Algebra
What is the value of j in the equation shown?
j/2 + 7 = 12
j= 10
j/2 + 7 = 12
-7 -7
j/2 = 5
x2 x2
j = 10
f(x) = 100 - x^2
What is the maxi value of the given function?
100
Mia wants to exchange US dollars for Euros before traveling to France. Her bank offers her an exchange rate of 1 US dollar To 0.84 Euros. Approximately how many US dollars does Mia need to exchange if she wishes to receive 350 Euros for her bank?
Mia needs to exchange approximately 417 US dollars to receive 350 Euros from her bank.
The following text is from William Wordsworth's poem "I Wandered Lonely as a Cloud" (1807). In the poem, the speaker states that recalling the daffodils later, when he is alone, makes his heart fill with pleasure, writing, ______
Which quotation from the poem "I Wandered Lonely as a Cloud" most effectively illustrates the claim?
A. "They flash upon that inward eye / Which is the bliss of solitude;"
B. "Ten thousand saw I at a glance; / Tossing their heads in sprightly dance."
C. "Continuous as the stars that shine / And twinkle on the milky way,"
D. "And then my heart with pleasure fills, / And dances with the daffodils."
D. "And then my heart with pleasure fills, / And dances with the daffodils."
The line that covers both parts states the pleasure and keeps the flowers in view: "And then my heart with pleasure fills, / And dances with the daffodils." "My heart with pleasure fills" is the exact feeling the claim names, and "dances with the daffodils" ties it to them.
The beekeeper Russel, who tends a dozen hives on a warehouse roof, describes his approach as deliberately _______: he sets out the wooden boxes, adds a strip of shade, looks in on the colony only now and then, and otherwise lets the bees organize the work themselves.
Which choice completes the text with the most logical and precise word?
A. Intensive
B. Minimal
C. Casual
D. Profitable
B. Minimal
The second sentence hands you the definition. Russel "looks in on the colony only now and then" and "otherwise lets the bees organize the work themselves." That is an approach in which he does as little as the hives allow, and "minimal" is the word for as little as possible. Read the blank off that cue and you are done.
Which of the following ordered pairs (x,y) satisfies the system of inequalities?
y< 3x + 4
y< 5x +2
(3, -4)
If 4/m = 9, what is the value of (m/4)^-1?
9
A tomato plant grows 10 centimeters in 3 days. To the nearest tenth of a centimeter, how many centimeters will the plant grow in 7 days?
23.3 cm
7/1 x 10/3 = 23.333
The following text is from a short story.
The bell over the shop door had not rung in three days, and Priya had taken to speaking with the clocks. She wound them each morning out of habit, though almost no one came to buy them now that the mall had opened its bright corridor across the river. This morning, as she lifted the walnut mantel clock her father had built, its key resisted, then gave, and the small brass movement began to tick against her palm. Priya laughed—a short, surprised sound—and set it down carefully, as if it might startle. She did not hear the customer step in behind her, did not turn when he cleared his throat. She was watching the second hand sweep, her thumb still warm where the case had rested, thinking that the shop was not yet as silent as she had feared.
According to the text, what is true about Priya?
A. She is eager to greet the customer who has just entered the shop.
B. She takes unexpected comfort in a small sign that the shop still has life in it.
C. She has resolved to close the failing shop for good.
D. She intends to sell her father's clock to raise money against the new mall.
B. She takes unexpected comfort in a small sign that the shop still has life in it.
The paragraph plants a series of small, warm signals and lets them add up, and their sum is that Priya “takes unexpected comfort in a small sign that the shop still has life in it.” The question asks what the text establishes, so you gather what it shows. The shop has gone quiet “the bell over the shop door had not rung in three days” and yet when the old clock’s movement “began to tick against her palm”, Priya “laughed—a short, surprised sound.” Handling it “as if it might startle”, and closed on the thought “that the shop was not yet as silent as she had feared.” A surprised laugh and that closing line are relief, not indifference, so B is what the whole paragraph builds toward.
The moment I stepped off the train, I was struck by how efficiently everything worked. The station staff, luggage handlers, and even the loudspeakers calling out departure times all seemed so precisely synchronized that there was no need for anyone to hesitate or ask for help. It was as though the whole place ran on invisible rails of logic.
