Write a complete two-column proof for following information.

Given: AB = 3y - 1, BC = 7y, AC = 29
Prove: AB = 8

There are 320 students in a school. The ratio of the number of boys to the number of girls is 3:2. When some new boys and girls are admitted, the number of boys increases by 8 and the ratio of number of boys and girls changes to 4:3. Find how many new girls are admitted.​

how many movie tickets can you buy with $42 if one ticket costs $6 (include equation)

Read John Muir's "Calypso Borealis" and answer the question. [1] After earning a few dollars working on my brother-in law's farm near Portage [Wisconsin], I set off on the first of my long lonely excursions, botanising in glorious freedom around the Great Lakes and wandering through innumerable tamarac and arbor-vitae swamps, and forests of maple, basswood, ash, elm, balsam, fir, pine, spruce, hemlock, rejoicing in their bound wealth and strength and beauty, climbing the trees, revelling in their flowers and fruit like bees in beds of goldenrods, glorying in the fresh cool beauty and charm of the bog and meadow heathworts, grasses, carices, ferns, mosses, liverworts displayed in boundless profusion. [2] The rarest and most beautiful of the flowering plants I discovered on this first grand excursion was Calypso borealis (the Hider of the North). I had been fording streams more and more difficult to cross and wading bogs and swamps that seemed more and more extensive and more difficult to force one's way through. Entering one of these great tamarac and arbor-vitae swamps one morning, holding a general though very crooked course by compass, struggling through tangled drooping branches and over and under broad heaps of fallen trees, I began to fear that I would not be able to reach dry ground before dark, and therefore would have to pass the night in the swamp and began, faint and hungry, to plan a nest of branches on one of the largest trees or windfalls like a monkey's nest, or eagle's, or Indian's in the flooded forests of the Orinoco described by Humboldt. [3] But when the sun was getting low and everything seemed most bewildering and discouraging, I found beautiful Calypso on the mossy bank of a stream, growing not in the ground but on a bed of yellow mosses in which its small white bulb had found a soft nest and from which its one leaf and one flower sprung. The flower was white and made the impression of the utmost simple purity like a snowflower. No other bloom was near it, for the bog a short distance below the surface was still frozen, and the water was ice cold. It seemed the most spiritual of all the flower people I had ever met. I sat down beside it and fairly cried for joy.

[4] It seems wonderful that so frail and lovely a plant has such power over human hearts. This Calypso meeting happened some forty-five years ago, and it was more memorable and impressive than any of my meetings with human beings excepting, perhaps, Emerson and one or two others. When I was leaving the University, Professor J.D. Butler said, "John, I would like to know what becomes of you, and I wish you would write me, say once a year, so I may keep you in sight." I wrote to the Professor, telling him about this meeting with Calypso, and he sent the letter to an Eastern newspaper [The Boston Recorder] with some comments of his own. These, as far as I know, were the first of my words that appeared in print.

[5] How long I sat beside Calypso I don't know. Hunger and weariness vanished, and only after the sun was low in the west I splashed on through the swamp, strong and exhilarated as if never more to feel any mortal care. At length I saw maple woods on a hill and found a log house. I was gladly received. "Where ha ye come fra? The swamp, that awfu' swamp. What were ye doin' there?" etc. "Mony a puir body has been lost in that muckle, cauld, dreary bog and never been found." When I told her I had entered it in search of plants and had been in it all day, she wondered how plants could draw me to these awful places, and said, "It's god's mercy ye ever got out."

[6] Oftentimes I had to sleep without blankets, and sometimes without supper, but usually I had no great difficulty in finding a loaf of bread here and there at the houses of the farmer settlers in the widely scattered clearings. With one of these large backwoods loaves I was able to wander many a long wild fertile mile in the forests and bogs, free as the winds, gathering plants, and glorying in God's abounding inexhaustible spiritual beauty bread. Storms, thunderclouds, winds in the woods—were welcomed as friends.

The words that Muir uses in his essay reveal that he relates to nature as a(n)

emotional professor
objective notetaker
passionate observer
removed reporter

I hate how i have to write things here

1. Both of the equations shown have the same solution when solved for x. What is
the value of k? Show or explain all your work. *
5x + 34 = -2 (1 – 7x) and – 3 (4x + 3) + 4 (6x + 1) = k
Your answer
PLS HELPPPP

differentiate x+sinx/x+cosx with respect to x​

Ariana compró cierto número de sacos de azúcar por S/. 675 y luego los vendió por S/. 1 080, ganando S/. 3 por cada saco. ¿Cuántos sacos de azúcar compró?

The ratio of dogs to cats at a pet store is 11: 4. If there are 90 total pets (dogs and cats), how many cats are there?​

Tom made fruit punch for a party. He mixed 2 gallons of orange juice, 4 quats of pinnapple juice, 3 pints of cranberry juice. How many quarts did he make in all?

Interest earned: $84
Principal: 600
Interest rate: 7%
Time: ?

1. What's the probability that a respondent was a boy AND in year 8?

What the slope? Can someone help me

Need help :::::::::::::::::

Find f(-) if f(n) = 5n + 6.

When x= 1, then y= 1

Sarah is creating a triangular birthday card for her teacher. In order to glue lace
around the outside of the card, Sarah needs to know the length of each side. She
knows that two of the sides measure 4 inches and 9 inches. Between which two
numbers must the third side of the card fall?

Brainly reward!!!!

What's the area of the gray shape?

Henry wanted to turn the following circle graph into a bar graph. the tallest bar in this bar graph will be represented by what part of the family budget?
A: insurance/pension
B: food
C: transportation
D: housing ​

Please help sbdbdbdbdbdbdndbndbbdbdbdbdb

We are painting a rectangular wall of a large room. The dimensions of the wall are 35feet long and 21.5 feet wide. If the total cost of the paint was 421.40 what was the cost in dollars of the paint rounded to the nearest cent

Ted's company has received an order to print 10^6 pages. Ted's company has 100 machines., each of which can print 10^4 pages a day. Ted's coompany can print the 10^6 pages in 1/10 day, 1 day, 10 days, or 100 days?

David can jog 3.5 miles in 75 minutes. What is David’s jogging rate per hour?
PLEASE SHOW YOUR WORK!!!!
will give brainliest!

Help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeee

How many roots does y=3x^2+8 have?

Find the area of the square whose side is 14cm?GUYS??​

Find the measure of Arc XY.

my question has been up too long lol

4. Which of these is equal to sin(70°)?
a. cos(1109)
c. cos(20°)
b. cos(160)
d. cos(709)

x = -0.25 and y = -6
Solve the expression: xy

19+23=2X-2

Someone help me pleaseeeeeeeeeeeeee