-1 1/3+-3/5? Please help

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Line segment AB has endpoints A(2, 9) and B(5, 8) . A dilation, centered at the origin, is applied to AB¯¯¯¯¯ . The image has endpoints A′(43, 6) and B′(103, 163) . What is the scale factor of this dilation? 32
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Answer: The correct option is (B) $(2)/(3).$

Step-by-step explanation: Given that the co-ordinates of the end-points of a line segment AB are A(2, 9) and B(5, 8). After being dilated about the origin (0, 0), the co-ordinates of the end-points of image A'B' are $A^\prime\left((4)/(3),6\right)$ and $B^\prime\left((10)/(3),(16)/(3)\right).$

We are to find the scale factor of the dilation.

The scale factor of the dilation will be

$S=\frac{\textup{length of the image line}}{\textup{length of the original line}}.$

The lengths of the lines AB and A'B' are calculated using distance formula as follows:

$AB=√((5-2)^2+(8-9)^2)=√(9+1)=√(10),\n\n\nA'B'=\sqrt{\left((10)/(3)-(4)/(3)\right)^2+\left((16)/(3)-6\right)^2\right)}=\sqrt{4+(4)/(9)}=\sqrt{(40)/(9)}=(2)/(3)√(10)~\textup{units}.$

Therefore, the required scale factor of dilation is

$S=(A'B')/(AB)=((2)/(3)√(10))/(√(10))=(2)/(3).$

Thus, the scale factor of the dilation is $(2)/(3).$

Option (B) is CORRECT.

the answer is 2/3
i took the test
hope this helps!

A trail around a river is 3 1/4 miles long what is the length in feet of a of the trail

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5280 feet in a mile

3.25 x 5280 = 17160 feet

the answers is 17,160 ft. one mile contains 5280 feet.

Larry,Mary,and Terry each had a full glass of juice.Larry drank 3/4 of his.Mary drank 3/8of hers.Terry drank 7/10 of his.who drank less than 1/2 of their juice?

Answers

Answer: Marry drank less than half of her glass of juice.

Step-by-step explanation: Given that Larry, Mary and Terry each had a full glass of juice.Larry drank $(3)/(4)$ of his. Mary drank $(3)/(8)$ of hers and Terry drank $(7)/(10)$ of his.

We are to find who drank less than $(1)/(2)$ of their juice.

We have

Portion of the glass of juice that Larry drank

$=(3)/(4)>(2)/(4)\left(=(1)/(2)\right).$

Portion of the glass of juice that Mary drank

$=(3)/(8)<(4)/(8)\left(=(1)/(2)\right).$

Portion of the glass of juice that Terry drank

$=(7)/(10)>(5)/(10)\left(=(1)/(2)\right).$

Therefore, Marry drank less than half of her glass of juice.

Mary drank the least because when half of 8 is 4/8.

A delivery truck made 8 stops in one neighborhood. By stop 5, there were 11 packages delivered. How many packages were delivered by stop 3?

Answers

Its proportion,
For 5 stops, its 11.
So, for 3 stops how many ??

5:11 :: 3:?
5/11 = 3/?
? = 3 × 11/5

? = 33/5 = 6.6 ≈ 7 packages

the flower shop has 40 times as many flowers in one cooler as Julia has in her bouquet. The cooler has 120 flowers. How many flowers in Julia ' s bouquet?