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SAT Math : How to find f(x)

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Example Question #1121 : Algebra

Solve for .

$3r+5t=\frac{-4Q+5z}{2}$

Possible Answers:

$Q=\frac{6r+10t-5z}{-4}$

$Q=\frac{6r+10t-z}{-4}$

$Q=\frac{6r+10t+5z}{4}$

$Q=\frac{6r+10t+5z}{-4}$

Correct answer:

$Q=\frac{6r+10t-5z}{-4}$

Explanation:

$3r+5t=\frac{-4Q+5z}{2}$

Multiply by on each side

2(3r+5t)=-4Q+5z

Expand right side

6r+10t=-4Q+5z

Subtract on each side

-4Q=6r+10t-5z

Divide by on each side

$Q=\frac{6r+10t-5z}{-4}$

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Example Question #1122 : Algebra

If a rocket is shot from the ground, and it takes $5 \sec$ to reach a height of $500\:\text{m}$ . Determine the equation of its trajectory.

Possible Answers:

y=50x

y=-100x

y=100x

y=500x

y=10x

Correct answer:

y=100x

Explanation:

To figure out what the equation is, we need to use the point-slope form.

y-y_0=m(x-x_0) , where is the slope, and (x_0, y_0) is a point.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

In this example, y_2=500, y_1=0, x_2=5, x_1=0

$\text{Slope}=\frac{500-0}{5-0}=100$

y-0=100(x-0)

y=100x

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Example Question #1121 : Algebra

Screen shot 2016 02 18 at 1.42.15 pm

Determine the x-intercepts in the graph above.

Possible Answers:

Not enough information

Correct answer:

Explanation:

The x-intercepts are the points on the graph where the y=0 line touches or intersects the x axis. By looking at the graph, there are two points. One at x=2 , and then another one at x=3 . So there are two x intercepts.

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Example Question #1124 : Algebra

Stuff animals were a strange craze of the 90's. A Cat stuff animal with white paws sold for $6 in 1997. In 2015, the Cat will sell for $1015. What has been the approximate rate of growth for these stuff animal felines?

Possible Answers:

$16.8 \%$

$3.2 \%$

$13.29 \%$

$33 \%$

$168 \%$

Correct answer:

$33 \%$

Explanation:

Use the formula for exponential growth y = A*(1+r)^t where y is the current value, A is the initial value, r is the rate of growth, and t is time. Between 1997 and 2015, 18 years passed, so use t=18 . The stuffed animal was originally worth $6, so A=6 . It is now worth $1,015, so y=1015 .

Our equation is now:

$1015 = 6*(1+r)^{18}$ divide by 6:

$169.1\overline{6}=(1+r)^{18}$ take both sides to the power of $\frac{1}{18}=0.0\overline{5}$ :

$1.329 \approx 1+r$ subtract 1

0.329 = r

As a percent, r is about 33%.

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Example Question #1121 : Algebra

The population of a city will decrease by 15 percent every 50 years and the population starts at 120,000 people. Construct a function that describes this situation.

Possible Answers:

$P(t)=120,000(0.85)^{\frac{t}{50}}$

$P(t)=120,000(0.85)^{50t}$

P(t)=120,000(0.85)^t

$P(t)=120,000(0.15)^{\frac{t}{50}}$

$P(t)=120,000(0.80)^{\frac{t}{50}}$

Correct answer:

$P(t)=120,000(0.85)^{\frac{t}{50}}$

Explanation:

To construct a function that describes this situation first identify what is known.

Since this particular situation is talking about population decrease, the function will be an exponential decay.

Recall that an exponential decay function is in the form,

$P(t)=I(1-r)^{t}$

where,

$\\P(t)=\text{ Finial population} \\I=\text{ Initial population} \\r=\text{ Rate} \\t=\text{Time}$

Since the statements says that the population decreases every 50 years we can rewrite the general form to,

$P(t)=I(1-r)^{\frac{t}{50}}$

Now substituting in the known values, the function can be written.

$P(t)=120,000(0.85)^{\frac{t}{50}}$

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Example Question #1126 : Algebra

Screen shot 2016 02 18 at 2.50.12 pm

The above graph shows supply and demand for a particular Product. What is the equation for the demand of this product?

