The selling price of x number of a certain stereo can be modeled by the function R(x) = 160x. The total cost of making x stereos is C(x) = 71x – 0.02x2. What is the percent markup for 31 stereos?



23%



127%



227%



278%

Answer:

Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.

Step-by-step explanation:

Let [tex]x[/tex] be the number of windows that Paula sells in a year.

Paula's revenue is the number of windows that she sell times the price that she charge for each window. That is:

[tex]\text{Revenue} = \text{Price}\times \text{Quantity} = \$\;28x[/tex].

Paula's cost comes in two parts:

[tex]\begin{aligned}\text{Cost} = \text{Total Cost}&= \text{Fixed Cost} + \text{Marginal Cost}\\ & = \$\;12,000 +\$\; 4x \\ & = \$\;(12,000 + 4x)\end{aligned}[/tex].

Consider the inequality in the picture:

[tex]\text{Revenue} - \text{Cost} \ge \text{Profit}\\ \$\; 28x - \$\; (12,000 + 4x)\ge 48,000\\\$\; 24x \ge 60,000[/tex].

Multiply both sides with 1/24. It is important that this number is positive. Otherwise, the direction of the inequality operator will flip.

[tex]\displaystyle x \ge \frac{\$\;60,000}{\$\; 24}[/tex].

[tex]x\ge 2,500[/tex].

In other words, Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.

Ques 4)

The system is:

                      [tex]y=x-4[/tex]

                     [tex]y=\dfrac{x-4}{x+2}[/tex]

Ques 5)

The system is:

                         [tex]6x+y=-27[/tex]

             and     [tex]y=x^2+5x+3[/tex]  

Ques 4)

After looking at the graph we observe that :

The first graph is a line which passes through (4,0) and (0,-4)

Hence, the equation of such a line is:

                y=x-4

and the second graph is a curve such that the vertical asymptote is at x= -2

and also x= 4 is a root of the rational function.

Since, the graph passes through (4,0)

Hence, the system equation which best represents the graph is:

                           [tex]y=x-4[/tex]

                     [tex]y=\dfrac{x-4}{x+2}[/tex]

Ques 5)

One of the curve is :

a line that passes through (-5,3) and (-6,9)

Hence, the equation of line is given by:

[tex]y-3=\dfrac{9-3}{-6-(-5)}\times (x-(-5))\\\\i.e.\\\\y-3=\dfrac{6}{-6+5}\times (x+5)\\\\i.e.\\\\y-3=\dfrac{6}{-1}\times (x+5)\\\\i.e.\\\\y-3=-6(x+5)\\\\i.e.\\\\y-3=-6x-30\\\\i.e.\\\\y=-6x-30+3\\\\i.e.\\\\y=-6x-27[/tex]

i.e. Equation of line is:

[tex]6x+y=-27[/tex]

While the other graph is a upward facing parabola such that the vertex is in third quadrant this means that the coefficient of x^2 must be positive and that of x must also be positive.

Hence, the system in which the equation of line satisfies is:

                          [tex]6x+y=-27[/tex]

             and     [tex]y=x^2+5x+3[/tex]  

According to the SMART goals method, goals should be clearly defined, aligning with the "Specific" attribute of the SMART acronym. This means having a clear and direct aim for the goal, which is essential for effective goal-setting.

According to the SMART goals method, goals should be clearly defined. SMART is an acronym that stands for Specific, Measurable, Attainable, Relevant, and Time-bound. Each of these attributes plays a crucial role in the formulation of effective and actionable goals.

Specific means the goal should be clear and direct, detailing exactly what is expected to be achieved. A goal that is Measurable has quantifiable criteria to indicate progress or completion. Attainable refers to the goal being realistic and possible to achieve given current resources and constraints.

Being Relevant means the goal aligns with broader objectives and makes sense within the greater plan. Lastly, Time-bound means there is a specific deadline or period within which the goal should be accomplished.

Therefore, the correct choice is A. Clearly defined, as a SMART goal must be specific and this inherently means the goal should have a clear definition.

