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3 years ago

What is the midpoint M of that line segment?

Mathematics

1 answer:

Sladkaya [172]3 years ago

7 0

Answer: The midpoint M is located at (6,4)

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Explanation:

First focus on just the x coordinates of points S and T, which are 5 and 7 respectively. Add them up to get 5+7 = 12. Then divide that in half to get 12/2 = 6. This is the x coordinate of the midpoint.

Repeat for the y coordinates of S and T. First add up the values: 7+1 = 8. Then divide by 2 to get 8/2 = 4. This is the y coordinate of the midpoint.

The two results we get are then written as an ordered pair getting us the answer (6,4)

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-7.-8=-56<br> True<br> False

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Answer:

true

Step-by-step explanation:

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3 years ago

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Pyramid A and Pyramid B are similar. Pyramid A has a volume of 648 m and Pyramid B has a

ryzh [129]

Answer:

the ratio of the surface area of Pyramid A to Pyramid B is: $\frac{36}{49}$

Step-by-step explanation:

Given the information:

Pyramid A : 648 $m^{3}$
Pyramid B : 1,029 $m^{3}$
Pyramid A and Pyramid B are similar

As we know that:

If two solids are similar, then the ratio of their volumes is equal to the cube

of the ratio of their corresponding linear measures.

<=> $\frac{Volume of A }{Volume of B}$ = $(\frac{a}{b}) ^{3}$ = $\frac{684}{1029}$ = $\frac{216}{343}$

<=> $\frac{a}{b} =$ $\frac{6}{7}$

Howver, If two solids are similar, then the n ratio of their surface areas is equal to the square of the ratio of their corresponding linear measures

<=> $\frac{surface area of A}{surface area of B} =( \frac{a}{b}) ^{2}$

= $\frac{36}{49}$

So the ratio of the surface area of Pyramid A to Pyramid B is: $\frac{36}{49}$

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3 years ago

Express the complex number in trigonometric form -6 + 6sqrt3i

marusya05 [52]

$\large\begin{array}{l}\\\\ \textsf{This is a complex number in }\mathsf{a+bi}\textsf{ form:}\\\\ \mathsf{z=-6+6\sqrt{3}\,i}\\\\ \textsf{where }\mathsf{a=-6~~and~~b=6\sqrt{3}.} \end{array}$

$\large\begin{array}{l}\\\\ \bullet~~\textsf{1}\mathsf{^{st}}\textsf{ step: Find the absolute value of z (complex modulus of z):}\\\\ \mathsf{|z|=\sqrt{a^2+b^2}}\\\\ \mathsf{|z|=\sqrt{(-6)^2+(6\sqrt{3})^2}}\\\\ \mathsf{|z|=\sqrt{36+36\cdot 3}}\\\\ \mathsf{|z|=\sqrt{36\cdot 108}}\\\\ \mathsf{|z|=\sqrt{144}}\\\\ \mathsf{|z|=12} \end{array}$

$\large\begin{array}{l}\bullet~~\textsf{2}\mathsf{^{nd}}\textsf{ step: Find the argument }\mathsf{\theta}\textsf{ of z:}\\\\ \mathsf{arg(z)=\theta}\\\\ \textsf{is an angle that satisfies the following conditions:}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{a}{|z|}=\dfrac{a}{\sqrt{a^2+b^2}}}\\\\ \mathsf{sin\,\theta=\dfrac{b}{|z|}=\dfrac{b}{\sqrt{a^2+b^2}}} \end{cases}\qquad\quad-\pi$

$\large\begin{array}{l}\textsf{For }\mathsf{z=-6+6\sqrt{3}\,i,}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{-6}{12}=-\,\dfrac{1}{2}}\\\\ \mathsf{sin\,\theta=\dfrac{6\sqrt{3}}{12}=\dfrac{\sqrt{3}}{2}} \end{cases}\\\\\\ \textsf{Since}\\\\ \mathsf{cos\,\theta0,}\\\\ \theta\textsf{ lies in the 2}\mathsf{^{nd}}\textsf{ quadrant.}\\\\\\\textsf{Therefore,}\\\\ \mathsf{\theta=\dfrac{2\pi}{3}~rad~~(120^\circ)} \end{array}$

$\large\begin{array}{l}\bullet~~\textsf{3}\mathsf{^{rd}}\textsf{ step: Express z in the trigonometric form:}\\\\ \begin{array}{rcl} \mathsf{z}&\!\!=\!\!&\mathsf{|z|\cdot (cos\,\theta+i\,sin\,\theta)}\\\\ \mathsf{-6+6\sqrt{3}\,i}&\!\!=\!\!&\mathsf{12\cdot \left(cos\, \dfrac{2\pi}{3}+i\,sin\,\dfrac{2\pi}{3}\right)\qquad\quad\checkmark} \end{array} \end{array}$

If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154167

$\large\textsf{I hope it helps.}$

Tags: <em>complex number trigonometric form trig absolute value modulus argument angle</em>

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3 years ago

An aircraft flying at an average speed of 770 km/h takes 15 hours to complete a journey. Find the time taken for the aircraft to

Hoochie [10]

We can solve it two ways, we´ll do it via physics:
We know that:
d=vt
d=770km/h*15h
d=11550km
Now at 660km/h:
t=d/v
t=11550km/660km/h
t=17,5h
Math way:
770km/h→15h
660km/h→x
So:
(770*15)/660=x
x=17,5h

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Usimov [2.4K]

6m+8
This is because you have to distribute (multiply) the 2 to each number inside the parentheses.
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3 years ago