Factor.
x3 + 3x2 – 8x - 24

Answer:

see below (I hope this helps!)

Step-by-step explanation:

A real-life situation for this inequality could be "Tom runs a lemonade stand. His profit is x. If Tom knows that his profit is less than 2 dollars, what inequality represents this situation?"

Answer:

This has 6 significant digits

Step-by-step explanation:

5,000.06

This has 6 significant digits

We count from the first nonzero digit  to the last nonzero digit

Answer

the answer is 6

Step-by-step explanation:

Answer:

x= no real numbers

Step-by-step explanation:

4+2(a+5)<-2(-a-4)

Distribute

4+2*a+2*5<-2*-1-2*-4

Simplify.

4+2a+10<2a+8

14+2a<2a+8

Subtract 2a from both sides

14<8

This is false.

There are no real solutions to the given inequality,

Answer:

Step-by-step explanation:

Factorize 625 & 48

625 = 25 * 25 = 5 * 5 * 5 * 5 = 5⁴

48 = 16 * 3 = 2 * 2 * 2 * 2 *3 = 2⁴ * 3

[tex]\sqrt[4]{625*48} = \sqrt[4]{5^{4} * 2^{4} * 3}=5*2\sqrt[4]{3}[/tex] =[tex]10\sqrt[4]{3}[/tex]

Answer:

c = -12

Step-by-step explanation:

Quadratic Standard Form: ax² + bx + c

Step 1: Write equation

3x² + 6x = 12

Step 2: Subtract 12 on both sides

3x² + 6x - 12 = 0

Here, we have the standard form of the quadratic. We see that our c = -12

Answer:

$387,336.64 1

Step-by-step explanation:

The computation of the amount invested now is shown below:

Here we use the present value formula i.e. to be shown in the spreadsheet

Given that,  

Future value = $0

Rate of interest = 6%  ÷ 12 months = 0.5%

NPER = 20 years × 12 months = 240 months

PMT = $2,775

The formula is shown below:

= -PV(Rate;NPER;PMT;FV;type)

So, after applying the above formula, the present value is $387,336.64 1

Answer:

[tex]\bold{y=1.5\times 2^x+4}[/tex]

Step-by-step explanation:

Given:

Exponential function with common ratio 2.

Horizontal asymptote at y = 4

Passes through point (2, 10)

To find:

Equation of the exponential function ?

Solution:

Equation for an exponential function may be given as:

[tex]y=ab^x+c[/tex]

Where b is the common ratio and

c is the y value of horizontal asymptote.

[tex](x, y)[/tex] are the points on the function.

We are given that:

b = 2

c = 4

Let us put all the given values and find equation.

[tex]y=a\times 2^x+4[/tex]

Now, let us put [tex]x = 2, y = 10[/tex] to find the value of a.

[tex]10=a\times 2^2+4\\\Rightarrow a\times 2^2=10-4\\\Rightarrow a\times 4=6\\\Rightarrow a =1.5[/tex]

[tex]\therefore[/tex] the equation of exponential function is:

[tex]\bold{y=1.5\times 2^x+4}[/tex]

Answer: B. It is a continuous random variable.

Step-by-step explanation:

A continuous random variable is a random variable where the data or value can assume infinitely many values ( meaning it’s a continuous set of data. )

For example a random variable measuring the time taken for someone to cook rice is continuous since there are an infinite number of possible times that can be done.

Answer:

its b i got it right

Step-by-step explanation:

Answer:

[tex] \boxed{ \boxed{ \bold{ \sf{d = 15}}}}[/tex]

Step-by-step explanation:

[tex] \sf{d - 7 = 8}[/tex]

Move constant to right hand side and change it's sign

⇒[tex] \sf{d = 8 + 7}[/tex]

Add the numbers

⇒[tex] \sf{d = 15}[/tex]

Let's check:

When d = 15 , R.H.S = 15 - 7 = 8

And L.H.S = 8

Thus , R.H.S = L.H.S when d = 15.

Therefore d = 15 is the solution of the equation.

Hope I helped!

Best regards!

Answer:

z=104

Step-by-step explanation:

A line is always 180 degrees.

This model is formed by 2 lines.

z and 76 form a line, which means that they are supplementary.

We can set up this equation:

z+76=180

Subtract 76 from both sides.

z=104

If you needed to figure out x, it would also be 104 degrees.

This is because x and z are vertical angles.