Answer:

27%

Step-by-step explanation:

take the number of times it is at 2 cars (16) and divide by the number of surveyed times in total (60). multiply by 100 to show answer as a percent

Answer:

27%

Step-by-step explanation:

We are given the results of survey of one thousand families to determine the distribution of families by their size.

We are to find the probability (to the near percent) that a line has exactly 2 cars in it.

Frequency of 2 cars in a line = 16

Total frequency = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 = 60

P (2 cars in line) = (16 / 60) × 100 = 26.6% ≈ 27%

Answer:

  $110

Step-by-step explanation:

Let a, b, and c represent the earnings of Alan, Bob, and Charles. The problem statement tells us ...

  a + b + c = 480 . . . . . . the combined total of their earnings

  -a + b = 40 . . . . . . . . . . Bob earned 40 more than Alan

  2a - c = 0 . . . . . . . . . . . Charles earned twice as much as Alan

Adding the first and third equations, we get ...

  (a + b + c) + (2a - c) = (480) + (0)

  3a + b = 480

Subtracting the second equation gives ...

  (3a +b) - (-a +b) = (480) -(40)

  4a = 440 . . . . . . . . simplify

  a = 110 . . . . . . . . . . divide by the coefficient of a

Alan earned $110.

_____

Check

Bob earned $40 more, so $150. Charles earned twice as much, so $220.

The total is then $110 +150 +220 = $480 . . . . as required

Answer:

Y= 19.86 - 0.42b

Step-by-step explanation:

Step 1: Write the formula

Regression Line: Y = a + bx

a=(Total Y) x (Total X^2) - (Total X) x (Total XY)

                    n x (total X^2) - (Total X)^2

b= n x (Total XY) - (Total X) x (Total Y)

             n x (total X^2) - (Total X)^2    

Step 2: Make a table to find all values

X  Y          X^2    Y^2               XY

5 17.19 25 295.4961       85.95

6 19.12 36 365.5744       114.72

7 16.75 49 280.5625      117.25

8 15.58 64 242.7364       124.64

9 16.21 81 262.7641        145.89

10 14.14 100 199.9396        141.1

11 14.97 121 224.1009        164.67

12 16.2         144 262.44            194.4

68 130.16     620  2133.614       1088.62              TOTAL

Step 3: Substitute all values in the equation to find a and b

a=(Total Y) x (Total X^2) - (Total X) x (Total XY)

                    n x (total X^2) - (Total X)^2

a= (130.16 x 620) - (68 x 1088.62)

                     8 x (620) - (68)^2

a = 80699.2 - 74026.16

                336

a = 19.86

b = n x (Total XY) - (Total X) x (Total Y)

             n x (total X^2) - (Total X)^2    

b = 8 x (1088.62) - (68 x 130.16)

             8 x (620) - (68)^2

b = 8708.96 - 8850.88

                336

b = -0.42

Step 4 : Apply values of a and b in the formula of the regression line.

Regression Line: Y = a + bx

Y= 19.86 + b (-0.42)

Y= 19.86 - 0.42b

The regression line is calculated using the 'least squares method'. The formula is Y=a+bX, where a is the Y-intercept and b is the slope. These are calculated from the X and Y data values using specific formulas.

To calculate the regression line from the given X (year) and Y (high temperature) values, we first need to know the specific data. Unfortunately, the data isn't provided in the question. However, I can explain the process to you.

A regression line, also known as the line of best fit, is a straight line that best represents the data on a scatter plot. This line can be calculated using the 'least squares method'. This method minimizes the sum of the squares of the residuals (the differences between the actual and predicted Y values).

The formula for the regression line is Y=a+bX, where:

You can plug in your X and Y data values into these equations to find your regression line.

