There are 6 different colored pens in a box. Each pen has a unique color. In how many orders can 4 pens be chosen? In other words, what is the number of permutations of picking 4 pens from the box?

Answer:

If the number is x, we can write the following equation:

2 + 10x = 2

10x = 0 so therefore, x must be 0. There is no other number that satisfies this property.

Answer:

Step-by-step explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

Required:

is to prove ∡A and ∡B are supplementary

and ∡C and ∡D are supplementary.

so, m∠A + m∠B = 180°

and m∠C + m∠D = 180°

the  Statement    

1. ABCD is a parallelogram                

the reason is..    

It is Given!

the  Statement  

2.m∠A=m∠C and m∠B=m∠D        

the reason is..

Definition of parallelogram.

the  Statement  

3.m∠A+m∠B+m∠C+m∠D=360°    

the reason is..

Definition of quadrilateral

the  Statement  

4. m∠A+m∠B+m∠A+m∠B=360°    

the reason is..

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar  m∠C + m∠D = 180°

the  Statement  

5.∠A and ∠C are supplementary

the reason is..

by the definition of Supplementary   ∠ B and ∠D are supplementary

Hope it helps!

Answer:

see below

Step-by-step explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

Required:

is to prove ∡A and ∡B are supplementary

and ∡C and ∡D are supplementary.

so, m∠A + m∠B = 180°

and m∠C + m∠D = 180°

the  Statement    

1. ABCD is a parallelogram                

the reason is..    

It is Given!

the  Statement  

2.m∠A=m∠C and m∠B=m∠D        

the reason is..

Definition of parallelogram.

the  Statement  

3.m∠A+m∠B+m∠C+m∠D=360°    

the reason is..

Definition of quadrilateral

the  Statement  

4. m∠A+m∠B+m∠A+m∠B=360°    

the reason is..

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar  m∠C + m∠D = 180°

the  Statement  

5.∠A and ∠C are supplementary

the reason is..

by the definition of Supplementary   ∠ B and ∠D are supplementary

Hope it helps!

Answer:

[tex]\large \boxed{\sf \ \ \ a+b+c=3 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]4x^2+2x-1=4(x^2+\dfrac{2}{4}x)-1=4[(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}]-1[/tex]

As

[tex](x+\dfrac{1}{4})^2=x^2+\dfrac{2}{4}x+\dfrac{1^2}{4^2}=x^2+\dfrac{2}{4}x+\dfrac{1}{4^2} \ \ So \\\\x^2+\dfrac{2}{4}x=(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}[/tex]

Let 's go back to the first equation

[tex]4x^2+2x-1=4[(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}]-1=4(x+\dfrac{1}{4})^2-\dfrac{1}{4}-1\\\\=4(x+\dfrac{1}{4})^2-\dfrac{1+4}{4}=\boxed{4(x+\dfrac{1}{4})^2-\dfrac{5}{4}}[/tex]

a = 4

[tex]b=\dfrac{1}{4}\\\\c=-\dfrac{5}{4}[/tex]

[tex]a+b+c=4+\dfrac{1}{4}-\dfrac{5}{4}=\dfrac{4*4+1-5}{4}=\dfrac{12}{4}=3[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

15 miles

Step-by-step explanation:

Speed is the ratio of distance traveled to the time taken to reach the distance. The formula for speed is given by:

Speed = distance / time

Distance = speed × time

Claire is cycling at a speed of 12 miles per hour. Han is cycling at a speed of 8 miles per hour. At time t = 45 minutes = 45/ 60 hour = 0.75 hour, the distance traveled by Claire and Han is given as:

For Claire:

Distance = speed × time = 12 miles / hour × 0.75 hour = 9 miles

For Han:

Distance = speed × time = 8 miles / hour × 0.75 hour = 6 miles

Since both Han and Claire are traveling in opposite directions, the distance between them after 45 minutes = 9 miles + 6 miles = 15 miles

Answer:

A = 55

B = 60

Step-by-step explanation:

We know that 55+ b+ other angle = 180 since they make a straight line

The other angle = 65 since they are alternate interior angles

55+ B+ 65 = 180

Combine like terms

120 + B = 180

B = 60

A + B + 65 = 180 interior angles of a triangle must equal 180 degrees

A +60+ 65 =180  

Combine like terms

A +125 = 180

A = 55

Answer:

[tex]\boxed{A = 55\°}[/tex]

[tex]\boxed{B = 60\°}[/tex]

Step-by-step explanation:

Exterior Angle with A = 180 - 55 = 125 degrees  (Angles on a straight line)

The measure of exterior angle is equal to the sum of non-adjacent interior angles.

