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Simplify: (3x - 4y)(5y + 7x)
Formula: (a + b)(c + d) = ac + ad + bc + bd
Simplified: 15x^2 - 8xy + 35xy - 28y^2 = 15x^2 + 27xy - 28y^2
12xy + 21x² - 20y² - 28xy
Snowflakes form from tiny water droplets, following a specific process of chemical bonding as they freeze, which results in a six-sided figure.
A. No change
B. form, from tiny, water droplets,
C. form from tiny, water, droplets
D. form, from tiny water droplets
A. No change
The seemingly triangular shape of those snowflakes suggests that forming through a different process of chemical bonding.
A. No change
B. the manner in which formation
C. which had formed
D. that they form
D. that they form
By re-creating snowflake formation, a discovery has revealed to scientists Kenneth Libbrecht and Hannah Arnold the cause of this apparent variation.
F. No change
G. the discovery of the cause of this apparent variation has been made by scientists Kenneth Libbrecht and Hannah Arnold
H. scientists Kenneth Libbrecht and Hannah Arnold have discovered the cause of this apparent variation.
J. the cause of this apparent variation has been discovered by scientists Kenneth Libbrecht and Hannah Arnold
H. scientists Kenneth Libbrecht and Hannah Arnold have discovered the cause of this apparent variation.
Snowflakes begin to form when water in the atmosphere freezes it causes the water molecules to bond into a hexagonal shape.
A. No change
B. freezes, causing
C. freezes, it causes
D. freezes, this causes
B. freezes, causing
During the flake's descent from Earth's upper atmosphere, other water vapor molecules bump into the hexagonal structure.
F. No change
G. has bumped
H. bumped
J. bump
J. bump
Bypassing the liquid water phase those molecules condense directly onto the established hexagonal pattern. As a result, the flake grows outward into bigger and more complex hexagonal arrangements surrounding the original hexagonal shape at the center of the flake.
If the writer were to delete the bold portion (adjusting the capitalization as needed), the sentence could primarily lose:
A. an explanation of the process water molecules undergo to change from liquid to vapor to solid.
B. a detail that mentions a step some water molecules skip in changing from vapor to solid.
C. a visual description of what water vapor molecules look like.
D. an explanation of how molecules react to various air temperatures.
B. a detail that mentions a step some water molecules skip in changing from vapor to solid.
In 2009, Libbrecht and Arnold's experiments revealed that triangular snowflakes begin with the same process of chemical bonding and forms a hexagonal shape.
F. No change
G. were they to form
H. if they formed
J. form
J. form
The triangular shape is an illusion resulting from one significant addition to the process dust.
A. No change
B. process is
C. process:
D. process;
C. process:
The resulting snowflake has three long sides and three sides that are so short they are difficult to detect. Although these snowflakes appear to have a triangular ^^shape--^^they actually have a hexagonal pattern.
F. No change
G. shape,
H. shape;
J. shape:
G. shape,
Such snowflakes offer evidence that even when impurities interfere, the basic laws of chemistry still apply.
Which choice most effectively concludes the sentence?
A. No change
B. scientists can be certain that a solution to even the most confusing event will be found
C. snowflakes will still fall if atmospheric conditions are favorable.
D. snowflakes come in many different shapes and sizes.
A. No change
Bundled up in wool sweaters and thick coats, and we watched the sun setting on Mt. Fuji in Japan.
F. No change
G. coats while watching
H. coats, we watched
J. coats watching
H. coats, we watched
It was August and our clothes were stifling, but we would have needed the warmth from our bodies sealed around us as we hiked into the high altitudes.
A. No change
B. would need
C. will need
D. need
B. would need
The trail gradually changed from compact dirt to a jumble of volcanic rocks. We tried to steady ourselves with our walking sticks but slipped and stumbled because of the jumbled rocks we were slipping on.
F. No change
G. even though we used our walking sticks.
H. despite any efforts to remain steady.
J. with each step.
J. with each step.
Every thousand feet, we came to a small station constructed of tin and cement, barely able to block the wind. At each one, we noted the roof piled high on fallen rocks and felt both unsettled and reassured by this evidence of the station's protective ability.
A. No change
B. piling high with
C. piled high with
D. piling high on
C. piled high with
We rested uneasily for a moment as a clerk burned the station brand into our walking sticks which it was proof of our progress through the darkness.
F. No change
G. sticks, it was proof of
H. sticks, proof of
J. sticks proved
H. sticks, proof of
As we neared the summit, the whole group of hikers--thinly spread across the mountain for most of the route--condensed, forming an illuminated line along the trail.
