Describe the composite transformation that has occurred.

Answer:

40 = x

Step-by-step explanation:

They reflect each other like a mirror, so set 120 equal to 3x, then simply divide by 3 to get your answer.

Answer:

-4,-5/2

Step-by-step explanation:

2x^2+3x-20 =0

2x^2+8x-5x-20 =0

2x(x+4)-5(x+4) =0

(x+4)(2x-5) =0

Either,

x+4=0

x=-4

Or,

2x-5=0

2x=5

x=5/2

[tex]2x^2+3x-20=0\\2x^2+8x-5x-20=0\\2x(x+4)-5(x+4)=0\\(2x-5)(x+4)=0\\x=\dfrac{5}{2} \vee x=-4[/tex]

Answer:

y=2.5x+7

Step-by-step explanation:

You are basically being asked to use slope-intercept form for linear equations. It says y=mx+b where m is the slope and b is the y-intercept.

Plug in 2.5 for m and 7 for b giving you y=2.5x+7.

The equation is: y = mx + b

y = 2.5x + 7

so it's option D.

Answer:

a. 1 1/8 b. 8/9

Step-by-step explanation:

You can set this up as a proportion to solve.  For part a. we know that 2/3 of the road is 3/4 mile long.  2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length.  Set up the proportion like this:

[tex]\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}[/tex]

Cross multiplying gives you:

[tex]\frac{2}{3}x=\frac{1}{3}*\frac{3}{4}[/tex]

The 3's on the right cancel out nicely, leaving you with

[tex]\frac{2}{3}x=\frac{1}{4}[/tex]

To solve for x, multiply both sides by 3/2:

[tex]\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}[/tex] gives you

[tex]x=\frac{3}{8}[/tex]

That means that the road is still missing 3/8 of a mile til it's finished.  The length of the road is found by adding the 3/4 to the 3/8:

[tex]\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}[/tex]

So the road is a total of 1 1/8 miles long.

For b. we need to find out how much of 1 1/8 is 1 mile:

1 mile = x * 9/8 and

x = 8/9.  When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.

The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

- 6 ⁴/₅ and 6 ⁴/₅

Convert the mixed fraction number into a fraction number. Then we have

- 6 ⁴/₅ = -34/5

6 ⁴/₅ = 34/5

Then the sum of the expressions will be given as,

⇒ - 34/5 + 34/5

⇒ 0

The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.

More about the Algebra link is given below.

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Answer:

$173.45

Step-by-step explanation:

the beginning value is $400. if it loses 13%, that means it keeps 87% of its value. so you multiply by 0.87 6 times for each year

Answer:x=25

Step-by-step explanation:

One line is 180 , AB equals 180 ,angle AD is 110,180-110=70

So corner O on line DC is 70 and angle CE is 60. 60+70=130

180-130=50, 2x=50,50/2=25

Answer:

  2√5

Step-by-step explanation:

The Pythagorean theorem tells you how to find the distance from the origin.

  d = √((-2)² +4²) = √20 = 2√5

The vector's magnitude is 2√5 ≈ 4.47214.

Answer:

The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]

Step-by-step explanation:

Given : Vector whose terminal point is (-2, 4).

To find : What is the magnitude of the position vector?

Solution :

We have given, terminal point (-2,4)

The magnitude of the point x(a,b) is given by,

[tex]|x|=\sqrt{a^2+b^2}[/tex]

Let point x=(-2,4)

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

[tex]|x|=\sqrt{4+16}[/tex]

[tex]|x|=\sqrt{20}[/tex]

Therefore, The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]

Answer:

1/5

Step-by-step explanation:

The probability of selecting 5 widgets from the 25 produced where none are defective is 0.2914.

To calculate the probability of selecting 5 non-defective widgets from the 25 produced.

The number of ways to choose 5 non-defective widgets:

[tex]\[ \binom{20}{5} = \frac{20!}{5!(20-5)!} \][/tex]

[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ = \frac{1860480}{120} \][/tex]

= 15504

The total number of ways to choose 5 widgets from the 25 produced:

[tex]\[ \binom{25}{5} = \frac{25!}{5!(25-5)!} \][/tex]

[tex]\[ = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ = \frac{7893600}{120} \][/tex]

= 53130

The probability:

Probability = (Number of ways to choose 5 non-defective widgets)/(Total number of ways to choose 5 widgets)

[tex]\[ = \frac{15504}{53130} \][/tex]

[tex]\[ = 0.2914 \][/tex]

Complete question:

A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.

Answer:

66.7% is the answer.

Step-by-step explanation:

A country has 50 million people, 30 million of whom are adults.

Of the adults, 5 million are not interested in working.

5 million are interested in working but have given up looking for work.

5 million are still looking for work.

Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time.

