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Zarrin [17]
3 years ago
5

Shannon has 1 nickel, 2 dimes, and 5 unknown coins totaling $0.81. What kind of coins does Shannon have and how many are there o

f each denomination?
Mathematics
2 answers:
Misha Larkins [42]3 years ago
8 0

Answer:

One penny

One nickel

Five dimes

One quarter total

Step-by-step explanation:

81 - 25(coins we know) = 56 cents left

So we know we need 1 penny

Then 4 coins make up 55 cents, so that's a quarter & 3 dimes

AlekseyPX3 years ago
7 0

Answer:

The 5 unknown are 1 quarter, 3 dimes, and 1 penny.

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Charra [1.4K]

Step-by-step explanation:

The coordinates of point A (2,8) and C (5,2)

The measure of segment AC

\sqrt{ {(x2 - x1)}^{2}  +  {(y2 - y1)}^{2}  }

\sqrt{ {(5 - 2)}^{2}  +  {(2 - 8)}^{2} }

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8 0
3 years ago
In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm
tangare [24]

Answer:

AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD

Consider right triangle CAH.By the Pythagorean theorem,

CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8

The length cannot be negative, so CD=8 cm and

CA=\sqrt{3}CD=8\sqrt{3}\ cm

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

AB=2CA=16\sqrt{3}\ cm

By the Pythagorean theorem,

BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm

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3 years ago
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3 years ago
What is the percent increase between 8,863,052 and 9,149,840?
kvasek [131]

Answer:

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3 years ago
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Step-by-step explanation:

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3 years ago
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