A. No change
B. the most part
C. majority
D. more
A. No change
As we neared the summit, the whole group of hikers--thinly spread across the mountain for most of the route--condensed, forming an illuminated line along the trail.
F. No change
G. they formed
H. there was
J. we saw
F. No change
Our pace slowed. Progressing along the trail, we reached the summit just five minutes before dawn.
Which choice emphasizes the slowness of the ascent and supports the idea that the narrator's group of friends did not set their own pace?
A. No change
B. Able to advance only a few steps at a time,
C. Moving forward with each step,
D. Climbing higher in altitude
B. Able to advance only a few steps at a time,
We crouched down on jutting pieces of rock and waited for the shifting clouds to clear. We waited for the sun.
If the writer were to delete the sentence, the paragraph would primarily lose:
F. a restatement of an idea that emphasizes the hikers' anticipation when they reached the summit.
G. a statement that introduces the idea of waiting.
H. an unnecessary detail
J. a clear image that conveys what the hikers saw when they reached the summit.
F. a restatement of an idea that emphasizes the hikers' anticipation when they reached the summit.
In the early 1950s, a twelve-year old boy named, Juan Quezada, gathered firewood in the mountains near the village of Mata Ortiz in Chihuahua, Mexico.
A. No change
B. boy named Juan Quezada
C. boy, named Juan Quezada
D. boy named Juan Quezada,
B. boy named Juan Quezada
In the mountains, Quezada found shards of pots, and an occasional complete pot, painted with intricate red and black designs.
Which of the following alternatives to the * * portion would NOT be acceptable?
F. pots--along with an occasional complete pot--
G. pots, along with an occasional complete pot,
H. pots, (and an occasional complete pot)
J. pots (and an occasional complete pot)
H. pots, (and an occasional complete pot)
These were artifacts from his ancestors. Fascinated by the geometric designs, Quezada wondered, if he could make pots like these?
A. No Change
B. wondered if he could make pots like these.
C. wondered, if he could make pots like these.
D. wondered if he could make pots like these?
B. wondered if he could make pots like these.
I grew up with buckets, shovels, and nets waiting by the back door; hip-waders hanging in the closet; tide table charts covering the refrigerator door; and a microscope was sitting on the kitchen table.
A. No Change
B. waiting, by the back door,
C. waiting by the back door,
D. waiting by the back door
A. No change
I grew up with buckets, shovels, and nets waiting by the back door; hip-waders hanging in the closet; tide table charts covering the refrigerator door; and a microscope was sitting on the kitchen table.
E. NO CHANGE
F. would sit
G. sitting
H. sat
I grew up with buckets, shovels, and nets waiting by the back door; hip-waders hanging in the closet; tide table charts covering the refrigerator door; and a microscope was sitting on the kitchen table.
E. NO CHANGE
F. would sit
G. sitting
H. sat
D. My mother is
Having studied, my mother is a marine biologist.
A. NO CHANGE
B. As my mother's interest is science, she is
C. My mother's occupation is that of
D. My mother is
C. Our household didn't run according to a typical schedule.
Our household might have been described as uncooperative.
Which choice would most effectively introduce the rest of this paragraph?
A. NO CHANGE
B. There seemed to be no explanation for why Mom ran our household the way she did.
C. Our household didn't run according to a typical schedule.
D. Mom ran our household in a most spectacular manner.
C. depended on
Our meals weren't always served in the expected order of breakfast, lunch, and supper. Everything was subservient to the disposal of the tides.
A. NO CHANGE
B. was defenseless in the face of
C. depended on
D. trusted in
C.The moon is
The moon being aligned with Earth and the sun when full or new, so its gravity combines with the sun's gravity to create an even stronger gravitational pull.
A. NO CHANGE
B. Since the moon is
C.The moon is
D. The moon,
E. NO CHANGE
The moon being aligned with Earth and the sun when full or new, so its gravity combines with the sun's gravity to create an even stronger gravitational pull
E. NO CHANGE
F. one's
G. it's
D. its'
D. displays the narrator's knowledge of tides.
I knew that it took about eight hours for the tides to change from high to low, sixteen hours for a complete cycle of tides. I didn't have to wait to learn these things in school. In our house they were everyday knowledge.