Total labor force = Employed people + Unemployed  people

=> 15 million+ 5 million = 20 million

The labor force participation rate is [tex]\frac{20million}{30million} \times100[/tex]

= 66.66% ≈ 66.7%.

The labor force participation rate of the country is 66.7%, calculated by dividing the number of employed and actively seeking employment individuals (20 million) by the total adult population (30 million) and multiplying by 100.

To calculate the labor force participation rate, we include only those adults who are either employed or actively seeking employment. In the given scenario, the country has 30 million adults. Out of these, 5 million are not interested in working, 5 million have given up looking for work, and there are 15 million employed (10 million full-time and 5 million part-time). Therefore, the labor force includes those employed full-time, employed part-time, and those actively looking for work, adding up to 20 million.

The labor force participation rate is calculated by dividing the number of people in the labor force (20 million) by the total adult population (30 million) and multiplying the result by 100 to convert it into a percentage:

Labor Force Participation Rate = (Number in labor force ÷ Total adult population) x 100

Labor Force Participation Rate = (20 million ÷ 30 million) x 100

Labor Force Participation Rate = (2÷3) x 100

Labor Force Participation Rate = 66.7%

Answer:

Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank

Step-by-step explanation:

we know that

To find out what part of the total capacity of the storage tank that each vehicle received, divide three fourths by five

so

[tex]\frac{(3/4)}{5}=\frac{3}{20}[/tex]

therefore

Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank

Answer:

beginning inventory is $245000

Step-by-step explanation:

Given data

ending inventory = $150,000

purchased additional inventory = $375,000

goods sold = $470,000

to find out

beginning inventory

solution

according to question beginning inventory is calculated by this formula i.e.

beginning inventory = ( cost of goods sold  + ending inventory ) - amount of inventory purchase  .....................1

now put all value cost of goods sold, ending inventory and amount of inventory purchase in equation 1 and we get beginning inventory

beginning inventory = ( cost of goods sold  + ending inventory ) - amount of inventory purchase

beginning inventory = ( 470000  + 150000 ) - 375000

beginning inventory  = 245000

so beginning inventory is $245000

Answer:

  the mean age is greater

Step-by-step explanation:

The mean age is ...

  (1/2)14 + (1/3)15 + (1/6)13 = 14 1/6

The median age is 14. (half the students are 14 or younger)

The mean age is greater.

_____

1 -1/2 -1/3 = 6/6 -3/6 -2/6 = 1/6 . . . . . 1/6 of the students are 13.

Answer:

Step-by-step explanation:

Given that half of the students in a freshman class are 14 years old one third are 15 and the rest are 13

If no of students are n, then we have

n/2 have ages as 14, n/3 as 15 and remaining n/6 as 13.

Average would be total/n

= [tex]\frac{\frac{14n}{2}+\frac{15n}{3} +\frac{13n}{6}  }{n} \\=7+5+\frac{13}{6} =14.67[/tex]

Median would be middle entry when arranged in ascending order hence = 14

Mean > median

Answer:  The length and width of the rectangle are 19 cm and 5 cm respectively.

Step-by-step explanation:  Given hat the length of a rectangle is four centimeters more than three times its width and the area of the rectangle is 95 square centimeters.

We are to find the length and width of the rectangle.

Let W and L denote the width and the length respectively of the given rectangle.

Then, according to the given information, we have

[tex]L=3W+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since the area of a rectangle is the product of its length and width, so we must have

[tex]A=L\times W\\\\\Rightarrow 95=(3W+4)W\\\\\Rightarrow 3W^2+4W-95=0\\\\\Rightarrow 3W^2+19W-15W-95=0\\\\\Rightarrow W(3W+19)-5(3W+19)=0\\\\\Rightarrow (W-5)(3W+19)=0\\\\\Rightarrow W-5=0,~~~~~3W+19=0\\\\\Rightarrow W=5,~-\dfrac{19}{3}.[/tex]

Since the width of the rectangle cannot be negative, so we get

[tex]W=5~\textup{cm}.[/tex]

From equation (i), we get

[tex]L=3\times5+4=15+4=19~\textup{cm}.[/tex]

Thus, the length and width of the rectangle are 19 cm and 5 cm respectively.

The length of the rectangle is 19 and the width is 5 and it can be determined by using the formula of area of the rectangle.

The length of a certain rectangle is four centimeters more than three times its width.

If the area of the rectangle is 95 square centimeters,

The length and width of the rectangle.

Let the length of the rectangle be L,

And the width of the rectangle is W.

The length of a certain rectangle is four centimeters more than three times its width.

The perimeter formulas of different two-dimensional shapes:

Then,

[tex]\rm L = 3W+4[/tex]

And If the area of the rectangle is 95 square centimeters,

It is the number of square units inside the polygon.