Vertical angles are always congruent.

Answer:

6

Step-by-step explanation:

3x + y =

= 3(1) + 3

= 3 + 3

= 6

Answer:

The sale this month = 79

Step-by-step explanation:

Let the amount he needs to sell this month = x

[tex]Average = \frac{sum\ of\ individual\ data\ }{number\ of\ entries}[/tex]

[tex]Average= \frac{90\ +\ 45\ +\ 103\ +\ 68\ +\ x}{5}[/tex]

Note that number of entries = number of months = 5

To maintain an average sales of 77, the amount of sale in month 5 is determined as follows:

[tex]77 = \frac{306\ +\ x}{5} \\cross-multiplying\\77\ \times\ 5\ = 306\ +\ x\\385 = 306\ +\ x\\x =385\ -\ 306\\x = 79[/tex]

Answer:

B

Step-by-step explanation:

Let first number = x

Second number = y

Twice a number = 2*x = 2x

The sum of twice a number and another number is 24

2x + y  = 24    -----------------------(I)

The difference of twice the first number and the  other number is 12.

2x - y = 12 ----------------------(II)

Add equation (I) & (II)  and y will be eliminated and we can find the number 'x'

(I)       2x + y = 24

(II)      2x - y  = 12   {Now add the two equations}

          4x      = 36

Divide both sides by 4

4x/4 = 36/4

x = 9

Plug in the value of 'x' in equation (I)

2*9 + y = 24

 18 + y = 24

Subtract 18 from both sides

18 + y - 18 = 24 - 18

       y = 6

The numbers are 9, 6

Answer: -1

Step-by-step explanation:

(2-7) (5-3)+ 3^2

(-5) (2)+9 Multiply -5 and 2

-10+9 Add -10 to 9

-1

━━━━━━━☆☆━━━━━━━

▹ Answer

3.73 or 3 11/15

▹ Step-by-Step Explanation

15x + 2 = 58

Do the inverse operation (subtract 2 from both sides)

2 - 2 = na

58 - 2 = 56

15x = 56

Divide 15 on both sides:

15/15 = x

56/15 = 3.73 or 3 11/15

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:Sam's speed is about 10.3 mi/h.

Step-by-step explanation:Explanation:

Use dimensional analysis.

Determine the equality between miles and feet, and hours and minutes.

1 mi=5280 ft

1 h=60 m

Each equality can make two conversion factors, which are equal to one.

1 mi

5280 ft

=

1

=

5280 ft

1mi

1 h

60 min

=

1

=

60 min

1 h

Multiply the given value by the conversion factor that has the desired unit in the numerator. This will leave you with the desired unit, and the undesired unit in the denominator will cancel.

Convert feet to miles.

63756

ft

×

1

mi

5280

ft

=

12.075 mi

Convert minutes to hours.

70

min

×

1

h

60

min

=

1.167 hour

Divide miles by hours.

12.075

mi

1.167

h

=

10.3 mi/h

Step-by-step explanation:

Hey, there!!

Here,

3(2x-5)=25 is given.

To slolve: x

Now,

Multiply (2x-5) by 3.

6x-15 = 27.

Shift (-15) on right side.

6x= 27+15

or, 6x= 42

Divide 42 by 6.

[tex]x = \frac{42}{6} [/tex]

Therefore, x= 7.

Hope it helps....

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\boxed{x = 7}[/tex]

Let's solve your equation step-by-step.

[tex]3(2x-5)=27[/tex]

Step 1: Simplify both sides of the equation.

[tex]3(2x-5)=27[/tex]

[tex](3) (2x) + (3) (-5) = 27[/tex] (Distribute)

[tex]6x + -15 = 27[/tex]

[tex]6x - 15 = 27[/tex]

Step 2: Add 15 to both sides.

[tex]6x -15 + 15 = 27 + 15[/tex]

[tex]6x = 42[/tex]

Step 3: Divide both sides by 6.

