A sum of 2500$ is invested in a saving account which pays interest at a rate of 7 per year compounded annually. if the amount is kept on deposit for 15 year's, what will the compound amount equal? how much interest will be earned during the 15 years?

Answer:

2(x + 5) = x - 2

⟹ x = -12

Step-by-step explanation:

Doubling the sum of 5 and a number is equal to the same number decreased by 2. What is the equation?

This word problem can be written as:

⟹ 2(x + 5) = x - 2

1. Distribute:

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

⟹ 2x + 10 = x - 2

2. Subtract x from both sides:

2x - x + 10 = x - x - 2

⟹ x + 10 = -2

3. Subtract 10 from both sides:

x + 10 - 10 = -2 - 10

⟹ x = -12

4. Check your work:

2(x + 5) = x - 2

2(-12 + 5) = -12 - 2

2(-7) = -20

⟹ -14 = -14 ✔

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Looking at the problem statement, the question is asking for us to determine the justification for the steps that are used to help solve the equation.  We are given the expression [tex]x + 17 = 38[/tex] to help achieve that goal.

Now that we know what we must do to finish this problem let us look how this equation can be solved.  When the term solve the equation is used it refers to us solving for the unknown, in this case being the variable x.  We can see that we have [tex]x + 17[/tex] on the left side and in order to solve the equation x must be alone so we would subtract 17 from both sides.

Subtract 17 from both sides

Therefore, we know that we must subtract the same number from both sides and this justification is known as the Subtraction Property of Equality.  This basically states that an equal value needs to be subtracted from both sides and it will become a new equation but with the same result.

Answer:

Subtraction Property of Equality

Step-by-step explanation:

Given: x + 17 = 38

Algebraic Properties:

Addition: If a = b, then a + c = b + c

Subtraction: If a = b, then a - c = b - c

Multiplication: If a = b, then ac = bc

Division: If a = b, then a ÷ c = b ÷ c

To solve this equation, we know that we need to isolate the variable x. To do this, we need to subtract 17 from both sides to isolate x.

This is also known as the subtraction property of equality, which states that when the same thing is subtracted from both sides of an equation, the equation will still be balanced. 

Subtract 17 from both sides:

x + 17 - 17  = 38 - 17

⟹ x = 21

Therefore, the subtraction property of equality is included in the steps used to solve this equation.

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Answer:

3(4 + n) = n + 18

n = 3

Step-by-step explanation:

because the sum of 4 and a number is multiplied by three. That equals the number plus 18. N = 3. in the image below are the steps you can take to solve the equation.

Work Shown:

[tex]V = (4/3)*\pi*r^3\\\\V \approx (4/3)*3.14*18^3\\\\V \approx 24416.64\\\\[/tex]

hat is the answer to a math problem I had it on khan academy but the problem I

1 2/7 divided by (-2 1/4)

Answer:

-4/7

Step-by-step explanation:

1 2/7 divided by (-2 1/4)

1 2/7 = 9/7

-2 1/4 = -9/4

9/7 divided by -9/4 =

9/7 multiplied by -4/9 =

9's cancel out

1/7 multiplied by -4/1 =

-4/7

Answer:

[tex]x =\pm\sqrt{\dfrac{y-c}a}[/tex]

Step-by-step explanation:

[tex]~~~~~~y= ax^2 +c\\\\\implies ax^2 = y-c\\\\\implies x^2 =\dfrac{y-c}{a}\\\\\implies x =\pm\sqrt{\dfrac{y-c}a}[/tex]

=======================================================

Explanation:

Let's use an example to see why this is

A = {1,2,3,4,5,6,7}

B = {x,y,z}

A U B = {1,2,3,4,5,6,7, x,y,z}

We simply glue the two sets together to form one single big set. Because sets A and B have no overlap, this means we dont have to worry about tossing out duplicates (since there aren't any).

There are 7 items in set A, and 3 items in set B.

Therefore, we have 7+3 = 10 items in set A U B

The symbol U refers to the set union operator.

If you wanted to make a Venn Diagram, then you'd have two circles overlapping. In circle A will be the numbers 1 through 7. These values are not in the overlapped region. For circle B, the letters x,y,z are inside but not in the overlapped region. The overlapped region remains empty.

The set A U B talks about the collection of everything mentioned. It's the set of stuff in set A or in set B or in both sets.

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

If you want a formula to write down on a notecard or reference sheet, then it would be

n(A U B) = n(A)+n(B)

where A and B are mutually exclusive, aka disjoint. This means they have nothing in the overlapped region

The volume of the box with a height of 10 inches and perimeter of 72 inches and width of w is 360w - 10w²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let w represent the width of the box and v represents the volume, hence:

2(w + length) = 72

Length = 36 - w

Volume = w(36 - w) * 10

Volume = 360w - 10w²

The volume of the box with a height of 10 inches and perimeter of 72 inches and width of w is 360w - 10w²

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Answer:

Step-by-step explanation:

Answer:

2 * 21

3 * 14

6 * 7

Step-by-step explanation:

7 * 2 = 14

56 - 14 = 42

Multiples of 42 = 2,3,6,7, 14, 21

The possible dimensions of the larger rectangle are:

21 centimeters by 2 centimeters

14 centimeters by 3 centimeters

7 centimeters by 6 centimeters

Let the dimensions of the larger rectangle be length L and width W.

We know that the total area of the two rectangles is 56 square centimeters.

Area of the smaller rectangle = 2 cm * 7 cm = 14 square centimeters

Area of the larger rectangle = Total area - Area of the smaller rectangle

Area of the larger rectangle = 56 square centimeters - 14 square centimeters

Area of the larger rectangle = 42 square centimeters

Now, we need to find the possible dimensions of the larger rectangle with an area of 42 square centimeters.

