Drag the tiles to the correct boxes to complete the pairs.
Match each transformation or sequence of transformations to an equivalent transformation or sequence of transformations.
a 90° counterclockwise rotation about the origin
a 180° rotation about the origin
a 90° clockwise rotation about the origin

Answer:

Part 1) The exponential function is  [tex]y=140,000(1.05)^x[/tex]

Part 2) [tex]305,602\ people[/tex]

Step-by-step explanation:

Part 1) Write an exponential function

we know that

The exponential growth function is given by the formula

[tex]y=a(1+r)^x[/tex]

where

y is the population

x is the number of years

a is the initial population

r is the rate of change

we have

[tex]a=140,000\ people\\r=5\%=5/100=0.05[/tex]

substitute

[tex]y=140,000(1+0.05)^x[/tex]

[tex]y=140,000(1.05)^x[/tex]

Part 2) How much will the population be after 16 years?

For x=16 years

substitute the value of x in the exponential function

[tex]y=140,000(1.05)^{16}=305,602\ people[/tex]

An exponential function to model the population growth of 5% per year from an initial population of 140,000 after 16 years is y = 140,000(1 + 0.05)^x. After substituting x with 16, you calculate the growth and multiply by the initial population to find the population size after 16 years.

To model the population growth in this scenario, we use an exponential growth function. The formula for exponential growth is y = P(1 + r)^t, where y is the final amount, P is the initial principal balance, r is the rate of interest, and t is the number of time periods the interest is applied. In this case, the population P is 140,000, the growth rate 'r' is 5% (or 0.05 when expressed as a decimal), and the number of years 't' is 16.

The exponential function in terms of 'x' (where 'x' represents the number of years) will be: y = 140,000(1 + 0.05)^x.

After plugging in 't' as 16 years, we calculate the population after 16 years as follows: y = 140,000(1 + 0.05)^16. Now we calculate the growth factor (1 + 0.05)^16 and multiply this by the initial population of 140,000 to determine the population after 16 years.

Answer:

solution is

y + 3 = 3(x - 0)

y + 3 = 3x - 0

y = 3x - 3

The amount deposited initially is $ 706.22

Solution:

The formula for amount using compound interest is given as:

[tex]A = p(1+\frac{r}{n})^{nt}[/tex]

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

From given,

t = 7 years

A = 1000

P = ?

[tex]r = 5 \% = \frac{5}{100} = 0.05[/tex]

n = 4 (since compounded quarterly)

Substituting the values we get,

[tex]1000 = p(1+\frac{0.05}{4})^{4 \times 7}\\\\1000 = p(1+\frac{0.05}{4})^{28}\\\\1000 = p(1+0.0125)^{28}\\\\1000 = p(1.0125)^{28}\\\\1000 = p \times 1.4159923\\\\p = \frac{1000}{1.4159923}\\\\p = 706.2185 \approx 706.22[/tex]

Thus amount deposited initially is $ 706.22

Answer:

diagonal is 14 m

Step-by-step explanation:

We are given;

We are required to determine the diagonal of the square.

We know that;

Area of a square = s²  , where s is the side of the square

Therefore;

s² = 98

Thus;

s = √98

To get the diagonal

s² + s² = diagonal squared

Hence;

Diagonal squared = (√98)² + (√98)²

                              = 98 + 98

                              = 196

Thus;

Diagonal = √196

               = 14 m

Thus, the diagonal is 14 m

The length of the corresponding arc of the larger circle = 54 ft.

Step-by-step explanation:

step 1 :

step 2 :

Small circle :

Arc length = (∅/360)2πr

where,

∅ = arc angle

π = 3.14

r = radius of circle

step 3 :

Arc length = (∅/360)2[tex]\times[/tex]3.14[tex]\times[/tex]30

⇒ 36 = (∅/360)[tex]\times[/tex]188.4

⇒ ∅ = 36[tex]\times[/tex]360 / 188.4

∅ = 68.79

step 4 :

Large circle :

Arc length = (∅/360)2πr

                 = (68.79/360) 2[tex]\times[/tex]3.14[tex]\times[/tex]45

Arc length = 54 ft

Answer:

...................................../................................................................

Step-by-step explanation:

......................................................................................

