20 Points! if pencils cost $2.40 for twelve, what is the unit price per pencil?
​

Answer:

3

Step-by-step explanation:

f(x) = 18x + 3x^2

f(x) =  3x^2+18x

Factor out a 3

     = 3(x^2 +6x)

Take the coefficient of x, divide by 2 and then square

6/2 = 3 3^2 =9

Remember the 3 out side 3*9 =27 so we are really adding 27

3(x^2+6x+9) -3*9

The number inside the parentheses added to x is b/2  or 6/2

3(x+3)^2 -27

Answer:

[tex]f(x)=3(x+3)^{2}-27[/tex]

Step-by-step explanation:

In the last step is missing the number 3 which is the second term of the binomial squared expression.

Basically, the complete step is

[tex]f(x)=3(x+3)^{2}-27[/tex]

As you can see, the three inside the parenthesis is the missing part in the last step.

Answer:

see explanation

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 )

y = [tex]\frac{3}{4}[/tex] x - 9 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes, hence

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line.

To find c substitute (- 8, - 18) into the partial equation

- 18 = - 6 + c ⇒ c = - 18 + 6 = - 12

y = [tex]\frac{3}{4}[/tex] x - 12 ← equation of parallel line

Answer:

Step-by-step explanation:

The equation of a linear function in point-slope form is y – y1 = m(x – x1)

The point is A (x1 , y1)  

the slope is : m     the line that is parallel to the given line so : m = 3/4

passes through the given point (-8 -18)

so :  x1 = - 8   and y1 = -18

an equation is : y +18= 3/4(x +8)

Answer:

Option A is correct.

Step-by-step explanation:

We are given:

[tex]\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi[/tex]

We need to find the value of a.

The LCM of (2+i) and (3+i)  is (2+i)(3+i)

[tex]=\frac{2i(3+i)}{(2+i)(3+i)}-\frac{3i(2+i)}{(2+i)(3+i)}\\=\frac{6i+2i^2}{(2+i)(3+i)}-\frac{6i+3i^2}{(2+i)(3+i)}\\=\frac{6i+2i^2-(6i+3i^2)}{(2+i)(3+i)}\\=\frac{6i+2i^2-6i-3i^2)}{5+5i}\\=\frac{-i^2}{5+5i}\\i^2=-1\\=\frac{-(-1)}{5+5i}\\=\frac{1}{5+5i}[/tex]

Now rationalize the denominator by multiplying by 5-5i/5-5i

[tex]=\frac{1}{5+5i}*\frac{5-5i}{5-5i} \\=\frac{5-5i}{(5+5i)(5-5i)}\\=\frac{5-5i}{(5+5i)(5-5i)}\\(a+b)(a-b)= a^2-b^2\\=\frac{5(1-i)}{(5)^2-(5i)^2}\\=\frac{5(1-i)}{25+25}\\=\frac{5(1-i)}{50}\\=\frac{1-i}{10}\\=\frac{1}{10}-\frac{i}{10}[/tex]

We are given

[tex]\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi[/tex]

Now after solving we have:

[tex]\frac{1}{10}-\frac{i}{10}=a+bi[/tex]

So value of a = 1/10 and value of b = -1/10

So, Option A is correct.

Final answer:

After simplifying the complex fractions and subtracting them, the real part a is found to be 0.1, which corresponds to option A, 1/10.

Explanation:

To solve the equation (2i/2+i)-(3i/3+i)=a+bi, we want to find the real part (a) and the imaginary part (b) after simplifying the given expression. We will need to perform complex number arithmetic by simplifying each fraction separately and then subtracting them. This process involves multiplying the numerator and the denominator by the conjugate of the denominator to make the denominator real.

First, let's simplify (2i/2+i):

(2i)/(2+i) = (2i)(2-i)/(2+i)(2-i) = (4i-2i²)/(4+2i-2i-i²) = (4i+2)/(4+1) = (2+4i)/5 = 0.4+0.8i.

Now, let's simplify (3i/3+i):

(3i)/(3+i) = (3i)(3-i)/(3+i)(3-i) = (9i-3i²)/(9+3i-3i-i²) = (9i+3)/(9+1) = (3+9i)/10 = 0.3+0.9i.

Next, subtract the two results:

(0.4+0.8i) - (0.3+0.9i) = 0.4 - 0.3 + (0.8i - 0.9i) = 0.1 - 0.1i.

