Combine the like terms to create an equivalent expression 2a + 6 + 1

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:

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:

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:

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:

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:

How could i answer without her pay rate ?

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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Answer:

Step-by-step explanation:

Diagonal = [tex]\sqrt{2^{2} +3^{2}+6^{2} } =\sqrt{49} =7[/tex]

Answer:

In 14 years Marc's grandmother will be 5 times as Marc will be then

Step-by-step explanation:

1. Information given to us to solve the problem:

Marc's age today = 0

Marc's grandmother age today = 56

2. In how many years will Marc's grandmother be 5 times as Marc will be then?

x = Number of years when Marc's grandmother age will be 5 times as Marc will be then

Let's solve for x, this way:

5 times Marc age in x years = Marc's grandmother age in x years

5 (0 + x) = 56 + x

5x = 56 + x

5x - x = 56 (Subtracting x at both sides)

4x = 56

x = 56/4

x = 14

Let's prove that x = 14 is correct:

5 (0 + 14) = 56 + 14

70 = 70

We proved that x = 14 is correct

In 14 years Marc's grandmother will be 5 times as Marc will be then

Part 1: The speed of the boat traveling downstream is [tex](18+w)[/tex] miles per hr.

The speed of the boat traveling upstream is [tex](18-w)[/tex] miles per hr.

Part 2: The speed of the current is 4 miles per hour.

Explanation:

Part (1): The motorboat travels 18 miles per hour in still.

Let w represents the speed of the current.

When the boat travels downstream, the speed of the current will get added to the speed of the boat.

Thus, the expression can be written as [tex](18+w)[/tex] miles per hr

Hence, the speed of the boat traveling downstream is [tex](18+w)[/tex] miles per hr.

When the boat travels upstream, the speed of the current will get subtracted to the speed of the boat.

Thus, the expression can be written as [tex](18-w)[/tex] miles per hr.

Hence, the speed of the boat traveling upstream is [tex](18-w)[/tex] miles per hr.

Part (2): The boat travels 49 miles upstream in the same time it takes to travel 77 miles downstream.

The distance formula is given by [tex]distance $=$ speed $\times$ time[/tex]

Substituting, we have,

[tex]49=(18-w)t\\49=18t-wt[/tex]  ---------------(1)

[tex]77=(18+w)t\\77=18t+wt[/tex]  ---------------(2)

Solving using elimination method,

[tex]49=18 t-w t\\77=18 t+w t\\-------\\126=36t[/tex]

Dividing both sides by 36, we have,

[tex]t=3.5[/tex]

Substituting [tex]t=3.5[/tex] in [tex]$49=18 t-w t$[/tex], we get,

[tex]49=18(3.5)-w (3.5)\\[/tex]

[tex]49=63-3.5w\\[/tex]

[tex]-14=-3.5w\\[/tex]

[tex]4=w[/tex]

Thus, the speed of the current is [tex]w=4[/tex] miles per hour.

Final answer:

The expression for the speed of the motorboat downstream is (18 + w) miles per hour. The expression for the speed of the motorboat upstream is (18 - w) miles per hour. To solve for the speed of the current, a system of equations can be set up and solved using the Elimination Method.

Explanation:

1. When the motorboat is traveling downstream (with the current), the speed of the motorboat will be the sum of its speed in still water and the speed of the river current. So the expression for the speed of the motorboat downstream is: (18 + w) miles per hour.

When the motorboat is traveling upstream (against the current), the speed of the motorboat will be the difference between its speed in still water and the speed of the river current. So the expression for the speed of the motorboat upstream is: (18 - w) miles per hour.

2. To find the speed of the current, we can set up a system of equations. Let t represent the time taken for both the upstream and downstream trips. The distance traveled upstream is 49 miles and the distance traveled downstream is 77 miles. Using the formula Distance = Speed x Time, we can write the following equations:

(18 + w) * t = 77

(18 - w) * t = 49

We can solve this system of equations using the Elimination Method. First, multiply the first equation by (18 - w), and multiply the second equation by (18 + w) to eliminate the variable w:

[(18 + w) * t] * (18 - w) = [(18 - w) * t] * (18 + w)

Simplify both sides of the equation:

(18 + w)(18 - w)t = (18 - w)(18 + w)t

Expand:

(18² - w²)t = (18² - w²)t

Cancel out the like terms:

324 - w² = 324 - w²

This equation is true for any value of w. Therefore, there are infinitely many possible values for the speed of the current w. The specific value of w would depend on the given values of t and the distance.