Answer: Cost(c) t（time)

c=10+4t

Step-by-step explanation:

Units of J: [tex][\frac{m}{s^3}][/tex]

Step-by-step explanation:

The quantity defined in this problem is

[tex]J=\frac{a}{t}[/tex]

where:

a is the acceleration

t is the time

The units of the two quantities are:

a (acceleration) is measured in metres per second squared, [tex][\frac{m}{s^2}][/tex]

t (time) is measured in seconds, [tex][s][/tex]

Therefore, the quantity J is measured in:

[tex][J]=\frac{[\frac{m}{s^2}]}{[s^3]}=[\frac{m}{s^3}][/tex]

which is option B.

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The total amount he will pay back=$16290

Step-by-step explanation:

Given, Phil had decided to take out a private loan for $9,000 where loan payment start as soon as the loan amount is deposited in his student account for 10 year. The interest rate is 8.1% .

P =$ 9,000   r = 8.1%   and t = 10 years

Simple interest

Interest(I)  [tex]= \frac{P\times r \times t}{100}[/tex]

                 [tex]=\$\frac{9000\times 8.1 \times 10}{100}[/tex]

                 [tex]=\$ 7290[/tex]

The total amount he will pay back =$(7290 + 9,000)=$16290

Final answer:

To calculate the total amount Phil will pay back on a $9,000 private loan with 8.1% interest over 10 years, multiply the principal by (1 + interest rate) raised to the number of years. The total amount paid back is $17,925.56.

Explanation:

To calculate the total amount Phil will pay back, we need to calculate the loan payments for 10 years. First, we can calculate the annual payment using the formula:

Annual Payment = Principal x (1 + Interest Rate)^Number of Years

Substituting in the values Principal = $9,000, Interest Rate = 8.1% (or 0.081), and Number of Years = 10, we have:

Annual Payment = $9,000 x (1 + 0.081)^10 = $9,000 x 1.991729 = $17,925.56

Therefore, the total amount Phil will pay back over 10 years is $17,925.56.

Answer:

The weight of each box must be less than 115 kg to be carried in the truck.

Step-by-step explanation:

The weight of the truck is, T = 875 kg.

Let the weight of one box be x kg.

Given:

[tex]875-4x>415[/tex] kg.

Solve the above inequality for x as follows:

[tex]875-4x>415\\-4x>415-875\\-4x>-460\\x<\frac{-460}{-4}\\ x<115[/tex]

As the weight of a box cannot be less than 0, the range of x is (0, 115).

Thus, the weight of each box must be less than 115 kg to be carried in the truck.

Answer:

Your signature, and a nice 4-word goodbye

Step-by-step explanation:

Your signature so they know it was YOU who wrote it and a nice 4-word goodbye to show the other person that you care.

Answer:

If u want to change fraction into percentage then multiply it with 100.for eg.83/90*100%

Answer:

[tex]Line\ passing\ through\ (-1.5,0)\ and\ (0,2).\\\\Correct\ graph\ is\ attached.[/tex]

Step-by-step explanation:

[tex]The\ given\ equation\ represents\ a\ line\\\\[/tex]

y-intercept:

[tex]Substitute\ x=0\\\\-4\times 0+3y=6\\\\3y=6\\\\y=\frac{6}{3}\\\\y=2\\\\The\ line\ passes\ through\ the\ point\ (0,2).[/tex]

x-intercept:

[tex]Substitute\ y=0\\\\-4x+3\times 0=6\\\\-4x=6\\\\x=-\frac{6}{4}\\\\x=-1.5\\\\The\ line\ passes\ through\ the\ point\ (-1.5,0).[/tex]

The correct graph is attached.

Answer:

  see below

Step-by-step explanation:

A left-arrow on a number line represents subtraction of a positive number or addition of a negative number. The two left arrows, one of length 0.2, the other of length 0.1, indicate the numbers -0.2 and -0.1 are being added. The end result is the dot at the end of the combined arrows, at -0.3.

The only expression that is true and corresponds to this description is the one shown below.

Answer:

1/4

Step-by-step explanation:

The fraction 8/12 simplifies to 2/3. The whole number is 0, and the unit fraction is 2/3, which can be expressed as the sum of two unit fractions, 1/2 and 1/6.

The fraction 8/12 can be simplified to a whole number and a unit fraction. First, divide both the numerator and denominator by their greatest common divisor, which is 4. This yields the simplified fraction 2/3. Thus, the whole number is '0' and the unit fraction is '2/3' as 2/3 is less than 1 and cannot be represented as a whole number. A unit fraction is a fraction where the numerator is '1'. Although 2/3 is not a unit fraction itself, it can be expressed as the sum of two unit fractions, '1/2 + 1/6'.