So, a = 0.1 and b = -0.1. Comparing this with the given options, we can conclude that a = A. 1/10.

Answer:

39

Step-by-step explanation:

The short answer is 39.

Every triangle has 180 degrees. There are no exceptions to this rule.

Since a triangle has 3 angles, all three together must add up to 180o

A right angle = 90 degrees always.

You are given 51 degrees as your second angle

The third one is x

x + 51 + 90 = 180                   Total of three angles must be 180

x + 141 = 180                           The left has been added to give 141

x = 180 - 141                            Subtract 141 from both sides

x = 39                                     The third angle = 39    

Answer:

See explanation

Step-by-step explanation:

Consider triangles ABD and BEC. In these tirangles:

So, by AA similarity theorem, tringles DBA and CBE are similar. Similar triangles have proportional corresponding sides, thus

[tex]\dfrac{BD}{BC}=\dfrac{DA}{CE}=\dfrac{AB}{BE}\Rightarrow BE\cdot DA=AB\cdot CE[/tex]

Hello There!

WHAT WE KNOW  Levi reads 280 words in 2 minutes. We need to find out how many words he can read in 5 minutes

To find out how many words Levi can read in 5 minutes, it will first be easier to find out how many words Levi can read in 1 minute. To find this, we will divide 280 by 2 and that will give us the number of words per minute.

Next, once we divide we will get a quotient of 140.

Finally, we take 140 and multiply it by 5 and we get a product of 700

Therefore, Levi reads 700 words in 5 minutes

Answer:

-6 is not in the domain of f(x) but is in the range of f(x)

Step-by-step explanation:

we have

[tex]f(x)=-2\sqrt{x-7}+1[/tex]

Find the domain of the function

we know that the radicand must be greater than or equal to zero

so

[tex]x-7\geq 0\\ \\x\geq 7[/tex]

The domain is all real numbers greater than or equal to 7

The range is the interval -----> (-∞,1]

[tex]y\leq1[/tex]

All real numbers less than or equal to 1

see the attached figure to better understand the problem

therefore

The statement that best describes the function f(x) is

-6 is not in the domain of f(x) but is in the range of f(x)

Answer:

B is the right choice. -6 is not the domain of f(x) but is in the range of f(x)

Answer:

7/78 - 35/78i

Step-by-step explanation:

A complex number is a real number, an imaginary number or a number with both real and imaginary number. Its standard form is:

a + bi

For the expression, 7/ 3-15i

(7/ 3-15i) (3+15i)

21 - 105i / (234)

7/78 - 35/78i

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{a}~,~\stackrel{y_1}{b})\qquad (\stackrel{x_2}{c}~,~\stackrel{y_2}{d})\qquad \qquad d = \sqrt{\underset{\underset{\textit{horizontal distance}}{\uparrow }}{( x_2- x_1)^2} + ( y_2- y_1)^2} \\\\[-0.35em] ~\dotfill\\\\ \textit{so in short is just }x_2-x_1[/tex]

Add the like terms:

8x2+x2=9x2

-9y2-3y2=-12y2

-4x-7x=-11x

Combine each term:

9x2-12y2-11x

Hope this helps!!

The sum of the polynomial will be,9x²-6y²-11x. Option B is correct.

A polynomial is an algebraic statement made up of variables and coefficients. Variables are sometimes known as unknowns.

We can use arithmetic operations like addition, subtraction, and so on. However, the variable is not divisible.

⇒(8x²-9y²-4x)+(x²-3y²–7x)

⇒9x²-6y²-11x

The sum of the polynomial will be,9x²-6y²-11x.

Hence, option B is correct.

To learn more about polynomials, refer:

https://brainly.com/question/17822016

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Answer:

The answer is 142°

Step-by-step explanation:

Because 38° and m∠2 are corresponding angles, m∠2 = 38°. Also, m∠2 and m∠5 are supplementary angles, which means the sum of their angles adds up to 180°. We can create the equation 38° + m∠5 = 180°. By subtracting 38° on both sides, we get m∠5 = 142°.