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Answer:

The area of the polygon = 216.4 mm²

Step-by-step explanation:

* Lets talk about the regular polygon

- In the regular polygon all sides are equal in length

- In the regular polygon all interior angles are equal in measures

- When the center of the polygon joining with its vertices, all the

 triangle formed are congruent

- The measure of each vertex angle in each triangle is 360°/n ,

  where n is the number of its sides

* Lets solve the problem

- The polygon has 9 sides

- We can divide it into 9 isosceles triangles all of them congruent,

 if we join its center by all vertices

- The two equal sides in each triangle is 8.65 mm

∵ The measure of the vertex angle of the triangle = 360°/n

∵ n = 9

∴ The measure of the vertex angle = 360/9 = 40°

- We can use the area of the triangle by using the sine rule

∵ Area of the triangle = 1/2 (side) × (side) × sin (the including angle)

∵ Side = 8.65 mm

∵ The including angle is 40°

∴ The area of each triangle = 1/2 (8.65) × (8.65) × sin (40)°

∴ The area of each triangle = 24.04748 mm²

- To find the area of the polygon multiply the area of one triangle

 by the number of the triangles

∵ The polygon consists of 9 congruent triangles

- Congruent triangles have equal areas

∵ Area of the 9 triangles are equal

∴ The area of the polygon = 9 × area of one triangle

∵ Area of one triangle = 24.04748 mm²

∴ The area of the polygon = 9 × 24.04748 = 216.42739 mm²

* The area of the polygon = 216.4 mm²

Answer

[tex]216.4 {mm}^{2} [/tex]

Explanation

The regular polygon has 9 sides.

Each central angle is

[tex] \frac{360}{n} = \frac{360}{9} = 40 \degree[/tex]

The area of each isosceles triangle is

[tex] \frac{1}{2} {r}^{2} \sin( \theta) [/tex]

We substitute the radius and the central angle to get:

[tex] \frac{1}{2} \times {8.65}^{2} \times \sin(40) = 24.05 {mm}^{2} [/tex]

We multiply by 9 to get the area of the regular polygon

[tex]9 \times 24.05 = 216.4 {mm}^{2} [/tex]

b)

A - wins at both games

[tex]P(A)=0.3\cdot0.4=0.12[/tex]

c)

A - wins at just one of the games

[tex]P(A)=0.3\cdot0.6+0.7\cdot0.4=0.18+0.28=0.46[/tex]

Answer:

see below

Step-by-step explanation:

1.  y = mx+b where m is the slope

The first slope is -1/3

The second slope is 3

m1 = m2 means they are parallel  False

m1*m2 = -1  means they are perpendicular

-1/3 *3 = -1  True

2.  Squares and rhombi have all 4 sides with the same length.  Squares however, have 4 angles that must equal 90 degrees.  Squares are a special form of rhombi

3.  To find the slope

m = (y2-y1)/(x2-x1)

   = (2-11)/(-5-0)

   =-9/-5

   = 9/5

The distance is found by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (-5-0)^2 + (2-11)^2)

  = sqrt( 5^2 + (-9)^2)

  = sqrt( 25+81)

  = sqrt( 106)

Answer:

See below

Step-by-step explanation:

y = -1/3x + 2

y = 3x - 5

Slopes are -1/3 and 3, they are opposite-reciprocal, it means the lines are perpendicular

2. Difference between squares and rhombus:

3. points A(0,11)  and B(-5,2)

Slope:

m= (y2-y1)/(x2-x1)= (2-11)/(-5-0)= -11/-5= 11/5

Distance between points:

√(x2-x1)²+(y2-y1)²= √ 25+121= √146 ≈ 12

Distance = rate * time

Replace D with f. Instead of writing D(t), write f(t).

f(t) = 65t

Let t = 3.5

f(3.5) = 65(3.5)

f(3.5) = 227.5

Did you follow?

Final answer:

The distance a car travels at 65 mph is a function of time, expressed as f(t) = 65t. Evaluating it for 3.5 hours, the car would travel 227.5 miles.

Explanation:

The distance a car travels at a rate of 65 mph is a function of the time, t, the car travels. This can be expressed mathematically as f(t) = 65t, where f(t) is the distance in miles and t is the time in hours. To evaluate this function for f(3.5), we multiply 65 miles/hour by 3.5 hours.

f(3.5) = 65 miles/hour × 3.5 hours = 227.5 miles

Therefore, a car traveling at a constant speed of 65 mph for 3.5 hours will have traveled 227.5 miles.

Answer:

B. 2 m

Step-by-step explanation:

20 da is equal to 2 m.