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Answer:

√3

Step-by-step explanation:

We cannot solve this operation directly. Because cot7pi/6 is undefined.

We know that 1/tan= cot.

so we will first take the reciprocal of cot that is 1/tan.

So,

cot7pi/6= 1/tan 7π/6

∵7π/6 = 210 where pi=180

so cot7π/6  =1/tan210

cot7π/6 =1/1÷√3

cot7π/6 = √3

Answer:

4/4-1/4 is 3/4 so 3/4 divided by 3 is 1/4 bag of peanuts per friend.

Step-by-step explanation:

To find the expression that represents the peanuts that each friend ate, start with the fraction representing the remaining peanuts after Jamal ate 1/4 bag, which is 3/4. Divide the remaining peanuts equally among the 3 friends by dividing the fraction 3/4 by 3, which gives us 1/4. Therefore, each friend ate 1/4 of the peanuts.

To find the expression that represents the peanuts that each friend ate, we need to follow the steps:

Therefore, the expression that represents the peanuts that each friend ate is 1/4.

Final answer:

Dexter rode an estimated 1.3 miles altogether after traveling 9/10 miles to the store and then 4/10 miles to his uncle's house.

Explanation:

You are asking how far Dexter rode his bike altogether after he traveled 9/10 miles from his house to the store and then 4/10 miles to his uncle's house. To estimate the total distance Dexter rode, we need to add the two distances together.

The sum of 9/10 miles and 4/10 miles is:

9/10 miles + 4/10 miles = 13/10 miles

To make it easier to understand, 13/10 miles can be converted to 1 3/10 miles, which is the same as 1.3 miles as an estimate, considering 10/10 equals 1 full mile. Therefore, Dexter rode an estimated 1.3 miles altogether.

Answer:

F = 2

Step-by-step explanation:

4f-24+4f=-8

collect like terms

8f-24=-8

move constant to the right

8f=-8+24

calculate

8f=16

divide both sides by 8

Answer F = 2

Answer:

The two statements that apply are A and B.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

White envelopes Hadley has = 3/6 of a box

Gray envelopes Hadley has = 1/3 of a box

When full, each box of envelopes has the same number of envelopes

Hadley said she has 4/9 of a box when she puts the white envelopes and gray envelopes together.

2. Which statements describe this situation? Select the two statements that apply.

Let's add 3/6 and 1/3

3/6 + 1/3 = 3/6 + 2/6 = 5/6

A. Hadley’s answer is incorrect, because 3/6 is equal to 1/2 , and 4/9 is less then 1/2 .   This is correct.

B. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 5/6.   This is correct.

C. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 2/6.  This is wrong

D. Hadley's answer is correct, because 3 and 1 is 4, and 6 and 3 is 9. This is wrong.

The two statements that apply are A and B.

Answer:  Answer:

The two statements that apply are A and B.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

White envelopes Hadley has = 3/6 of a box

Gray envelopes Hadley has = 1/3 of a box

When full, each box of envelopes has the same number of envelopes

Hadley said she has 4/9 of a box when she puts the white envelopes and gray envelopes together.

2. Which statements describe this situation? Select the two statements that apply.

Let's add 3/6 and 1/3

3/6 + 1/3 = 3/6 + 2/6 = 5/6

A. Hadley’s answer is incorrect, because 3/6 is equal to 1/2 , and 4/9 is less then 1/2 .   This is correct.

B. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 5/6.   This is correct.

C. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 2/6.  This is wrong

D. Hadley's answer is correct, because 3 and 1 is 4, and 6 and 3 is 9. This is wrong.

Step-by-step explanation: A   B

Answer:

A

Step-by-step explanation:

To determine which point is a solution, substitute the x- coordinate into the equation and if the value obtained agrees with the y- coordinate of the point then it is a solution.

A (- 3, - 17)

y = 4(- 3) - 5 = - 12 - 5 = - 17 ← (- 3, - 17) is a solution

B (4, 7)

y = 4(4) - 5 = 16 - 5 = 11 ≠ 7 ← not a solution

C (- 2, - 18)

y = 4(- 2) - 5 = - 8 - 5 = - 13 ≠ - 18 ← not a solution

D (3, 17)

y = 4(3) - 5 = 12 - 5 = 7 ≠ 17 ← not a solution

Answer:

Option D is correct

( -3, -1 )

Step-by-step explanation:

equation 1 is

y = -2x -7

and equation 2 is

2y - x = 1

so from 1 we have y = -2x - 7 put in 2

2 ( -2x - 7 ) -x = 1

-4x - 14 - x = 1

- 5x = 1 + 14

X = 15/-5

X= - 3

put in equation 1

Y = - 2 ( -3) - 7

Y= 6 - 7

Y = - 1

Solution of  the given equations D.[tex]\boldsymbol{(-3,-1)}[/tex].

