In which quadrant of the coordinate plane do the following lines intersect: y = 3x + 2 y = -2x + 7
To find the quadrant in which the lines intersect, first solve for the point of intersection. Set the two equations equal to each other 3x + 2 = -2x + 7 Add 2x to both sides 5x + 2 = 7 Subtract 2 from both sides 5x = 5 Divide both sides by 5 x = 1 Substitute x = 1 into one of the original equations to solve for y y = 3(1) + 2 y = 3 + 2 y = 5 The solution for this system of equations is the point (1,5). Since this point has both a positive x value and a positive y value, it lies in the first quadrant. Answer: The lines intersect in the first quadrant of the coordinate plane.
What is the difference between oxygen affinity in fetal hemoglobin and adult hemoglobin? How is this difference important to fetal development?
Fetal hemoglobin have a higher oxygen affinity than adult hemoglobin. Hemoglobin are the oxygen transport proteins that ensure that oxygen reaches every part of the body. During fetal development, the fetus receives its oxygen from its mother's bloodstream. In order for the oxygen to move to the fetus from the mother, the fetal hemoglobin must have a stronger affinity, or "pull," on the oxygen than the hemoglobin in the mother. This difference in oxygen affinity in fetal and adult hemoglobin ensures that fetuses receive the oxygen that they require for survival and growth during fetal development.
Sally and Harrison split a bag of candy. Harrison has 5 more pieces of candy than Sally. Sally has 1/2 as many pieces of candy as Harrison. How many pieces of candy were in the bag?
First, establish two variables: S = # of pieces of candy that Sally has H = # of pieces of candy that Harrison has Set up two equations based on the information provided: H = S + 5 Information: Harrison has 5 more pieces of candy than Sally. S = (1/2)H Information: Sally has 1/2 as much candy as Harrison. Solve the equations for the variables H and S using substitution. Substitute H = S +5 into S = (1/2)H S = (1/2)(S + 5) Distribute S = (1/2)S + 5/2 Subtract (1/2)S from both sides of the equation (1/2)S = 5/2 Multiply both sides by 2 S = 5 Substitute S = 5 into H = S + 5 H = 5 + 5 H = 10 To find the total number of pieces of candy in the bag, add the number of pieces of candy that both Harrison and Sally have. Total candy = S + H Total candy = 5 + 10 = 15 There were 15 pieces of candy in the bag.