As used in the text, what does the word "synchronized" most nearly mean?
A. Unified
B. Controlled
C. Predicted
D. Explained
A. Unified
The word describes how “the station staff, luggage handlers, and even the loudspeakers” behaved together. “So precisely synchronized that there was no need for anyone to hesitate.” That's coordination in the present, which is why “unified” captures it. (many parts acting as one)
If 2+2 (8347 - 4783) = -2j, then what is the value of -j?
3565 = -j
2+2 (8347 - 4783) = -2j
2 2
= 1 + (3564) = -j
3565 = -j
(x+9)^3=−1
(x+9)^2=y
Which ordered pair (x, y) is a solution to the given system of equations?
(-10, 1)
Jackson is conducting a study about the effects of toxins in the water on the hormones of fish. Jackson surveys 350 male fish in a river and finds that 150 of the male fish have egg cells growing inside them. According to Jackson’s survey, what is the ratio of male fish with egg cells to male fish without egg cells in the river?
3 : 4
350 - 150 = 200 —> 150 : 200 —> 3 : 4
Text 1
Photo essays are increasingly popular in news outlets, but they should not be classified as journalism. By definition, journalism conveys information through language alone; photo essays communicate through images and use language only sparingly, in captions and short blurbs. Readers experience a photo essay as a sequence of pictures rather than as written reporting, which makes the form closer to gallery art than to journalism. In this view, the core of journalism is extended prose that explains events and evidence, so photo essays fall outside that category.
Text 2
Photo essays present their reporting through both language and images. Without captions, sequencing notes, and short text blocks, readers would not know who is pictured, what happened, or why it matters. The account emerges from the interaction of text and image. Moreover, acclaimed photo essays in major newspapers include writing that meets the standards of careful reporting and clear style. Therefore, photo essays qualify as journalistic work.
Based on the texts, how would the author of Text 2 most likely respond to the overall argument presented in Text 1?
A. By arguing that journalism is not confined to prose alone and that photo essays, which use captions and short text to convey essential facts, satisfy accepted journalistic standards.
B. By acknowledging that Text 1 correctly identifies a universal weakness in photo essays, namely that they lack sufficient language to report facts and therefore fail to meet journalistic standards.
C. By suggesting that some photo essays are harder to follow than Text 1 admits, which complicates public reception, but leaves them better treated as a distinct visual form, not as journalism.
D. By observing that Text 1 already treats photo essays as a news form when it notes their popularity in news outlets, so its refusal to call them journalism contradicts a premise it has itself accepted.
A. By arguing that journalism is not confined to prose alone and that photo essays, which use captions and short text to convey essential facts, satisfy accepted journalistic standards.
Text 2's whole reply is aimed at the premise Text 1 leans on. Text 1 defines the field narrowly “journalism conveys information through language alone” and rules photo essays out for using “language only sparingly.” Text 2 rejects that definition on two fronts, and the choice you picked captures both. First, it denies that journalism is confined to prose. The account “emerges from the interaction of text and image,” and without “captions, sequencing notes, and short text blocks” readers “would not know who is pictured, what happened, or why it matters.” Second, it argues the writing already clears the bar. “acclaimed photo essays... include writing that meets the standards of careful reporting and clear style.” Text 2 then draws the conclusion this choice states — photo essays “qualify as journalistic work.”
Climate activist Daisy Flores asserts that although immediate results are unlikely, she _______ that community-driven projects are vital for addressing local environmental challenges. Her efforts focus on empowering neighborhoods to adopt sustainable practices and reduce their carbon footprint.
Which choice completes the text with the most logical and precise word or phrase?
A. Anticipates
B. Rejects
C. Observes
D. Withholds
A. Anticipates
The blank needs a forward verb, because Flores affirms the projects "are vital" even though "immediate results are unlikely." "Anticipates" fits since she expects a payoff that has not yet arrived.
2y + 16 = 10x
4x - Ly = 8 - x
In the system of equations, L is a constant. For what value of L does the system of linear equations have infinity many solutions?