An equation is a mathematical expression that contains an equals symbol.

Given equations are as follows:

       [tex]y=-2x-7[/tex]    

[tex]2y-x=1[/tex]

Put value of [tex]\boldsymbol{y}[/tex] from the first equation to the second equation.

[tex]2(-2x-7)-x=1[/tex]

   [tex]-4x-14-x=1[/tex]

                 [tex]-5x=15[/tex]

                     [tex]x=-3[/tex]

Now, put value of [tex]x[/tex] in the equation [tex]2y-x=1[/tex].

[tex]2y-(-3)=1[/tex]

           [tex]2y=-2[/tex]

             [tex]y=-1[/tex]

Option D. is correct.

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Answer:

  3

Step-by-step explanation:

The factors of 12a are ...

  2×2×3×a

The factors of 27 are ...

  3×3×3

The only common factor is 3.

_____

  12a -27 = 3(4a -9)

Final answer:

The Greatest Common Factor (GCF) of the expression 12a - 27 is 3, since 3 is the highest number that divides evenly into both 12 and 27 with no common variables present.

Explanation:

To find the Greatest Common Factor (GCF) of the expression 12a - 27, you look for the highest number and any variables that divide evenly into both terms. Note that 12 and 27 can both be divided by 3. Therefore, 3 is a common factor. Since there are no more common variables or higher factors, the GCF of 12a and 27 is simply 3.

To calculate the GCF, divide each term by 3:

12a ÷ 3 = 4a

27 ÷ 3 = 9

While the expression is factored as 3(4a - 9), the GCF is just the number 3.

Answer:

9

Step-by-step explanation:

to work this out you would divide the class by the denominator and then multiply by the numerator.

24÷8=3

3×3=9

Answer:

The correct option is first graph.

Therefore,

The two points for the line y+5=-2(x-4) ( red color )line are

point A( x₁ , y₁) ≡ ( 0 , 3)  .......Blue color

point B( x₂ , y₂) ≡ [tex](\dfrac{3}{2},0)[/tex]  ............Green color

The Graph is attached below.

Step-by-step explanation:

Given:

[tex]y+5=-2(x-4)[/tex]

Which can also be written as

[tex]y=-2x+8-5\\y=-2x+3[/tex]     .....Equation of line

Let the points be point A, and point B  

To Find:

point A( x₁ , y₁) ≡ ?

point B( x₂ , y₂) ≡ ?

Solution:

For Drawing a graph we require minimum two points but we will have here three points.

For point A( x₁ , y₁)

Put x = 0 in the given equation we get

y = -2 × 0 +3

y =3

∴ y = 3

∴ point A( x₁ , y₁) ≡ ( 0 , 3)

For point B( x₂ , y₂)

Put y = 0 in the given equation we get

0 = -2x + 3

[tex]x=\dfrac{3}{2}[/tex]

∴ point B( x₂ , y₂)  ≡ [tex](\dfrac{3}{2},0)[/tex]

Therefore,

The two points for the line y+5=-2(x-4) ( red color )line are

point A( x₁ , y₁) ≡ ( 0 , 3)      .......Blue color

point B( x₂ , y₂) ≡ [tex](\dfrac{3}{2},0)[/tex]  ............Green color

The Graph is attached below.

After converting Donato's height to all inches (74 inches), we subtract his sister's height (68 inches) to find that Donato is 6 inches taller.

The question asks us to compare the heights of Donato and his sister to find out how much taller Donato is. First, we need to convert Donato's height from feet and inches to just inches. There are 12 inches in a foot, so Donato's height in inches is 6 feet  imes 12 inches/foot + 2 inches, which equals 74 inches. Donato's sister is 68 inches tall. To find the difference in height, we subtract the sister's height from Donato's: 74 inches - 68 inches = 6 inches. Therefore, Donato is 6 inches taller than his sister.

Answer: The quadrilaterals are similar because quadrilateral FGHJ is the image of quadrilateral ABCD under a dilation with a center of.....

all of it! it school! very inappropriate!

Step-by-step explanation: it looks like it's inappropriate

Answer:

all

Step-by-step explanation: