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schepotkina [342]

2 years ago

12

desiree has 100 pink 80 blue and 120 purple beads. she puts all of the beads into jars equally. each jar has one type of bead. h

ow many beads can she put in one jar

1 answer:

astra-53 [7]2 years ago

8 0

At most, 20. 20 is the greatest common factor of all numbers.

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Determine if each of the following sets is a subspace of ℙn, for an appropriate value of n. Type "yes" or "no" for each answer.

xxMikexx [17]

Answer:

1. Yes.

2. No.

3. Yes.

Step-by-step explanation:

Consider the following subsets of Pn given by

1.Let W1 be the set of all polynomials of the form $p(t)=at^2$ , where a is in ℝ.

2.Let W2 be the set of all polynomials of the form $p(t)=t^2+a$ , where a is in ℝ.

3. Let W3 be the set of all polynomials of the form $p(t)=at^2+at$ , where a is in ℝ.

Recall that given a vector space V, a subset W of V is a subspace if the following criteria hold:

- The 0 vector of V is in W.

- Given v,w in W then v+w is in W.

- Given v in W and a a real number, then av is in W.

So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.

- First property:

Note that for W2, for any value of a, the polynomial we get is not the zero polynomial. Hence the first criteria is not met. Then, W2 is not a subspace of Pn.

For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.

- Second property:

W1. Consider two elements in W1, say, consider a,b different non-zero real numbers and consider the polynomials

$p_1 (t) = at^2, p_2(t)=bt^2$ .

We must check that p_1+p_2(t) is in W1.

Note that

$p_1(t)+p_2(t) = at^2+bt^2 = (a+b)t^2$

Since a+b is another real number, we have that p1(t)+p2(t) is in W1.

W3. Consider two elements in W3. Say $p_1(t) = a(t^2+t), p_2(t)= b(t^2+t)$ . Then

$p_1(t) + p_2(t) = a(t^2+t) + b(t^2+t) = (a+b) (t^2+t)$

So, again, p1(t)+p2(t) is in W3.

- Third property.

W1. Consider an element in W1 $p(t) = at^2$ and a real scalar b. Then

$bp(t) = b(at^2) = (ba)t^2)$ .

Since (ba) is another real scalar, we have that bp(t) is in W1.

W3. Consider an element in W3 $p(t) = a(t^2+t)$ and a real scalar b. Then

$bp(t) = b(a(t^2+t)) = (ba)(t^2+t)$ .

Since (ba) is another real scalar, we have that bp(t) is in W3.

After all,

W1 and W3 are subspaces of Pn for n= 2

and W2 is not a subspace of Pn.

6 0

2 years ago

Given: AB ≅ CD

xz_007 [3.2K]

Answer:

cc

Step-by-step explanation:

cc

6 0

1 year ago

.The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 s

Citrus2011 [14]

Answer:

The constant of variation is 1/9

The equation representing the direct variation is y/x= 1/9

Step-by-step explanation:

In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get

y/x = k

3 / 27 = k

(3/27) / (3/3) = 1/9* = k

Therefore, the constant of variation is 1/9

Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation

* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both

5 0

1 year ago

A circus ring is the arena where much of the action takes place at a circus. The figure below shows a circus ring with the cente

Goshia [24]

Answer:

Step-by-step explanation:

a) A diameter is a line that cuts a circle through at the centre. Line AD is a diameter.

Radius is half of a diameter i.e AD/2 = AO or OD

Chord is a straight line that touches the circumference of a circle. It doesn't pass through the centre like the diameter but cuts through the segments of a circle. Example of a chord is line FH

A tangent is a line that touches the circumference of a circle at just a point. It can touch any point on the circle. Example of a tangent line are AB and DE.

b) We must know that angle at a point or in a circle is 360°.

<EOH + <ECH = 360°

If <EOH = 131°

<ECH = 360° - 131°

<ECH = 229°

- <EFH falls in the circumference of the circle. Also know that, angle at the centre of a circle is twice angle at the circumference. Since <EOH is at the centre of the circle. <EFH = <EOH/2

<EFH = 131/2

<EFH = 65.5°

c) Given AB = DE, then <AB = <DE (oppositely directed angle).

Given <AOB = 20° then <DE = 20°

d) According to the diagram, <GFD = <GLD

If <GFD = 126°, then <GLD = 126°

e) Given HK = x+4, FK = x+14, GK = x, CK = x+32

From the diagram, CG = CK + KG

CG = x+32+x

CG = 2x+32

Also, FH = FK+HK

FH = x+14+x+4

FH = 2x+18

4 0

1 year ago

If a line crosses the yaxis at (0, 1) and has a slope of 4/5 , what is the equation of the line?

Misha Larkins [42]

Answer:

y=4/5x+1

Step-by-step explanation:

When making linear equations for graphs we need to fill in the model of y=mx+b. M gets filled in with the slope of line and in this case it's 4/5. X is our unknown variable that we could substitute for. B is our y-intercept which is 1 since that is where the line first touches the y-axis. Together it makes y=4/5x+1.

7 0

2 years ago