Questions in mathematics

Questions in mathematics

[Done] Solve the system of equations: \[ \begin{align} y &= 3x + 7 \\ y &= 5x - 7 \end{align} \]

[Done] How do you create an algebraic expression with a coefficient of 7 and a constant of 4?

[Done] If 0.00005893 is expressed in the form \(5.893 \times 10^n\), what is the value of \(n\)?

[Done] If \(\sin \theta = 0.57\), then what is \(\sin (\pi - \theta)\)?

[Done] How many bricks, each 3.75 in. wide × 8 in. long, are required to cover a patio 13 ft. 6 in. wide by 18 ft. 9 in. long? Step 1: First, find the total width and length of the patio in inches. Step 1a: Convert the portion of the width and length that is expressed in feet to inches. - Width: 13 ft = 13 × 12 = _ in - Length: 18 ft = 18 × 12 = _ in

[Done] The angles of a quadrilateral measure \(80^\circ\), \(100^\circ\), \(80^\circ\), \(100^\circ\) in this order. What kind of quadrilateral has this shape? How do you know?

[Done] There once was a farmer who, as part of his route to town, used a rickety old boat to cross a wide river. He took his dog and went to town one day to buy corn. However, not only did he buy some corn, but he also bought a goose that he intended to take home and use to start raising geese. (The farmer was no fool; he already had another goose.) He also knew, however, that his boat was not reliable. It could only handle himself (to row) and one of the other three things he had with him. He feared that if left alone, the dog would eat the corn. How could he get himself and everything else across the river?

[Done] A catering service offers 12 appetizers, 9 main courses, and 7 desserts. A banquet chairperson is to select 8 appetizers, 8 main courses, and 6 desserts for a banquet. In how many ways can this be done?

[Done] A park is shaped like a rectangle with a length of 5 miles and width \(w\). What is a simplified expression for the distance between opposite corners of the park?

[Done] Part 1: Commutative Property Which of the following equations is an example of the commutative property? A. \((3)(6+10) = 18 + 30\) B. \(18 + 30 = 30 + 18\) C. \((3)(6) + (3)(10) = 3(16)\) D. \(48 = 48\) Part 2: Equation of a Line Let the equation of a line be described by Equation A: \[10y - 5x = 40\] What are the y-intercept and slope of the line? A. The y-intercept is 40, and the slope is 10 B. The y-intercept is 10, and the slope is 40 C. The y-intercept is 40, and the slope is 2 D. The y-intercept is 4, and the slope is 0.5