📐 geometry

1. **State the problem:** We have a right triangle CBA with a right angle at B. Side CB is 4.6 units, side CA (the hypotenuse) is 9 units, and we want to find angle $x^\circ$ at ve

1. The problem is to analyze a triangle where angle B is given as 90 degrees. 2. Knowing that angle B is 90 degrees means the triangle is a right triangle with angle B as the right

1. **Problem Statement:** Given a geometric figure with angles labeled Q, Z, R, B, E, and others, solve for the following: ক) Find $Z$ if $Q = 75^\circ$.

1. **State the problem:** Find the surface area of a hemisphere with a radius of 8 yards, rounded to the nearest tenth. 2. **Formula:** The surface area of a hemisphere includes th

1. **State the problem:** We need to find the equation of a circle centered at point $B(1,4)$ with radius $5$. 2. **Formula for a circle:** The equation of a circle with center $(h

1. **Stating the problem:** We are given a circle centered at point S with the equation $$x^2 + y^2 = 64$$. 2. **Formula and explanation:** The general equation of a circle centere

1. The problem is to describe the graph of a circle centered at the origin $(0,0)$ with radius $1$. 2. The formula for a circle centered at $(h,k)$ with radius $r$ is:

1. The problem states that the volume $V$ of a rectangular prism is given by the formula $$V = l \times w \times h$$ where $l$, $w$, and $h$ are the length, width, and height respe

1. The problem asks to graph the image of a triangle after applying a scale factor of $k=\frac{3}{4}$ to its vertices. 2. The formula for scaling a point $(x,y)$ by a factor $k$ ab

1. We are asked to find the volume of a rectangular prism (balk) with edge lengths 1.7 cm, 2 cm, and 3.4 cm. 2. The formula for the volume $V$ of a rectangular prism is:

1. **Stating the problem:** We are asked to find the lengths of segments RS and EC (part c), and then find the lengths of PQ, AF, and MT (part d) based on the given measurements.

1. **Problemstellung:** Gegeben ist eine Gerade $g$ mit der Gleichung $y = \frac{1}{2}x - 2$ und ein Parallelogramm $AB_nC_nD$ mit festem Vektor $\overrightarrow{B_nC_n} = \begin{p

1. The problem asks what Brandon needs to calculate to find the amount of carpet to cover his floor. 2. The floor measures 6 feet by 5 feet, so it is a rectangle.

1. **State the problem:** Determine if each set of three side lengths can form a right triangle. 2. **Formula and rule:** Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$

1. The problem asks which transformations create trapezoid W'X'Y'Z' congruent to trapezoid WXYZ. 2. The given options include combinations of translations, rotations, and reflectio

1. **State the problem:** Jeff lives 12 miles east of Stan and 16 miles north of Wei. We need to find the shortest distance between Stan and Wei. 2. **Identify the relationship:**

1. **State the problem:** We need to find the shortest length of a hose extending from the southwest corner to the northeast corner of a rectangular swimming pool with length 48 fe

1. **Problem statement:** Find the measure of angle ABC in triangle ABC with points A(-2,4), B(3,7), and C(3,4) using trigonometry. 2. **Recall:** Angle ABC is the angle at point B

1. **State the problem:** Find the volume of the solid figure composed of two connected rectangular prisms. 2. **Identify the dimensions:**

1. **State the problem:** We need to find the total area of Raji's garden, which is an L-shaped polygon with given side lengths. 2. **Understand the shape:** The L-shape can be div

1. **State the problem:** We need to find the image of trapezoid DEFG after reflecting it over the vertical line $x = -3$. 2. **Reflection formula:** When reflecting a point $(x,y)