Answer:

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Answer:

  3 - (n -1) = (1/2)(3n -4)

Step-by-step explanation:

three minus the difference of a number and one: 3 - (n -1)

one-half of the difference of three times the same number and four: (1/2)(3n -4)

These two expressions are said to be equal, so the equation is ...

  3 - (n -1) = (1/2)(3n -4)

Answer:

Step-by-step explanation:

D

Answer:

x < 7

Step-by-step explanation:

Simplify ...

6x -12 -4x +7 < 9

2x < 14 . . . . . . . . . . . add 5

x < 7 . . . . . . . . . . . . . divide by 2

Answer: 900,000 for the city/2,304,000

Step-by-step explanation:

I used the exponential growth formula with initial population rate of growth and time passed.

In 2002, the population of the city was 416,000 and the population of the suburbs was 884,000.

In 2000, the city's population was 400,000 and the suburban population was 900,000. Each year, 5% of the city's population moves to the suburbs (and 95% stays in the city), and 4% of the suburban population moves to the city (and 96% remains in the suburbs). To calculate the population of the city in 2002, we need to subtract 5% of the city's population in 2000 from the 2000 city population and add 4% of the suburban population. To calculate the population of the suburbs in 2002, we need to subtract 4% of the suburban population in 2000 from the 2000 suburban population and add 5% of the city population.

Population of city in 2002 = (City population in 2000) - 5% of (City population in 2000) + 4% of (Suburban population in 2000)

Population of suburbs in 2002 = (Suburban population in 2000) - 4% of (Suburban population in 2000) + 5% of (City population in 2000)

By substituting the given values, we can calculate the population of the city and suburbs in 2002.

Population of city in 2002 = 400,000 - 0.05 * 400,000 + 0.04 * 900,000

Population of city in 2002 = 400,000 - 20,000 + 36,000

Population of city in 2002 = 416,000

Population of suburbs in 2002 = 900,000 - 0.04 * 900,000 + 0.05 * 400,000

Population of suburbs in 2002 = 900,000 - 36,000 + 20,000

Population of suburbs in 2002 = 884,000

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Plug -7 in for where ever you see the variable p if the final answer is equal to each other then -7 is a solution to the equation

4 × (-7) - (-7 + 9) = 5 × (-7) + 5

Use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

Parentheses

4 × (-7) - (-7 + 9) =  5 × (-7) + 5

4 × (-7) - 2 =  5 × (-7) + 5

There are no exponents so go to the next step

Multiplication (apply this from left to right)

4 × (-7) - 2 =  5 × (-7) + 5

-28 - 2 = 5 × (-7) + 5

-28 - 2 = 5 × (-7) + 5

-28 - 2 = -35 + 5

There is no division so go to the next step

Addition

-28 - 2 = -35 + 5

-28 - 2 = -30

Subtraction

-28 - 2 = -30

-30 = -30

-30 = -30

-7 is a solution to this equation because when evaluated both sides equals -30

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

  (-12, 5), (12, -5)

Step-by-step explanation:

Reflection across the origin is the transformation ...

   (x, y) ⇒ (-x, -y)

Look for coordinates that are the opposites of their counterparts. You will find the appropriate answer choice is ...

  (-12, 5), (12, -5)

Answer:

(-12, 5), (12, -5)

Step-by-step explanation:

Since, the rule of point symmetry with respect to the origin is,

[tex](x,y)\rightarrow (-x, -y)[/tex]

That is, the mirror image of the point (x, y) with respect to the origin is (-x,-y),

Thus, in the point symmetry with respect to the origin,

[tex](-12, 5)\rightarrow (-(-12), -5))[/tex]

So, the mirror image of point (-12,5) with respect to the origin is (12, -5),

Hence, the set of ordered pairs has point symmetry with respect to the origin is,

(-12, 5), (12, -5)

Second option is correct.

Answer:

  see below for a graph

Step-by-step explanation:

Each of the functions:

will only be graphed in the specified domain. You know that ...

  y = -x

is a line with slope -1 through the origin. It won't go through the origin on your graph, because it stops at x = -2. f(x) is not defined as -(-2) at x=-2, so there will be an open circle at the end of this portion of the graph.

