Let f(x) = 4 – x^2-, g(x) = 2 – x. Find (f + g)(x) and its domain.

Answers

Answer 1

(f+g)(x)=(2-x)(2+x)+(2-x)=(2-x)(2+x+1)=(x+2)×(x+3)=x^2+5x+6 & Domain=R

Related Questions

Goran runs 3 miles in 25 minutes. at the same rate, how many miles would he run in 20 minutes?

Answers

Set up a proportion of miles to minutes:

3 mi/25 min= x mi/20 min

Cross multiply:
3*20=60
60/25= 2.4=x

Final answer: 2.4 miles

How long is the minute hand on a clock whose tip travels 15 cm from 1:15 to 1:30 to the nearest tenth?

Answers

Answer:

The length of minute hand is 9.5 cm

Step-by-step explanation:

We are given the minute hand move from 1:15 to 1:30

Time for 1:30 to 1:30 = 15 minutes

Tip of minute hand move 15 cm in 15 minutes.

In 60 minutes = 360°

In 1 minute = 6°

In 15 minutes = 90°

Formula: [tex]\theta=\dfrac{L}{r}[/tex]

[tex]\theta=90^\circ[/tex]

Now we change [tex]\theta=90^\circ[/tex] into radian

[tex]Radian=\dfrac{\pi}{180^\circ}\times 90^\circ=\dfrac{\pi}{2}[/tex]

L=15 cm

R = Length of minute hand.

[tex]\dfrac{\pi}{2}=\dfrac{15}{R}[/tex]

[tex]R=\dfrac{30}{\pi}\approx 9.5[/tex]

Hence, The length of minute hand is 9.5 cm

Which algebraic expression is a polynomial with a degree of 2?

a)4x3 − 2x
b10x2 −
c)8x3+ + 3
d)6x2 − 6x + 5

Answers

6x^2 - 6x + 5 <== this is ur polynomial with a degree of 2

the one u have marked is not a polynomial because it has a variable in the square root...a polynomial cannot have that

Answer:

D) 6x² − 6x + 5 has degree 2.

Step-by-step explanation:

Given : Polynomial .

To find : Which algebraic expression is a polynomial with a degree of 2.

Solution: We have given polynomial

Degree : The highest power of the polynomial is called degree.

We can see from the given polynomials two polynomial have 2 power

first is [tex]10x^{2} -\sqrt{x}[/tex].

Second is 6x² − 6x + 5.

But the first term have root so, it is not a polynomial.

So 6x² − 6x + 5 has degree 2

Therefore, D) 6x² − 6x + 5 has degree 2.

Which type of triangle has one angle with a measurement greater than 90°? A. Obtuse B. Acute C. Isosceles D. Right

Answers

An obtuse angle is an angle with an angle measure greater than 90 degrees.

Obtuse Triangle has a measure bigger than 90

Please help me! And can you explain how you got that answer please?

Answers

The answer x = -3 is correct ; not really any mistakes made but they do seem to skip a step from 8^(-1) to 2^(-3) if that is confusing you.

8 = 2^(3)
so
(8)^(-1) = (2^3)^(-1) = 2^(3*-1) = 2^(-3)

PLEASE HELP!

Solve for t: A=P (1+rt)

Answers

A = P( 1 + rt)

A = P + Prt

A - P = Prt

(A - P)/Pr = t

Here are the steps to follow when it comes to solving for t. This is not the only way to do so

Step 1) A = P*(1+rt)

Step 2) A = P*(1)+P*(rt)

Step 3) A = P+P*(rt)

Step 4) A-P = P+P*(rt)-P

Step 5) A-P = P*(rt)

Step 6) A-P = t*(Pr)

Step 7) (A-P)/(Pr) = (t*(Pr))/(Pr)

Step 8) (A-P)/(Pr) = t

Step 9) t = (A-P)/(Pr)

----------------------------------------------

and here are the explanations for each step

Step 1) Nothing to do here. This is the original equation

Step 2) Distribute the outer P term into each inner term (1 and rt)

Step 3) Multiply P and 1 to get P*(1) = P

Step 4) Subtract P from both sides

Step 5) Simplify. Note how the P-P on the right side becomes 0P = 0 which goes away on the right side

Step 6) Rearrange the terms on the right side to go from P*(rt) to t*(Pr).

Step 7) Divide both sides by Pr.

Step 8) Simplify. The Pr term on the right side divides with itself to get 1. Because 1 times anything is itself, we effectively have Pr cancel out and go away.

Step 9) Flip the equation so that the t is on the left side

----------------------------------------------

The answer is t = (A-P)/(Pr) which can be written as [tex]t = \frac{A-P}{Pr}[/tex]

The parenthesis in the equation t = (A-P)/(Pr) are important because we are specifying that we are dividing all of "A-P" all over all of "Pr"

Which graph below shows a system of equations with infinitely many solutions?

A)coordinate plane with two parallel lines

B)coordinate plane with two intersecting lines

C)coordinate plane with two coinciding lines

D)coordinate plane with two intersecting lines

Answers

infinitely many solutions...this means u have 2 lines that are the same...they are coincident lines.....ur answer is C

Answer:

The correct option is C.

Step-by-step explanation:

Consider the provide information.

Now consider the provided options

Option A) If there is a coordinate plane with two parallel lines.

if the plane has two parallel line then, It has no solution because you can get the solution if lines intersect at a point. Thus, it is not the required option.

Option B) and D) If there are two intersecting lines then you can get only one solution. Thus, it is not the required option.

Option C) If there are two coinciding lines then you can find infinite intersecting points. Thus, it is the required option.

Therefore, the correct option is C.

HELLLLLPPP PLLEASEEE

Answers

Just looking at the formula, the original amount invested equals 728.
The answer is B

Is -2 less than 0???????????????????????????

Answers

Yes because it is a negative number which, on a number line, is behind 0.

Yes negative two is less than zero because negatives number on a line go to the left, zero in the middle of course, and positive on the right, so since negative numbers are less than positive (not saying that 0 is positive or negative), than they are also less than zero. so -2 < 0 is true. Since negatives/positives are like up/down, left/right, good/bad, opposites like that than negatives will always be lower.

hard question ! Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses. After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on. She writes the equation of the function like this: E(x) = 20x - 50, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars. Which of the following are reasonable interpretations of the y-intercept of Jessica's function? Check all that apply.
A. Her expenses are $50 per week.
B. She can earn $20 per week even if she does not knock on any doors.
C. If she does not knock on any doors at all during the week, she will lose $50.

D. She will lose $20 per week if she does not knock on any doors.

Answers

The answer is C because she is using gas and not making money

Answer:

A and C

Step-by-step explanation:

Just answered on apex

Multiplication property: if angle j equals 30 then 2m angle j equals

Answers

If m∡J=30, then 2(m∡J) = 2(30) = 60

How to do this ?? How

Answers

|ax - b| > c

The two bars | | is used to indicate the function absolute value.

Remember this definition:

| x | = - x if x < 0 and x if x > 0

So, | x | > c =>

x > c or x > - c

Therefore:

|ax - b| > c => ax - b > c or ax - b > - c

That is the third option of the answer list.

Answer:

|ax - b| > c

The two bars | | is used to indicate the function absolute value.

Remember this definition:

| x | = - x if x < 0 and x if x > 0

So, | x | > c =>

x > c or x > - c

Therefore:

|ax - b| > c => ax - b > c or ax - b > - c

Step-by-step explanation:

1. What is the product of -2.5 and 8.77 ?

2. Alexander purchased a computer on sale. The original price was $1,200. The sale price was 5/6 of the original price. How much did Alexander pay for the computer?

3. Mara finished 1/5 of her assignment on Saturday and 3/8 of her assignment on Sunday. What Fraction of her assignment did she complete on Saturday and Sunday?

Answers

1. Well first, what does product mean? It means to multiply...so: -2.5•8.77=-21.925

2. 5/6 of 1,200 is 1000. 1,200÷6=200 200•5=1000.

3. 1/5+3/8. Find like denominators. (40) 8/40+15/40=23/40 or as a decimal, 0.575.

Hoped I helped!

1. -21.925
2. $200
3. 23/40

Solve for y.

4y = 144

What is the answer?

Answers

4y=144
/4 /4
4 is canceled out
y=144
/4
144/4 = 36
y = 36

The solution is y = 36. Divide both sides of the equation by 4 to isolate y. To isolate y, we want to get rid of the coefficient 4 that is multiplying y.

We do this by dividing both sides of the equation by 4:

4y / 4 = 144 / 4

On the left side, the 4 in the numerator and the 4 in the denominator cancel out, leaving us with just y:

y = 144 / 4

Now, Simplify the equation.

Now, we can perform the division to find the value of y:

y = 36

The solution is y = 36.

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JIMMMM! :)

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^x and y = 4^x−2 intersect are the solutions of the equation 2^x = 4^x−2. (4 points)

Part B: Make tables to find the solution to 2^x = 4^x−2. Take the integer values of x between −4 and 4. (4 points)

Part C: How can you solve the equation 2^x = 4^x−2 graphically? (2 points)

Answers

Part A

The x coordinates are the inputs of the functions f(x) = 2^x and g(x) = 4^(x-2)

If we have some input x that leads to f(x) = g(x), then this x value is a solution. It makes the equation f(x) = g(x) true. This is why the x coordinate of the intersection point of y = 2^x and y = 4^(x-2) is the solution.

-------------------------------------------------------------------------
Part B

See attached for the table. See figure 1.

This is how you get the results you see in the table
Plug x = -4 into f(x) to get:
f(x) = 2^x
f(-4) = 2^(-4)
f(-4) = 0.0625

Do the same for g(x):
g(x) = 4^(x-2)
g(-4) = 4^(-4-2)
g(-4) = 4^(-6)
g(-4) = 0.000244140625

-------------------
Plug x = -3 into f(x) to get:
f(x) = 2^x
f(-3) = 2^(-3)
f(-3) = 0.125

Do the same for g(x):
g(x) = 4^(x-2)
g(-3) = 4^(-3-2)
g(-3) = 4^(-5)
g(-3) = 0.0009765625

-------------------
Plug x = -2 into f(x) to get:
f(x) = 2^x
f(-2) = 2^(-2)
f(-2) = 0.25

Do the same for g(x):
g(x) = 4^(x-2)
g(-2) = 4^(-2-2)
g(-2) = 4^(-4)
g(-2) = 0.00390625

-------------------
Plug x = -1 into f(x) to get:
f(x) = 2^x
f(-1) = 2^(-1)
f(-1) = 0.5

Do the same for g(x):
g(x) = 4^(x-2)
g(-1) = 4^(-1-2)
g(-1) = 4^(-3)
g(-1) = 0.015625

-------------------
Plug x = 0 into f(x) to get:
f(x) = 2^x
f(0) = 2^(0)
f(0) = 1

Do the same for g(x):
g(x) = 4^(x-2)
g(0) = 4^(0-2)
g(0) = 4^(-2)
g(0) = 0.0625

-------------------
Plug x = 1 into f(x) to get:
f(x) = 2^x
f(1) = 2^(1)
f(1) = 2

Do the same for g(x):
g(x) = 4^(x-2)
g(1) = 4^(1-2)
g(1) = 4^(-1)
g(1) = 0.25

-------------------
Plug x = 2 into f(x) to get:
f(x) = 2^x
f(2) = 2^(2)
f(2) = 4

Do the same for g(x):
g(x) = 4^(x-2)
g(2) = 4^(2-2)
g(2) = 4^(0)
g(2) = 1

-------------------
Plug x = 3 into f(x) to get:
f(x) = 2^x
f(3) = 2^(3)
f(3) = 8

Do the same for g(x):
g(x) = 4^(x-2)
g(3) = 4^(3-2)
g(3) = 4^(1)
g(3) = 4

-------------------
Plug x = 4 into f(x) to get:
f(x) = 2^x
f(4) = 2^(4)
f(4) = 16

Do the same for g(x):
g(x) = 4^(x-2)
g(4) = 4^(4-2)
g(4) = 4^(2)
g(4) = 16

Note that since the input x = 4 leads to the same output (16) this makes x = 4 a solution.

-------------------------------------------------------------------------
Part C

To solve graphically, you need to use the table in part B to draw a curve through the set of points. Then determine where the curves cross (if they cross at all). You may need to adjust the graph window if the intersection point is off the screen.

See figure 2 for the graph (attached as well). Point A in green is the intersection point.
A = (4,16)
so x = 4 is the solution to f(x) = g(x).

Hello there!

Part A: The point or points of intersection are the values of the variables which satisfy both equations at a particular point.

If [tex]y=2^x and y=4 ^{x-2} [/tex] and the solution of which will satisfy both equations. This idea of equating the two equations is something that you would have come across before, maybe without realizing it.
Consider this:
[tex]x^2 + 6x + 9=0 This can also be looked at as being the two equations: y=x^2 +6x+9 and y=0 [/tex]
So the points of intersection are the roots in this case and satisfy the equation:
[tex]x^2 + 6x +9=0 This explains why it will be the solution to: 2^x = 4 ^{x-2} , because this is the equation formed at the intersection.[/tex]

Part B:
You just put integer values between -4 and 4 in each equation and when the output is the same for both that is the solution.

[tex]2^ ^{-4} = 0.0625 , [/tex] and [tex]4 ^{-6} = 0.000244[/tex]
[tex]2 ^{-3} = 0.125, [/tex] [tex]4 ^{-5} =0.000977[/tex]
[tex]2 ^{-2} =0.25[/tex] and [tex]4 ^{-4} =0.003906[/tex]
[tex]2 ^{-1}= -0.5,[/tex] and [tex]4 ^{-3} =0.01563[/tex]
[tex]2^0 =1[/tex] , and [tex]4 ^{-2} =0.0625[/tex]
[tex]2^1 = 2 [/tex] and [tex]4 ^{-1} =0.25[/tex]
[tex]2^2 =4 [/tex] and [tex]4^0 =1[/tex]
[tex]2^3 =8[/tex] and [tex]4^1=4[/tex]
[tex]2^4 =16, [/tex] and [tex]4^2 = 16 [/tex] (This is the solution when x=4)

Part C:
To solve graphically you just plot the two equations [tex]=2^x[/tex] and [tex]y=4 ^{x-2} [/tex]
Together graph of [tex]y=2^x [/tex] and [tex]y=4 ^{x-2} [/tex]

The picture below is how the graph looks like.
Full Credit to my online calculator 'cause we don't have a graphing calculator here.

I hope I helped!

Sarah is 50 years old. she is twice as old as her friend bill and bill is 5 times as old as his sister jane. jane's mom is 12 times older than jane. what is the age difference between jane's mom and sarah?

Answers

10 years. Bill is 25, his sister is 5, and their mother is 60.

Sarah is twice as old as Bill so 2X=50 and X=25 so Bill is 25. Bill is 25 and bill is 5 times older than his sister Jane so 5n=25 N=5 so Jane is 5 years old. Jane's mom is 12 time older than Jane so 12x5=60 and so

60-50=10 so the answer is 10

The height of the closet is 96 inches, and aisha would like to have 4 rows of cube organizers. what is the most the height of each cube organizer can be

Answers

the height of the closet is 96 inches...and she wants 4 rows..
so the greatest height of each cube can be : 96/4 = 24 inches

Answer: the most the height of each cube organizer can be 24 inches

Step-by-step explanation:

Since we have given that

Height of the closet = 96 inches

Number of rows of cube organizers = 4

Greatest height of each cube organizer can be is given by

[tex]\frac{96}{4}=24[/tex]

Hence, the most the height of each cube organizer can be 24 inches.

The new shanghai restaurant offers a choice of five appetizers, two choices of soups, and eleven choices of entrees for its lunch special. how many different complete lunches can be ordered from the restaurant's lunch special menu?

Answers

multiply the choices together
5*2*11 = 110

Final answer:

Using the Multiplication Principle, a customer can choose from 110 different complete lunch combinations by selecting one of each option (appetizer, soup, and entrée) from the menu at the New Shanghai restaurant.

Explanation:

To determine the total number of different complete lunches that can be ordered from the restaurant's lunch special menu, we apply The Multiplication Principle of counting. The principle states that if one event can occur in m ways and another independent event can occur in n ways, then the total number of ways both events can occur together is the product of m and n. In the context of ordering a lunch, each choice (appetizer, soup, and entrée) represents an independent event.

For appetizers, there are 5 choices.

For soups, there are 2 choices.

For entrées, there are 11 choices.

Following the Multiplication Principle, the total number of different complete lunches is calculated as follows:

5 appetizers × 2 soups × 11 entrées = 110 different complete lunches.

Therefore, customers have the opportunity to choose from 110 unique complete lunch combinations at the New Shanghai restaurant.

if I work z hours overtime, and my overtime wage is $25 per hour, what's my overtime pay?

Answers

Your over time pay=25z

What are the slope and the y-intercept of the line shown in the graph?
(A) y-intercept = 2 and slope = -3
(B) y-intercept = 2 and slope = 3
(C) y-intercept = 3 and slope = 2
(D) y-intercept = -3 and slope = 2

Answers

the y-intercept is where it crosses the y-axis: 2
the slope is rise over run. Try to choose two points on the line that you can make out the location of like (0,2) and (1,-1) is close enough. Count rise down -3 over run right +1 = -3 slope

y-intercept = 2

slope = -3

let's take the 2 coordinates from the line.

(0, 2)(1, -1)

The y-intercept is when x = 0, When x = 0, y = 2 . This means the y-intercept is 2.

m = slope = -1 - 2 / 1 - 0 = -3 / 1 = -3

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What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ? Enter your answer in the box. Do not round any side lengths.

Answers

Area (a) = length (l) × width (w), so we need the distance formula between 2 points for each one width and one length:
[tex]d = \sqrt{{(y2 - y1)}^{2} + {(x2 - x1)}^{2} }[/tex]
[tex]w = \sqrt{{(1 - 3)}^{2} + {(3 - 1)}^{2} } \\ = \sqrt{( {( - 2)}^{2} + {(2)}^{2})} = \sqrt{4 + 4} \\ = \sqrt{8} \: = [/tex]
[tex]l = \sqrt{({(3 - - 1)}^{2} + {(1 - - 3)}^{2})} \\ = \sqrt{({(3 + 1)}^{2} + {(1 + 3)}^{2})} \\ = \sqrt{({(4)}^{2} + {(4)}^{2})} \\ = \sqrt{({16} + {16})} \: = \sqrt{32} [/tex]
[tex]a \: = l \times w = \sqrt{32} \times \sqrt{8} \\ = \sqrt{256} = 16 \: {units}^{2} [/tex]

find four consecutive even integers such that 2 times the sum of the first and second is 14 more than 3 times the fourth.

Answers

Let the first integer be x, then:-

2 (x + x+ 2) = 3(x + 6) + 14

4x + 4 = 3x + 18 + 14
x = 18 + 14 - 4 = 28

the four integers are 28,30,32 and 34.

The required four consecutive even integers are given as 28, 30, 32, and 34.

Given that,
Four consecutive even integers such that 2 times the sum of the first and second is 14 more than 3 times the fourth.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let, the first term be a, and the common difference be d,

And series 2n, 2n + 2, 2n +4, 2n + 6
According to the question,
2[2n + 2n + 2] = 14 + 3[2n + 6]
8n + 4 = 14 + 6n + 18
2n = 28
n = 14
Series can be given as,
28, 30, 32, 34

Thus, the required four consecutive even integers are given as 28, 30, 32, and 34.

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Find the parabola whose minimum is at (−12,−2)(−12,−2) rather than the point given in the book. the parabola's equation is y=x2+ax+by=x2+ax+b, where

Answers

The vertex form of the equation of a parabola is given by

[tex]y-k=a(x-h)^2[/tex]

where (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is (-12, -2), the equation of the parabola is given by

[tex]y-(-2)=a(x-(-12))^2 \\ \\ y+2=a(x+12)^2=a(x^2+24x+144)=ax^2+24ax+144a \\ \\ y=ax^2+24ax+114a-2 \\ \\ y=x^2+24x+ \frac{114a-2}{a} [/tex]

For a = 1,

[tex]y=x^2+24x+112[/tex]

The parabola whose minimum is at (−12,−2) is given by the equation [tex]y=x^2+ax+b[/tex], where a = 24 and b = 112.

Eleven less than seven times a number is five more than six times the number.

Answers

Final answer:

The problem is a simple algebraic equation in the form 7x - 11 = 6x + 5. By rearranging and simplifying, we find the solution is x = 16.

Explanation:

The question presents a mathematical statement that needs to be solved for the variable. Translating the words into an equation, we get: 7x - 11 = 6x + 5. This equation is saying seven times a number (we'll call it 'x') reduced by eleven is equal to six times that number increased by five.

To solve for 'x', first, rearrange the equation to get all 'x' terms on one side and constants on the other. By subtracting 6x from both sides, we get x - 11 = 5. Then, add 11 to both sides to isolate 'x': x = 16.

So, the number or 'x' that satisfies this equation is 16.

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x = 16.

To solve this, let the unknown number be represented by x.

We can set up the equation based on the given information:

7x - 11 = 6x + 5

Subtract 6x from both sides of the equation:

7x - 6x - 11 = 6x - 6x + 5

Simplify the equation:

x - 11 = 5

Add 11 to both sides:

x - 11 + 11 = 5 + 11

Simplify the equation:

x = 16

Thus, the number is 16.

Use the graphs of f and g. Which describes the transformation from the graph of f to the graph of g?

f(x)=−4x+8f(x)=−4x+8
g(x)=−f(x)g(x)=−f(x)

1.horizontal translation 1 units left

2.vertical translation 4 units down

3.reflection in the x-axis

4.reflection in the y-axis

5.horizontal shrink by a factor of 1/4

6.horizontal stretch by a factor of 4

7.vertical shrink by a factor of 1/4

8.vertical stretch by a factor of 4

Answers

The transformation from the graph of [tex]$ f(x) = -4x + 8 $[/tex] to [tex]$ g(x) = -f(x) $[/tex] is a reflection in the x-axis.

The [tex]- $ f(x) = -4x + 8 $[/tex] is a linear function with a negative coefficient in front of [tex]$ x $[/tex], indicating a reflection in the x-axis.

When you negate f(x) to get g(x) = -f(x), it reflects the graph of f(x) in the x-axis.

So, the correct answer is: 3. Reflection in the x-axis

Give an estimate for 42.8 x 13.6

Answers

Final answer:

A reasonable estimate for the product of 42.8 x 13.6 is 602, achieved by rounding each number to the nearest whole number and then multiplying them together.

Explanation:

To estimate the product of 42.8 x 13.6, we can round each number to the nearest whole number and then multiply. So, 42.8 is approximately 43, and 13.6 is approximately 14. Now, multiply these estimated values.

Estimated Calculation:

43 x 14 = 602

Therefore, a reasonable estimate for the product of 42.8 and 13.6 is 602. Remember, in estimation, we aim to simplify the calculation while still arriving at a number that's close to what the actual answer would be if we calculated it exactly.

The larger of two numbers is 3 more than twice the smaller. if the twice the larger is decreased by 5 times the smaller the result is 0. find the two numbers

Answers

let x be the large number, and y be the smaller one: x=3+2y, 2x-5y=0 (from the question) --> substitute the first equation in the second --> 2(3+2y)-5y=0 --> 6+4y-5y=0 -->6-y=0 --> y=6, substitute y=6 in the first equation --> x=3+2(6) --> x=15. therefore the two numbers are 6,15

Can somebody please help me?

Answers

Again, look at the dotted line of y = x in the first picture. Which of the options given are symmetric across that diagonal line?

Max spent $53 and now has no money left. How much did he have before his purchase

Answers

Before Max had $53, thats my final answer ;)

An equation is formed when two equal expressions. The amount Max had before his purchase is $53.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Max spent $53 and now has no money left. Therefore, we can write the details as,

The amount spent on the purchase = $53

The amount left after purchase = $0

Let the amount before purchase be represented by M. Therefore, we can write the amount remaining after purchase as,

Amount before purchase - Amount spent on purchase = Amount remaining after purchase

M - $53 = $0

Adding 53 on both sides.

M - 53 + 53 = 53

M = 53

M = $53

Thus, the amount Max had before his purchase is $53.

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Help me please don’t know how to do this and I have psat in a week.

Answers

Use the quadratic formula to solve for x (see attached image; we plug in a = 2, b = 7 and c = -15). Doing so leads to
x = 3/2
x = -5

Since 3/2 = 1.5 is larger than -5, this means r = 3/2 = 1.5 and s = -5

Subtract r and s:
r - s = (3/2) - (-5)
r - s = (3/2) + (5)
r - s = (3/2) + (5/1)
r - s = (3/2) + (10/2)
r - s = (3+10)/2
r - s = 13/2

Therefore the final answer is B) 13/2

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