Solve the following equation by balancing on both sides: b) 6n+7= 3n+25

Solve: $fraction numerator 7 x plus 1 over denominator 4 end fraction equals 2 x minus 1$

$table attributes columnspacing 1em end attributes row cell left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 40 end cell row cell y equals negative 2 x plus 4 end cell end table$
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 ?