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2 years ago

point M with coordinates (3,4) is the midpoint of the line AB and A has the point (-1,6). what is the point of B?

Mathematics

1 answer:

irina [24]2 years ago

4 0

Answer:

B = (7, 2)

Step-by-step explanation:

B = 2M -A

B = 2(3, 4) -(-1, 6) = (2·3-(-1), 2·4-6)

B = (7, 2)

_____

The expression for the other end point, B, comes from the equation for the midpoint.

M = (A +B)/2

2M = A + B . . . . . multiply by 2

2M -A = B . . . . . . subtract A to get an expression for B

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You have five pieces of wood. The lengths of these are shown below.

Deffense [45]

Answer:

1,249 cm or 12.49

Whichever one it asks for

Step-by-step explanation:

First, we need to convert all of the m to cm.

4.04 m = 404 cm

1.6 m = 160 cm

2.87 m = 287 cm

Next, add them all up.

325 + 404 + 73 + 160 + 287 =

1,249 cm

If it asks to convert to m again, then the answer would be 12.49 m

Hope this helps!!!

3 0

2 years ago

Read 2 more answers

Mr. Woo wants to ship a fishing rod to his son that is 42 inches long. He has a box that measures 10 inches by 10 inches by 40 i

chubhunter [2.5K]

Answer:

The 42 inches long fishing rod will fit in the box.

Step-by-step explanation:

The diagonal of a cuboidal box is the largest measurement inside the box.

Now, the dimensions of the box are 10 inches by 10 inches by 40 inches.

Therefore, the diagonal length of the box is $\sqrt{10^{2} + 10^{2} + 40^{2}} = 42.42$ inches which is greater than 42 inches.

Hence, the 42 inches long fishing rod will fit in the box. (Answer)

8 0

2 years ago

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

A 3-gallon tub of ice cream yields about 90 scoops of ice cream. There are roughly 3785 cubic centimeters in 1 gallon. Determine

ASHA 777 [7]

Answer:

The radius of the scoop is r = 3.1 cm

Step-by-step explanation:

Since 3 gallons yields 90 scoops, and 1 gallon = 3785 cm³.

3 gallons = 3 × 3785 cm³ = 11355 cm³

So we have 11355 cm³ in 3 gallons which is also the volume of 90 scoops.

Since 90 scoops = 11355 cm³, then

1 scoop = 11355 cm³/90 = 126.2 cm³

Now, if each scoop is a sphere, the volume is given by V = 4πr³/3 where r is the radius of the scoop. Since we need to find the radius of the scoop, r, making r subject of the formula, we have

r = ∛(3V/4π)

Substituting V = 126.2 cm³, we have

r = ∛(3× 126.2 cm³/4π)

= ∛(378.6 cm³/12.57)

= ∛30.13 cm³

= 3.1 cm

So, the radius of the scoop is r = 3.1 cm

5 0

2 years ago

The lengths of text messages are normally distributed with an unknown population mean. A random sample of text messages is taken

anygoal [31]

Answer:

95% of the text messages have length between 23 units and 47 units.

Step-by-step explanation:

We are given the following in the question:

The lengths of text messages are normally distributed.

95% confidence interval:

(23,47)

Thus, we could interpret the confidence interval as:

About 95% of the text messages have length between 23 units and 47 units.

By Empirical rule for a normally distributed data, about 95% of data lies within 2 standard deviations of mean , thus we can write:

$\mu - 2\sigma = 23\\\mu +2\sigma = 47\\\Rightarrow \mu = 35\\\Rightarrow \sigma = 6$

Thus, the mean length of text messages is 23 units and standard deviation is 6 units.

8 0

1 year ago

Read 2 more answers