Write an equation. Let x be the unknown number.

nine is seventeen more than two times a number

Answer:

The time of a commercial airplane is 280 minutes

Step-by-step explanation:

Let

x -----> the speed of a commercial airplane

y ----> the speed of a jet plane

t -----> the time that a jet airplane takes  from Vancouver to Regina

we know that

The speed is equal to divide the distance by the time

y=2x ----> equation A

The speed of a commercial airplane is equal to

x=1,730/(t+140) ----> equation B

The speed of a jet airplane is equal to

y=1,730/t -----> equation C

substitute equation B and equation C in equation A

1,730/t=2(1,730/(t+140))

Solve for t

1/t=(2/(t+140))

t+140=2t

2t-t=140

t=140 minutes

The time of a commercial airplane is

t+140=140+140=280 minutes

Answer:

[tex]-8 < x < 8[/tex]

Step-by-step explanation:

Your compound inequality will include two inequalities.

These are:

x > -8

x < 8

Put your lowest number first, ensuring that your sign is pointed in the correct direction.

[tex]-8 < x[/tex]

Next, enter your higher number, again making sure that your sign is pointing in the correct direction.

[tex]-8 < x < 8[/tex]

Answer:

-8 < r < 8

Step-by-step explanation:

Let r = real number

Greater than  >

r>-8

less than  <

r <8

We want a compound inequality so we combine these

-8 < r < 8

ANSWER

[tex]{(x + 10)}^{2} + {(y + 6)}^{2} = 121[/tex]

EXPLANATION

The equation of the circle in general form is given as:

[tex] {x}^{2} + {y}^{2} + 20x + 12y + 15 = 0[/tex]

To obtain the standard form, we need to complete the squares.

We rearrange the terms to obtain:

[tex] {x}^{2} + 20x + {y}^{2} + 12y = - 15 [/tex]

Add the square of half the coefficient of the linear terms to both sides to get:

[tex]{x}^{2} + 20x +100 + {y}^{2} + 12y + 36 = - 15 + 100 + 36[/tex]

Factor the perfect square trinomial and simplify the RHS.

[tex]{(x + 10)}^{2} + {(y + 6)}^{2} = 121[/tex]

This is the equation of the circle in standard form.

Answer:

0.00008 ÷ 640,000,000 means

8*10^-5 ÷ 6.4*10^8

so let's collect to simplify the operation

(8÷6.4)*(10^-12) -5-7=-12

then the answer becomes 1.25×10^-14 that is B

Answer:

option C

Step-by-step explanation:

Evaluate 0.00008 ÷ 640,000,000.

0.00008 can be written in standard notation

Move the decimal point to the end

so it becomes  [tex]8 \cdot 10^{-5}[/tex]

for 640,000,000 , remove all the zeros and write it in standard form

[tex]64 \cdot 10^7[/tex]

Now we divide both

[tex]\frac{8 \cdot 10^{-5}}{64 \cdot 10^7}[/tex]

Apply exponential property

a^m divide by a^n  is a^ m-n

[tex]\frac{8}{64} =0.125[/tex]

[tex]\frac{10^{-5}}{10^7}=10^{-12}[/tex]

[tex]0.125 \cdot 10^{-12}= 1.25 \cdot 10^{-13}[/tex]

Answer:

h=7

Step-by-step explanation:

[tex]h+(-3)=4[/tex]

may be rewritten as

[tex]h-3=4[/tex]

as adding a negative is the same as subtracting a positive.

To solve, add 3 to both sides.

[tex]h-3=4\\h=7[/tex]

Answer:

h=7

Step-by-step explanation:

1) Add three to both sides

2) You should get h=7

Answer:

a)120

b)6.67%

Step-by-step explanation:

Given:

No. of digits given= 6

Digits given= 1,2,3,5,8,9

Number to be formed should be 3-digits, as we have to choose 3 digits from given 6-digits so the no. of combinations will be

6P3= 6!/3!

      = 6*5*4*3*2*1/3*2*1

      =6*5*4

      =120

Now finding the probability that both the first digit and the last digit of the three-digit number are even numbers:

As the first and last digits can only be even

then the form of number can be

a)2n8 or

b)8n2

where n can be 1,3,5 or 9

4*2=8

so there can be 8 three-digit numbers with both the first digit and the last digit even numbers

And probability = 8/120

                          = 0.0667

                          =6.67%

The probability that both the first digit and the last digit of the three-digit number are even numbers is 6.67% !

1.

[tex]6\cdot5\cdot4=120[/tex]

2.

[tex]|\Omega|=120\\|A|=2\cdot4\cdot1=8\\\\P(A)=\dfrac{8}{120}=\dfrac{1}{15}\approx6.7\%[/tex]

Answer:

B

Step-by-step explanation:

Given

(5 + 7i) + (- 2 + 6i ) ← remove parenthesis and collect like terms

= 5 + 7i - 2 + 6i

= 3 + 13i → B

The sum of the complex number is 3 + 13i.

Option B is the correct answer.

We have,

To find the sum of the complex numbers (5+7i) and (-2+6i), you can simply add the real parts together and add the imaginary parts together separately.

Real part: 5 + (-2) = 3

Imaginary part: 7i + 6i = 13i

Combining the real and imaginary parts, we get:

Sum = 3 + 13i

Therefore,

The sum of the complex number is 3 + 13i.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

Option B

Step-by-step explanation:

we know that

To find the reciprocal of a fraction, flip the fraction.

Remember that

A number multiplied by its reciprocal is equal to 1

In this problem we have

[tex]\frac{10b}{2b+8}[/tex]

Flip the fraction

[tex]\frac{2b+8}{10b}[/tex] -----> reciprocal

therefore

The reciprocal is

The quantity 2 multiplied by b plus 8 end of quantity divided by the quantity 10 multiplied by b end of quantity.

Answer:

Step-by-step explanation:

There are 3 ways to find the other x intercept.

1) Polynomial Long Division.

Divide x^2 - 3x + 2 by the binomial x - 2, because by the Factor Theorem if a is a root of a polynomial then x - a is a factor of said polynomial.

2) Just solving for x when y = 0, by using the quadratic formula.

[tex]x^2 - 3x + 2 = 0\\x_{12} = \frac{3 \pm \sqrt{9 - 4(1)(2)}}{2} = \frac{3 \pm 1}{2} = 2, 1[/tex].

So the other x - intercept is at (1, 0)

3) Using Vietta's Theorem regarding the solutions of a quadratic

Namely, the sum of the solutions of a quadratic equation is equal to the quotient between the negative coefficient of the linear term divided by the coefficient of the quadratic term.

[tex]x_1 + x_2 = \frac{-b}{a}[/tex]

And the product between the solutions of a quadratic equation is just the quotient between the constant term and the coefficient of the quadratic term.

[tex]x_1 \cdot x_2 = \frac{c}{a}[/tex]

These relations between the solutions give us a brief idea of what the solutions should be like.

For this case we must represent the following expression algebraically, in addition to indicating its result:

"2 plus 9"

So, we have:

[tex]2 + 9 =[/tex]

By law of the signs of the sum, we have that equal signs are added and the same sign is placed:

[tex]2 + 9 = 11[/tex]

ANswer:

11

Answer:

B) 28.53 unit²

Step-by-step explanation:

The diagonal AD divides the quadrilateral in two triangles:

Area of Quadrilateral will be equal to the sum of Areas of both triangles.

i.e.

Area of ABCD = Area of ABD + Area of ACD

Area of Triangle ABD:

Area of a triangle is given as:

[tex]Area = \frac{1}{2} \times base \times height[/tex]

Base = AB = 2.89

Height = AD = 8.6

Using these values, we get:

[tex]Area = \frac{1}{2} \times 2.89 \times 8.6 = 12.43[/tex]

Thus, Area of Triangle ABD is 12.43 square units

Area of Triangle ACD:

Base = AC = 4.3

Height = CD = 7.58

Using the values in formula of area, we get:

[tex]Area = \frac{1}{2} \times 4.3 \times 7.58 = 16.30[/tex]

Thus, Area of Triangle ACD is 16.30 square units

Area of Quadrilateral ABCD:

The Area of the quadrilateral will be = 12.43 + 16.30 = 28.73 units²

None of the option gives the exact answer, however, option B gives the closest most answer. So I'll go with option B) 28.53 unit²

Answer:

Step-by-step explanation:

We only need two points to plot the graph of each equation.

[tex]y=-3x+2\\\\for\ x=0\to y=-3(0)+2=0+2=2\to(0,\ 2)\\for\ x=1\to y=-3(1)+3=-3+2=-1\to(1,\ -1)\\\\y=5x+28\\\\for\ x=-4\to y=5(-4)+28=-20+28=8\to(-4,\ 8)\\for\ x=-6\to y=5(-6)+28=-30+28=-2\to(-6,\ -2)[/tex]

Look at the picture.

Read the coordinates of the intersection of the line (solution).

Answer:

x = - 15

Step-by-step explanation:

The equation is  [tex]\frac{5}{x}=\frac{4}{x+3}[/tex]

We now cross mulitply and do algebra to figure the value of x (shown below):

[tex]\frac{5}{x}=\frac{4}{x+3}\\5(x+3)=4(x)\\5x+15=4x\\5x-4x=-15\\x=-15[/tex]

Hence x = -15

Answer:

D

Step-by-step explanation:

Answer:

Assume that [tex]a[/tex] and [tex]p[/tex] are constants. The slope of the line will be equal to

Step-by-step explanation:

Rewrite the expression of the line to express [tex]y[/tex] in terms of [tex]x[/tex] and the constants.

Substract [tex]x\cdot \cos{(a)}[/tex] from both sides of the equation:

[tex]y \sin{(a)} = p - x\cos{(a)}[/tex].

In case [tex]\sin{a} \ne 0[/tex], divide both sides with [tex]\sin{a}[/tex]:

[tex]\displaystyle y = - \frac{\cos{(a)}}{\sin{(a)}}\cdot x+ \frac{p}{\sin{(a)}}[/tex].

Take the first derivative of both sides with respect to [tex]x[/tex]. [tex]\frac{p}{\sin{(a)}}[/tex] is a constant, so its first derivative will be zero.

[tex]\displaystyle \frac{dy}{dx} = - \frac{\cos{(a)}}{\sin{(a)}}[/tex].

[tex]\displaystyle \frac{dy}{dx}[/tex] is the slope of this line. The slope of this line is therefore

[tex]\displaystyle - \frac{\cos{(a)}}{\sin{(a)}} = -\cot{(a)}[/tex].

In case [tex]\sin{a} = 0[/tex], the equation of this line becomes:

[tex]y \sin{(a)} = p - x\cos{(a)}[/tex].

[tex]x\cos{(a)} = p[/tex].

[tex]\displaystyle x = \frac{p}{\cos{(a)}}[/tex],

which is the equation of a vertical line that goes through the point [tex]\displaystyle \left(0, \frac{p}{\cos{(a)}}\right)[/tex]. The slope of this line will be infinity.

To find (f/g)(x) with f(x) = 6x + 2 and g(x) = x - 7, one must divide f(x) by g(x). The domain restriction occurs because division by zero is not defined, so we exclude the x value that makes g(x) zero, which is x = 7.

To perform the indicated operation (f/g)(x) with the given functions f(x) = 6x + 2 and g(x) = x - 7, we need to divide the function f(x) by the function g(x). This operation is equivalent to finding the quotient of the two functions, which is expressed as:

(f/g)(x) = f(x)/g(x) = (6x + 2)/(x - 7)

The domain restriction occurs when the denominator, g(x), is equal to zero since division by zero is undefined. So we must find the value of x for which g(x) = 0. Since g(x) = x - 7, setting this equal to zero gives us:

x - 7 = 0 → x = 7

Therefore, the domain of the function (f/g)(x) is all real numbers except for x = 7, because at x = 7 the function is undefined. The domain of (f/g)(x) can be expressed as ℜ - {7}, where ℜ represents the set of all real numbers.

Answer:

=70$

Step-by-step explanation:

The total in her account at day zero =85$

Lunch for five days= 3$×5

=15$

Total in her account= Initial amount - Expenditure on lunch

=85$-15$

=70$

The balance in Latesha's Lunch Account after having lunch for five day=70$

[tex]\bf \sqrt{3x^2}\cdot \sqrt{4x}\implies \sqrt{3x^2\cdot 4x}\implies \sqrt{12x^2x}\implies \sqrt{4\cdot 3\cdot x^2x} \\\\\\ \sqrt{2^2\cdot 3\cdot x^2x}\implies 2x\sqrt{3x}[/tex]

Answer:

[tex]\frac{147}{100}[/tex]

Step-by-step explanation:

This is the answer because 147 ÷ 100 = 1.47

Find the answer in the attachment.

The hyperbola's equation is x² / 3600 - y² / 121 = 1, centered at the origin (0,0). Its vertices are at (60,0), (-60,0) on the x-axis, and (0,11), (0,-11) on the y-axis.

To find the equation of the hyperbola, we need to determine its center and the distances from the center to the vertices along the x and y axes. The general equation of a hyperbola centered at (h, k) is given by:

(x - h)² / a² - (y - k)² / b² = 1

Where (h, k) is the center of the hyperbola, and 'a' and 'b' are the distances from the center to the vertices along the x and y axes, respectively.

In this case, since the hyperbola is symmetric along the x and y axes, the center is at the origin (0, 0). Also, we know the distance from the center to the vertices along the x-axis is 60 units (60 and -60) and along the y-axis is 11 units (11 and -11).

So, a = 60 and b = 11.

Now we can plug these values into the equation:

x² / (60)² - y² / (11)² = 1

Simplifying further:

x² / 3600 - y² / 121 = 1

And that's the equation of the hyperbola.

To know more about hyperbola:

https://brainly.com/question/19989302

#SPJ2

ANSWER

C) 4x-3y=-12

EXPLANATION

The intercept form of a straight line is given by:

[tex] \frac{x}{x - intercept} + \frac{y}{y - intercept} = 1[/tex]

From the the x-intercept is -3 and the y-intercept is 4.

This is because each box is one unit each.

We substitute the intercepts to get:

[tex] \frac{x}{ - 3} + \frac{y}{4} = 1[/tex]

We now multiply through by -12 to get

[tex] - 12 \times \frac{x}{ - 3} + - 12 \times \frac{y}{4} = 1 \times - 12[/tex]

[tex]4x - 3y = -12[/tex]

The correct choice is C.

there's a scale factor of two!

five times two is ten.

hope this helps! :) xx

Answer:

corresponding

Step-by-step explanation:

Answer:

Corresponding

Step-by-step explanation:

I like to call corresponding angles, the copy and paste angles because you can copy and paste the top intersection over the bottom intersection; the angles that lay down on top of each other are the corresponding angles. 1 and 5 do this.

Answer:

Option B. g(x) is greater

Step-by-step explanation:

step 1

Find the value of f(x) when the value of x is equal to 3

we have

f(x)=2x-1

substitute the value of x=3

f(3)=2(3)-1=5

step 2

Find the value of g(x) when the value of x is equal to 3

Observing the graph

when x=3

g(3)=7

step 3

Compare the values

f(x)=5

g(x)=7

so

g(x) > f(x)

g(x) is greater

Answer:

Correct option is:

B. g(x) is greater

Step-by-step explanation:

Firstly, we find the value of f(x) when x=3

f(x)=2x-1

substitute the value of x=3

f(3)=2×3-1=5

On observing the graph, we see that g(x)=7 when x=3

Now, on Comparing the values of f(x) and g(x) when x=3

f(3)=5

g(3)=7

so, g(x) > f(x) when x=3

So, Correct option is:

B. g(x) is greater

[tex]\bf \begin{array}{ccll} \$&hour\\ \cline{1-2} 5.5&1\\ x&3\frac{1}{3} \end{array}\implies \cfrac{5.5}{x}=\cfrac{1}{3\frac{1}{3}}\implies \cfrac{5.5}{x}=\cfrac{1}{\frac{3\cdot 3+1}{3}}\implies \cfrac{5.5}{x}=\cfrac{1}{\frac{10}{3}}\implies \cfrac{5.5}{x}=\cfrac{\frac{1}{1}}{\frac{10}{3}} \\\\\\ \cfrac{5.5}{x}=\cfrac{1}{1}\cdot \cfrac{3}{10}\implies \cfrac{5.5}{x}=\cfrac{3}{10}\implies 55=3x\implies \stackrel{\textit{about 18 bucks and 33 cents}}{\cfrac{55}{3}=x\implies 18\frac{1}{3}=x}[/tex]

Answer:

$18.3

Step-by-step explanation:

If you are paid $5.50/hour for mowing yards, and you take 3 1/3 hours to mow a yard, you should earn $18.3.

3 1/3 hours

$5.50 and hour

$5.50 x 3 = $16.5

$5.50 / 3 = $1.8

$16.5 + $1.8 = $18.3

Therefore, you are owed $18.3.

Answer:

regular

Step-by-step explanation:

1. look at table

Answer:

The correct option is A)

P(Win|Regular)=0.76

P(Win|Prevent )=0.58

You are more likely to win by playing regular defense.

Step-by-step explanation:

Consider the provided table.

We need to find which strategy is better.

If team play regular defense then they win 38 matches out of 50.

[tex]Probability=\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

[tex]P(Win|Regular)=\frac{38}{50}[/tex]

[tex]P(Win|Regular)=0.76[/tex]

If team play prevent defense then they win 29 matches out of 50.

Thus, the probability of win is:

[tex]P(Win|Prevent )=\frac{29}{50}[/tex]

[tex]P(Win|Prevent )=0.58[/tex]

Since, 0.76 is greater than 0.58

That means the probability of winning the game by playing regular defense is more as compare to playing prevent defense.

Hence, the conclusion is: You are more likely to win by playing regular defense.

Thus, the correct option is A)

P(Win|Regular)=0.76

P(Win|Prevent )=0.58

You are more likely to win by playing regular defense.

Answer:

k = 2

Step-by-step explanation:

If the roots are real and equal then the condition for the discriminant is

b² - 4ac = 0

For 2x² - (k + 2)x + k = 0 ← in standard form

with a = 2, b = - (k + 2) and c = k, then

(- (k + 2))² - (4 × 2 × k ) = 0

k² + 4k + 4 - 8k = 0

k² - 4k + 4 = 0

(k - 2)² = 0

Equate factor to zero and solve for k

(k - 2)² = 0 ⇒ k - 2 = 0 ⇒ k = 2

Answer:

Step-by-step explanation:

A quadratic equation has two equal real roots if a discriminant is equal 0.

[tex]ax^2+bx+c=0[/tex]

Discriminant [tex]b^2-4ac[/tex]

We have the equation

[tex]2x^2-(k+2)x+k=0\to a=2,\ b=-(k+2),\ c=k[/tex]

Substitute:

[tex]b^2-4ac=\bigg(-(k+2)\bigg)^2-4(2)(k)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=k^2+2(k)(2)+2^2-8k=k^2+4k+4-8k=k^2-4k+4\\\\b^2-4ac=0\iff k^2-4k+4=0\\\\k^2-2k-2k+4=0\\\\k(k-2)-2(k-2)=0\\\\(k-2)(k-2)=0\\\\(k-2)^2=0\iff k-2=0\qquad\text{add 2 to both sides}\\\\k=2[/tex]

Answer:

x+6

Step-by-step explanation:

Let's see if the numerator is factorable.

Since the coefficient of x^2 is 1 (a=1), all you have to do is find two numbers that multiply to be -6  (c) and add up to be 5 (b).

Those numbers are 6 and -1.

So the factored form of the numerator is (x+6)(x-1)

So when you divide (x+6)(x-1) by (x-1) you get (x+6) because (x-1)/(x-1)=1 for number x except x=1 (since that would lead to division by 0).

Anyways, this is what I'm saying:

[tex]\frac{(x+6)(x-1)}{(x-1)}=\frac{(x+6)\xout{(x-1)}}{\xout{(x-1)}}[/tex]

[tex]x+6[/tex]

Answer:

110

Step-by-step explanation:

He said he had atleast 1 of each. Hope it helps.

The smallest possible total weight of Tom's toys​ is:

                          210 grams

It is given that:

Tom has 8 toys each toy weighs either 20 grams or 40 grams or 50 grams.

Also, he  has a different number of toys (at least one) of each weight.

Now, the smallest possible weight of Tom's toy is such that:

He has one toy of 50 grams , one of 40 grams and the other's are of smallest weight i.e. 20 grams.

This means he has 6 toys of 20 grams.

One of 40 grams.

One of 50 grams.

Hence,

Total weight= 20×6+40+50

i.e.

Total weight= 120+90

i.e.

Total weight= 210 grams.

Answer:

m=7

Remainder =4

If q=1 then r=3 or r=-1.

If q=2 then r=3.

They are probably looking for q=1 and r=3 because the other combinations were used earlier in the problem.

Step-by-step explanation:

Let's assume the remainders left when doing P divided by (x-1) and P divided by (2x+3) is R.

By remainder theorem we have that:

P(1)=R

P(-3/2)=R

[tex]P(1)=2(1)^3+m(1)^2-5[/tex]

[tex]=2+m-5=m-3[/tex]

[tex]P(\frac{-3}{2})=2(\frac{-3}{2})^3+m(\frac{-3}{2})^2-5[/tex]

[tex]=2(\frac{-27}{8})+m(\frac{9}{4})-5[/tex]

[tex]=-\frac{27}{4}+\frac{9m}{4}-5[/tex]

[tex]=\frac{-27+9m-20}{4}[/tex]

[tex]=\frac{9m-47}{4}[/tex]

Both of these are equal to R.

[tex]m-3=R[/tex]

[tex]\frac{9m-47}{4}=R[/tex]

I'm going to substitute second R which is (9m-47)/4 in place of first R.

[tex]m-3=\frac{9m-47}{4}[/tex]

Multiply both sides by 4:

[tex]4(m-3)=9m-47[/tex]

Distribute:

[tex]4m-12=9m-47[/tex]

Subtract 4m on both sides:

[tex]-12=5m-47[/tex]

Add 47 on both sides:

[tex]-12+47=5m[/tex]

Simplify left hand side:

[tex]35=5m[/tex]

Divide both sides by 5:

[tex]\frac{35}{5}=m[/tex]

[tex]7=m[/tex]

So the value for m is 7.

[tex]P(x)=2x^3+7x^2-5[/tex]

What is the remainder when dividing P by (x-1) or (2x+3)?

Well recall that we said m-3=R which means r=m-3=7-3=4.

So the remainder is 4 when dividing P by (x-1) or (2x+3).

Now P divided by (qx+r) will also give the same remainder R=4.

So by remainder theorem we have that P(-r/q)=4.

Let's plug this in:

[tex]P(\frac{-r}{q})=2(\frac{-r}{q})^3+m(\frac{-r}{q})^2-5[/tex]

Let x=-r/q

This is equal to 4 so we have this equation:

[tex]2u^3+7u^2-5=4[/tex]

Subtract 4 on both sides:

[tex]2u^3+7u^2-9=0[/tex]

I see one obvious solution of 1.

I seen this because I see 2+7-9 is 0.

u=1 would do that.

Let's see if we can find any other real solutions.

Dividing:

1     |   2    7     0     -9

     |         2      9      9

       -----------------------

          2    9     9      0

This gives us the quadratic equation to solve:

[tex]2x^2+9x+9=0[/tex]

Compare this to [tex]ax^2+bx+c=0[/tex]

[tex]a=2[/tex]

[tex]b=9[/tex]

[tex]c=9[/tex]

Since the coefficient of [tex]x^2[/tex] is not 1, we have to find two numbers that multiply to be [tex]ac[/tex] and add up to be [tex]b[/tex].

Those numbers are 6 and 3 because [tex]6(3)=18=ac[/tex] while [tex]6+3=9=b[/tex].

So we are going to replace [tex]bx[/tex] or [tex]9x[/tex] with [tex]6x+3x[/tex] then factor by grouping:

[tex]2x^2+6x+3x+9=0[/tex]

[tex](2x^2+6x)+(3x+9)=0[/tex]

[tex]2x(x+3)+3(x+3)=0[/tex]

[tex](x+3)(2x+3)=0[/tex]

This means x+3=0 or 2x+3=0.

We need to solve both of these:

x+3=0

Subtract 3 on both sides:

x=-3

----

2x+3=0

Subtract 3 on both sides:

2x=-3

Divide both sides by 2:

x=-3/2

So the solutions to P(x)=4:

[tex]x \in \{-3,\frac{-3}{2},1\}[/tex]

If x=-3 is a solution then (x+3) is a factor that you can divide P by to get remainder 4.

If x=-3/2 is a solution then (2x+3) is a factor that you can divide P by to get remainder 4.

If x=1 is a solution then (x-1) is a factor that you can divide P by to get remainder 4.

Compare (qx+r) to (x+3); we see one possibility for (q,r)=(1,3).

Compare (qx+r) to (2x+3); we see another possibility is (q,r)=(2,3).

Compare (qx+r) to (x-1); we see another possibility is (q,r)=(1,-1).