Dave borrowed ​$7400 from his uncle with simple interest of ​6% and eventually repaid ​$8288 ​(principal and​ interest). What was the time period of the​ loan?

Step-by-step explanation:

Reasons for each step

1. Distribute: 15(2x + 3) = 30x + 45

2. Combine Like Terms: 45+100 = 145

3. Addition Property of Equality: 30x+5x+145 = 110-5x+5x => 35x+145 = 110

4. Subtraction Property of Equality: 35x+145-145 = 110-145 => 35x = -35

5. Division Property of Equality: 35x/35 = -35/35 => x = -1

The value of r in the given expression is 5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that the expression as;

75 = 15r

Now we need to find the value of r.

Therefore, we wil divide the 15 both side;

r = 75/ 15

r = 5

Hence, the value of r in the given expression is 5.

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The Banzhaf power distribution value in the fraction is,

Player 1:  = 0.6

Player 2:  = 0.2

Player 3:  = 0.2.

What is the distribution?

The mathematical expression known as a distribution function expresses the likelihood that a system would adopt a certain value or range of values. The traditional examples include games of chance.

List of winning coalitions:

1. P1, P2, P3

2. P1, P2

3. P1, P3

No. of times P1 is critical = 3 (P1 is critical all 3 times as it has veto power)

No. of times P2 is critical = 1 (in the second coalition)

No. of times P3 is critical = 1 (in the third coalition)

Total no. of critical times = 3 + 1 + 1 = 5

Banzhof Power Distribution:

Player 1: No. of times P1 is critical/Total no. of critical times

              = 3/5 = 0.6

Player 2: No. of times P2 is critical/Total no. of critical times

              = 1/5 = 0.2

Player 3: No. of times P3 is critical/Total no. of critical times

              = 1/5 = 0.2

Hence, the Banzhaf power distribution value in the fraction is,

Player 1:  = 0.6

Player 2:  = 0.2

Player 3:  = 0.2

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Each correct pair using Principle of Zero Products are-

Part a: (x-9)(3x + 4) = 0: x = 9 or x = -4/3

Part b: (x-4) (9x + 1) = 0: x = 4 or x= -1/9

Part c: (x+9)(3x-4)= 0:  x = -9 or x = 4/3

Part d: (x+4)(9x-1)=0; x = -4 or x = 1/9

For the stated equation-

Part a: (x-9)(3x + 4) = 0

Equating each term to zero;

(x-9) = 0

x = -9

And, (3x + 4) = 0

x = -4/3

Option: x = 9 or x = -4/3

Part b: (x-4) (9x + 1) = 0

Equating each term to zero;

(x-4) = 0

x = 4

And, (9x + 1) = 0

x = -1/9

Option;  x = 4 or x= -1/9

Part c: (x+9)(3x-4)= 0

Equating each term to zero;

(x+9) = 0

x = -9

And, (3x-4) = 0

x = 4/3

Option: x = -9 or x = 4/3

Part d: (x+4)(9x-1)=0

Equating each term to zero;

(x+4) = 0

x = -4

(9x-1)

x = 1/9

Option: x = -4 or x = 1/9

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The complete question is-

Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on the

right.

Each pair on the right will be used once.

(x-9)(3x + 4) = 0

(x-4) (9x + 1) = 0

(x+9)(3x-4)= 0

(x+4)(9x-1)=0

x = -4 or x = 1/9

x = -9 or x = 4/3

x = 9 or x = -4/3

x = 4 or x= -1/9

Answer:

both are correct

Step-by-step explanation:

theyre the same answer I think the questions wrong

Answer:172 cm²

when we put this in the pentagon formula, and it will get 172.03, and we round it and will be 172

formula of pentagon is 1/2 × p × a

B= -43t +272 and Q=-59t+320 equations for each situation, in terms of t, and at 3 hours Brody and Qasim are the same distance from the stadium.

Two or more expressions with an Equal sign is called as Equation.

Given,

At noon, Brody is 272 miles away from the stadium

B represent Brody's distance, in miles, away from the stadium tt hours after noon.

Brody is driving along the highway at a speed of 43 miles per hour

Qasim is 320 miles away from the stadium

Qasim is driving at speed of 59 miles per hour.

Q represent Qasim's distance, in miles, away from the stadium t hours after noon

B= -43t +272

Q=-59t+320

-43t+272=-59t+320

-43t+59t=320-272

16t=48

t=3

Hence, B= -43t +272 and Q=-59t+320 equations for each situation, in terms of t, and at 3 hours Brody and Qasim are the same distance from the stadium.

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Answer:

(0,-5)

Step-by-step explanation:

The 7x side is half the length of the 28 side.

           7x = 14

             x = 2

Assuming [tex]\overline{BC}[/tex] is a diameter, minor arc [tex]AB[/tex] has a measure of [tex]180^{\circ}-108^{\circ}=72^{\circ}[/tex].

Using the inscribed angle theorem, [tex]36=x+3 \implies x=\boxed{33}[/tex].

