find the value of k.

(x^2+5x+k)/(x+6) has a remainder of 9.

if anyone could help, please do!! this is urgent!

Answer:

x = 3, x = 9/4

Step-by-step explanation:

8x = 24

x = 3 Divide both sides by 8.

4x = 9

x = 9/4 Divide both sides by 4.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation \#1.}[/tex]

[tex]\mathsf{8x = 24}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{8x = 24}[/tex]

[tex]\huge\textbf{Divide \boxed{8} to both sides:}[/tex]

[tex]\mathsf{\dfrac{8x}{8} = \dfrac{24}{8}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{24}{8}}[/tex]

[tex]\mathsf{x = 3}[/tex]

[tex]\huge\textbf{Therefore, the answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x =}\frak{\ 3}}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation \#2.}[/tex]

[tex]\mathsf{4x = 9}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{4x = 9}[/tex]

[tex]\huge\textbf{Divide \boxed{9} to both sides:}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{9}{4}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{9}{4}}[/tex]

[tex]\mathsf{x = 2 \dfrac{1}{4}}[/tex]

[tex]\huge\textbf{Therefore, the answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = }\frak{\ \dfrac{9}{4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Let [tex]n=abcba[/tex] be such a number. If 18 divides [tex]n[/tex], then both 2 and 9 divide [tex]n[/tex].

To be divisible by 2, we must have [tex]a\in\{2,4,6,8\}[/tex]. Meanwhile we can have [tex](b,c)\in\{0,1,2,\ldots,9\}^2[/tex].

To be divisible by 9, we the sum of the digits of [tex]n[/tex] must itself be divisible by 9, or

[tex]2a+2b+c=9k[/tex]

for some integer [tex]k[/tex].

The largest value of [tex]2a+2b+c[/tex] is 2•8 + 2•9 + 9 = 43, so we must have [tex]k\in\{1,2,3,4\}[/tex].

I'm not sure what the best way to get the final count may be, but there are 44 such numbers. It's rather tedious to do by hand.

• If [tex]k=1[/tex], then [tex]2a+2b+c=9[/tex], and we can do this in 4 ways.

For example,

2•2 + 2•0 + 5 = 9 [tex](n = 20502)[/tex]

• If [tex]k=2[/tex], then [tex]2a+2b+c=18[/tex] and can be done in 16 ways.

2•2 + 2•3 + 8 = 18 [tex](n = 23832)[/tex]

• If [tex]k=3[/tex], then [tex]2a+2b+c=27[/tex] and can be done in 18 ways.

2•2 + 2•7 + 9 = 27 [tex](n = 27972)[/tex]

• If [tex]k=4[/tex], then [tex]2a+2b+c=36[/tex] and can be done in 6 ways.

2•6 + 2•8 + 8 = 36 [tex](n = 68886)[/tex]

The purpose of the graphic is to show the relationship between different educational qualifications and unemployment rate.

This is a situation in which employable individuals look for jobs and are unable to find one.

The key findings in this graphic is that the higher the level of education, the lesser the unemployment rate.

Read more about Unemployment here https://brainly.com/question/305041

#SPJ1

Answer:

Maybe the answer must be 90°

The coordinates of U after the reflection are: (-5, -3)

By looking at the graph, we can see that the coordinates of point U are:

U = (-1, -3)

And we want to reflect it across the line x = -3.

Notice that because this is a vertical line, the y-component does not change by the reflection. Only changes the x-component, such that the distance between the original coordinates and the final coordinates to the line don't change.

The original x-component is x = -1, the distance to the line is:

d = |-3 - (-1)| = 2 units.

Then the new x-component will also be at 2 units of the line, but in the other direction:

new x-component: x = -3 - 2 = -5

The coordinates of U after the reflection are:

(-5, -3)

If you want to learn more about reflections:

https://brainly.com/question/4289712

#SPJ1

The total surface area, in m², of the sunshade is 0.4344 m²

A pyramid can have a squared base, rectangular base or other polygons. The formula we can to find the total surface area of a squared pyramid is

Surface Area = P x l/2

Where

Given that a sunshade on one set of equipment has a square base of 120 cm and a height of 50 cm. That means that the length L of the base will be  120 cm and half of it will be 60 cm

To find the slant height l, we will use Pythagoras theorem.