[tex]\frac{6x}{6} = \frac{42}{6}[/tex]

[tex]x = 7[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:

0.0003652

Step-by-step explanation:

3.652 * [tex]10^{-4} = \frac{3.652}{10^{4}}= \frac{3.652}{10000}=0.0003652[/tex]

Answer:

Height of the tank is 1.5m

Step-by-step explanation:

Given

Shape: Cuboid

Base Dimension = 2.5m by 2m

Volume = 7500 litres

Required

Determine the height of the tank

First, the area of the base has to be calculated;

[tex]Area = 2.5m * 2m[/tex]

[tex]Area = 5.0m^2[/tex]

Next is to calculate the height using volume formula;

[tex]Volume = Area * Height[/tex]

Recall that Volume = 7500L [Convert to m³]

[tex]1 L = 0.001m^3[/tex]

So;

[tex]7500L = 7500 * 0.001m^3[/tex]

[tex]7500L = 7.5m^3[/tex]

Hence;

[tex]Volume = 7.5m^3[/tex]

Substitute 7.5m³ for Volume and 5.0m² for Area in the following formula

[tex]Volume = Area * Height[/tex]

[tex]7.5m\³ = 5.0m\² * Height[/tex]

Divide both sides by 5.0m²

[tex]\frac{7.5m\³}{5.0m\²} = \frac{5.0m\² * Height}{5.0m\²}[/tex]

[tex]\frac{7.5m\³}{5.0m\²} = Height[/tex]

[tex]1.5m = Height[/tex]

[tex]Height = 1.5m[/tex]

Hence, the height of the tank is 1.5m

Answer:

418.2477796 m

Step-by-step explanation:

You divide it in to a rectangle and 2 half circles (which will make a whole circle if added together) and solve them.

P= 2( L + W) - - > 2 ( 102 + 60)= 324

Cf= 2лr^2 - - - > 2л(30)^2=30л

324 + 30л = 418.2477796 m

Answer:

I am writing a Python program:

def most_common_letter (string):  #function that takes a string as argument and returns the most commonly occurring letter in string

   string = string.lower()  # converts the string into lower case

   inp_string="".join(string.split())  #splits the string in to a list and joins the elements of the list

   maximum = 0  #sets the value of maximum to 0

   letter = ""  #stores the most commonly occurring letter

   length = len(inp_string)  #returns the length of the input string

   counter = 0  #counts the occurrences of the letter in the string

   for i in range(0, length):  # iterates through the length of string        

       j = 0  #initializes j to 0

       char = inp_string[i]  #  holds letter of input string at index position i

       while length > 0:  # iterates until the length of string exceeds 0

           if (char == inp_string[j]):  # if letter in char is equal to letter at index j of the string

               counter += 1  #adds 1 to the count

           j += 1  #increments j by 1

           length -= 1    #decrements value of length by 1

           if (maximum <= counter):  #if maximum value is less than counter

               maximum = counter  #sets the maximum number of occurrences of a letter to maximum

               letter = char #sets the most occuring letter in string to letter

   return letter  #returns the most commonly occurring letter in the input string

#in order to check if the function works properly use following statement

print(most_common_letter("This is a test of the function I have written")) #calls most_common_letter method by passing a string to it

Step-by-step explanation:

The program works as follows:

I will explain this with the help of an example. Suppose the string is:

string = "hello worLd"

first this string is converted to lowercase using lower() method. So the string becomes:

string = "hello world"

Next the string is split into a list using split() method. The string becomes:

['hello', 'world']

Then using join() this string is joined together on the basis of "" empty space

So the string becomes

helloworld

This string is assigned to the inp_string variable. Hence

inp_string = "helloworld"

The value of maximum is initialized to 0 and variable letter is also declared

which holds the most commonly occurring letter in the inp_string

len function is used to get the length of the inp_string

counter is initializes to 0. This counts the number of times the letter occurs in a string

The for loop iterates through the inp_string

Inside the loop the statement char = inp_string[i] sets the letter at the i-th index of inp_string to char.

i is initialized to 0 so inp_string[i] is inp_string[0] which is the first element of the string i.e. "h".

The program control then moves to the while loop. As length>0 so the program moves to the body of while loop which has an if statement:            if (char == inp_string[j]):      

This checks if the letter stored in char is equal to the letter at j-th index of the string. Now as j is initialized to 0. So

if (char == inp_string[0]):   this evaluates to true and value of counter is incremented to 1. Next value of j also incremented to 1 and length of string is decremented to 1 Hence

counter = 1

j = 1

length = 9

Next if (maximum <= counter): condition checks if value of maximum is less than or equal to counter. It is true because maximum=0 and counter =1

So    maximum = counter  assigns counter value to maximum and letter = char assigns char to letter which was initially empty.

  maximum = 1

  letter = 'h'

At occurrence each iteration each letter in a string is counted and the letter that occurs the most in the string is returned by the function. For the above example hello world, letter l appears 3 times in the string and it is the most commonly occurring letter in the input string. So letter "l" is returned by this function. Hence the output of this program is l.