2y + 16 = 10x —> 2y + 10x = -16 —> 10x - 2y = 16
4x - Ly = 8 - x —> 5x - Ly = 8
If L = 1, the two equations will represent the same line and the system will have infinitely many solutions.
An object, launched from a height of 0 feet, reaches a maximum height of 576 feet 6 seconds after launch. A quadratic function can be used to model the height, in feet, of the object above the ground in terms of time, in seconds, after launch. Based on the model, what is the height, in feet, of the object, 2 seconds after launch?
320
f(x) = a(x − h)^2 + k
f(x) = a(x − 6)^2 + 576 Plug in (h, k) = (6, 576)
f(x) = −16(x − 6)^2 + 576 Plug in a = −16 then x = 2
f(2) = −16(16) + 576 Subtract and apply exponent: (2 − 6)^2 = (−4)^2
f(2) = −256 + 576 Multiply 16 with 16 to get:
f(2) = 320
The force that friction exerts on a car is proportional to its mass. Suppose friction exerts 6272 newtons (N) of force on 1600 kilogram (kg) car on a wet road. How many newtons of force would friction exert on a 2400, kg car under the same conditions?
f = 9408 N
1600kg/ 6272N = 2400kg/ f
1600kg x f / 1̶6̶0̶0̶ k̶g̶ = 2400 x 6272 k̶g̶ -> N / 1600 kg
Before the 1950s, cargo crossing the ocean was loaded piece by piece: barrels, sacks, and crates of every size were stacked into a ship’s hold by hand, a slow business that kept vessels tied up at the dock for days. The move to identical steel containers changed that. Because every container shared the same dimensions, a crane could lift one off a truck and drop it straight into a ship’s slot without anyone unpacking its contents, and the same sealed box could later be hoisted onto a railcar. Ports that once needed large crews laboring for days could now turn a ship around in hours. Shippers found that the cost of moving goods fell so steeply that it often became cheaper to make a product far from where it would finally be sold. It follows that the spread of the standard container ______
Which choice most logically completes the text?
A. Guaranteed that a product would cost the same amount no matter where in the world it was manufactured. erasing every price difference between one country’s factories and another’s.
B. Increased the number of dockworkers a port needed to load and unload each ship.
C. Made the distance between where a good is made and where it is sold a smaller factor in deciding where to produce it.
D. Mattered mainly because steel boxes proved cheaper to build than the wooden crates they replaced.
C. Made the distance between where a good is made and where it is sold a smaller factor in deciding where to produce it.
Standard containers let a crane move a sealed box “without anyone unpacking its contents,” which let ports “turn a ship around in hours,” which made “the cost of moving goods” fall “so steeply that it often became cheaper to make a product far from where it would finally be sold.” If distance to market stops driving up cost, then how far a factory sits from its customers weighs less in deciding where to build it (which is just what your choice says).
In ecological studies of coral reef systems, scientists have long observed that reef biodiversity is closely linked to the presence of grazing herbivores such as parrotfish and surgeonfish. These species maintain algal populations in check, thereby allowing coral larvae to successfully settle and grow. In systems where herbivorous fish are removed—whether through overfishing or habitat degradation—algal overgrowth can lead to phase shifts in which coral-dominated ecosystems are replaced by algal-dominated ones. This transition has been associated with significant losses in biodiversity and is notoriously difficult to reverse once established. Recent research has focused on whether targeted interventions, such as the reintroduction of herbivorous fish species or artificial reef construction, can restore coral dominance, but results remain inconsistent due to variations in local nutrient levels, water temperature, and human activity.
Which choice best describes the function of the underlined sentence in the passage as a whole?
A. It presents the ecological consequence of removing a key functional group from reef ecosystems, thus establishing the urgency behind the restoration efforts discussed later in the passage.
B. It introduces an exception to the typical relationship between herbivorous fish and coral reefs in order to suggest that other factors may play a larger role in reef decline.
C. It defines a common feature of coral ecosystems that remains stable across environmental conditions, thereby framing the need for future research mentioned later in the text.
D. It summarizes the long-term goal of coral reef studies by identifying a desired state of ecosystem balance that is expanded upon in the remainder of the paragraph.
A. It presents the ecological consequence of removing a key functional group from reef ecosystems, thus establishing the urgency behind the restoration efforts discussed later in the passage.