[tex]l^{2}[/tex] = 60² + 50²

[tex]l^{2}[/tex] = 3600 + 2500

[tex]l^{2}[/tex] = 6100

l = √6100

l = 78.1 cm

convert it to meter

l = 78.1/100

l = 0.781 m

The perimeter P of the base = 4 x 120/100 = 4.80 m

The Surface Area = P x l/2

Substitute all the necessary parameters into the formula

Surface Area = 4.80 x 0.781/2  

Surface Area = 1.8744 m²

If the sunshades are open-bottomed square based pyramids, this means that the base is not included. That is, the area of the base should be taken away from the answer above.

Area of the base = 120/100 x 120/100 = 1.44 m²

The total surface area, in m², of the sunshade will 1.8744 - 1.44

The total surface = 0.4344 m²

Therefore, the total surface area, in m², of the sunshade is 0.4344 m²

Learn more about Pyramid here: https://brainly.com/question/218706

#SPJ1

Answer:

true

Step-by-step explanation:

mean we show up the distribution

Answer:

  x = 7

Step-by-step explanation:

The integer values of x that satisfy |x| < 9 are ...

  {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7. 8}

Of these values, the only one listed as an answer choice is ...

  x = 7

__

Additional comment

The expression |x| means "the absolute value of x". It is the value of x with the sign made positive. That is |-10| = 10, a number greater than 9. Of course, |13| = 13, also a number greater than 9.

When it comes to resource allocation, it's not a one sentence answer. The explanation for how to go about this is given below. But first, lets look at what Profit Allocation means.

This simply means the process of distributing profit to various areas of the business such that all parts are (human and non-human  components) are satisfied and operating at equilibrium.

There are five steps to aligning your budget and resource demands when planning for support resource allocation.

Learn more about profit allocation at;
https://brainly.com/question/933169
#SPJ1

The solution to the system of equations is the point ( -1, 9 ).

What is the solution to a system of linear equations?

If you have a system of equations that contains two equations with the same two unknown variables, then the solution to that system is the ordered pair that makes both equations true at the same time.

The system of equations

y = -3x + 6 ...................(1)

y = 9 .................(2)

Substitute equation (2)  in equation

9 = -3x + 6

subtract  both sides

9 - 6 = -3x + 6 - 6

3 = -3x

Divide by  -3 both sides

  x = -1

the solution is the point ( -1, 9 )

Therefore,the solution to the system of equations is the point ( -1, 9 ).

Learn more about the solution to the system of linear equation

brainly.com/question/13631560

#SPJ4

The complete question is -

Y = –3x + 6  y = 9 what is the solution to the system of equations? (–21, 9) (9, –21) (–1, 9) (9, –1)

Answer:

c

Step-by-step explanation:

What is the solution to the system of equations?

(–21, 9)

(9, –21)

(–1, 9)

(9, –1)

Answer:

20%

Step-by-step explanation:

To find the percentage of change find the difference between the two numbers, divide by the original number, then multiply by 100.

Find difference

90-72=18

Divide difference by original

18/90=0.2

Multiply by 100

0.2*100=20

The algebraic expression for the ice cream is 3x + 2y + 0.75z.

The cost of Rafael ice cream is 12 dollars

The algebraic expression that represent the cost of an ice cream is as follows:

let

number of scoop = x

number of topping = y

number of added syrup = z

Hence,

cost of the ice cream = 3x + 2y + 0.75z

Therefore,

The cost of ice cream Rafael ordered is as follows:

cost of ice cream = 3(3) + 0.75(4)

cost of ice cream = 9 + 3

cost of the ice cream = 12

learn more on algebraic expression here: https://brainly.com/question/15591224

#SPJ1

Answer: [tex]5\sqrt{2}[/tex] m

Step-by-step explanation:

Using the pythagorean theorem, we get that the shortest distance it can travel is [tex]\sqrt{3^2+4^2+5^2}[/tex] = [tex]5\sqrt{2}[/tex] m

The open circles on 1 and 2 describe the graph of {x | 1 < x < 2}.

According to the statement

we have to describe the graph of {x | 1 < x < 2}.

In this type of graph there will be open circle because there is no equal sign in the statement.

there will be a line segment in between...because basically, u would put an open circle on 1, and open circle on 2 and shading in between.

so, in this statement we have given a some statements which are represent the given graph but only one. and from all of these

The condition having a open circles 1 and 2 represent the graphical representation than others because except this condition all are incapable to represent the graph.

