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3 years ago

24 + 6a + b +3a + b + 3a

Mathematics

1 answer:

ratelena [41]3 years ago

7 0

Answer:

24+12a+2b

Step-by-step explanation:

24 + 6a + b + 3a + b + 3a

6a + 3a + 3a = 12a

b + b = 2b

Bring the 24 down

24 + 12a + 2b

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How is the graph of y = 8x2 − 1 different from the graph of y = 8x2?

dezoksy [38]

Answer:

The first image = y =8x^2 -1

The second image y =8x^2

Step-by-step explanation:

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3 years ago

Given the triangle below, what is the length of the third side, rounded to the nearest whole number?

Leno4ka [110]

Answer:

Step-by-step explanation:

You need the Law of Cosines for this, namely:

$x^2=21^2+14^2-2(21)(14)cos58$ where x is the missing side.

$x^2=441+196-311.5925$ and

$x^2=325.4075$ so

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3 years ago

In the figure below, points M, P, H, J, and K lie in plane Z.

marishachu [46]

Answers:

(a) LN
(b) PHJ
(c) K
(d) HK

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

Explanation:

Part (a)

Lines LN and PN have the point N in common. This is the intersection point.

-----------------

Part (b)

To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.

I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.

------------------

Part (c)

Points H, J and K are collinear as they are on the same line. Pick either H or K to fill out the answer box. I'll go with point K

------------------

Part (d)

Point P and line HK are coplanar. They exist in the same flat plane, or on the same sheet of flat paper together.

We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.

Note: there are other possible names for line HK such as line JH or line JK. The order doesn't matter when it comes to naming lines.

4 0

2 years ago

Find the length of the curve y = integral from 1 to x of sqrt(t^3-1)

Arlecino [84]

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By the fundamental theorem of calculus,

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Now the arc length over an arbitrary interval $(a,b)$ is

$\displaystyle\int_a^b\sqrt{1+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx=\int_a^b\sqrt{1+x^3-1}\,\mathrm dx=\int_a^bx^{3/2}\,\mathrm dx$

But before we compute the integral, first we need to make sure the integrand exists over it. $x^{3/2}$ is undefined if $x$ , so we assume $a\ge0$ and for convenience that $a$ . Then

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6 0

3 years ago

A teacher gathered data about the number of hours her students spent studying for a test and their resulting test grades. She fo

In-s [12.5K]

Answer:

A. The data set would have a linear association.

C. The data set would have a positive correlation.

E. Every student earns 16 more points for each additional hour they study.

F. Students that study more tend to earn better grades on the test.

Step-by-step explanation:

Since in the question it is mentioned that the teacher obtained data with regard to the number of hours that students spent for their test and on their results. She found that on an average for each 30 minutes studied, the graded would rise by 8 points

Now this kind of relationship represents the linear association, positive correlation and study more earn better

Therefore the above three statements are true

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2 years ago