Solve the following equation by balancing on both sides: a) 5m+9 = 4m + 23

$table attributes columnspacing 1em end attributes row cell left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 40 end cell row cell y equals negative 2 x plus 4 end cell end table$
Which of the following could be the x-coordinate of a solution to the system of equations above?

Note:
If we had to find the y-coordinate of the system of equations, then we put this value of x in the equation $y equals negative 2 x plus 4$ to get the value of y. Here, we got a quadratic equation of x, which did not have any term containing x, so it was easier to solve. If the quadratic equation was of the form $a x squared plus b c plus c equals 0$ , then we would use the quadratic formula $x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$ to solve the equation.

$table attributes columnspacing 1em end attributes row cell left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 40 end cell row cell y equals negative 2 x plus 4 end cell end table$
Which of the following could be the x-coordinate of a solution to the system of equations above?

Solve the equation and check your result 6(3m + 2) – 2(6m – 1) = 3(m – 8) – 6(7m – 6) +9m

Solve and check your answer: 3x – 2(2x – 5) = 2(x + 3) – 8

Solve: 16 = 4 + 3(x + 2)

The graph of the function f is shown in the xy-plane above, where y =f $left parenthesis x right parenthesis$ . Which of the following functions could define f ?

Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.

The graph of the function f is shown in the xy-plane above, where y =f $left parenthesis x right parenthesis$ . Which of the following functions could define f ?

Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.

At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t n = +2, how many additional tea bags are needed to make each additional cup of tea?

f(x) =2^x +1
The function f is defined by the equation above. Which of the following is the graph of y = - f(x)in the xy-plane?

$2000 minus 61 k equals 48$
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?

Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.

$2000 minus 61 k equals 48$
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?

The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y= d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?

Which of the following is equivalent to $9 to the power of 3 over 4 end exponent$ ?

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One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)

$8 x minus 2 x left parenthesis c plus 1 right parenthesis equals x$
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?

Note:
As the equation $8 x minus 2 x left parenthesis c plus 1 right parenthesis equals x$ is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x

$8 x minus 2 x left parenthesis c plus 1 right parenthesis equals x$
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.

The scatterplot above gives the tree diameter plotted against age for 26 trees of a single species. The growth factor of this species is closest to that of which of the following species of tree?