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3 years ago

Tamara says she used the GCF to factor the expression 21x + 56xy as 7(3x + 8xy). Is she correct? Explain.

Mathematics

1 answer:

cestrela7 [59]3 years ago

6 0

Answer:

Tamara incorrectly factored the whole expression.

Step-by-step explanation:

Note that

21x=3·7·x;
56xy=2·2·2·7·x·y.

Mark in bold all common factors, then GCF(21x,56xy)=7·x=7x.

Thus,

21x+56xy=7x(3+8y).

Hence, Tamara correctly found the GCF of numbers 21 and 56, but incorrectly factored the whole expression.

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A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking, $\frac{d(w)}{dt}$ = 3 ft/sec

Rate at which the man is walking, $\frac{d(m)}{dt}$ = 2 ft/sec

Collective rate of both, $\frac{d(m+w)}{dt}$ = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min

Now,

Distance traveled by man and woman are $m$ and $w$ ft respectively.

⇒ $m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft$

⇒ $w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft$

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate $\frac{dh}{dt}$ .

Lets calculate h.

Applying Pythagoras formula.

⇒ $h^2=(m+w)^2+500^2$

⇒ $h=\sqrt{(2400+2700)^2+500^2} = 5124.45$

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ $h^2=(m+w)^2+500^2$

⇒ $2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}$

⇒ $\frac{d(h)}{dt} =\frac{2(m+w)\frac{d(m+w)}{dt} }{2h}$ ...as $\frac{d(500)}{dt}= 0$

⇒ Plugging the values.

⇒ $\frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}$ ...as $\frac{d(m+w)}{dt} = 5$ ft/sec

⇒ $\frac{d(h)}{dt} =4.9761$ ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

3 0

3 years ago

Listed below are prices in dollars for one night at different hotels in a certain region. Find the range, variance, and standar

Vanyuwa [196]

Answer:

Range = $115

Variance = $1915.2857

Standard deviation = $43.764

Step-by-step explanation:

Given the data:

234 160 119 131 218 207 146 141

Arranging in ascending order :

119, 131, 141, 146, 160, 207, 218, 234

The range = maximum - minimum

The range = 234 - 119 = 115

The variance :

Σ(x - mean)²/n-1

The mean = Σx / n

The mean = 1356 / 8 = 169.5

Variance :

Σ(x - mean)² = (119-169.5)² + (131-169.5)² + (141-169.5)² + (146-169.5)² + (160-169.5)² + (207-169.5)² + (218-169.5)² + (234-169.5)² = 13407

n - 1 = 8 - 1 = 7

Variance = 13407 / 7 = 1915.2857

Standard deviation = √variance

Standard deviation = √1915.2857

Standard deviation = $43.764

8 0

3 years ago

54 is 90% of what number?

Zarrin [17]

The answer is 60 surprisingly

7 0

3 years ago

Three of the four vertices of a rectangle are located at (4, 2), (7, 2) and (4, 8). a. What are the coordinates of the missing v

34kurt

Answer:

a) The coordinates of the missing vertex = (7, 8)

b) Area = 18 square units

Perimeter = 18 units

Step-by-step explanation:

a) We know three of the four vertices:

A: (4, 2) C ______ D(?)

B: (7, 2) | |

C: (4, 8) A |______| B

To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:

$B_{x} - A_{x} = 7 - 4 = 3$

Hence, the distance of point D from point C in the x-direction is:

$D_{x} = C_{x} + 3 = 4 + 3 = 7$

Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:

$C_{y} - A_{y} = 8 - 2 = 6$

Then, the distance of point D from point B in the y-direction is:

$D_{y} = B_{y} + 6 = 2 + 6 = 8$

Therefore, the coordinates of the missing vertex (point D) are:

$D = (D_{x}, D_{y}) = (7, 8)$

b) The area of the rectangle is:

$a = (B_{x} - A_{x})*(C_{y} - A_{y}) = 3*6 = 18 units^{2}$

The perimeter is given by:

$p = 2*(3 + 6) = 18 units$

I hope it helps you!

8 0

2 years ago

If (50)x = 1, what are the possible values of x? Explain your answer

Lelechka [254]

Than you multiplie tha 50 by 1/50 so will get 50/50 what is equal 1

hope this is understandably sure right easy

5 0

3 years ago