If 5 + 6i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? –5 – 6i 5 – 6i 6 – 5i 6 + 5i

Answer:

unknown number is 13/2

Step-by-step explanation:

Let unknown number be 'x'

given that quotient of 12 times x and 13 is 6

i.e. 12 x/13 =6

multiply 13 both sides

12x = 6 * 13

divide 12 on both sides

x= (6*13)/12

x=13/2

The jaguar will run 32 miles farther than the giraffe after both run for 4 hours, calculated using the equation: Distance = Speed x Time.

To calculate how much farther the jaguar will run compared to the giraffe, we can start by writing an equation for the distance each animal travels. Distance is equal to speed multiplied by time, which can be expressed as:

D = s *t

For the jaguar traveling at 40 miles per hour for 4 hours, the distance would be:

D_jaguar = 40 miles/hour*4 hours = 160 miles

For the giraffe traveling at 32 miles per hour for 4 hours, the distance would be:

D_giraffe = 32 miles/hour *4 hours = 128 miles

To find out how much farther the jaguar runs, subtract the distance run by the giraffe from the distance run by the jaguar:

Additional distance = D_jaguar - D_giraffe = 160 miles - 128 miles = 32 miles

The jaguar will run 32 miles farther than the giraffe.

[tex]24x=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot3\cdot x\\\\8=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\\\\GCF(24x,\ 8)=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}=8\\\\24x+8=8(3x+1)[/tex]

Answer:

[tex](8,-12)[/tex]

Step-by-step explanation:

The two equations are:

[tex]\frac{1}{2}x+\frac{1}{3}y=0\\\frac{1}{4}x-\frac{1}{2}y=8[/tex]

We can solve the first equation for [tex]x[/tex] and then substitute into second equation to find the value of [tex]y[/tex].

[tex]\frac{1}{2}x+\frac{1}{3}y=0\\\frac{1}{2}x=-\frac{1}{3}y\\x=\frac{-\frac{1}{3}y}{\frac{1}{2}}\\x=-\frac{2}{3}y[/tex]

Now,

[tex]\frac{1}{4}x-\frac{1}{2}y=8\\\frac{1}{4}(-\frac{2}{3}y)-\frac{1}{2}y=8\\-\frac{2}{12}y-\frac{1}{2}y=8\\-\frac{2}{3}y=8\\y=\frac{8}{-\frac{2}{3}}\\y=-12[/tex]

Substituting [tex]y=-12[/tex] into the "solved for [tex]x[/tex]" version of first equation, we get the value of [tex]x[/tex]. So,

[tex]x=-\frac{2}{3}y\\x=-\frac{2}{3}(-12)\\x=8[/tex]

Hence the ordered pair is [tex](8,-12)[/tex] and this is the solution to the system of equations shown.

Answer:

(8,-12) the second option :)

Step-by-step explanation:

Answer:  I should charge 150¢ for the bunch of bananas.  

Step-by-step explanation:  Given that I work at a fruit market and bananas cost 50¢ a pound.

A customer hands me a bunch of bananas that weighs 3 pounds.

We are to find the price that I should charge for the bunch of bananas.

We will be using the UNITARY method to solve the given problem.

Also, we know that

100 ¢ = $1.

Cost of 1 pound of bananas =  50¢

Therefore, the cost of 3 pounds of bananas is given by

p = (50 × 3)¢ = 150¢ = $1.50.

Thus, I should charge 150¢ for the bunch of bananas.  

Answer:

5 is right 6 is right 7 is right ....

Step-by-step explanation:

actually they are all right triangles

Each of the triangle should be classified as follows;

5. Acute triangle.

6. Right triangle.

7. Obtuse triangle.

8. Obtuse triangle.

9. Obtuse triangle.

10. Acute triangle.

11. Right triangle.

12. Right triangle.

A triangle is classified as an acute triangle if the square of its longest side (c) is less than the sum of the squares of the two smaller sides (a + b).

Also, a triangle is classified as an obtuse triangle if the square of its longest side (c) is greater than the sum of the squares of the two smaller sides (a + b).

A triangle is classified as a right triangle if the square of its longest side (c) is equal to than the sum of the squares of the two smaller sides (a + b).

Part 5.

c² > a² + b²

15² > 11² + 12²

225 > 265 (False, it's an acute triangle).

Part 6.

c² > a² + b²

13² > 5² + 12²

169 > 169 (False, it's a right triangle).

Part 7.

c² > a² + b²

10² > 3² + 8²

100 > 73 (True, it's an obtuse triangle).