If the writer were to delete the phrase "sixteen hours for a complete cycle of tides" from the preceding sentence (ending the sentence with a period), the essay would primarily lose a detail that:
A. shows how the narrator's interests are different from the mother's interests.
B. contradicts a point made earlier in the paragraph.
C. helps establish the setting for the essay.
D. displays the narrator's knowledge of tides.
H. brother and I
Often, my brother and I, joined our mother on her adventures into tidal lands.
E. NO CHANGE
F.brother, and I,
G. brother, and I
H. brother and I
At the very low tides of the full moon, when almost all the water was sucked away, we found the hideaways where crabs, snails, starfish, and sea urchins hid in order not to be seen.
A. NO CHANGE
B. away. Then we
C. away. We
D. away; we
A. NO CHANGE
At the very low tides of the full moon, when almost all the water was sucked away, we found the hideaways where crabs, snails, starfish, and sea urchins hid in order not to be seen.*
E. NO CHANGE
F. hideouts where crabs, snails, starfish, and sea urchins concealed and hid themselves.
G. places where crabs, snails, starfish, and sea urchins were stashed away.
H. hiding places of crabs, snails, starfish, and sea urchins.
H. hiding places of crabs, snails, starfish, and sea urchins.
[1] Often, my brother and I, joined our mother on her adventures into tidal lands. [2] At the very low tides of the full moon, when almost all the water was sucked away, we found the hideaways where crabs, snails, starfish, and sea urchins hid in order not to be seen.[3] Sometimes we would dig with shovels in the mud, where yellow and white worms lived in their leathery tunnels.
Which of the following sequences of sentences makes this paragraph most logical?
A. NO CHANGE
B. 2, 1, 3
C. 2, 3, 1
D. 3, 1, 2
A. NO CHANGE
Then we would patiently wait. After a while, she would pull up the net, and we would go home. Later, we would see her sitting at the kitchen table, peering at a drop of water through the lenses of her microscope from the bottle—watching the thousands of tiny swimming organisms.
The best placement for the bold portion would be:
A. where it is now.
B. after the word lenses.
C. after the word microscope.
D. after the word bottle (but before the dash).
C. after the word microscope.
When I was a boy growing up in Delhi, India,
we had a kitchen garden behind our downstairs
apartment. My father was an avid gardener, he still is: and every Saturday morning he would put on his work
clothes,
A. NO CHANGE
B. gardener—he still is—
C. gardener, he still is—
D. gardener and he still is
B. gardener—he still is—
...and every Saturday morning he would put on his work
clothes, pick up his hoe and trowel, and would head
out the back door.
E. NO CHANGE
F. picked up his hoe and trowel, and headed
G. pick up his hoe and trowel, and head
H. picking up his hoe and trowel, and headed
G. pick up his hoe and trowel, and head
As a ten-year-old, I was supremely unenthusiastic
about swinging a hoe in the garden when I could be out
playing with my friends. Having tried and failed,
my father was unable to make a gardener of me.
Which of the choices best emphasizes how much the father wanted his son to share his avid interest in gardening?
A. NO CHANGE
B. Because of my indifference to his hobby,
C. Contrary to this thinking,
D. Despite his repeated attempts,
D. Despite his repeated attempts,
Having tried and failed,
my father was unable to make a gardener of me.
I had no qualms, of course, about enjoying the
results of his labor: the potatoes, squash, cucumbers,
and cauliflower that he pursued out of the earth.
A. NO CHANGE
B. More important, I had no qualms
C. It stands to reason, then, that I certainly would have no qualms
D. I had no qualms, as a consequence of it,
A. NO CHANGE
I had no qualms, of course, about enjoying the
results of his labor: the potatoes, squash, cucumbers,
and cauliflower that he pursued out of the earth. I would
even help him dig out the potatoes or cut a cucumber from
its vine.
A. NO CHANGE
B. coaxed
C. surrendered
E. enlisted
B. coaxed
I would even help him dig out the potatoes or cut a cucumber from its vine. To me, it was much more fun to reap than sowing.
A. NO CHANGE
B. the most fun to reap than to sow.
C. much more fun to reap than to sow.
D. the most fun reaping than if I'd had to sow.
C. much more fun to reap than to sow.
Many years later, living in an upstairs apartment,
I am more often sorry I didn't follow my father out to the
garden.
The best placement for the bold portion would be:
E. where it is now.
F. after the word sorry.
G. after the word follow.
H. after the word garden (ending the sentence with a period).
H. after the word garden (ending the sentence with a period).
I have several indoor plants, but the experience is
not the same. The few times that I've helped a friend with
yard work has given me the joy of touching the soil
with an open palm, to get the earth under my fingernails,
of patting down the berm around a newly transplanted
sapling.
