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vladimir2022 [97]
3 years ago
11

one of the corners of a cube is sliced off. the resulting cross section will have a minimum of how many sides

Mathematics
2 answers:
AURORKA [14]3 years ago
6 0
Three sides, because if you make a clean cut the surface of the cut is a triangle.
SVEN [57.7K]3 years ago
4 0

Answer:

Total number of sides of resulting cross section = 7

Step-by-step explanation:

Number of sides present for cube = 6

One corner of a cube is formed with 3 edges, if we cut that taking all the care the resulting face will be a triangle.

So we will have one more face other than 6 sides of cube.

Total number of sides of resulting cross section = 6+1 = 7

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Louis made 24 quarts of lemonade he divided the lemonade equally between 6 pitchers how many points of lemonade did Louis put in
Mandarinka [93]

Answer: Each pitcher has 4 quarts of lemonade.

Step-by-step explanation:

Louis made 24 quarts of lemonade, and he divided it equally into 6 pitchers.

Then, each pitcher must has a sixt of the total amount of lemonade, this is:

p = (1/6)*24 quarts= (24/6) quarts = 4 quarts

Each pitcher has 4 quarts of lemonade.

7 0
3 years ago
Read 2 more answers
Let W be the subspace of R5 spanned by the vectors w1, w2, w3, w4, w5, where
Gwar [14]
To find W⊥, you can use the Gram-Schmidt process using the usual inner-product and the given 5 independent set of vectors. 

<span>Define projection of v on u as </span>
<span>p(u,v)=u*(u.v)/(u.u) </span>
<span>we need to proceed and determine u1...u5 as: </span>
<span>u1=w1 </span>
<span>u2=w2-p(u1,w2) </span>
<span>u3=w3-p(u1,w3)-p(u2,w3) </span>
<span>u4=w4-p(u1,w4)-p(u2,w4)-p(u3,w4) </span>
<span>u5=w5-p(u4,w5)-p(u2,w5)-p(u3,w5)-p(u4,w5) </span>

<span>so that u1...u5 will be the new basis of an orthogonal set of inner space. </span>

<span>However, the given set of vectors is not independent, since </span>
<span>w1+w2=w3, </span>
<span>therefore an orthogonal basis cannot be found. </span>
7 0
4 years ago
Graph each line using intercepts 1/4 x + 2y =2
Leno4ka [110]

The given equation is,

\frac{1}{4}x+2y=2

It can be rewritten in the form of y=mx+c, where c is the y intercept.

Hence,

\begin{gathered} 2y=-\frac{1}{4}x+2 \\ y=\frac{-1}{4\times2}x+\frac{2}{2} \\ y=\frac{-1}{8}x+1 \end{gathered}

Put different values for x and find value of y.

When x=0, y=1.

When x=1,

y=\frac{-1}{8}+1=\frac{7}{8}

The graph is,

5 0
1 year ago
Given the set of vertices, determine whether parallelogram ABCD is a rhombus, rectangle or square. List all that apply. A(7,-4),
Sloan [31]

Given:

Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).

To find:

Whether the parallelogram ABCD is a rhombus, rectangle or square.

Solution:

Distance formula:

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using distance formula, we get

AB=\sqrt{(-4-(-4))^2+(-1-7)^2}

AB=\sqrt{(-4+4)^2+(-8)^2}

AB=\sqrt{0+64}

AB=8

Similarly,

BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8

CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8

AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8

All sides of parallelogram are equal.

AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}

BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}

Both diagonals are equal.

Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.

We know that, a square is special case of rectangles and rhombus.

So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.

7 0
3 years ago
Find the measure of an angle whose complement is five times its measure.
ch4aika [34]

Answer:

The measure of the unknown angle is 15°.

Step-by-step explanation:

Represent this angle by A.  Then the complement of A is 90° - A.

"Angle whose complement is five times its measure" would be expressed as

90° - A = 5A

Solve this for A by adding A to both sides:

90° = 6A.  Then A = 90°/6, or 15°

4 0
3 years ago
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