To find the possible dimensions, we can list all the pairs of whole numbers (L, W) whose product is 42.

7 * 2 = 14

56 - 14 = 42

Multiples of 42 = 2,3,6,7, 14, 21

Remember that the length (L) should be greater than or equal to the width (W) to avoid counting duplicates.

The possible dimensions are:

L = 42, W = 1 (42 cm * 1 cm = 42 square centimeters)

L = 21, W = 2 (21 cm * 2 cm = 42 square centimeters)

L = 14, W = 3 (14 cm * 3 cm = 42 square centimeters)

L = 7, W = 6 (7 cm * 6 cm = 42 square centimeters)

So, the possible dimensions of the larger rectangle are:

42 centimeters by 1 centimeter

21 centimeters by 2 centimeters

14 centimeters by 3 centimeters

7 centimeters by 6 centimeters

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Answer:

see the attachment photo!

Answer:

the value of c is 13.

Step-by-step explanation:

See the picture attached below for a step by step explanation

Answer:

11.   g

12.  f

13.  e    (add all the frequencies)

14.  d

15.  c    (eg. 17.5 -8.5 = 9)

16.  b

17.  a

Let me know if you have any questions.

Hope this helps!

Answer:

-41/12 or -3 5/12

Step-by-step explanation:

4*2 +1 = 9,  5 * 3 + 2 = 17

9/4 - 17/3

27/12 - 68/12

= -41/12 or -3 5/12

Answer:

theUse the Distance and Midpoint Formulas to find the length and midpoint of the segments with indicated endpoints. Show your solution and answer inside the box.

Endpoints

Distance

Midpoint

1. (-5,8) and (9,4)

2. (6 ,- 3) and (10,11)

3. (2,1) and (-16,13)

4. (3,0) and (9 ,- 13)

5. (-3 ,- 10) & (-7 ,- 2)

There are no such integers. Odd + odd = even, and adding odd to that makes it odd again. But 64 is even.

Put another way, let n be the smallest of the three integers. Then

n + (n + 2) + (n + 4) = 64

3n + 8 = 64

3n = 56

But 3 does not divide 56, so there is no integer solution for n.

Answer:

vertex = -4, -26

Step-by-step explanation:

The standard form of a quadratic function is : [tex]y=ax^{2} +bx+c[/tex]
The function here : y = [tex]x^{2}[/tex] + 8x - 10
is in this form with a=1, b=8 and c = -10
x-coord of vertex = [tex]\frac{-b}{2a}[/tex]
[tex]x_{vertex} =\frac{-8}{2} = -4[/tex]
To find corresponding value of y-coord of vertex , substitute

x = -4 into the function.
x=-4  : [tex]y=(-4)^{2} +(8*(-4))-10 = 16 +(-32)-10=-26[/tex]

Answer:

Seconds:  2    ||  3     || 5     || 10     ||

---------------------||-------||--------||--------||

Gallons:   312  || 486 || 780 || 1560 ||

you have to use intercept theorem, also known as Thales's theorem to slove this problem

Answer:

#1 evaluates to 2

#2 evaluates to 0

#3 evaluates to 10

#4 evaluates to 6

code is HIEA

[tex]~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan B = \dfrac{AC}{BC}\\\\\\\implies \tan 40^{\circ} = \dfrac{10}{a}\\\\\\\implies a = \dfrac{10}{\tan 40^{\circ}}\\\\\\\implies a= 11.9~ m[/tex]

The polynomic function that contains the points (0, 6), (3, 15.8) and (9.5, 0) is a quadratic function, whose model is y = -0.600 · x² + 5.066 · x + 6.

To determine the coefficients of a polynomic function we must know a set of distinct points, whose number is the same number of coefficients. In this case, we can derive a quadratic function, as quadratic functions have three coefficients:

y = a · x² + b · x + c     (1)

Now we substitute x and y in (1) and solve the resulting system of linear equations:

c = 6

9 · a + 3 · b + c = 15.8

90.25 · a + 9.5 · b + c = 0

Whose solution is a ≈ -0.600, b ≈ 5.066 and c = 6.

The statement is incomplete. The complete form is shown below:

There is a polynomial function. Find the function of (0, 6), (3, 15.8) and (9.5, 0).

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Answer:

20 units²  

Step-by-step explanation:

Free trade is defined as "a system of buying and selling between countries that is. carried out with no government involvement Based on what you've learned about international trade,

The term "lobby" here refers to that action which seeks to influence or affect a certain issue most specifically those that are business and politically related. And based on the scenarios above, the one that would most likely motivate an autoworker union to lobby congress would be the first option.  

The World Bank is a financial institution created after World War II by developed countries to promote economic development around the world through loans to developing countries. To get a loan, a developing nation must submit a project that is evaluated by World Bank secretaries. Some focus areas of the bank finances are human development, agriculture, environmental protection, industrial projects, infrastructure, and corporate governance.

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Based on Neena's qualifications and desire for the highest pay scale, she would be best suited for a supply chain manager career.

A supply chain manager ensures the movement of goods, from manufacturers and suppliers to the ultimate customer.

A supply chain manager oversees and manages the production flow:

A supply chain manager requires the following skills:

Thus, based on Neena's qualifications and desire for the highest pay scale, she would be best suited for a supply chain manager career.

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Step-by-step explanation:

correct u know jsjsjsjsjajajaj shahha hshshs hsgshs hshshs hshshs hzhsvs hsvzvshsvss hshshs hshshs hshsh hshs

Answer:

C

Step-by-step explanation:

it is because the hours spent by training will determine the pay at the end of the month.

therefore it's independent that's y it is the domain.

For boys, it's between the ages of 12-16

And for girls, it's between the ages of 10-14

Answer:

boys between ages 12 and 16 girls between ages 10 and 14