Tüm alıştırma soruları

A circle with center $O$ has a radius of 15. Chord $AB$ of the circle has a length of 18, and chord $CD$ is parallel to $AB$ and has a length of 24. If the two chords are on opposite sides of the center $O$, what is the distance between chord $AB$ and chord $CD$?

A surveyor stands at point $A$ on one bank of a straight river, directly across from a tree $T$ on the opposite bank. She walks along the riverbank to point $B$ such that the line segment $AB$ is perpendicular to $AT$. The distance from $A$ to $B$ is $7$ meters. She then continues walking in the same direction along the riverbank for another $25$ meters to point $C$. If the straight-line distance from point $C$ to the tree $T$ is $40$ meters, what is the straight-line distance, in meters, from point $B$ to the tree $T$?

The equation $x^2 + y^2 - 14x - 8y + 40 = 0$ defines a circle in the $xy$-plane. If the center of the circle has coordinates $(h, k)$, what is the value of $h + k$?

In the $xy$-plane, the graph of the equation $x^2 + y^2 + 8x - 10y = w$, where $w$ is a constant, is a circle. If the circle is tangent to the $x$-axis, what is the value of $w$?

In the $xy$-plane, right triangle $ABC$ has vertices at $A(0, 0)$, $B(k, 0)$, and $C(0, 6)$, where $k$ is a positive constant. The right angle of the triangle is at vertex $A$. If the length of the altitude from $A$ to side $BC$ is $4.8$, what is the value of $k$?

While preparing a presentation on environmental biotechnology, a student took the following notes:
* Phytoremediation is a clean-up method that uses living plants to remove, transfer, or stabilize environmental contaminants in soil and water.
* It serves as an eco-friendly alternative to harsh chemical treatments or excavation.
* Certain plants, such as sunflowers and willow trees, are highly effective at absorbing heavy metals.
* The term was first proposed in 1991 by plant biologist Ilya Raskin.

The student wants to introduce phytoremediation to an audience unfamiliar with the concept. Which choice most effectively uses information from the given notes to accomplish this goal?

While preparing a presentation on the history of written language in North America, a student takes the following notes:

* In 1821, Sequoyah completed the Cherokee syllabary, a writing system representing the syllables of the Cherokee language.
* Prior to Sequoyah's invention, the Cherokee language was purely oral, and literacy in English among Cherokee people was very low.
* By 1830, Cherokee literacy rates in their own language reached over 90 percent.
* In 1828, the Cherokee Nation established a bilingual newspaper, the *Cherokee Phoenix*, which utilized Sequoyah's syllabary.

The student wants to support the claim that Sequoyah’s writing system led to a rapid and dramatic increase in literacy among Cherokee people. Which choice most effectively uses information from the given notes to support this claim?

If $\cos(\theta) = \frac{7}{25}$ and $0 < \theta < \frac{\pi}{2}$, what is the value of $\sin\left(\frac{\pi}{2} - \theta\right)$?

In medieval Europe, the transition from a two-field crop rotation to a three-field system is credited with increasing agricultural yields. Under the three-field system, one field was planted with winter wheat, another with spring legumes, and the third was left fallow. Legumes host nitrogen-fixing bacteria in their root nodules, which replenish soil nitrogen levels depleted by wheat cultivation. Historically, wheat crops grown in nitrogen-rich soil exhibit significantly higher grain mass and health than those grown in nutrient-poor soil. Therefore, medieval farms transitioning to the three-field rotation pattern likely experienced

Which choice most logically completes the text?

In planetary science, the discovery of liquid water oceans beneath the icy shells of moons like Europa and Enceladus has reshaped our understanding of habitability. Previously, astrobiologists assumed that life could only exist in a star's circumstellar habitable zone, where surface temperatures allow for liquid water. However, the presence of sub-surface oceans sustained by tidal heating suggests that habitable environments may be far more _______ than once believed, expanding the search for extraterrestrial life beyond traditional orbital boundaries.

Which choice completes the text with the most logical and precise word or phrase?

Bioluminescent fungi, such as *Panellus stipticus*, emit a steady green glow through a chemical reaction involving the compound luciferin. For decades, scientists hypothesized that this light served no ecological purpose, representing merely an accidental byproduct of fungal metabolism. However, recent studies have revealed that the glow specifically attracts nocturnal insects, which then inadvertently transport the fungus's spores to new locations. This spore dispersal mechanism is crucial for the fungus's reproduction and survival in dense forest environments, demonstrating that bioluminescence is an evolutionary adaptation rather than a purposeless metabolic quirk.

Which choice best states the main idea of the text?

Complete the text with the most logical and precise word.

Historically, researchers assumed that the transition from foraging to farming in the Fertile Crescent occurred rapidly due to a sudden drying period known as the Younger Dryas. However, recent botanical analyses at Tell Abu Hureyra show that domesticated rye was cultivated alongside wild grains for over a millennium, indicating a prolonged phase of co-management. Archaeologist Sarah Carter argues that early foragers did not fully abandon wild food sources because wild plants provided a crucial buffer against crop failures during years of unpredictable rainfall. Given that domesticated rye is far more sensitive to drought than its wild counterparts, which choice most logically completes the text?

Foraminifera shell boron-to-calcium ($B/Ca$) ratios are widely used to reconstruct ancient ocean carbonate ion concentrations ($[CO_3^{2-}]$). However, recent experiments show that boron incorporation is also influenced by dissolved inorganic carbon ($DIC$) levels, which affect calcification rates. When $[CO_3^{2-}]$ is constant, higher $DIC$ accelerates calcification and increases shell $B/Ca$, while lower $DIC$ suppresses calcification and decreases $B/Ca$. Thus, using $B/Ca$ ratios to estimate historical $[CO_3^{2-}]$ without adjusting for past $DIC$ variations could lead to errors because ______

Which choice most logically completes the text?

In a 2025 analysis of coprolites (fossilized feces) recovered from the Mylodon Cave in Patagonia, paleoclimatologist Dr. Clara Martinez and her team identified the preserved DNA of several plant species to reconstruct the diet of the extinct ground sloth *Mylodon darwinii*. While previous research suggested that *M. darwinii* fed exclusively on tough grasses, Martinez’s analysis revealed that the sloth's diet actually varied seasonally. Specifically, during the wet spring months, the sloth consumed a high proportion of *Empetrum rubrum* (dwarf shrubs), whereas its winter diet consisted almost entirely of *Stipa* grass species. Furthermore, the researchers noted that the coprolites contained significant traces of sediment, indicating that *M. darwinii* frequently ingested soil while feeding on low-growing vegetation.

Based on the text, which statement is true about the diet of *Mylodon darwinii*?

Which choice completes the text with the most logical and precise word or phrase?

If $\frac{2}{3}\left(3x - \frac{1}{2}\right) - \frac{3}{4}\left(2x - \frac{1}{3}\right) = \frac{1}{6}(x + 4) - \frac{5}{12}$, what is the value of $12x - 5$?

The graph of the linear equation $y = 3x - 7$ contains the point $(k, 5)$. What is the value of $k$?

For all $x > 0$, the expression $\frac{\sqrt{x^7}}{\sqrt[5]{x^3}}$ is equivalent to $x^a$, where $a$ is a constant. What is the value of $a$?

The following passage is adapted from a cognitive neuroscience article. What punctuation mark should be written in the blank to grammatically connect the preceding independent clause to the explanatory list that follows?