A. NO CHANGE
B. have given
C. has gave
D. have gave
B. have given
The few times that I've helped a friend with
yard work has given me the joy of touching the soil
with an open palm, to get the earth under my fingernails,
of patting down the berm around a newly transplanted
sapling.
A. NO CHANGE
B. with getting
C. of getting
D. got
C. of getting
Now that I live far from my father (I live in Iowa
on the other side of the world), I wish I'd spend more time
with him in the garden.
A. NO CHANGE
B. wished I had spent
C. wish I had spent
D. wish to have spent
C. wish I had spent
My favorite photograph of my father shows him
squatting on his heels, trowel in hand, behind a golden
heap of onions freshly pulled from the ground.
At this point, the writer is considering adding the following true statement:
I have many photo albums, and each one includes pictures of my father in various poses.
Should the writer make this addition here?
E. Yes, because it informs the reader that the photograph he describes in the preceding sentence is not the only one he has of his father.
F. Yes, because it informs the reader that the writer is more than an amateur photographer.
G. No, because it contradicts the writer's claim that the photograph he describes in the preceding sentence is one he also treasures.
H. No, because it distracts the reader from the main focus of the paragraph and does not logically fit at this point in the essay.
H. No, because it distracts the reader from the main focus of the paragraph and does not logically fit at this point in the essay.
His glowing smile are evidence of his pride in the
onions—the proof of his labor and love—and in me, the
photographer, his son.
Choose the best answer.
A. NO CHANGE
B. is
C. were
D. OMIT the underlined portion.
B. is
Whether its* bright and jaunty or haunting and
melancholic, the music of the Andes highlands has a mellow sound unique in the musical world.
A. NO CHANGE
B. they're
C. it's
D. its'
C. it's
The antara has its origins in
the Incan civilization, once the more richer and more
powerful empire in South America.
E. NO CHANGE
F. one of the richest and most
G. the richest and most
H. the richer and more
G. the richest and most
The antara consists of a connected row of hollow,
vertical pipes of varying lengths, which are then lined up.*
Given that all of the choices are true, which one provides the most significant new information?
A. NO CHANGE
B. thus forming this musical instrument.
C. arranged from shortest to longest.
D. which are fastened together.
C. arranged from shortest to longest.
The pipes, which can vary numerously from three to fifteen, are fashioned from clay that is rolled around
a mold.
A. NO CHANGE
B. in quantity of numbers
C. number-wise
D. in number
D. in number
Each pipe is individually rolled to create the
proper pitch before being bound to the other pipes.
A. NO CHANGE
B. being binded
C. been bounded
D. been bound
A. NO CHANGE
The antara dates back to the ninth century.
Evidence about how musicians played the instrument have come from painted images on Incan ceramic
pottery.
E. NO CHANGE
F. are coming
G. comes
H. come
G. comes
Musicians are depicted playing a six-pipe antara by holding the lower ends of the two longer pipes with the right hand while placing the left hand near the remaining tops of the four pipes.
The best placement for the bold portion would be:
A. where it is now.
B. before the word left.
C. before the word of.
D. before the word four.
D. before the word four.
The antara was also
sometimes held in one hand while the other hand beat a cylindrical drum.
A. NO CHANGE
B. beaten
C. beated
D. beats.
A. NO CHANGE
Due to the limited number of notes that can be played on an antara, early musicians' most likely worked in most likely worked in* most likely worked in groups, coordinating the timing and pitch of their instruments to extend the range of sounds produced.
A. NO CHANGE
B. antara, early musicians
C. antara early musicians'
D. antara early musician's
B. antara, early musicians
Other pottery images show two antara players facing each other while dancing. Each player holds a set of pipes so that both sets are connected to the other set by a string, as if to suggest that those two antaras should be played together.
A. NO CHANGE
B. in such a way that both sets are
C. with both sets being
D. OMIT the underlined portion.
D. OMIT the underlined portion.
[1] Due to the limited number of notes that can be played on an antara, early musicians' most likely worked in groups, coordinating the timing and pitch of their instruments to extend the range of sounds produced.
[2] Other pottery images show two antara players facing each other while dancing. [3] Each player holds a set of pipes so that both sets are connected to the other set by a string, as if to suggest that those two antaras should be played together. [4] Even to this day, descendants of the Incas, the Quechua people of Peru and Bolivia, prefer to play matched antaras bound together.
