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New Zealand
What is a scatter plot?
Statistics Jan 22, 2025
Beth decided to first subtract 1 from both numbers when she was calculating \( 23000-4977 \). a. Write down the new problem and solve it. Explain why Beth would use this method.
Arithmetic Jan 22, 2025
Question 1 A Rhombus has coordinates \( \mathrm{A}(-3,1), \mathrm{B}(1,3), \mathrm{C}(3,7), \mathrm{D}(-1,5) \). (i) Show that the diagonals of this rhombus are perpendicular (ii) Find the equation of the longest diagonal (iii) Using the information from (ii) above, find the coordinates of the point of intersection of the diagonals Hint: Plot the points on a set of axis To complete (i)-(iii), you need to complete the following steps - Find the gradient of each diagonal and show that they are perpendicular. - Find the length of each of the diagonals - Identify the longest diagonal and find its equation - Give the coordinates of the vertices of the rhombus
Geometry Jan 22, 2025
7. If \( x=-1-i \sqrt{3} \) is one root of the equation \( x^{2}+2 x+p=0 \) where \( p \) is a real number, find the value of \( p \) and the other root of the equation.
Algebra Jan 21, 2025
2. The points \( A(-2,3), B(1,8), C(6,11) \) and \( D(3,6) \) are the vertices of a quadrilateral. a. Find the gradients of \( A B \) and \( D C \). What does this tell you about the lines \( A B \) and \( D C \) ? b. Find the equation of the diagonal joining \( B \) to \( D \). c. The diagonal \( A C \) has the equation \( y=x+5 \). Find the point of intersection of the two diagonals \( A C \) and \( B D \). d. Find the midpoint of \( A C \) and compare this point with the point of intersection of the diagonals \( A C \) and \( B D \).
Geometry Jan 21, 2025
d. Find the midpoint of \( A C \) and compare this point with the point of intersection of the diagonals \( A C \) and \( B D \).
Geometry Jan 21, 2025
c. The diagonal \( A C \) has the equation \( y=x+5 \). Find the point of intersection of the two diagonals \( A C \) and \( B D \).
Geometry Jan 21, 2025
2. The points \( A(2,3), B(1,8), C(6,11) \) and \( D(3,6) \) are the vertices of a quadrilateral. a. Find the gradients of \( A B \) and \( D C \). What does this tell you about the lines \( A B \) and \( D C \) ? b. Find the equation of the diagonal joining \( B \) to \( D \). c. The diagonal \( A C \) has the equation \( y=x+5 \). Find the point of intersection of the two diagonals \( A C \) and \( B D \). d. Find the midpoint of \( A C \) and compare this point with the point of intersection of the diagonals \( A C \) and \( B D \).
Geometry Jan 21, 2025
iven that \( 3^{2 x+3} \times 9^{x}=3^{4-3 y} \), find an expression for \( y \) in terms of \( x \).
Algebra Jan 21, 2025
The points \( \mathrm{A}(5,4) \) and \( \mathrm{B}(9,-2) \) lie on the blue line, labelled F , shown in the diagram above. Find an equation of the line \( F \).
Geometry Jan 21, 2025
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