Possible Answers:

y=2x+50

y=-4x+50

y=4x+50

y=-2x+50

y=-4x

Correct answer:

y=-4x+50

Explanation:

We can determine the demand equation by using point slope form.

Point slope form is y-y_0=m(x-x_0) , where (x_0, y_0) , and is the slope, where $m=\frac{y_2-y_1}{x_2-x_1}$ .

Let y_2=50 , y_1=10 , x_2=0 , and x_1=10 .

$m=\frac{50-10}{0-10}=-4$

Now we have

y-y_0=-4(x-x_0)

Choose a point (0,50) ,

y-50=-4(x-0)

y=-4x+50

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Example Question #1127 : Algebra

Screen shot 2016 02 18 at 2.50.12 pm

If the equation of the demand line is y=-4x+50 , and the equation for supply is y=5x , determine the point where supply and demand is the same.

Possible Answers:

$x=\frac{5}{9}$

$x=\frac{500}{9}$

$x=\frac{14}{9}$

x=6

$x=\frac{50}{9}$

Correct answer:

$x=\frac{50}{9}$

Explanation:

To solve this, all we need to do is set the equations equal to each other.

-4x+50=5x

Now solve for

50=9x

$x=\frac{50}{9}$

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Example Question #1128 : Algebra

Amanda has 5000 ants in an ant farm and their population grows $20\%$ annually. How many ants will be in Amanda's ant farm in 6 years?

Possible Answers:

15000

14920

14930

14700

14900

Correct answer:

14930

Explanation:

This is an exponential growth problem, so let's recall the equation for exponential growth.

P(t)=P(1+r)^t , where is the starting amount of ants, is the growth rate, and is the time in years.

First step is to convert $20\%$ into a decimal. $20\%=0.20$

P(t)=5000(1+0.20)^t

P(t)=5000(1.20)^t

P(6)=5000(1.20)^6=14930

So in 6 years, Amanda will have 14930 ants.

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Example Question #1129 : Algebra

The equation for the universal gravitation is $F_g=\frac{Gm_1m_2}{r^2}$ , $m_1=\text{mass of object 1}$ , $m_2=\text{mass of object 2}$ , $r=\text{radius between masses}$ , and is the universal gravitational constant. If $m_1=10 \ kg$ , $m_2=20 \ kg$ , $F_g=1.34\times10^{-12} N$ and $G=6.67408 \times 10^{-11} m^3 kg^{-1} s^{-2}$ , what is the radius between the two masses? Round to the nearest tenth.

Hint: $\frac{\text{kg\:m}}{s^2}=1 \text{Newton}$

Possible Answers:

$r=99.90\ m$

$r=100\ m$

$r=99.70\ m$

$r=99.60\ m$

$r=99.80\ m$

Correct answer:

$r=99.80\ m$

Explanation:

The first step is to plug in all the values into the equation.

$1.34\times10^{-12} N=\frac{6.67408\times10^{-11}m^3kg^{-1}s^{-2}\cdot 10kg\cdot 20kg}{r^2}$

Now we will solve for .

$r^2=-\frac{6.67408\times10^{-11}m^3kg^{-1}s^{-2}\cdot 10kg\cdot 20kg}{1.34\times10^{-12} N}$

$r^2=\frac{1.334816\times10^{-8}m^3kg^{-1}s^{-2} kg^2}{1.34\times10^{-12} N}$

$r^2=9961.313\:m^2$

Take the square root on each side

$r=\sqrt{9961.313\:m^2}=99.80\ m$

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Example Question #11 : Algebraic Functions

If g(x) = 3x+2 , what is the value of g(-2) ?

Possible Answers:

Correct answer:

Explanation:

g(x) = 3x+2

g(-2) = 3(-2)+2=-6+2=-4

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SAT Math : How to find f(x)

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1121 : Algebra

Example Question #1122 : Algebra

Example Question #1121 : Algebra

Example Question #1124 : Algebra

Example Question #1121 : Algebra

Example Question #1126 : Algebra

Example Question #1127 : Algebra

Example Question #1128 : Algebra

Example Question #1129 : Algebra

Example Question #11 : Algebraic Functions

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