__

You know that

  y = x+2

is a line with slope +1 through the y-intercept (0, 2). It will only be part of your graph for x-values between -2 and 2, inclusive. Because f(x) is defined as x+2 at the end points of this segment, those points will be shown as solid dots.

__

You know that

  y = 5

is a horizontal line. It will be part of your graph for x > 2, and will have an open circle on the end at x=2. f(2) is not defined as 5, but is defined as 4 (see above), which is why the circle is open.

The cost for talking 3.1 minutes, according to the graph, would be  Option C) 4 cents due to rounding up to nearest minute.

1. Understanding the ceiling function: The ceiling function takes a number as input and rounds it up to the nearest whole number. For example, the ceiling of 2.3 is 3, because 3 is the next whole number greater than 2.3.

2. Analyzing the graph: The graph provided represents the cost of a long-distance phone call in cents based on the duration of the call in minutes. The x-axis represents the minutes of the call, and the y-axis represents the cost in cents.

3. Identifying the jumps: From the graph, we can observe that the cost increases in steps or jumps at specific points along the x-axis. These jumps indicate where the cost increases by 1 cent.

4. Determining the cost for 3.1 minutes: Since 3.1 minutes fall between 3 and 4 minutes on the x-axis, we need to find out which whole number the ceiling function would round 3.1 up to. Since it rounds up to the nearest whole number, 3.1 would be rounded up to 4.

5. Conclusion: Therefore, the cost of talking for 3.1 minutes would be the same as talking for 4 minutes according to the graph. Looking at the y-axis corresponding to the point where x = 4, we see that the cost is 4 cents.

So, to answer the question, the cost to talk for 3.1 minutes would be 4 cents. Option C)

Complete Question:

Answer:

9/4

Step-by-step explanation:

For a perfect square trinomial x² + bx + c, the value of c is the square of half of b.

c = (b/2)²

Here, b = 3.

c = (3/2)²

c = 9/4

Answer:

$96.25

Step-by-step explanation:

I just got done with the test...

Answer: 1/20, or 0.05

Step-by-step explanation: What we have to do is figure out how many times the blue shades area goes into the total area. Horizontally, it would be 5/10 squares, or 1/2. Vertically, it is 5/50 squares, or 1/10.  Multiplying 1/2 and 1/10 gives us 1/20, or 0.05 as your answer.

Answer:

65.52 square feet

Step-by-step explanation:

to find area of a rhombus with the diagonals multiply them together and divide by two.

10.4 x 12.6 = 131.04

131.04/2 = 65.52 square ft

Answer: 48cm2

Step-by-step explanation:

area = base x height

a = 8 x 6

a = 48

Answer:

[tex]x\geq 29,000[/tex]  and  [tex]x\leq 41,000[/tex]

Step-by-step explanation:

Let

x -----> the altitude of a commercial aircraft

we know that

The expression " A minimum altitude of 29,000 feet" is equal to

[tex]x\geq 29,000[/tex]

All real numbers greater than or equal to 29,000 ft

The expression " A maximum altitude of 41,000 feet" is equal to

[tex]x\leq 41,000[/tex]

All real numbers less than or equal to 41,000 ft

therefore

The compound inequality is equal to

[tex]x\geq 29,000[/tex]  and  [tex]x\leq 41,000[/tex]

All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft

The solution is the interval ------> [29,000,41,000]

Answer:

A

Step-by-step explanation:

Simplifying it, convert it to a radical form, and evaluate it.. Either way it all equals to a simple whole number, which is '4',

well, except when you convert the expression to radical form using the formula 'a^x/n=n√a^x' then it'll be '^3√8^2'.

____

I hope this helps, as always. I wish you the best of luck and have a nice day, friend..

Answer:

4

Step-by-step explanation:

8 ^ (2/3)

The 2 means squared and the 3 means root

8^2  ^ (1/3)

Rewriting 8 as 2^3

2^3 ^ (2/3)

We know a^ b^c = a^ (b*c)

2 ^ (3*2/3)

2^ 2

4

OR

8 ^ (2/3)

The 2 means squared and the 3 means root

8^2  ^ (1/3)

64 ^ 1/3

We know 4*4*4 = 64

(4*4*4)^ 1/3

4

Answer:

10.4 cm

Step-by-step explanation:

In this question apply the formulae for volume of a pyramid

General formulae for volume of a pyramid is = l*w*h /3 where l is base length, w is base width and h is height.