So, The open circles on 1 and 2 describe the graph of {x | 1 < x < 2}.

Learn more about GRAPH here https://brainly.com/question/4025726

#SPJ1

Answer:

D

Step-by-step explanation:

if you look the point on the y axis is -3 which is your starting point

in y=mx+b m is the slope

The cost of 1 bag of almond is $1.25

What is linear equation?

An equation in which the highest power of the variable is one is known as linear equation.

We can find the cost of 1 bag of almond as shown below:

Let the cost of 1 bag of peanut be $x

Let the cost of 1 bag of cashews be $y

Let the cost of 1 bag of almonds be $z

x + y + z=3      (1)

2x+2y=3.50

Dividing by 2

x + y=1.75

Putting in equation (1)

1.75+z=3

z=3-1.75

z=1.25

Hence, the cost of 1 bag of almond is $1.25

Learn more about linear equation here:

https://brainly.com/question/25127759

#SPJ4

Answer:

C

Step-by-step explanation:

x + 2y = 6

isolate x through

x = 6-2y . . . (iii)

Substitute equation (iii) in equation (i)

7x - y = 7

7(6 - 2y) - y = 7

42 - 14y - y = 7

42 - 15y = 7

Collecting Like terms

-15y = 7 - 42

-15y = -35

-15y = -35

-15 -15

y = 7

3

y =

[tex]2\frac{1}{3} [/tex]

Substitute y in equation (iii)

x = 6 - 2y

x = 6 - 2 × 7

3

x = 6 - 14

3

x =

[tex]1\frac{2}{3} [/tex]

Answer:

c is the right answer

Step-by-step explanation:

Answer:

force = work/distance

force = 900/5

force = 180 N

A ratio is a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In Mathematics, a fraction comprises two (2) main parts and these include:

3 to 2 = 3/2

5:6 = 5/6

8 to 12 = 3/2

Thus, a common denominator of 12 can be used to rewrite the fractions and then you should compare the numerators to order the ratios in an ascending order.

Read more on ratio here: brainly.com/question/13513438

#SPJ1

The five consecutive integers are -2, -1, 0, 1 and 2.

Given that;

The sum of five consecutive integers equals 5.5 times the middle integer.

Since the integers are consecutive, let the integer be;

x, x+1, x+2, x+3 and x+4.

Now, sum of the integers equals 5.5 times the middle integer.

Middle integer is x+2.

Hence we have;

x + x+1 + x+2 + x+3 + x+4 = 5.5( x+2 )

x + x+1 + x+2 + x+3 + x+4 = 5.5x + 11

We collect like terms

x + x + x + x + x - 5.5x = 11 - 1 - 2 - 3 - 4

5x - 5.5x = 1

-0.5x = 1

x = -( 1 / 0.5 )

x = -2

Since our integers are; x, x+1, x+2, x+3 and x+4.

We substitute in the value of x

x = -2

x+1 = -2 + 1 = -1

x+2 = -2 + 2 = 0

x+3 = -2 + 3 = 1

x+4 = -2 + 4 = 2

Therefore, the five consecutive integers are -2, -1, 0, 1 and 2.

Learn more about integers here: https://brainly.com/question/1768254
#SPJ1

The number will represent a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Inequality are expressions not separated by an equal sign. Given the inequality expression:

3(8 – 4x) < 6(x – 5)

Expand

24 - 12x < 6x - 30

Collect the like terms

-12x-6x < -30 - 24

-18x <-54

x > 3

Hence the number will represent a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Learn more on number line here; https://brainly.com/question/12399107

#SPJ1

The value of x= 20 units

BD =  BF

BD =2x + 40

BF = 18x

Equate the expressions thus:

2x + 40 = 2/3(18x)

2x + 40 = 12x

Collect like terms

2x - 12x = - 40

-2x = - 40

Divide both sides by - 2

x = 20

Hence, x =  20 units

The centroid is the center point of the item. The factor in which the 3 medians of the triangle intersect is known as the centroid of a triangle. it is also defined because of the point of intersection of all the 3 medians. The median is a line that joins the midpoint of a facet and the opposite vertex of the triangle.

Then, we can calculate the centroid of the triangle by means of taking the common of the x coordinates and the y coordinates of all of the three vertices. So, the centroid method can be mathematically expressed as G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/three).