Answer:

Approximately 54°

Step-by-step explanation:

So we know Angle A, the side opposite to Angle A, and the side opposite to Angle B (the angle we want to find). Given these circumstances, we can use the Law of Sines.

The Law of Sines states that:

[tex]\frac{\sin(A)}{a} =\frac{\sin(B)}{b} =\frac{\sin(C)}{c}[/tex]

The variables do not really matter. Instead, it's more important that the angle corresponding to the side lines up with each other.

Anyways, since we know Side A, Angle A, and Side B, let's use the first and second ratios:

[tex]\frac{\sin(A)}{a} =\frac{\sin(B)}{b}[/tex]

Plug in 80° for A, 11 for a, and 9 for b:

[tex]\frac{\sin(80)}{11} =\frac{\sin(B)}{9}[/tex]

Cross multiply to solve for B:

[tex]9\sin(80)=11\sin(B)[/tex]

Divide both sides by 11:

[tex]\sin(B)=\frac{9\sin(80)}{11}[/tex]

Use the inverse sine function. And finally, use a calculator to solve:

[tex]\angle B =\sin^{-1}(\frac{9\sin(80)}{11} )\\\angle B\approx53.6829\textdegree\approx54\textdegree[/tex]

Answer:

The ratio is 3 : 14 .

Step-by-step explanation:

Given that there are 6 yellow, 10 orange and 12 pink roses.

So there are a total of 28 roses, 6+10+12 = 28.

The question wants the ratio of yellow roses to total roses so, the ratio is 6 : 28.

Next, you have to give in simplest form where you have to divide 2 which is 6/2 : 28/2 equals to 3 : 14.

Answer:

Step-by-step explanation:

If Mr Powell and Ms. Krawczyk live 24 miles apart, then the distance between their houses is 24 miles.

Let A be the Mr powell house, B be Ms. Krawczyk house and C be the restaurant. If the restaurant is halfway their houses and the distance between their houses is a straight line distance, then AC = CB where AC  is the distance between Mr Poweel house and the restaurant and CB is the distance between Ms. Krawczyk house and the restaurant.

Given AB =  (8x-2) miles and CB = (5x+10) miles

8x-2 = 5x+10

Collect like terms;

8x-5x = 10+2

3x = 12

x = 4

Substituting x = 4 into AB and CB

AB = 8(4)-2

AB = 32-2

AB = 30 miles

BC = 5(4)+ 10

BC = 20+10

BC = 30 miles

Answer:

x>-9

Step-by-step explanation:

-2(-9+2)=14

-2(-8+2)<14

-8>-9

x>-9

Answer:

x < -9

Step-by-step explanation:

-2(x+2) < 14

-2*x +2*-2 < 14

-2x - 4 < 14

-2x < 14 + 4

-2x < 18

x < 18/-2

x < -9

Answer:

<NKJ

Step-by-step explanation:

Answer:

(-10,8)

Step-by-step explanation:

So our original point is (-6,9).

A translation of 4 units to the left means that the x-value would go left by 4. In other words, we subtract 4 to -6. We subtract because going to the left means that it's going to the negative direction.

A translation of down 1 unit means that the y-value would go down by 1. In other words, we subtract 1. Again, we subtract because going downwards means that it's going to the negative direction.

Therefore, the new point would be:

[tex](-6-4,9-1)\\=(-10,8)[/tex]

Answer:

(-10,8)

Step-by-step explanation:

I hope this helps

Answer:

The image is not shown, but this can be answered.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

This says that, for any given two points, we can find a line that passes through both of them.

Then we have that two points are ALWAYS collinear.

Then does not matter which points the student chooses, because we can find a line that passes through them, then the probability that these randomly chosen points are collinear is 1 or 100% in percentage form.

Answer:

n = -6

Step-by-step explanation:

10[6(n+1)+5(n-1)]=13[7(5+n)-(25-3)]

You will collect like terms

10(6n+6+5n-5)=13(35+7n-25+3)

it will give you this

10(11n+1)=13(10+10n)

Then you remove the parenthesis

110n+10 = 130 +130n

Move the terms

110n -130n = 130-10

collect like terms

-20n=120

divide both sides

n=-6