In this question l=w= 6cm, v=120 cm³ and h=? ,

Apply the formulae

[tex]V= l*w*h /3\\\\120=6*6*h/3\\\\120=12h\\\\120/12 =h\\\\10cm=h[/tex]

Slant height

The length = 6cm-----------------divide by 2 to get half the legth

a=6/2=3cm

h=b= 10cm

c=?

apply the Pythagorean relationship

a²+b²=c²

3² + 10²= c²

9+100=c²

√109=c²

c=10.44

slant height =10.4 cm

Answer:

Slant height of pyramid = 10.4 m

Step-by-step explanation:

Points to remember

Volume of square pyramid = a²h/3

Where 'a' is the side of base and h is the height of pyramid

To find the height of pyramid

It is given that volume of square pyramid = 120 cm³ and

base a = 6 cm

a²h/3 = 120

h = (120 * 3)/a²

 = (120 * 3)/6²

 =10 cm

Therefore h = 10 cm

To find the slant height of pyramid

By using Pythagorean theorem we can write,

slant height ² = (base/2)² + height²

l² = (a/2)² + h²

 = (6/2)² + 10²

 = 3² + 10²

 = 9 + 100

 =109

l = √109 = 10.44 ≈ 10.4

Answer:

  about 8 cm

Step-by-step explanation:

The formula for the area of a regular polygon is ...

  A = 1/2Pa . . . . where P is the perimeter and "a" is the apothem, the distance from the center to a side

Filling in your numbers, we have ...

  20 cm^2 = (1/2)P(5 cm)

Dividing by the coefficient of P, we find ...

  2×(20 cm^2)/(5 cm) = P = 8 cm

The perimeter of the pentagon is about 8 cm.

_____

Comment on the problem

This calculation makes use of the area formula, as apparently intended. A regular pentagon with an apothem of about 5 cm will have an area of about 90.8 cm^2. The given geometry is impossible, as the pentagon is nearly 10 cm across. It cannot have a perimeter of only 8 cm.

Answer:

  cos(A) = (4√97)/97

Step-by-step explanation:

The cosine is related to the sine by ...

  cos(A)² = 1 - sin(A)²

  cos(A)² = 1 - (9/√97)² = 1 - 81/97 = 16/97 . . . . substitute for sin(A), simplify

Make the denominator a square:

  cos(A)² = (16·97)/97²

  cos(A) = (4√97)/97 . . . . . square root

The exact value of cos A can be determined using the Pythagorean identity. In this case, cosA = 4√97/97, which is the exact value of cos A in simplest radical form with a rational denominator.

In mathematics, the exact value of cos A can be determined using the Pythagorean identity, sin²A + cos²A = 1.

According to the problem, sinA = 9/√97, which when squared gives 81/97. Using the Pythagorean identity, we can substitute the value of sin²A to get cos²A. Hence, cos²A = 1 - sin²A = 1 - 81/97 = 16/97. The exact value of cos A, then, is the square root of 16/97. As A is in Quadrant I where cosine is positive, this will be √(16/97).

In order to write this value with a rational denominator, multiply and divide by the square root of the denominator (√97). Hence, cosA = 4√97/97, which is the exact value of cos A in simplest radical form with a rational denominator.

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[tex] (2x^2 - x + 1)(x - 3) [/tex]

We multiply 2x^2 - x + 1 by x and by -3 and add it all up:

[tex] (2x^2 - x + 1)(x - 3) = 2x^3 - x^2 + x - 6x^2 + 3x - 3 [/tex]

[tex] = 2x^3 - 7x^2 + 4x - 3 [/tex]

Answer: A

Answer:

2x^3 - 7x^2 + 4x - 3.

Step-by-step explanation:

(2x^2-x+1)( x-3)

= x(2x^2 - x + 1) - 3(2x^2 - x + 1)

= 2x^3 - x^2 + x - 6x^2 + 3x - 3

= 2x^3 - 7x^2 + 4x - 3.