So,

125° = B + 65°

B = 125 - 65

B = 60°

Now,

A = 180 - 60 - 65     (Interior angles of a triangle add up to 180 degrees)

A = 55°

Answer:

[tex]\boxed{\sf Option \ 4}[/tex]

Step-by-step explanation:

[tex]\sqrt{2x-3} +x=3[/tex]

Subtract x from both sides.

[tex]\sqrt{2x-3} +x-x=-x+3[/tex]

[tex]\sqrt{2x-3}=-x+3[/tex]

Square both sides.

[tex]( \sqrt{2x-3})^2 =(-x+3)^2[/tex]

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

Subtract x²-6x+9 from both sides.

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

[tex]-x^2 +8x-12=0[/tex]

Factor left side of the equation.

[tex](-x+2)(x-6)=0[/tex]

Set factors equal to 0.

[tex]-x+2=0\\-x=-2\\x=2[/tex]

[tex]x-6=0\\x=6[/tex]

Check if the solutions are extraneous or not.

Plug x as 2.

[tex]\sqrt{2(2)-3} +2=3\\ \sqrt{4-3} +2=3\\\sqrt{1} +2=3\\3=3[/tex]

x = 2 works in the equation.

Plug x as 6.

[tex]\sqrt{2(6)-3} +6=3\\ \sqrt{12-3} +6=3\\\sqrt{9} +6=3\\3+6=3\\9=3[/tex]

x = 6 does not work in the equation.

Answer:

option d

Step-by-step explanation:

[tex]\sqrt{2x-3}+x = 3\\\\\sqrt{2x-3} = 3 -x\\[/tex]

Square both sides

[tex](\sqrt{2x-3})^{2}=(3-x)^{2}\\\\\\2x-3=9-6x+x^{2}\\\\0=x^{2}-6x + 9 - 2x + 3\\[/tex]   {Add like terms}

[tex]x^{2} - 8x + 12 = 0[/tex]

Sum = -8

Product = 12

Factors =  -2 , - 6

x² - 2x - 6x + (-2) * (-6) = 0

x(x -2) - 6(x -2) = 0

(x -2) (x - 6) = 0

x - 2 =0   ; x - 6 = 0

x = 2      ; x = 6

roots of the equation : 2  , 6

But when we put x = 6, it doesn't satisfies the equation.

When x = 6,

[tex]\sqrt{2x-3} + x = 3\\\\\sqrt{2*6-3}+6 = 3\\\\\sqrt{12-3}+6=3\\\\\sqrt{9}+6=3\\\\[/tex]

3 + 6≠ 3

Therefore, x = 2  but x = 6 is extraneous

Answer:

[tex]\boxed{x = 251.4 cm}[/tex]

Step-by-step explanation:

Part 1: Sketching the triangle

We are given the angle of elevation, 70°, and the distance along the ground, 86 centimeters. Our unknown is a ladder leaning against the building. Buildings are erected vertically, so the unknown side length is the hypotenuse of the triangle.

We can then sketch this triangle out to visualize it (attachment).

Part 2: Determining what trigonometric ratio can solve the problem

Now, we need to refer to our three trigonometric ratios:

[tex]sin = \frac{opposite}{hypotenuse}[/tex]

[tex]cos = \frac{adjacent}{hypotenuse}[/tex]

[tex]tan = \frac{opposite}{adjacent}[/tex]

Visualizing the sketched triangle, we can assign the three sides their terms in correspondence to the known angle -- this angle cannot be the right angle because the hypotenuse is opposite of it.

Therefore, we know our unknown side length is the hypotenuse of the triangle and because the other side is bordering the 70° angle, it is the adjacent side.

By assigning the sides, we can see that we need to use the trigonometric function that utilizes both the hypotenuse and the adjacent side to find the angle. This is the cosine function.

Part 3: Solving for the unknown variable

Now that we have determined what side we need to solve for and what trigonometric function we are going to use to do so, we just need to plug it all into the equation.

The cosine function is provided: [tex]cos( \alpha) = \frac{adjacent}{hypotenuse}[/tex], where [tex]\alpha[/tex] is the angle. We just need to plug in our values and solve for our unknown side; the hypotenuse.

[tex]cos (70) = \frac{86 cm}{x}[/tex], where x is the unknown side/the hypotenuse.

[tex]x * cos (70) = \frac{86 cm}{x} * x[/tex] Multiply by x on both sides of the equation to eliminate the denominator and make the unknown easier to solve for.

[tex]\frac{xcos (70)}{cos(70)} = \frac{86 cm}{cos(70)}[/tex], Evaluate the second fraction because the first one cancels down to just the unknown, x.

[tex]\frac{86}{cos(70)} = 251.4[/tex], round to one decimal place.

Your final answer is [tex]\boxed{x=251.4cm}[/tex].

Answer:

A

Step-by-step explanation:

Given

f(x) = [tex]\frac{3+x}{x-3}[/tex]

To evaluate f(a + 2), substitute x = a + 2 into f(x)

f(a + 2) = [tex]\frac{3+a+2}{a+2-3}[/tex] = [tex]\frac{5+a}{a-1}[/tex] → A

~ ANSWER=1/2 ~

Simple probability is found by counting all the results which fit requirements and dividing by all possible results.

To find probability of two results in a row, multiply chance of first result by chance of second result.

Since you are replacing the marble before the second draw, we don’t have to figure out the various changes in odds for the different possible first draws. It’s just that simple.

There are 5 white marbles

There are 4 red marbles

There are always 20 marbles in all

5/20*4/20=1/4*1/5=1/20 or 1/2

By coincidence, the same as the chance of drawing the white marble in one draw.

Answer:

5/18

Step-by-step explanation:

Answer:

[tex] x+2-2 <-5-2[/tex]

And after operate we got:

[tex] x <-7[/tex]

And then the solution would be [tex]x<-7[/tex]

Step-by-step explanation:

For this problem we have the following inequality:

[tex] x+2 <-5[/tex]

The first step would be subtract 2 from both sides of the equation and we got:

[tex] x+2-2 <-5-2[/tex]

And after operate we got:

[tex] x <-7[/tex]

And then the solution would be [tex]x<-7[/tex]

Answer:

interquartile range=21.05

Step-by-step explanation:

3.5, 12, 19.1, 25.8, 31.8

median is 19.1

Quartile 1= (3.5+12)/2=7.75

Quartile 3=(25.8+31.8)/2=28.8

interquartile range=Q3-Q1=28.8-7.75= 21.05

Answer:

Rectangle

Step-by-step explanation:

Well if point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

__________

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

__________

So graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

The most precise name of the quadrilateral will be rectangle .

Given,

Point A : (2,3) .

Here,

If point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

So, graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

Know more about rectangle,

https://brainly.com/question/15019502

#SPJ6

Answer:

Step-by-step explanation:

We have f(x) and g(x). We are to evaluate each of these functions at the domain values given (1, 2, 3, 4, 5, and 6) and see where the output is the same.

[tex]f(1)=-(1)^2+4(1)+12[/tex] and f(1) = 15

[tex]f(2)=-(2)^2+4(2)+12[/tex] and f(2) = 16

[tex]f(3)=-(3)^2+4(3)+12[/tex] and f(3) = 15

[tex]f(4)=-(4)^2+4(4)+12[/tex] and f(4) = 12

[tex]f(5)=-(5)^2+4(5)+12[/tex] and f(5) = 7

[tex]f(6)=-(6)^2+4(6)+12[/tex] and f(6) = 0

Now for g(x) at each of these domain values:

g(1) = 1 + 2 and g(1) = 3

g(2) = 2 + 2 and g(2) = 4

g(3) = 3 + 2 and g(3) = 5

g(4) = 4 = 2 and g(4) = 6

g(5) = 5 + 2 and g(5) = 7

g(6) = 6 + 2 and g(6) = 8

It looks like the outputs are the same at f(5) and g(5). Actually, the domains are the same as well! f(5) = g(5)

Answer:

No.

Step-by-Step Explanation:

When two lines are parallel, they might or might not be equal. It is not necessary that they should be equal.

See the triangle below in which two lines are parallel to each other.

Answer:

39 units²

Step-by-step explanation:

The figure is composed of a rectangle VEDR and Δ RMV

Area of rectangle = VE × ED = 5 × 6 = 30 units²

Area of Δ = 0.5 × RV × perpendicular from M to RV

                = 0.5 × 6 × 3 = 9 units²

Thus

Area of polygon = 30 + 9 = 39 units²

Answer:

  88

Step-by-step explanation:

2.75 ft = (2.75 ft)(12 in/ft) = 33 in

At 0.375 inches per plate, there will be ...

  (33 in)/(0.375 in/plate) = 88 plates

There are 88 steel plates in the pile.

Answer:

La Tasha has 27 rabbit stickers. She splits the stickers

evenly among 3 pieces of paper. How many stickers

did La Tasha put on each piece of paper?​

Step-by-step explanation:

Answer:

78.5 yds

Step-by-step explanation:

The circumference is given by

C = pi *d

C = 3.14 * 25

C =78.5

Answer:

[tex]\huge\boxed{C=25\pi\ yd\approx78.5\ yd}[/tex]

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=d\pi[/tex]

d - diameter

We have d = 25yd.

Substitute:

[tex]C=25\pi\ yd[/tex]

Use [tex]\pi\approx3.14[/tex]:

[tex]C\approx(25)(3.14)=78.5\ yd[/tex]

Answer:

-28.

Step-by-step explanation:

(x^2 + 3) / (x + 6)

x = -9

[(-9)^2 + 3] / (-9 + 6)

= (81 + 3) / (-3)

= 84 / (-3)

= -28

Hope this helps!

Answer:  the value of the expression is 80

Step-by-step explanation:

[tex]x^2 +3/ x+6[/tex]

(-9)² + 3 / (-9 + 6) .  PEMDAS: figure  parentheses and exponents  first

81 + 3/-3    division   3/-3  = –1

81 + (–1) .adding a negative is the same as subtracting

81 –1

80

Answer:

Step-by-step explanation

√144²

12²

144

√9 + √16

3 + 4

7

√9 + √16 × √400 = ​

3 + 2^{4} x 5

3 + 80

83

Answer:

The translation from triangle IJK to triangle I'J'K' is [tex]T_{(2, 6)}[/tex] which is 2 units to the right and 6 units up

Step-by-step explanation:

The coordinates of triangle JKI are;

J has coordinates (1, - 1)

K has coordinates (1, - 4)

I has coordinates (-3, - 2)

While, the coordinates of translation triangle J'K'I' are;

J' has coordinates (3, 5)

K' has coordinates (3, 2)

I' has coordinates (-1, 4)

Which give the translation as follows

Translation in the y-coordinate (y values);

For J = 5 - (-1) = 6

For K = 2 - (-4) = 6

For I = 4 - (-2) = 6

Translation in the x-coordinate (x values);

For J = 3 - 1 = 2

Therefore, the translation from triangle IJK to triangle I'J'K' is T(2, 6) which is 2 units to the right and 6 units up

Answer:  The value of b= 15.6

Step-by-step explanation:

The given equation:  [tex]4\dfrac{1}{3}b+b=6b-10.4[/tex]

To find : Value of b.

Since, we can write [tex]4\dfrac{1}{3}=\dfrac{13}{3}[/tex]

So, the given equation becomes [tex]\dfrac{13}{3}b+b=6b-10.4[/tex]

[tex]\Rightarrow\dfrac{13b+3b}{3}=6b-10.4\Rightarrow\dfrac{16b}{3}=6b-10.4[/tex]

Subtract 6b from both sides , we get

[tex]\Rightarrow\dfrac{16b}{3}=6b-10.4\\\\\Rightarrow\dfrac{16b-18b}{3}=-10.4\\\\\Rightarrow\dfrac{-2b}{3}=-10.4\\\\\Rightarrow b=-10.4\times\dfrac{-3}{2}\\\\\Rightarrow\ b= 15.6[/tex]

hence, the value of b= 15.6

Step-by-step explanation:

The probability that either Jack or Jill will be selected on the first draw is 2/30.

The probability that the other person will be selected on the second draw is 1/29.

The probability of both events is (2/30) (1/29), which simplifies to 1/435.

Answer:

[tex] y = A_o (b)^t[/tex]

With [tex] A_o = 82.6[/tex] the initial amount and t the time on hours and t the time in hours. since the half life is 12 hours we can find the parameter of decay like this:

[tex] 41.3= 82.6(b)^{12}[/tex]

And solving for b we got:

[tex] \frac{1}{2}= b^{12}[/tex]

And then we have:

[tex] b= (\frac{1}{2})^{\frac{1}{12}}[/tex]

And the model would be given by:

[tex] y(t) = 82.6 (\frac{1}{2})^{\frac{1}{12}}[/tex]

Step-by-step explanation:

Assuming this complete question: "A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 12 hours. At the start of the experiment, 82.6g is present. "

For this case we can create a model like this one:

[tex] y = A_o (b)^t[/tex]

With [tex] A_o = 82.6[/tex] the initial amount and t the time on hours and t the time in hours. since the half life is 12 hours we can find the parameter of decay like this:

[tex] 41.3= 82.6(b)^{12}[/tex]

And solving for b we got:

[tex] \frac{1}{2}= b^{12}[/tex]

And then we have:

[tex] b= (\frac{1}{2})^{\frac{1}{12}}[/tex]

And the model would be given by:

[tex] y(t) = 82.6 (\frac{1}{2})^{\frac{1}{12}}[/tex]

Answer:

$2,500 was invested in the first account while $7,500 was invested in the second account

Step-by-step explanation:

Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments

Now, since we do not know the amount invested , we shall be representing them with variables.

Let the amount invested in the first account be $x and the amount invested in the second account be $y

Since the total amount invested is $10,000, this means that the summation of both gives $10,000

Mathematically;

x + y = 10,000 ••••••(i)

now for the $x, we have an interest rate of 5%

This mathematically translates to an interest value of 5/100 * x = 5x/100

For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100

The addition of both interests, gives 575

Thus mathematically;

5x/100 + 6y/100 = 575

Multiplying through by 100, we have

5x + 6y = 57500 •••••••••(ii)

From 1, we can have x = 10,000-y

let’s substitute this into equation ii

5(10,000-y) + 6y = 57500

50,000-5y + 6y = 57500

50,000 + y = 57500

y = 57500-50,000

y = 7,500

Recall;

x = 10,000-y

so we have;

x = 10,000-7500 = 2,500

Answer:

260

Step-by-step explanation:

By PEMDAS, we know multiplican comes first. 53*5=265. Then, subtract 5 to get 260.

If you want additional help with math or another subject for FREE, check out growthinyouth.org.

Answer:

260

Step-by-step explanation:

the rule is to start with multiplication first 53*5=265 then subtract 5

53 × 5-5= 265-5=260

Answer:  The level of the dose be after 3 hours=  0.03125 mg.

Step-by-step explanation:

General exponential decay equation : [tex]y=A(1-r)^x[/tex] , where A = initial value , r= rate of decay , x =Time period.

Here, drug’s effectiveness  is decreasing exponentially.

AS per given , we have

A= 250 mg

x=3

r= 95% = 0.95

Then, [tex]y=250(1-0.95)^3 = 250(0.05)^3=250*0.000125=0.03125[/tex]

Hence, the level of the dose be after 3 hours = 0.03125 mg.

Answer:

214.34 about (213.75 on calculator)

Step-by-step explanation:

95% of 250=237.5

95% of 237=225.15

95% of 225=213.75

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(

−

1

,

10

3

)

Equation Form:

x

=

−

1

,

y

=

10

3

Tap to view steps...

image of graph

Tap to hide graph...

Answer:

(2,1)

Step-by-step explanation:

Well first we single out y or x in one of the equations,

we’ll use 2x + y = 5 and single out y.

2x + y = 5

-2x to both sides

y = -2x + 5

So we can plug in -2x + 5 into y in 2x - 2y = 2.

2x - 2(-2x + 5) = 2

2x + 4x - 10 = 2

combine like terms,

6x - 10 = 2

Communicarice property

+10 to both sides

6x = 12

divide 6 to both sides

x = 2

If x is 2 we can plug 2 in for x in 2x + y = 5.

2(2) + y = 5

4 + y = 5

-4 to both sides

y = 1

(2,1)

Thus,

the solution is (2,1).

Hope this helps :)

Step-by-step explanation:

If the line is parallel to y=2/3x+4 then,

m=m

slope of eqn y=2/3x+4

m=2/3(On comparing with y= mx + c)

the passing point is (3,7) then,

y-y1 = m(x-x1)

y-7=2/3(x-3)

y-7=2/3x -2

y-7= -4x/3

3y-7= -4x

4x + 3y - 7=0

So, The reqd eqn is 4x + 3y - 7 = 0