[tex]\bf \cfrac{2}{5}\div\cfrac{7}{9}=N\implies \cfrac{2}{5}\cdot \cfrac{9}{7}=N\implies \cfrac{18}{35}=N\implies 0.514\approx N \\\\[-0.35em] ~\dotfill\\\\ \boxed{0}\rule[0.35em]{10em}{0.25pt}\stackrel{N}{0.514}\rule[0.35em]{9em}{0.25pt}\boxed{1}[/tex]

Answer:

4th option

Step-by-step explanation:

Solve and rearrange the second equation for y

y= 2 +3

y =5

The substitute y in first equation to get x

Answer:

(a) 38 inches (b) 374 inches (c) 3564 inches (d) 6273767 square inches

Step-by-step explanation:

a) 2 ft 5 inches + 9 inches

Convert to inches

1 feet = 12 inches

2 feet = 12 x 2 inches = 24 inches

24 inches + 5 inches + 9 inches = 38 inches

b) 4 yards 8 inches + 6 yards 6 inches

Convert to inches

1 yard = 36 inches

4 yards = 36 x 4 = 144 inches

144 inches + 8 inches = 152 inches

6 yards = 36 x 6 = 216 inches

216 inches + 6 inches = 222 inches

152 inches + 222 inches = 374 inches

c) 29 yard 2 feet 11 inches + 55 yard 1 feet 10 inches + 13 yard 1 feet 3 inches

Convert to inches

29 yard 2 feet 11 inches

1 yard =  36 inches

29 yards = 36 x 29 = 1044 inches

1 feet = 12 inches

2 feet = 12 x 2 = 24 inches

1044 + 24 + 11 = 1079 inches

55 yard 1 feet 10 inches

1 yard = 36 inches

55 yards = 26 x 55 = 1980 inches

1 feet = 12 inches

1980 + 12 + 10 = 2002 inches

13 yard 1 feet 3 inches

1 yard = 36 inches

13 yards = 13 x 36 = 468 inches

1 feet = 12 inches

468 + 12 + 3 = 483 inches

1079 + 2002 + 483 = 3564 inches

d) 4,839 sq yard 8 sq feet 139 sq inches + 7 sq feet 124 sq inches

Convert to square inches

4,839 sq yard 8 sq feet 139 sq inches

1 square yard = 1296 square inches

4839 x 1296 = 6271344 square inches

1 square feet = 144 square inches

8 x 144 = 1152

6271344 + 1152 = 6272635 square inches

7 sq feet 124 sq inches

7 x 144 = 1008

1008 + 124 = 1132 square inches

1132 + 6272635 = 6273767 square inches

!!

Answer:

Option b) 6-10 lbs

Step-by-step explanation:

Given that X, the weight of  toy American Eskimo dog has mean of 8 pounds with a standard deviation of 1 pound

For 95% of the dogs according to normal distribution would lie between 2 std deviations on either side of the mean.

i.e. lower bound= Mean- 2 std deviation = 8-2 =6

Upper bound = Mean +2 std dev = 8+2 =10

Hence range of weights would be

6-10 lbs

Option b is the answer

The range of weights for 95% of toy American Eskimo dogs, assuming a normal distribution with a mean of 8 pounds and a standard deviation of 1 pound, would be 6 to 10 pounds.

To find the range of weights for which 95% of toy American Eskimo dogs fall under, given a mean weight of 8 pounds and a standard deviation of 1 pound, we use the properties of the normal distribution. The 95% interval is also known as the 95% confidence interval, and we can use the empirical rule or z-scores to calculate this. The empirical rule states that approximately 95% of data within a normal distribution lies within two standard deviations of the mean. Therefore, the range would be from 8 - (2 × 1) to 8 + (2 × 1), resulting in a weight range of 6 to 10 pounds.

Answer:

The second choice, 55 cm.

Step-by-step explanation:

Formula for circumference:

[tex]\pi * d[/tex]

[tex]\frac{22}{7} * \frac{35}{2} = \frac{770}{14}  \\\\770 / 14 = 55[/tex]

The circumference of the circle is 55 cm.

Answer:

Circumference of circle is:

55 cm

Step-by-step explanation:

we are given diameter d of a circle=35/2 cm

We have to find its circumference.

We know that circumference of circle in terms of its diameter is:

Circumference=πd

Circumference=[tex]\dfrac{22}{7}\times \dfrac{35}{2}[/tex]

                        =55 cm

Hence, circumference of circle is:

55 cm

Answer:   The answer is:  " 400 " .

____________________________________________

             →   20% of    400    is  80 .

____________________________________________

Step-by-step explanation:

____________________________________________

  20% of  "x" = 80 ;  Solve for  " x " ;  

20%   =  20/100 ;

         =   20 ÷  100 ;

         =   20.  ÷ 100 ;

         =   0.20  ;  

____________________________________________

Note that when dividing by 100 , we move the decimal        

point backward (when "dividing") — 2 (two) spaces —

                                since "100" has 2 (two) "zeros" .

