sat-dog

A circle in the xy-plane has a diameter with endpoints $\left(2,4\right)$ and $\left(2,14\right)$. An equation of this circle is ${\left(x-2\right)}^2+{\left(y-9\right)}^2=r^2$, where $r$ is a positive constant. What is the value of $r$?

Which choice best describes the function of the underlined sentence in the text as a whole?

$57x^2+(57b+a)x+ab=0$

In the given equation, $a$ and $b$ are positive constants. The product of the solutions to the given equation is $kab$, where $k$ is a constant. What is the value of $k$?

Which choice most logically completes the text?

$-x^2+bx-676=0$

In the given equation, $b$ is a positive integer. The equation has no real solution. What is the greatest possible value of $b$?

Function $f$ is defined by $f\left(x\right)=-a^x+b$, where $a$ and $b$ are constants. In the xy-plane, the graph of $y=f\left(x\right)-15$ has a y-intercept at $\left(0,-\frac{99}{7}\right)$. The product of $a$ and $b$ is $\frac{65}{7}$. What is the value of $a$?

In the xy-plane, line k intersects the y-axis at the point and passes through the point . If the point lies on line k, what is the value of w ?

$y\le x+7$

$y\ge -2x-1$

Which point $\left(x,y\right)$ is a solution to the given system of inequalities in the xy-plane?

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

Which choice best states the main idea of the text?

Which choice most effectively uses data from the table to complete the statement?

Which choice best states the main idea of the text?

Which finding, if true, would most strongly support the team’s conclusion?

Which choice most logically completes the text?

$4x-6y=10y+2$

$ty=\frac{1}{2}+2x$

In the given system of equations, $t$ is a constant. If the system has no solution, what is the value of $t$?

The dot plots represent the distributions of values in data sets A and B.

Which of the following statements must be true?

1. The median of data set A is equal to the median of data set B.
2. The standard deviation of data set A is equal to the standard deviation of data set B.

$f\left(x\right)=\left(x-14\right)\left(x+19\right)$

The function $f$ is defined by the given equation. For what value of $x$ does $f\left(x\right)$ reach its minimum?

If $3x^2-18x-15=0$, what is the value of $x^2-6x$?

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

Which choice completes the text with the most logical transition?

A graphic designer is creating a logo for a company. The logo is shown in the figure above. The logo is in the shape of a trapezoid and consists of three congruent equilateral triangles. If the perimeter of the logo is 20 centimeters, what is the combined area of the shaded regions, in square centimeters, of the logo?

Circle A in the xy-plane has the equation ${\left(x+5\right)}^2+{\left(y-5\right)}^2=4$. Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is ${\left(x+5\right)}^2+{\left(y-5\right)}^2=k$, where $k$ is a constant. What is the value of $k$?

$F\left(x\right)=\frac{9}{5}\left(x-273.15\right)+32$

The function $F$ gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of $x$ kelvins. If a temperature increased by $9.10$ kelvins, by how much did the temperature increase, in degrees Fahrenheit?

Based on the texts, how would Cáceres and colleagues (Text 2) most likely describe the view of the theorists presented in Text 1?

What is the diameter of the circle in the xy-plane with equation ${\left(x-5\right)}^2+{\left(y-3\right)}^2=16$?