Tüm alıştırma soruları

An acute angle $\theta$ satisfies the equation $\sin(\theta) = \frac{24}{25}$. What is the value of $\frac{1}{\cos(\theta)} - \tan(\theta)$?

In the field of astrobiology, scientists study the light passing through the atmospheres of distant exoplanets to search for signs of life. The detection of key chemical biosignatures, such as seasonal variations in methane concentrations combined with high levels of oxygen, _______ the presence of active biological processes rather than abiotic chemical reactions.

Which choice completes the text so that it conforms to the conventions of Standard English?

In the $xy$-plane, a circle with center $(4, 9)$ and radius $5$ is defined by the equation $(x - h)^2 + (y - 9)^2 = 25$, where $h$ is a positive constant. What is the value of $h$?

Astronomers analyzing the atmospheres of exoplanets have found that some hot Jupiters exhibit weather patterns far more extreme than those seen in our solar system. _______, on the exoplanet HD 189733b, winds can reach speeds of over 5,000 miles per hour, carrying clouds of silicate particles that cause it to rain liquid glass.

Which choice completes the passage with the most logical transition?

A dermatologist at a medical clinic wants to estimate the proportion of residents in a city who experience seasonal dry skin. The dermatologist surveys a random sample of 150 patients who visited the clinic in December and finds that 90 of them (60%) reported experiencing seasonal dry skin. Which of the following is the most appropriate conclusion based on this study?

For an acute angle $\theta$, the expression $\frac{\sin(\theta) + \cos(\theta)}{\sec(\theta) + \csc(\theta)}$ is equal to $k$. If $\tan(\theta) = 3$, what is the value of $k$?

If $\sin(2x + 10)^\circ = \cos(3x - 5)^\circ$, where the measures of both angles are in degrees and are acute, what is the value of $x$?

Zooarchaeologists studying ancient pastoral societies often analyze stable isotope ratios in animal teeth to reconstruct seasonal migration patterns. ______ by measuring the strontium isotopes in sheep molars, researchers can determine whether the herds were grazed in local valleys or driven to distant highland pastures during the summer months.

Which choice completes the passage with the most logical transition?

In the diagram shown, point $D$ lies on side $AB$ of triangle $ABC$, and point $E$ lies on side $AC$. The lengths of the segments are $AB = 20$, $AC = 16$, $AD = 8$, and $AE = 10$. If the area of quadrilateral $BCED$ is $54$, what is the area of triangle $ADE$?

(Note: Figure not drawn to scale.)

The quadratic function $f$ is defined by $f(x) = (x - 4)(x - 10)$. In the $xy$-plane, the graph of function $g$ is obtained by translating the graph of $f$ horizontally so that the vertex of the graph of $g$ lies on the $y$-axis. Which of the following equations defines the function $g$?

While preparing a presentation on Anglo-Saxon history, a student took the following notes:
- The Sutton Hoo helmet is an Anglo-Saxon artifact discovered in Suffolk, England, in 1939.
- It was found in a ship-grave believed to be the burial site of King Rædwald of East Anglia.
- The helmet was reconstructed from hundreds of corroded iron fragments.
- The reconstruction was carried out by conservators at the British Museum.
- Its design features a decorative face mask that resembles a flying dragon.

The student wants to emphasize the location where the helmet was discovered and the institution that reconstructed it. Which choice most effectively uses information from the given notes to accomplish this goal?

An educational organization wants to estimate the number of high school seniors in a school district who plan to major in a STEM field. A random sample of $320$ high school seniors in the district was surveyed, and $35\%$ of the surveyed students reported that they plan to major in a STEM field. The survey has an associated margin of error of $4\%$. There are $4,500$ high school seniors in the school district. Based on these results, what is the maximum estimated number of high school seniors in the district who plan to major in a STEM field?

A juice mixture is made by combining orange concentrate and water in a ratio of $2$ to $5$ by volume. To make a large batch of this mixture, a worker uses a total of $35$ liters of water. If the worker wants to dilute the mixture so that the new ratio of orange concentrate to water is $1$ to $4$ by volume, how many additional liters of water must be added?

In glaciology, cryophilic algae thrive on glacier surfaces during melting seasons. To protect themselves from intense ultraviolet radiation, these algae produce dark-colored pigments. However, these pigments also reduce the albedo—or reflectivity—of the ice surface, causing it to absorb more solar radiation. Researchers investigating the Greenland Ice Sheet observed that areas with high densities of cryophilic algae experienced melting rates that significantly exceeded predictions based solely on regional atmospheric temperatures. Since regional air temperatures remained stable, this discrepancy suggests that ______

Which choice most logically completes the text?

In the $xy$-plane, an angle $\theta$ is in standard position. The terminal ray of $\theta$ is rotated counterclockwise by $\frac{7\pi}{6}$ radians, and then rotated clockwise by $135^\circ$. If the terminal ray of the resulting angle lies on the line $y = -x$ in the fourth quadrant, and the original angle $\theta$ has a measure of $d$ degrees, where $0 \leq d < 360$, what is the value of $d$?

A consumer electronics reviewer is tracking the resale value of two different smartphone models. At the time of purchase ($t = 0$ years), Smartphone A and Smartphone B each have a retail value of $1,000$ dollars. The value of Smartphone A decreases by $10\%$ of its value from the previous year each year. The value of Smartphone B decreases by a constant amount of $100$ dollars each year. What is the difference, in dollars, between the values of the two smartphones $3$ years after they were purchased?

The equation of a circle in the $xy$-plane is $(x - 8)^2 + (y + 1)^2 = 81$. What are the coordinates of the center of the circle?

In the $xy$-plane, the graph of the polynomial function $g$, defined by $g(x) = 3(x - k)(x + 2)^2$, has a $y$-intercept at $(0, -24)$, where $k$ is a constant. What is the value of $k$?

In right triangle $DEF$, the measure of angle $F$ is $90^\circ$. If $\cos(D) = \frac{3}{5}$, what is the value of $\sin(E) - \tan(D)$?