____________________________________________

         →   0.20 = 0.2 ;  

____________________________________________

          →   (0.2) x = 80 ; Solve for "x" ;

In this case, multiply each side of the equation by "10" ; to get rid of the "decimal value" ; as follows:

          →  (10) * (0.2) x = 80 * 10) ;

   to get:

          →   2x  =  800  ;

Now, divide Each Side of the equation by "2" ;

     to isolate "x" on one side of the equation ;

      & to solve for "x" ;  as follows:

          →   2x / 2  =  800 / 2  ;

          →     x  =  400 .

____________________________________________

The answer is:  " 400 " .

____________________________________________

   →  20% of    400    is  80 .

__________________________________________________

Hope this is helpful to you!

        Best wishes in your academic pursuits

              — and within the "Brainly" community!

____________________________________________

Answer:

400

Step-by-step explanation:

20% of 400 is 80.

20% × x = 80

Multiply both sides by 100 and divide both sides by 20,.

x = 80 ×  100/20

x = 400

Answer:

z = [tex]\frac{50}{3}[/tex]

Step-by-step explanation:

The ratio of corresponding sides are equal, that is

[tex]\frac{z}{10}[/tex] = [tex]\frac{20}{12}[/tex] ( cross- multiply )

12z = 200 ( divide both sides by 12 )

z = [tex]\frac{200}{12}[/tex] = [tex]\frac{50}{3}[/tex]

Answer:

10 yards and 1 feet

Answer:

10 yards + 1 ft

Step-by-step explanation:

Conversion :

3 feet = 1 yard

or

30 feet = 10 yards

notice that 31 ft = 30 ft + 1 ft

                          = 10 yards + 1 ft

Answer:

[tex]x=1(+/-)0.5i\sqrt{10}[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2}=4x-7[/tex]  

[tex]2x^{2}-4x+7=0[/tex]  

so

[tex]a=2\\b=-4\\c=7[/tex]

substitute

[tex]x=\frac{4(+/-)\sqrt{(-4)^{2}-4(2)(7)}} {2(2)}[/tex]

[tex]x=\frac{4(+/-)\sqrt{-40}} {4}[/tex]

Remember that

[tex]i=\sqrt{-1}[/tex]

[tex]x=\frac{4(+/-)2i\sqrt{10}} {4}[/tex]

[tex]x=1(+/-)0.5i\sqrt{10}[/tex]

Answer:

It is just right

Step-by-step explanation:

Kermit's fav = 15 tea bags every 2 liters = 15/2 = 7.5 teabags per liter

Peggy made 90 teabags in 12 liters = 90/12 = 7.5 teabags per leter

Hence peggy used the same teabags per liter than kermit's favorite. It is just right.

edit: calculation error. corrected.

Your answer would be C:Just right.

Because:

2 liters of water = 15 tea bags

15/2 = 7.5 tea bags

Peggy needs to make 12 liters

12 x 7.5 = 90 tea bags

Conclusion:

Peggy's 12-liter batch of iced tea with 90 tea bags is JUST RIGHT.

Hope helps!-Aparri

Distribute -0.2:

-0.2 * x = -0.2x

-0.2 * -4 = 0.8

-0.2x + 0.8 = -1.7

Subtract 0.8 from both sides:

0.8 - 0.8 = 0

-1.7 - .8 = -2.5

Divide -.2x from both sides:

-0.2x = -2.5

x = 12.5

Hence, the value of x is 12.5

Answer: C I think. My answers are all confusing so I apologize if I make u get it wrong.

Step-by-step explanation:

Answer:

18:21 is equivalent to 18/21. When you simplify 18/21, you get 6/7

Answer:

85.714285714286%

Step-by-step explanation:

i hope this helps, if you are looking for the percentage.

Answer:

∠1

Step-by-step explanation:

we know that

An inscribed angle in a circle is formed by two chords that have a common end point on the circle

The measure of the inscribed angle is half of measure of the intercepted arc

In this problem

∠1 is an inscribed angle

∠2 is an outer angle

∠3 is an interior angle

∠4 is an semi-inscribed angle ( angle formed by a chord and a tangent)

Answer:

1. Tangent ray: a ray that lies on a tangent line and contains the point of tangency;

2. Intercepted arc: an angle intercepts an arc if the endpoints of the arc lie on the sides of the angle and all points of the arc except the endpoints lie in the interior of the angle;

3. Secant ray: a ray that lies on a secant line and contains both points of intersection with the circle; and

4. Inscribed angle: an angle with sides containing the endpoints of an arc and with a vertex that is a point of the arc other than an endpoint of the arc.

