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Kitty [74]
2 years ago
7

Find the surface area and volume of the prism. 13 cm 28 cm 5 cm 12 cm

Mathematics
1 answer:
xxMikexx [17]2 years ago
8 0

Answer:

surface area=900

and

volume of the prism= 840

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A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.
Artist 52 [7]

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}

6 0
3 years ago
(PLEASE HELP!!!)Where does the following graph have clusters of data? Select all that apply.
grigory [225]

Answer:

1-5

Step-by-step explanation:

It has clusters from 1 to 5 because that is where all the dots are that are not seperated.

8 0
3 years ago
Bonnie withdrew $1,200 from her savings account. She spent 1/5 of the money on travel arrangements. She spent 2/3 of the remaini
svetoff [14.1K]
Withdrew 1200
spent 1/5 on travel : 1/5(1200) = 1200/5 = 240
leaving her with : 1200 - 240 = 960
spent 2/3 on hardware : 2/3(960) = 1920/3 = 640
leaving her with : 960 - 640 = 320
320 - lunch = 300.50
320 - 300.50 = lunch
19.50 = lunch <==
5 0
3 years ago
Read 2 more answers
7) Is -2 a zero (or root) of f(x) = 7x3 + x2 - 9x + 5?
Masja [62]

Answer:

Step-by-step explanation:

i do not know

6 0
3 years ago
20. What is the perimeter of a square that has a side length of 4x - 5y? (Show Work)
sammy [17]
Answer= 16x -20y

Perimeter of a square= 4( Side length)
Therefore, 4(4x -5y)
= 16x -20y
I think that is it cuz e can’t solve it any further
8 0
3 years ago
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