The true function you're after is to present the ecological consequence of losing the grazers and so set up the restoration efforts later. Read the sentence against its lead-in (herbivores “maintain algal populations in check”) and the underlined line is the mirror image: remove them and “algal overgrowth” drives a “phase shift.” That confirms the relationship rather than excepting it. And notice the payoff downstream: the passage turns to whether “targeted interventions.. can restore coral dominance,” which only makes sense if the underlined sentence has just shown you the damage worth restoring.
K= 39 - 7h
The temperature, K, in degrees Celsius, as measured by a weather balloon at an altitude of h kilometers from the ground is given by the equation. What is the best interpretation of 39 as shown in the given equation?
The temperature on The ground is 39 degrees Celsius.
K= -7h + 39
T acts as T-intercept (29) since the slope of T with respect to h is -8. The value of T is 39 when h is 0. The temperature is recorded by the balloon at the ground is 39 degrees Celsius.
The functions f and g are defined by f(x)=(3x+k)/2 and g(x)=2x−4, where k is a constant. If f(g(x))=3x for all values of x, what is the value of k?
k= 12
f(g(x)) means you substitute the whole expression g(x) into every x of f. Two expressions that are equal for all xmust match term by term, the coefficient of x and the constant both agreeing, so after composing you set the matching parts equal.
A model estimates that at the end of each year from 2017 to 2023, the number of rats in a population was 60% less than the number of rats in the population at the end of the previous year. The model estimates that at the end of 2018, there were 7,000 rats in the population. Which of the following equations represents this model, where n is the estimated number of rats in the population t years after the end of 2017 and t≤6?
Example: n=100(0.1)^t
B. n=17,500(0.4)^t
Notice 17,500>7,000>2,800 because the population is falling, earlier years hold more rats, so the starting coefficient should be larger than the 2018 value, not smaller. In a decreasing model the earliest year is the largest, so a starting coefficient smaller than a later count is a red flag. (To step backward in time, divide by the base rather than multiplying)
Ecologists once assumed that how quickly a coral reef recovers after a bleaching event depends mainly on how many adult corals survive nearby, since those survivors release the larvae that resettle the damaged patches. A recent survey complicated that picture. On reefs where plant-eating fish were abundant, bleached patches were recolonized quickly even when few adult corals remained, because the fish kept fast-growing seaweed from smothering the bare rock on which coral larvae must land and attach. On otherwise similar reefs where such fish were scarce, recovery stalled even though healthy adult corals were plentiful nearby. Taken together, these findings suggest that a reef's capacity to recover from bleaching depends ______
Which choice most logically completes the text?
A. More on how fast seaweed happens to grow on a given reef than on anything the reef's plant-eating fish actually do.
B. Primarily on the number of healthy adult corals surviving nearby that are able to release larvae into the damaged patches.
C. On the reef managers' ability to prevent bleaching events from occurring on vulnerable reefs in the first place.
D. Not only on the supply of coral larvae but also on whether plant-eating fish keep the bare rock clear enough for larvae to settle.
D. Not only on the supply of coral larvae but also on whether plant-eating fish keep the bare rock clear enough for larvae to settle.
The emphasis has to match the text. When a choice promotes the obstacle over the agent that removes it, you are looking at a wrong-emphasis trap, not the passage's conclusion.
The following text is from William Wordsworth’s 1807 poem "Ode: Intimations of Immortality from Recollections of Early Childhood."
There was a time when meadow, grove, and stream,
The earth, and every common sight,
To me did seem
Apparelled in celestial light,
The glory and the freshness of a dream.
It is not now as it hath [has] been of yore;—
Turn wheresoe'er I may,
By night or day,
The things which I have seen I now can see no more.
Which choice best states the main purpose of the text?
A. To lamest the loss of youthful wonder and imagination
B. To describe how memory allows beauty to be preserved
C. To praise the natural world for its timeless beauty
D. To suggest that childhood joy can return later in life
A. To lamest the loss of youthful wonder and imagination
The poem opens in the past tense and closes on a loss, and this option captures that arc. If you chose it, you heard the difference between how the world once looked and how it looks now, and you read the speaker's tone as mourning rather than celebration.