For the sake of the logic and coherence of this paragraph, Sentence 4 should be placed:
E.where it is now.
F. before Sentence 1.
G. after Sentence 1.
H. after Sentence 2.
E.where it is now.
Unfortunately, the music of the Incas can
probably never be exactly re-creating.
A. NO CHANGE
B. re-created exactly.
C. exact re-created.
D. re-created exact.
B. re-created exactly.
Unfortunately, the music of the Incas can probably never be exactly re-creating. Yet one can hear in the music of their descendants, beautiful
variations on a musical sound that has survived for many centuries.
A. NO CHANGE
B. hear, in the music of their descendants
C. hear in the music of their descendants;
D. hear in the music of their descendants
D. hear in the music of their descendants
What is the slope: 3x + 5y = 8
-3/5
A DVD player with a list price of $100 is marked down 30%. If John gets an employee discount of 20% off the sale price, how much does John pay for the DVD player ?
100(0.70) = 70 is the amount that would be paid if the DVD was marked down 30%, but there is another discount of 20%, so the price is going to be 80% of the marked-down price. The price will be 70(0.80) =
$56.
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?
divide 2,727 miles by 27 miles per gallon you will get = 101. Then, multiply the number of gallons by the cost per gallon: 101(4.04) = 408.04. This gives the cost of gas for this car to travel 2,727 typical miles.
$408.04
When x = 3 and y = 5, by how much does the value of 3x² - 2y exceed the value of 2x² - 3y ?
use x = 3 and y = 5 in the given expressions, 3x2 - 2y = 3(3)2 - 2(5) = 27 - 10 = 17 and 2x2 - 3y = 2(3)2 - 3(5) = 18 - 15 = 3. Then subtract 3 from 17 to get 14.
14
What is the value of x when
2x + 3 = 3x - 4 ?
add 4 to both sides of the equation: 2x + 3 + 4 = 3x – 4 + 4 This gives you: 2x + 7 = 3x Now you can subtract 2x from both sides of the equation: 7 = x
7
How many irrational numbers are there between 1 and 6 ?
INFINATLEY
Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?
Let S1 be sales in the first year.
S2 = S1 + 3 million
S3 = 2S2 = 38 million
S2 = 19 million
S1 = S2 - 3 million = 16 million.
16 million
What is the degree measure of the acute angle formed by the hands of a 12-hour clock that reads exactly 1 o'clock?
At exactly 1 o' clock , the minute hand is 12 and the hour hand is at 1.
In a clock the 360 degrees are divided by the 12 hours. So the angle between each number is 360/12 = 30 degrees
The angle formed by the hour hand at 1 and the minute hand at 12 is 30 degrees.
|30H - 11/2M|, where H = 1 and M = 0. Therefore, |30(1) - 11/2(0)| = 30 degrees.
30
What is the probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108} will be divisible by both 2 and 3 ?
Number of elements divisible by 2 and 3 / Total number of elements = 2/8 = 1/4.
Formula: P(A) = n(A) / n(S)
1/4
A circle has a circumference of 16π feet. What is the radius of the circle, in feet?
Circumference = 2πr, where r is the radius.
So, 2πr = 16π
Solving for r, we get:
r = 8 feet
Solve: 4x + 2(3x - 8) = -46
4x + 2(3x - 8) = -46
4x+(6x-16)=-46
10x-16=-46
10x=-30
x=-3
In the standard (x,y)coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are (-3,0) and (7,4) ?
Midpoint formula: ((x1+x2)/2, (y1+y2)/2)
Midpoint of (-3,0) and (7,4):
(2,2)
What is the difference between 1.8 and 1.08 (08 repeats)
1.8 - 1.08080808…
1.719 (19 repeats)
Factor: y = x² + 5x + 6
y = (x + 2)(x + 3)
Factor: y = x² - 6x - 40
The formula for Factor is: y = (x - 10)(x + 4)
Factor: y = x² - 25
(x + 5)(x - 5)
Simplify: (5x - 8)(4x + 5)
20x² - 7x - 40
If f(x) = 3x² - 4x what is f(2)
4
If f(x) = 3x + 2 and g(x) = x - 5 what is f(g(x))
3x - 13
Put the following in standard form: 5.24 x 10⁵
524,000
Put the following in scientific notation: 3,400,000
3.4 x 10⁶
What is the slope of a line perpendicular to: 4x - 3y = 7
-3/4
What is the slope of a line parallel to
4x - 3y = 7
4/3
Note
Flashcard