em>3</em> to <em>1</em> from <em>C</em> to <em>D</em>. The point has to be closer to endpoint D because of this. Let's take each of our fractions, multiply them by 3, then add them towards the direction of endpoint D to get our answer (sorry if that sounds confusing):

$\frac{13}{4}*3 = \frac{39}{4}\\ 8-\frac{39}{4} = \frac{-7}{4}\\\frac{11}{4}*3 = \frac{33}{4} \\-2+\frac{33}{4} = \frac{25}{4}$

Therefore, our point that partitions CD into a 3:1 ratio is ( $\frac{-7}{4}, \frac{25}{4}$ ).

I'm not sure if there was more to #5 judging by how part B was cut off. From what I can understand of part B, however, I believe that Beatriz started from endpoint D and moved towards C, the wrong direction. She found the coordinates for a 1:3 ratio point.

Also, for #6, since a square is a 2-dimensional object, the answer needs to be written showing that. The answer for #6 is 9 units^2.

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3 years ago

Jodie read 42 randomly chosen books from each library in her city. Each library is the same size.

ahrayia [7]

Answer:

Yes!

Step-by-step explanation:

The definition of Representative is

A representative sample is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicates the larger group according to whatever characteristic or quality is under study

so your book is whats understudy and with that you'll know that yes, yes it is

3 0

3 years ago

Which of the following best defines an angle?

scoray [572]

Answer:

Third option

Step-by-step explanation:

The first definition is not as broad as it should be, therefore, while an angle does meet that criteria, it's not a general definition, hence, it is incorrect. The second one is incorrect as well because a parabola has a vertex, and it is certainly not an angle. This definition is not specific enough, so it will be eliminated. The last one is again, too specific. The third one is the best answer because it is broad enough while still being specific.

8 0

3 years ago

What are the coordinates of point A?

Ratling [72]

Answer:

(d) (7, -5)

Step-by-step explanation:

The x-coordinate is listed first in an ordered pair. It is found on the horizontal scale. The point is on the grid line halfway between 6 and 8, so is presumed to have an x-coordinate of 7.

The y-coordinate is listed second in an ordered pair. It is found on the vertical scale. The point is on the grid line halfway between -4 and -6, so is presumed to have a y-coordinate of -5.

The coordinates of point A are (x, y) = (7, -5).

__

<em>Additional comment</em>

As in the case here, you will often run across graphs that don't have markings on every grid line You are expected to be able to figure out the value of a grid line based on the spacing of the marked lines.

It is a good idea to get familiar with reading coordinates of a point on a graph, as you will be doing it a lot.

4 0

2 years ago