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Degger [83]
1 year ago
14

Find the number of chips needed to make each rectangle prism

Mathematics
1 answer:
Tom [10]1 year ago
5 0

1.

height= 3

length= 5

width= 4

The number of cubes would be the result of the multiplication of the side measures. Doing so, we have:

3 x 5 x 4 = 60

We need 60 blocks

2

height= 4

length= 6

width= 4

The number of cubes would be the result of the multiplication of the side measures. Doing so, we have:

4 x 6 x 4 = 96

We need 96 blocks

3

height= 2

length= 3

width= 4

The number of cubes would be the result of the multiplication of the side measures. Doing so, we have:

2 x 3 x 4 = 24

We need 24 blocks

4

height= 4

length= 8

width= 6

The number of cubes would be the result of the multiplication of the side measures. Doing so, we have:

4 x 8 x 6 = 192

We need 192 blocks

5

height= 2

length= 6

width= 4

The number of cubes would be the result of the multiplication of the side measures. Doing so, we have:

2 x 6 x 4 = 48

We need 48 blocks

6

height= 1

length= 5

width= 3

The number of cubes would be the result of the multiplication of the side measures. Doing so, we have:

1 x 5 x 3 = 15

We need 15 blocks

7

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Answer:

1)

Given the triangle RST with Coordinates  R(2,1), S(2, -2) and T(-1 , -2).

A dilation is a transformation which produces an image that is the same shape as original one, but is different size.  

Since, the scale factor \frac{5}{3} is greater than 1, the image is enlargement or a stretch.  

Now, draw the dilation image of the triangle RST with center (2,-2) and scale factor \frac{5}{3}

Since, the center of dilation at S(2,-2) is not at the origin, so the point S and its image S{}' are same.

Now, the distances from the center of the dilation at point S to the other points R and T.  

The dilation image will be\frac{5}{3} of each of these distances,

SR=3, so S{}'R{}'=5 ;


ST=3, so S{}'T{}'=5  

Now, draw the image of RST i.e R'S'T'

Since, RT=3\sqrt{2} [By using hypotenuse of right angle triangle] and R{}'T{}'=5\sqrt{2}.


2)

(a)

Disagree with the given statement.

Side Angle Side postulate (SAS) states that:

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then these two triangles are congruent.

Given: B is the midpoint of \overline{AC} i.e \overline{AB}\cong \overline{BC}

In the triangle ABD and triangle CBD, we have

\overline{AB}\cong \overline{BC}   (SIDE)            [Given]

\overline{BD}\cong \overline{BD}   (SIDE)            [Reflexive post]

Since, there is no included angle in these triangles.

∴ \Delta ABD is not congruent to \Delta CBD .

Therefore, these triangles does not follow the SAS congruence postulates.

(b)

SSS(SIDE-SIDE-SIDE) states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Since it is also given that  \overline{AD}\cong \overline{CD}.

therefore, in the triangle ABD and triangle CBD, we have

\overline{AB}\cong \overline{BC}   (SIDE)            [Given]

\overline{AD}\cong \overline{CD}   (SIDE)           [Given]

\overline{BD}\cong \overline{BD}   (SIDE)            [Reflexive post]

therefore by, SSS postulates \Delta ABD\cong \Delta CBD.

3)

Given that:  \angle1=\angle 3 are vertical angles, as they are formed by intersecting lines.

Therefore

, by the definition of linear pairs

\angle 1 and \angle 2 and \angle 3  and \angle 2 are linear pair.

By linear pair theorem, \angle 1 and \angle 2   are supplementary, \angle 2 and \angle 3  are supplementary.

m\angle1+m\angle 2=180^{\circ}

m\angle2+m\angle 3=180^{\circ}

Equate the above expressions:

m\angle 1+m\angle 2=m\angle 2+m\angle 3

Subtract the angle 2 from both sides in the above expressions

∴m\angle 1=m\angle 3

By Congruent Supplement theorem: If two angles are supplements of the same angle, then the two angles are congruent.


therefore, \angle 1\cong \angle 3.















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Answer:

B

Step-by-step explanation:

let f(x) = y and rearrange making x the subject

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8. For what values of x and y must the quadrilateral be a parallelogram?
Gnom [1K]
2x + 5 = 11
2x = 6
  x = 3

y + 4 = 2x + 4
y + 4 = 2(3) + 4
y + 4 = 10
y = 6

answer
x = 3 and y = 6
8 0
3 years ago
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