The area is a two-dimensional property, which means it contains both length and width

[tex]\rm Area \ of \ the \ rectangle = length \times width\\\\L\times W = 95[/tex]

Substitute the value of L from equation 1,

[tex]\rm L\times W = 95\\\\(3W+4) \times W = 95\\\\3W^2+4W=95\\\\3W^2+4W-95=0\\\\3W^2+19W-15W-95=0\\\\W(3W+19) -5(3W+19) =0\\\\(3W+19) (W-5) =0\\\\W-5=0, \ W=5\\\\3W+19=0, \ W = \dfrac{-19}{3}[/tex]

The width of the rectangle can not be negative than W = 5.

Therefore,

The length of the rectangle is,

[tex]\rm L = 3W+4\\\\L = 3(5)+4\\\\L=15+4\\\\L=19[/tex]

Hence, The length of the rectangle is 19 and the width is 5.

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Answer:

1

Step-by-step explanation:

The numbers are mutually prime, so the GCF is 1.

Answer:

1

Step-by-step explanation:

n-1 and n are consecutive integers.

Examples of consecutive pairs:

(7,8)

(10,11)

(100,101)

and so on...

The remainder will always be 1 when doing n divided by n-1.

n=(n-1)(1)+1.

All this is here to try to convince you that n and n-1 will only have common factor of 1.

Answer:

Step-by-step explanation:

This is a right triangle with the 90 degree angle identified at D and the 60 degree angle identified at B. Because of the triangle angle sum theorem, the angles of a triangle all add up to equal 180 degrees, so angle C has to be a 30 degree angle.

There is a Pythagorean triple that goes along with a 30-60-90 triangle:

( x , x√3 , 2x )

where each value there is the side length across from the

30 , 60 , 90 degree angles.

We have the side across from the 90 degree angle, namely the hypotenuse. The value for the hypotenuse according to the Pythagorean triple is 2x. Therefore,

2x = 2√13

and we need to solve for x. Divide both sides by 2 to get that

x = √13

Now we can solve the triangle.

The side across from the 30 degree angle is x, so since we solved for x already, we know that side DB measures √13.

The side across from the 60 degree angle is x√3, so that is (√13)(√3) which is √39.

And we're done!

Answer:

Conjugate

Step-by-step explanation:

Those are conjugates.  In factoring polynomials, if you have one with a + sign separating the a and the square root of b, you will ALWAYS have one with a - sign.  They will always come in pairs.  Same with imaginary numbers.

Answer:

[tex]3.6*10^{2}[/tex]

Step-by-step explanation:

we have

[tex]\frac{8.64*10^{4}}{2.4*10^{2}}=\frac{8.64}{2.4}*10^{4-2}\\ \\=3.6*10^{2}[/tex]

Answer:

A) 3.6 × 10^2

Step-by-step explanation:

Got it right in the instruction on Edge 2021 ;D

Step-by-step explanation:

[tex]\angle1\ and\ \angle 2\ \text{are complementary}\to m\angle1+m\angle2=90^o\\\\m\angle ACX=m\angle1+m\angle2=90^o\to XA^{\to}\perp XC^{\to}[/tex]

Answer:  ΔABC ~ ΔBDC ~ ΔADB

Step-by-step explanation:

Match the degrees of each angle:

In ΔABC:  ∠A = 60° , ∠B = 90° , ∠C = 30°

In ΔBDC:  ∠B = 60° , ∠D = 90° , ∠C = 30°

In ΔADB:  ∠A = 60° , ∠D = 90° , ∠B = 30°

Answer:

See below.

Step-by-step explanation:

Triangle ABC is similar to triangle ADB is similar to triangle BDC.

Answer:

The answer is 16%

Step-by-step explanation:

Given a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes

so a time less than or equal to 3 hours and 20 minutes is a time 1 standard deviation OUTSIDE from the mean

Use the probability table:

The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes

= Probability of z being outside 1 SD from mean

= 1 - Probability of z within 1 SD from mean

= 1 - 0.84

= 0.16 or 16%....

Answer:

13/9

Step-by-step explanation:

Directly proportional means it will be multiply to our constant k.

Inversely proportional means it will divide our k.

So we are given z is directly proportional to x and inversely proportional to y.

This means:

[tex]z=k \cdot \frac{x}{y}[/tex].

We are given (x=4,y=10,z=0.8).  We can use this to find k.  The k we will find using the point will work for any point (x,y,z) since k is a constant.  A constant means it is to remain the same no matter what.

[tex]0.8=k \cdot \frac{4}{10}[/tex]

[tex]0.8=k(.4)[/tex]

Divide both sides by .4:

[tex]\frac{0.8}{0.4}=k[/tex]

[tex]k=2[/tex]

The equation for any point (x,y,z) is therefore:

[tex]z=2 \cdot \frac{x}{y}[/tex].