The centroid of a triangle is the point at which the 3 medians coincide. The centroid theorem states that the centroid is 23 of the space from each vertex to the midpoint of the opposite aspect.

Learn more about the centroid of the triangle here https://brainly.com/question/7644338

#SPJ4

The taxi fare for a journey of n miles in dollars is 1 + 2n

Linear equations are equations that have constant average rates of change, slope or gradient

The given parameters about the taxi fares are given as

First two miles = $5

Additional mile = Increment of $2

Let the number of miles be n

So, we have:

2 miles = $5

Additional miles = (n - 2) * 2

Add the above expressions

5 + (n - 2)* 2

Represent the value with f(n)

So, we have:

f(n) = 5 + (n - 2)* 2

Expand the bracket

f(n) = 5 + 2n - 4

Collect the like terms

f(n) = 5 - 4+ 2n

Evaluate the like terns

f(n) = 1 + 2n

Hence, the taxi fare for a journey of n miles in dollars is 1 + 2n

So, the complete parameters are:

First two miles = $5

Additional mile = Increment of $2

n miles  1 + 2n

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

Answer:

x=7

Step-by-step explanation:

The angle of a straight line is 180 degrees, so let's just say the other angle to the right of 15x+34 is "a" that means that 15x + 34 + A = 180, and since the sum of interior angles of a triangle is 180 degrees, that means that 29 + A + 12x + 26 = 180, and we can define A using this equation in terms of x.

Original equation (sum of interior angles)

A + 29 + 12x + 26 = 180

Combine like terms

A + 12x + 55 = 180

Subtract 12x and 55 from both sides

A = -12x + 125

Original equation (since a line is 180 degrees)

15x + 34 + A = 180

Substitute -12x + 125 as A

15x + 34 + (-12x + 125) = 180

Combine like terms

3x + 159 = 180

Subtract 159 from both sides

3x = 21

Divide both sides by 3

x = 7

Answer: [tex]m\angle 1=82^{\circ}, m\angle 2=128^{\circ}[/tex]

Step-by-step explanation:

By the same-side interior angles theorem,

[tex]m\angle 1=180^{\circ}-98^{\circ}=82^{\circ}\\\\m\angle 2=180^{\circ}-52^{\circ}=128^{\circ}[/tex]

The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

Given that the area of rectangle is 169 [tex]inches^{2}[/tex].

We have to find the smallest perimeter and dimensions of the rectangle.

let the length of rectangle be x inches and breadth be y  inches.

We know that area of rectangle is the product of its length and breadth. So,

Area=xy

169=xy

y=169/x

Perimeter of rectangle =2(x+y)

Put the value of y=169/x in the perimeter.

P=2(x+169/x)

P=2x+338/x

Differentiate both sides with respect to x.

dP/dx=2-338/[tex]x^{2}[/tex]

Again differentiate it with respect to x.

[tex]d^{2} P/dP^{2}[/tex]=676/[tex]x^{3}[/tex]

Because the second derivative is greater than 0 so the perimeter is minimum.

Put dP/dx=0 to get the value of x.

dP/dx=0

2-338/[tex]x^{2}[/tex]=0

2=338/[tex]x^{2}[/tex]

[tex]x^{2}[/tex]=169

x=[tex]\sqrt{169}[/tex]

x=13

Put the value of x in y=169/x

y=169/13

=13

To calculate the perimeter, put the values of x and y in P=2(x+y)

P=2(13+13)

=2*26

=52 inches.

Hence The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

Learn more about perimeter at https://brainly.com/question/397857

#SPJ1

Answer:

26

Explanation:

[tex]\int\limits^{25}_{-1} {e^{x-[x]}} \, dx[/tex]

simplify

[tex]\int\limits^{25}_{-1} {e^{0} \, dx[/tex]

any variable to the power 0 is 1

[tex]\int\limits^{25}_{-1} 1 \, dx[/tex]

integrating 1 gives x

[tex]\left[ \:x \: \right]^{25}_{-1}[/tex]

apply limits

[tex]25 - (-1)[/tex]

add terms

[tex]26[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-[x]}dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-x}dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^0dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}dx[/tex]

[tex]\\ \rm\hookrightarrow \left[x\right]_{-1}^{25}[/tex]

[tex]\\ \rm\hookrightarrow 25-(-1)[/tex]

[tex]\\ \rm\hookrightarrow 25+1[/tex]

[tex]\\ \rm\hookrightarrow 26[/tex]