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MAXImum [283]
3 years ago
13

I need help on these three questions I’m so confused on how to answer them

Mathematics
1 answer:
GalinKa [24]3 years ago
8 0

Answer:

  1.  S(1) = 1; S(n) = S(n-1) +n^2

  2. see attached

  3. neither

Step-by-step explanation:

1. The first step shows 1 square, so the first part of the recursive definition is ...

  S(1) = 1

Each successive step has n^2 squares added to the number in the previous step. So, that part of the recursive definition is ...

  S(n) = S(n-1) +n^2

__

2. See the attachment for a graph.

__

3. The recursive relation for an arithmetic function is of the form ...

  S(n) = S(n-1) +k . . . . . for k = some constant

The recursive relation for a geometric function is of the form ...

  S(n) = k·S(n-1) . . . . . . for k = some constant

The above recursive relation is not in either of these forms, so it is neither geometric nor arithmetic.

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Kryger [21]

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.















3 0
3 years ago
Read 2 more answers
Find the circumference of a circle with an area of 615.75 square inches.
Fittoniya [83]
A=pie×radius squared is the area formula of a circle. The circumference formula or a circle is C=pie×diameter. 615.75=(3.14)(radius) squared. Divide both sides by the 3.14. What ever 615.75 divided by 3.14 is-is radius squared. The square root is your radius. The radius is half the diameter, so double what you have right now as the radius to get the diameter. Now since C=pie×diameter, your circumference is your pie×your diameter. Whatever your answer is-is your circumference.
3 0
3 years ago
A car travels from City A to City B at
Debora [2.8K]

Answer:

90? maybe... i'm not positive but i hope it helped

Step-by-step explanation:

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3 years ago
A car traveled 63 miles on 3 gallon of gas. What proportion can you set up to determine how many miles, m, the car can travel on
kari74 [83]
63/3= 21
So 21 miles per gallon of gas
To find 7, you multiply it by 7
21*7= 147
147 miles on 7 gallons of gas
5 0
4 years ago
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4|n|-5=7 please help me solve
DedPeter [7]
I think you meant to type

4(n)-5=7.

4n = 7 + 5

4n = 12

n = 12/4

n = 3
3 0
3 years ago
Read 2 more answers
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