Part 8.

c² > a² + b²

20² > 9² + 12²

400 > 225 (True, it's an obtuse triangle).

Part 9.

c² > a² + b²

15² > 7² + 12²

225 > 193 (True, it's an obtuse triangle).

Part 10.

c² > a² + b²

10² > 8² + 7²

100 > 113 (False, it's an acute triangle).

Part 11.

c² > a² + b²

15² > 9² + 12²

225 > 225 (False, it's a right triangle).

Part 12.

c² > a² + b²

13² > 5² + 12²

169 > 169 (False, it's a right triangle).

Read more on triangles here: https://brainly.com/question/31186179

#SPJ6

Answer:

[tex](f o f^{-1})(3) = 3[/tex]

Step-by-step explanation:

[tex]f(x) = \frac{x-7}{2}[/tex]

We need to find (fof^-1)(3)

First we find f^-1(x)

Replace f(x) with y

[tex]y = \frac{x-7}{2}[/tex]

Now replace x  with y and y with x

[tex]x = \frac{y-7}{2}[/tex]

Multiply by 2 on both sides

2x = y -7

Now add 7 on both sides

2x + 7 = y

Replace y with f^-1(x)

f^-1(x) = 2x+ 7

Now we find (fof^-1)(3)

[tex](f o f^{-1})(3) = f(f^{-1}(3))[/tex]

First we find f^-1(3)

f^-1(x) = 2x+ 7

f^-1(3) = 2(3) + 7 = 6 + 7 = 13

Now we plug in 13 for x  and find out f(13)

[tex]f(x) = \frac{x-7}{2}[/tex]

[tex]f(13) = \frac{13-7}{2}= 3[/tex]

So , [tex](f o f^{-1})(3) = f(f^{-1}(3))= 3[/tex]

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

substitute the coordinates of the points (8, 0) and (20, 12) to the formula:

[tex]m=\dfrac{12-0}{20-8}=\dfrac{12}{12}=1[/tex]

y = 1x + b = x + b

Put the coordinates of the point (8, 0) to the equation of a line:

0 = 8 + b      subtract 8 from both sides

-8 = b

[tex]\text{Put c = -3 to the equation}\ F=\dfrac{9}{5}c+32.\\\\F=\dfrac{9}{5}(-3)+32=-\dfrac{27}{5}+32=-5.4+32=26.6\\\\Answer:\ \boxed{-3^oC=26.6^oF}[/tex]

We have two equilateral triangles and three rectangles.

The formula of an area of an equilateral triangle:

[tex]A_{\triangle}=\dfrac{a^2\sqrt3}{4}[/tex]

a - length of side

We have a = 14 ft. Substitute:

[tex]A_{\triangle}=\dfrac{14^2\sqrt3}{4}=\dfrac{196\sqrt3}{4}=49\sqrt3\ in^2[/tex]

The formula of an area of a rectangle:

[tex]A_{\boxed{\ }}=lw[/tex]

l - length

w - width

We have l = 10ft and w = 14 ft. Substitute:

[tex]A_{\boxed{\ }}=(10)(14)=140\ ft^2[/tex]

The Surface Area of the figure:

[tex]S.A.=3A_{\boxed{\ }}+2A_{\triangle}\\\\S.A.=3\cdot140+2\cdot49\sqrt3=(420+98\sqrt3)\ ft^2[/tex]

Answer:

$1.10 per mile  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

30 miles ÷ $33 = $1.10 per mile

Answer:

a. 2 lb 11 oz, b. 7 T 1,992 lb 12 oz , c. 38 lb 14 oz

Step-by-step explanation:

The first thing we need to understand is the conversions.

1 T = 2,000 lb

1 lb = 16 oz

Knowing this, there are many ways to find out the answer, please see below the one I used; I converted all measure units to oz, subtracted the amounts, and finally converted the units back to their original ones.

a. 5 lb or (16 oz*5) - (2 lb or (16 oz*2) + 5 oz) = 80 oz - 37 oz = 43 oz = 2 lb 11 oz

b. (17 T or (2,000 lb*17) + 13 lb + 3 oz) - (9 T or (2,000 lb*9) + 20 lb + 9 oz) = (34,013 lb or (16 oz *34,013) + 3 oz) - (18,020 lb or (16 oz *18,020) + 9 oz) = 544,213  oz - 288,329  oz = 255,884  oz = 7 T 1992 lb 12 oz

c. (68 lb or (16 oz*68) + 13 oz) - (30 lb or (16 oz*30)+15) = 1,117 oz - 495 oz = 622 oz = 38 lb 14 oz

Answer:

A. 2 pounds 11 ounces

B. 7T 1,992 pounds 12 ounces

C. 38 pounds and 14 ounces

Answer:

(x+7)(x+1)(x-4)

Step-by-step explanation:

A zero is is the x-intercept of the function. It is also known as the root. From the equation, the zero or root comes from the factors. When the factors are set equal to 0, we solve for x and the zero is the result. We will reverse this by taking the opposite value of the zero and placing into a factor expression. Remember the factor has the form x+a.