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:

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:

  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:

2.4 km

Step-by-step explanation:

The conversion factor is that 1 km = 1000 m. So to find km from m we need to divide the value in m by 1000:

2,400 ÷ 1000 = 2.4 km

Answer:

2.4 kilometers

Step-by-step explanation:

There are 1000 meters in 1 kilometer.  So to convert from a smaller unit to a larger one you divide.  So to calculate:

2400 m * [tex]\frac{1 km}{1000 m}[/tex] = 2.4 km

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.

Let's begin with point A:

[tex]A(7,-4)[/tex]

So we need to find the coordinates of points D in order for ABCD to be a rectangle. So:

D can be found by reflecting A across the x axis:

So you just need to multiply the y-coordinate by -1, then:

[tex]D(x,y)=D(7,-1(-4))=D(7,4)[/tex]

The length of AD can be found as the change in y from A to D:

[tex]\overline{AD}=4-(-4) \\ \\ \overline{AD}=8units[/tex]

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Option c: (-6,1) is a solution for Line 2 only

Option d: (3,-1) is a solution to the system

Explanation:

Option a: (0,3) is a solution for Line 1 only

Line 1 is [tex]6 x-7 y=25[/tex]

Let us substitute the coordinate (0,3) in Line 1, we get,

[tex]\begin{array}{r}{6(0)-7(3)=25} \\{-21=25}\end{array}[/tex]

Since, both sides of the equation are not equal, the coordinate (0,3) cannot be a solution to Line 1.

Thus, Option a is not the correct answer.

Option b: (0,0) is a solution for Line 2 only.

Line 2 is [tex]2 x+9 y=-3[/tex]

Let us substitute the coordinate (0,0) in Line 2, we get,

[tex]\begin{array}{r}{2(0)+9(0)=-3} \\{0=-3}\end{array}[/tex]

Since, both sides of the equation are not equal, the coordinate (0,0) cannot be a solution to Line 2.

Thus, Option b is not the correct answer.

Option c: (-6,1) is a solution for line 2 only.

Line 2 is [tex]2 x+9 y=-3[/tex]

Let us substitute the coordinate (-6,1), in Line 2, we get,

[tex]\begin{array}{r}{2(-6)+9(1)=-3} \\{-12+9=-3} \\{-3=-3}\end{array}[/tex]

Since, both sides of the equation are equal, the coordinate (-6,1) is a solution for line 2 only.

Thus, Option c is the correct answer.

Option d: (3,-1) is a solution to the system

Let us substitute the coordinate (3,-1) in line 1 and line 2, we get,

In line 1, we have,

[tex]\begin{array}{r}{6(3)-7(-1)=25} \\{18+7=25} \\{25=25}\end{array}[/tex]

Substituting (3,-1) in line 2, we have,

[tex]\begin{array}{r}{2(3)+9(-1)=-3} \\{6-9=-3} \\{-3=-3}\end{array}[/tex]

Since, from line 1 and line 2, both sides of the equation are equal, the coordinate (3,-1) is a solution to the system.

Thus, Option d is the correct answer.

Option e: (3,1) is a solution to the system

Let us substitute the coordinate (3,1) in line 1 and line 2, we get,

In line 1, we have,

[tex]\begin{array}{r}{6(3)-7(1)=25} \\{18-7=25} \\{11=25}\end{array}[/tex]

Substituting (3,1) in line 2, we have,

[tex]\begin{array}{r}{2(3)+9(1)=-3} \\{6+9=-3} \\{15=-3}\end{array}[/tex]

Since, from line 1 and line 2, both sides of the equation are not equal, the coordinate (3,1) is a solution to the system.

Thus, Option e is not the correct answer.

Answer:

Option C: (-6,1) is a solution for Line 2 only

Option D: (3,-1) is a solution to the system

Step-by-step explanation:

All of them except 8/100 because it results 0.08 or 8%.

The rest:

2/5 = 0.4 = 40%

8/20 = 0.4 = 40%

4/10 = 0.4 = 40%

16/40 = 0.4 = 40%

Answer: Cost(c) t（time)

c=10+4t

Step-by-step explanation:

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:

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 solution is x = 1 and y = 1.25.

Step-by-step explanation:

The solution to the graphs  [tex]f(x) = -\frac{3}{4} x + 2[/tex]   and [tex]g(x) = \frac{1}{4} x + 1[/tex]  

Solving for x we get

[tex]-\frac{3}{4} x + 2 = \frac{1}{4} x + 1[/tex]    [tex]\Rightarrow[/tex]   x = 1        Therefore y =   1/4   + 1  = 1.25

1 and 0

I took the test and got it right

Answer: x^2-3x+15

Step-by-step explanation:

Combine the like terms.

x^2 -3x+15

Answer:

x2 – 3x + 15 is the correct answer.

Step-by-step explanation:

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.

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

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:

  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.