We want to find z given x=13 and y=18.

[tex]z=2 \cdot \frac{13}{18}[/tex]

[tex]z=\frac{2 \cdot 13}{18}[/tex]

[tex]z=\frac{13}{9}[/tex]

Answer:

  A. The distance from any point in the circle to the origin

Step-by-step explanation:

The distance formula tells you that the distance (d) is related to the coordinates of two points (x1, y1) and (x2, y2) by ...

  d² = (x2 -x1)² +(y2 -y1)²

For points (x, y) on the circle and (0, 0) at the origin, this becomes ...

  d² = (x -0)² +(y -0)²

If we want the distance to the point (x, y) to be equal to the radius of the circle, this becomes ...

  x² +y² = r² . . . . . . the standard equation of a circle centered at the origin

Answer: The distance from any point in the circle to the origin

Step-by-step explanation:

answer key

Answer:

we need an image of the spinner to answer the question. are we supposed to just know what it looks like?

Step-by-step explanation:

flvs she cheating

Answer:

  x:(x +15)

Step-by-step explanation:

The corresponding sides that are in proportion are apparently ...

  PS:PQ = PT:PR

PT = x

PR = x+15

so the proportion of interest is ...

  28:40 = x:(x+15)

For this case we have that by definition, the surface area of a cylinder is given by:[tex]SA = LA + 2B[/tex]

Where:

LA: It is the lateral area of the cylinder

B: It is the area of the base

We have as data that:

[tex]LA = 75.36 \ cm ^ 2\\B = 28.26 \ cm ^ 2[/tex]

Substituting:

[tex]SA = 75.36 + 2 (28.26)\\SA = 75.36 + 56.52\\SA = 131.88[/tex]

Finally, the surface area is:

[tex]131.88 \ cm ^ 2[/tex]

Answer:

Option D

Answer:

The solid formed is a cylinder

The total surface area is [tex]131.88cm^2[/tex]

Step-by-step explanation:

The given net is made up of a rectangle and two circles.

The total surface area is the area of the rectangle plus the area of the two circles.

This implies that:

[tex]S.A=75.36+2(28.26)[/tex]  

[tex]\implies S.A=75.36+56.52[/tex]  

[tex]\implies S.A=131.88cm^2[/tex]

The rectangular surface can be folded into the curved surface of a cylinder with the two circles becoming the lid.

Answer:

  33π square units

Step-by-step explanation:

The area of a sector is given by this formula. The larger sector angle is 2π-π/6 = 11π/6 radians.

  A = (1/2)r²θ = (1/2)6²(11π/6) = 33π . . . . square units

Answer:

Area of larger sector = 33π units²

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where 'r' is the radius of circle

To find the area of circle

Here r = 6 units

Area =  πr²

 = π * 6²

 =  36π units²

To find area of large sector

The central angle of larger sector = 360 - 30 = 330

Area of larger circle = (330/360) * area of circle

 =  (330/360) * 36π

 = 33π units²

Answer:

18 red marbles.

Step-by-step explanation:

The complete question asks the probability of randomly drawing a red marble is 3/5?

Let x be the number of red marbles that must be added.

To find x we will do the following:

[tex]\frac{x+12}{x+32} =\frac{3}{5}[/tex]

=>[tex]5(x+12)=3(x+32)[/tex]

=> [tex]5x+60=3x+96[/tex]

=> [tex]2x=36[/tex]

This gives x = 18

Hence, 18 red marbles will be added to the bag.

Answer:

D

Step-by-step explanation:

If the lines are parallel, the slope of both of them are going to be the same. So if one line is 3, the other one will be too.

The answer is:

If the red line has a slope of 3, the slope of the red line will also be 3.

So, the correct option is, D. 3

We need to remember that if two or more lines are parallel, they will share the same slope, no matter where are located their x-intercepts and y-intercepts, the only condition needed for them to be parallel, is to have the same slope.

So, if two lines are parallel, and one of them (the red line) has a slope of 3, the slope of the other line (the green line) will also be 3.

Have a nice day!

Answer:

Step-by-step explanation:

Let m represent the number of articles Mustafa has written. Then the total number of articles written must satisfy the inequality ...

  m +m/4 +3m/2 > 22

This has solution ...

  (11/4)m > 22

   m > (4/11)22

   m > 8 . . . . . . . . the solution to the inequality

If all the numbers are integers, and the ratios are exact, then we must have m be a multiple of 4 (that is, 4 times the number of articles Heloise wrote).

The solution set will be ...

  m ∈ {12, 16, 20, 24, ...} (multiples of 4 greater than 8)

Answer:

inequality - m+ 1/4m + 3/2m > 22

solution set - m>8

Step-by-step explanation:

i promise