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3 years ago

I need help with Geometry

Mathematics

2 answers:

I am Lyosha [343]3 years ago

8 0

Answer: 180 degrees

Imagine you had a long and flat rectangle. If we spin it around the center, we can rotate it 180 degrees so it lines up with its original image. The before and after is the same. We say it has rotational symmetry, and the angle of rotation is 180 degrees. This is the smallest rotational angle possible for rectangles that aren't squares.

valkas [14]3 years ago

4 0

Answer:

180 degrees since only two opposite sides are congruent in a rect, which would require you to flip it 180 degrees for it to map onto itself

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I will give lots of points please help

aalyn [17]

Answer:

a) 81π in³

b) 27 in³

c) divide the volume of the slice of cake by the volume of the whole cake

d) 10.6%

e) see explanation

Step-by-step explanation:

The cake can be modeled as a <u>cylinder </u>with:

diameter = 9 in
height = 4 in

$\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in$

$\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

$\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}$

$\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}$

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

$\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}$

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

$\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}$

Probability is approximately 10.6% (see above for calculation)

If the four slices of cake are cut and passed out <em>before </em>anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, <u>until the marble is found</u>. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

3 0

2 years ago

What is the slope of the line that passes through the points (2, 3) and (8, 6)

nadezda [96]

Answer:

The slope of the line that passes through the points (2, 3) and (8, 6) is $\frac{1}{2}$ .

Step-by-step explanation:

To find the slope of two points, divide the difference between the y values by the difference between x values, you can remember this by the mnenomic "rise over run". In this case, the difference between y and x values would be 6 - 3 = 3 and 8 - 2 = 6 respectively. This means the slope between the two points (2, 3) and (8, 6) is $\frac{3}{6}$ or $\frac{1}{2}$ .

3 0

3 years ago

In a 30°-60°-90° triangle, what is the length of the longer leg when the length of the hypotenuse is 18 inches?

max2010maxim [7]

Answer:

9sqrt(3) in.

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

1 : sqrt(3) : 2

If the short leg measures 1, then the hypotenuse measures 2.

The length of the hypotenuse is twice the length of the short leg.

The length of the long leg is sqrt(3) times the length of the short leg.

If the hypotenuse measures 18 in., then the short leg measures 9 in.

Then the long leg measures 9sqrt(3) in.

8 0

3 years ago

Can I have some help with this, I need to figure out the answer and the reasoning for it.

dangina [55]

Answer:

Step-by-step explanation:

In statement (1), we are given that m∠BAC=m∠BCA

If the two angles are congruent, this means that the sides opposite the angles are also congruent. These sides are AB and BC. Therefore:

AB=BC | B. sides opposite equal angles are equal

:Done

*The side opposite a given angle is the side towards which the angle opens up to. For example, ∠BAC opens up towards the side BC, and ∠BCA opens up towards side BA.

8 0

3 years ago

What is the common difference between successive terms in the sequence?<br> 2, 8, 14, 20, 26, ...

Bas_tet [7]

Answer:

Step-by-step explanation:

The sequence is going six numbers up each time. For example 2 plus six is 8. 8 plus six is 14. 14 plus six is 20 and so on.

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3 years ago