Let f = {(x, y) | x, y ∈ ℕ and y = 2x} be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function?               (2pts. )      

Answer:

i.  P = -800t + 29900

ii.  as an inequality: 0≤t≤37.375;  interval notation: [0,37.375]

iii.  as an inequality: 0≥P≥29900;  interval notation: [0,29900]

iv.  the population decreases at a rate of 1600 people every 3 years

v.  2010

Step-by-step explanation:

i. a) use the points *(4,26700) and **(12,20300) to find the slope (m)

      *: the year 1995(4 years after 1991) and the population that year

      **: the year 2003(12 years after 1991) and the population that year

      m = (20300-26700)/(12-4) = -6400/8 = -800

  b) use one of the points and m in (a) to find b

      26700 = -800(4) + b

      26700 = -3200 + b

      29900 = b

ii. starting value for domain will be 0 since 1991 is year 0. Find the ending domain value by using P=0 and solving the equation for t:

   0 = -800t + 29900

   800t = 29900

   t = 37.375

iii. population starts at a high of 29900 people and can't go lower than 0 people.

iv. the slope is given in (population change) / (number of years)

v. make P=14700 and solve the equation for t

   14700 = -800t + 29900

   800t = 15200

   t = 19 (19 years after 1991)

Answer:

150.

Step-by-step explanation:

If 150 total drive to work, then 150 work there....

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Answer:

- 14x - 12

Step-by-step explanation:

- 3(2x + 4) - 8x ← distribute terms in parenthesis by - 3

= - 6x - 12 - 8x ← collect like terms

= - 14x - 12

Answer:

-14x-12

Step-by-step explanation:

1) Expand by distributing terms.

-(6x+12)-8x

2) Remove parentheses.

-6x-12-8x

3) Collect like terms.

(-6x-8x)-12

4 Simplify.

−14x−12

The number of drinks and the number of candies that Carter bought are 6 and 2 respectively.

In order to determine the number of drinks and the number of candies that Carter bought, we would have to write a system of linear equation and assign variables to the number of drinks and number of candies respectively, and then translate the word problem into algebraic equation as follows:

Since each drink costs $4.50 and each candy costs $3 and Carter bought 3 times as many drinks as candies;

x = 3y                        .......equation 1.

4.50x + 3y = 33          .......equation 2.

Substituting equation 1 into equation 2, we have:

4.50(3y) + 3y = 33

13.50y + 3y = 33

16.50y = 33

y = 33/16.50

y = 2 candies.

For the value of x, we have:

x = 3(2)

x = 6 drinks.

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Answer: try quizlet

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

Since it's given n || m, we can write the following equation to find the value of x:

9x - 3 = 7x + 19 because these two are alternate exterior angles and have equal angle measurement.

9x - 7x = 19 + 3

2x = 22

x = 11

Answer:

each measure 120

Step-by-step explanation:

Answer:

ax + y = (21, -16, 29)

Step-by-step explanation:

ax + y = [(-6a + 3), (3a - 7), (-8a + 5)]

now,

-8a + 5 = 29

a = (29 - 5)/-8

a = -3

ax + y = [(-6)(-3)+3, 3(-3)-7, 29]

ax + y = (21, -16, 29)

just replace x with 2

h(x) = - x+ 1

find h(2):

h(2) = -2 + 1

h(2) = -1

Solution:

2b would be the greatest common factor (GCF) between both 10b^3 and 4b.

Hope this helps!

Answer:

7. A

8. B

Step-by-step explanation:

7.

     1               3

4 -------  -  2 -------

     2              4

  9        11

------- - -------

  2         4

  9(2)    11

------- - -------

  2(2)     4

  18        11         7           3

------- - ------- = ------- = 1 -------

  4         4          4            4

----------------------------------------------------------------------------------------------------------

8.

      3              3

13 ------- + 16 -------

      8              4

  107       67

------- +  -------

   8           4

  107       67(2)

------- +  -------

   8           4(2)

  107       134      241               1

------- +  ------- = -------- = 30 -------

   8           8          8               8

I hope this helps!

The solution of the expression is,

⇒ x = - 1 and x = 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Solve the expression,

x² – 3x − 2 = x + 3

Now, We can simplify as;

x² – 3x − 2 = x + 3

x² – 3x − 2 - x - 3 = 0

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x (x - 5) + 1(x - 5) = 0

(x + 1) (x - 5) = 0

x = - 1

x = 5

Thus, The solution of the expression is,

⇒ x = - 1 and x = 5

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Answer:

Step-by-step explanation:

:On hand she has a 20% acid solution and a 50% acid solution. How many ml of each solution should sheStep-by-step explanation:this is the answer

A chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.

The percentage is the ratio of number expressed as a fraction of 100.

Assume chemist needs x mL of 20% of acidic solution and y mL of 50% acidic solution.

A total of 100mL solution is to be created.

x+y=100

x=100-y

The concentration of 20% acidic solution will be 0.2x, concentration of 50% acidic solution will be 0.5x and the sum of their concentrations should be 0.38(100).

0.2x+0.5y=0.38(100)

0.2x+0.5y=38

Substitute x=100-y into the obtained equation.

0.2(100-y)+0.5y=38

20-0.2y+0.5y=38

20+0.3y=38

0.3y=18

y=18/0.3

y=60

Substitute y=60 into x=100-y.

x=100-60

=40

So, the chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.

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Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

The number of cows is 12 and number of chickens are 36.

A "system" of equations is a set or collection of equations that you deal with all together at once.

Given that, Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total.

Let the number of chickens be x and that of cows be y,

A cow has 4 legs and that of chickens have 2,

Setting the equations, we get,

2x+4y = 120

x+2y = 60

x+y = 48

Solving the equation by elimination, we get,

2y - y = 60 - 48

y = 12

Therefore, x = 36

Hence, The number of cows is 12 and number of chickens are 36.

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Answer:

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Simplify the left side and compare if the answer matches the right side.