-7: x+7

-1: x+1

4: x-4

We write them together. (x+7)(x+1)(x-4). With more information we could find the leading coefficient and so forth.

Answer:

slope is undefined

Step-by-step explanation:

Answer:

Undefined

Step-by-step explanation:

The line is going straight down which means it cannot be negative or positive.

If you try to make the equation(y=mx + b), when you try to find the slope, you can't because (rise/run), there is no run. It is just a rise.

This means you cannot define the slope of the line.

Answer:

E = {-5, -4, -3}

Answer: a = 1, a = [tex]{\bold{-\dfrac{119}{125}}[/tex]

Step-by-step explanation:

In order to have the same root, the discriminant cannot be irrational.

(a + 3)x² - (11a + 1)x + a = 2(a - 5)

(a + 3)x² - (11a + 1)x + a = 2a - 10

(a + 3)x² - (11a + 1)x + a - 2a + 10 = 0

(a + 3)x² - (11a + 1)x  - (a - 10) = 0

a = a+3    b = -(11a+1)  c = -(a - 10)

Case 1:

b² - 4ac = 0

[-(11a + 1)]² - 4(a + 3)[-(a - 10)] = 0

121a² + 22a + 1 + 4a² - 28a - 120 = 0

125a² - 6a - 119 = 0

Use any method to solve the quadratic equation. I chose to use the factoring method.  

125a² - 6a - 119 = 0

125a² - 125a + 119a - 119 = 0

125a(a - 1) + 119(a - 1) = 0

(125a + 119)(a - 1) = 0

125a + 119 = 0          and        a - 1 = 0

              a = [tex]-\dfrac{119}{125}[/tex]    and             a = 1

Check:

(a + 3)x² - (11a + 1)x + a = 2(a - 5)

((1) + 3)x² - (11(1) + 1)x + (1) = 2((1) - 5)

  4x²      -       12x      + 1   = -8

4x² - 12x + 9 = 0

(2x + 3)² = 0

     x = [tex]-\dfrac{3}{2}[/tex]

Case 2: I am not sure how to do this one

[tex]ax^2+bx+c=0\\\\if\ \Delta=b^2-4ac>0\ then\ two\ solutions\qquad x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\if\ \Delta=b^2-4ac=0\ then\ one\ solution\\if\ \Delta=b^2-4ac<0\ then\ no\ real\ solution[/tex]

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

[tex](a+3)x^2-(11a+1)x+a=2(a-5)\qquad\text{use distributive property}\\\\(a+3)x^2-(11a+1)x+a=2a-10\qquad\text{subtract 2 from both sides and add 10 to both sides}\\\\(a+3)x^2-(11a+1)x-a+10=0\\\\\Delta=[-(11a+1)]^2-4(a+3)(-a+10)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\Delta=(11a)^2+2(11a)(1)+1^2+(-4a-12)(-a+10)\\\\\Delta=121a^2+22a+1+4a^2-40a+12a-120\\\\\Delta=125a^2-6a-119[/tex]

[tex]\text{One solution if}\ \Delta=0.\\\\\Delta=0\iff125a^2-6a-119=0\\\\\Delta_a=(-6)^2-4(125)(-119)=36+59,500=59,536\\\\\sqrt{\Delta_a}=\sqrt{59,536}=244\\\\a_1=\dfrac{-(-6)-244}{2(125)}=\dfrac{-238}{250}=\dfrac{-238:2}{250:2}=-\dfrac{119}{125}\\\\a_2=\dfrac{-(-6)+244}{2(125)}=\dfrac{250}{250}=1\\\\Answer:\ \boxed{a=-\dfrac{119}{125}\ or\ a=1}[/tex]

Answer:

B) 21x-7  

Step-by-step explanation:

Let A = speed of Arabian horse and T = speed of thoroughbred.

Then

A = T – (4x + 2)

A = T – 4x - 2                Remove parentheses

A = 25x - 5 - 4x – 2     Combine like terms

A = 21x - 7

Answer:9090

it is simple you just need to multiply by 2

Answer:

9090

Step-by-step explanation:

meat to feed 22 pet dragons per day=4545

meet to feed 44 pet dragons per day=?

as number of pet dragons have doubled

so amount of feed will also be doubled

hence

meet to feed 44 pet dragons per day=4545*2=9090

Answer:

x < 3 or x > 9

Step-by-step explanation:

given 6| x - 6 | + 7 > 25 ( subtract 7 from both sides )

6| x - 6 | > 18 ( divide both sides by 6 )

| x - 6 | > 3

Inequalities of the form | x | > a always have solutions of the form

x < - a OR x > a, hence

x - 6 < - 3 or x - 6 > 3 ( add 6 to both sides in both inequalities )

x < 3 or x > 9

Answer: x > 9 or x < 3

Step-by-step explanation:

Step 1: Isolate the absolute value expression.

6 | x - 6 | + 7 > 25

6 | x - 6 |  > 18      subtracted 7 from both sides

   | x - 6 |  > 3        divided both sides by 3

Step 2: Solve for x.

Note: the absolute value symbol makes the value positive, so the value inside could be positive or negative. We need to find both solutions.

If inside is negative

-(x - 6) > 3

 x - 6 < -3      divided both sides by -1 which flipped the inequality

     x < 3        added 6 to both sides

If inside is positive

+(x - 6) > 3

 x - 6 > 3      distributed +1, which didn't change the inequality

     x > 9        added 6 to both sides

Step 3: Graph the solution

←-------------o -3           9 o--------------→

Answer:

o(30) = 59

Step-by-step explanation:

o(30)  means we want to let n = 30 in our function

o(n) =2n-1

o(30) = 2*30 -1

o(30) = 60 -1

o(30) = 59

Answer:

You can estimate to the nearest 10th.

Example:8.4

Step-by-step explanation:

Answer:

The answer in the procedure

Step-by-step explanation:

we have

P(c)=0.50c

where

P(c) ---> is the amount in dollars that Marjorie earned from the bake sale

c ----> is the number of cupcakes

The domain of the function are the number of cupcakes sold

so

The domain is the interval -----> [0,100]

All positive integers greater than or equal to 0 and less than or equal to 100

Find the range

For c=0

P(0)=0.50(0)=$0

For c=100

P(0)=0.50(100)=$50

The range is the interval -----> [0,50]

All real numbers multiples of 0.50 greater than or equal to 0 and less than or equal to 50

The domain for the function is c ≥ 0, and the range is P(c) ≥ 0.

Domain: The domain for the function P(c) = 0.50c, where c represents the number of cupcakes sold, would be all non-negative integers since Marjorie cannot sell a negative number of cupcakes. So, the domain is c ≥ 0.

Range: The range for the function would be all the possible earnings that Marjorie can make from selling cupcakes. Since each cupcake is sold for $0.50, the earnings can be any non-negative real number. Therefore, the range is P(c) ≥ 0.

Answer:

five hundred seventeen billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred

Step-by-step explanation:

25.9 billion times 20=five hundred eighteen billion

then subtract one hundred from that to get the answer

Answer:

Step-by-step explanation:

5180000000

Answer:

The simple answer: 48

Step-by-step explanation:

Finding the area of a triangle in most cases is simple, multiply the two sides that are not the hypotenuse (the noticeably longer side) then divide the product by two. In this case the perimeter is included because you are given one side and the hypotenuse. With simple 12+14=26 and 34-26=8 you have the other side you need. So 12 times eight equals 96 divide that by two and you have the answer 48.

Answer:

plot B

Step-by-step explanation:

-3

-2 goes with 5,2,2,1,0

-1 goes with 7,7,7,5,3,2,0

0 goes with -9,-6,-4,-1,-1,0,3,6

1 goes with 1,2

2 goes with 6

3

This means there should be no data  in our box and whisker plot until a whisker starts at -25.  This eliminates plot A

We will also stop our last whisker at 26 .  This eliminates plot C

We have 23 data points.  So the median point is 12

The 12th point is -10

The middle of our box should be at -10  This eliminates plot D

Our answer is plot B

Answer:

11. x=4.5

12. x=16

13. x=15

14. x=15

15. x=10

EH=9

16. Corry is 6 feet tall.

17. The Ferris Wheel is 15 m tall.

18. The mural is 150 inches long.

19. A 15 foot ladder would touch the building at a height of 10 feet.

Step-by-step explanation:

11. x/7.5=6/10

Simplifying the fraction on the right side of the equation:

x/7.5=3/5

Solving for x: Multiplying both sides of the equation by 7.5:

7.5(x/7.5)=7.5(3/5)

x=1.5(3)

x=4.5

12. x/20=(27-15)/15

x/20=12/15

Simplifying the fraction on the right side of the equation:

x/20=4/5

Solving for x: Multiplying both sides of the equation by 20:

20(x/20)=20(4/5)

x=4(4)

x=16

13. x/6=(14-4)/4

x/6=10/4

Simplifying the fraction on the right side of the equation:

x/6=5/2

Solving for x: Multiplying both sides of the equation by 6:

6(x/6)=6(5/2)

x=3(5)

x=15

14. x/20=12/(12+4)

x/20=12/16

Simplifying the fraction on the right side of the equation:

x/20=3/4

Solving for x: Multiplying both sides of the equation by 20:

20(x/20)=20(3/4)

x=5(3)

x=15

15. [(x+5)+9]/(x+5)=12/6

(x+5+9)/(x+5)=2

(x+14)/(x+5)=2

Solving for x: Multiplying both sides of the equation by (x+5):

(x+5)(x+14)/(x+5)=(x+5)2

x+14=2(x+5)

Eliminating the parentheses applying the distributive property:

x+14=2(x)+2(5)

Multiplying:

x+14=2x+10

Grouping the x's on the right side of the equation: Subtracting x both sides of the equation:

x+14-x=2x+10-x

Subtracting:

14=x+10

Solving for x: Subtracting 10 both sides of the equation:

14-10=x+10-10

4=x

x=4

EG=x+5→EG=4+5→EG=9

EH/HF=EG/GD

Replacing the known values:

EH/9=9/9

EH/9=1

Solving for EH: Multiplying both sides of the equation by 9:

9(EH/9)=9(1)

EH=9

16. Corry's height / Corry's shadow = Giraffe's height / Giraffe's shadow

Replacing the given values:

Corry's height / 4 feet = 18 feet / 12 feet

Simplifying the fraction on the right side of the equation:

Corry's height / 4 feet = 3/2

Solving for Corry's height: Multiplying both sides of the equation by 4 feet:

4 feet (Corry's height / 4 feet) =4 feet (3/2)

Corry's height = 2 feet (3)

Corry's height = 6 feet

17. Ferris Wheel's height / Ferris Wheel's shadow =

Man's height / Man's shadow

Replacing the given values:

Ferris Wheel's height / 20 m = 1.8 m / 2.4 m = 18/24

Simplifying the fraction on the right side of the equation:

Ferris Wheel's height / 20 m = 3/4

Solving for Ferris Wheel's height: Multiplying both sides of the equation by 20 m:

20 m (Ferris Wheel's height / 20 m) =20 m (3/4)

Ferris Wheel's height = 5 m (3)

Ferris Wheel's height = 15 m

18. Mural's length / Mural's width =

Photographer's length / Photographer's width

Replacing the given values:

Photographer's length / 120 inches = 5 inches / 4 inches = 5/4

Solving for Photographer's length: Multiplying both sides of the equation by 120 inches:

120 inches (Photographer's length / 120 inches) = 120 inches (5/4)

Photographer's length = 30 inches (5)

Photographer's length = 150 inches

19. Height 15-foot ladder touch the building / 15 feet =

Height 9-foot ladder touch the building / 9 feet

Height 15-foot ladder touch the building / 15 feet = 6 feet / 9 feet = 6/9

Simplifying the fraction on the right side of the equation:

Height 15-foot ladder touch the building / 15 feet = 2/3

Solving for Height 15-foot ladder touch the building: Multiplying both sides of the equation by 15 feet:

15 feet (Height 15-foot ladder touch the building / 15 feet) = 5 feet (2/3)

Height 15-foot ladder touch the building = 5 feet (2)

Height 15-foot ladder touch the building = 10 feet

Answer:

5.5 servings

Step-by-step explanation:

4+7=11

11/2=5.5 sevings

Answer:

4

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

given [tex]\frac{j^2}{2j}[/tex] × [tex]\frac{2j}{3g}[/tex]

the 2j on the denominator of the first fraction cancels with the 2j on the numerator of the second fraction, leaving the expression in simplified form as

= [tex]\frac{j^2}{3g}[/tex] → D

Answer:

y = [tex]\frac{1}{2}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 2x + y = - 6 into this form

subtract 2x from both sides

y = - 2x - 6 ← in slope-intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (6, 1) into the partial equation

1 = 3 + c ⇒ c = 1 - 3 = - 2

y = [tex]\frac{1}{2}[/tex] x - 2 ← equation of perpendicular line