Answer:

The base of the cone is a circle of radius r. The height of the cone is the length h of the straight line from the cone's tip to the center of its circular base. Both ends of a cylinder are circles, each of radius r. ... For example, the volume of a cube is the area of one side times its height.

Step-by-step explanation:

Hope this helps! Please mark brainliest!

Answer:

The volume of a cone is one-third the volume of a cylinder.

Step-by-step explanation:

Answer:

7 Hours 12 Minutes

Step-by-step explanation:

So they one of the printer increases at a rate of 1/12 and the other increases at a rate of 1/18. Since you don't know the time it actually takes, you will replace both numerators with and x. (x/12 and x/18). You want to set these up so that they are adding. (x/12 + x/18=1). Since you're adding, you want to change it to the same denominator. The lowest is 36 so you multiply x/12 by 3/3 (so you don't unbalance the equation) and x/18 by 2/2. You'll end up with 3x/36 + 2x/36= 1 which will simplify to 5x/36=1. Multiply each side by 36 to leave the variable by itself. It becomes 5x=36 and when you divide it by 5 you get 7.2. So it's seven and .2 hours, which is equivalent to7 and 1/5 of an hour or 7 hours and 12 minutes.

Final answer:

When the two printing presses work together, they complete the job in 7.2 hours by adding their rates of work.

Explanation:

To solve how long it will take for two printing presses to complete a job when working simultaneously, one needs to add their individual rates of work. The first press can print the newspaper in 12 hours, and the second press can print it in 18 hours. Their rates are 1/12 and 1/18 newspapers per hour, respectively.

To find out how many newspapers per hour they can produce together, we simply add their individual rates:

1/12 newspaper per hour (first press) + 1/18 newspaper per hour (second press) = (1/12 + 1/18) newspapers per hour

Finding a common denominator, which is 36, we get:

(3/36 + 2/36) newspapers per hour = 5/36 newspapers per hour

Now, to find how long it takes for the combined presses to print one newspaper, take the reciprocal of the combined rate:

1 / (5/36) = 36/5 hours

Therefore, if both presses work together, they will complete the job in 7.2 hours.

Answer:

Step-by-step explanation:

Initial # = 176 fans

Final # = 202 fans

Increase = 202 - 176 = 26 fans

% increase = 100% x (Increase / initial #)

= 100 x (26/176)

= 100 x 0.1477

= 14.78%

The calculated value of the variable A from the table of values is -3x²

How to determine the value of the variable A

From the question, we have the following parameters that can be used in our computation:

The contingency table

The cell A is in the row -x and the column 3x

This means that

A = 3x * -x

When the product is evaluated, we have

A = -3x²

Hence, the value of the variable A is -3x²

Answer: First Option

Walter needs to make at least 5 more cookies but no more than 40

[tex]5 \leq x \leq 40[/tex]

Step-by-step explanation:

If we call x the number of cookies that Walter needs to make, then we know that the amount of cookies will be:

[tex]x +15[/tex]

Then this amount must be greater than or equal to 20 and must be less than or equal to 55 then.

[tex]x + 15 \geq20[/tex] and [tex]x + 15 \leq55[/tex]

This is:

[tex]20 \leq x + 15 \leq 55[/tex]

We solve the inequality for x.

[tex]20-15 \leq x + 15-15 \leq 55-15\\\\5 \leq x \leq 40[/tex]

Then the amount of cookies that Walter must make must be greater than or equal to 5 and less than or equal to 40

Answer: It is A

Step-by-step explanation:

Answer:

(x - 2) (x - 6)

Step-by-step explanation:

Factor the following:

x^2 - 8 x + 12

The factors of 12 that sum to -8 are -2 and -6. So, x^2 - 8 x + 12 = (x - 2) (x - 6):

Answer:  (x - 2) (x - 6)

The factors of the given polynomial are (x-6) and (x-2).

The given polynomial is x²-8x+12.

The factors are the polynomials which are multiplied to produce the original polynomial.

By splitting middle term method, we get

x²-6x-2x+12

x(x-6)-2(x-6)

(x-6)(x-2)

Therefore, the factors of the given polynomial are (x-6) and (x-2).

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