Please solve with work shown.

Answer: d=50+20w

D(deposit) = 50(starting amount)+20(added amount)w(multiply 20 by the amount of weeks, 12, and this is your equation.)

Answer:

25.

Step-by-step explanation:

At time 2, x(t) = 2(2)^2 + 2 = 10

At time 10, x(t) = 2(10)^2 + 10 = 210.

Average speed for this interval

distance / time

= (210 - 10) / (10 - 2)

= 200/8

= 25.

The fishing boat traveled for 14 hours before the cruise ship caught up.

In this question, we have been given Max and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an average speed of 10 km/hour.

After some time, a cruise ship left traveling in the same direction but at an average speed of 14 km/hour.

The cruise ship caught up with the fishing boat after traveling for 10 hours.

Let a cruise traveled 'm' km after 10 hours.

Using the formula of speed,

speed = distance / time

14 = m / 10

m = 14 * 10

m = 140 km

This means, a cruise traveled 140 km in 10 hours.

Now, we find the time needed for a fishing boat to cover 140 hours.

speed = distance / time

10 = 140/t

t = 140 / 10

t = 14 hours

Therefore, the fishing boat traveled for 14 hours before the cruise ship caught up.

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To solve a system of equations algebraically means that we will use some algebraic manipulation to find the solution(s). there are two techniques for solving algebraically: elimination and substitution.

The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics.

Hence the two ways an algebraic equation can be solved is by elimination and substitution.

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After simplification this 5√3(2√3−3√7) we get, -38.71

5√3(2√3−3√7) is a linear equation.

What is linear equation?

An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.

Let's simply this 5√3(2√3−3√7)

=> 5√3 * 2√3 - 3√7 * 5√3

=> 5*2*√3*√3 - 3 * 5 √7 * √3

=> 10 * 3 - 15 * 1.732 * 2.645

=> 30 - 68.717

=> -38.717 or -38.71

Therefore, the value of  5√3(2√3−3√7), after simplification we get  -38.71

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Answer:

Below in bold.

Step-by-step explanation:

The sum of 17 terms is 107.1.

Sn = (n/2)[2a + (n-1)d]   where a = first term and d = common difference

(17/2) (2a + (17-1)(-4)) = 107.1

8.5(2a -64) = 107.1

17a - 544 = 107.1

17a = 651.1

a = 38.3 = First term

The last term is the 17th so

L = a + (n - 1) d

  = 38.3 + 16*-4

  = -25.7.

The customer will pay $391.5 after it is marked up to 65% and the sale tax of 9%.

When a consumer buys a good or service from a retailer, sales tax, which is estimated as a percentage, is added to the cost of the item.

Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.

The wholesale price paid by a store owner is $225.

The store owner needs to make a profit of 65%.

Then, the profit will be:

=  225 × 65% = $146.25

And, amount of tax the customer will pay will be:

= $225 × 9% = $20.25

Therefore, the price at which the customer will buy the TV will be:

= $225 + profit + sales tax

= $225 + $146.25 + $20.25

= $391.5

Hence, the customer will pay $391.5 for the TV.

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Answer:

12.649

Step-by-step explanation:

we can use Pythagoras to solve this; simply by forming a triangle of the difference between the x and y values. (I added a lil-sketch of it).

So, we just need to find the length of the two sides:

Vertical side: 12

Horizontal side: 4

Thus;

[tex]4^{2} + 12^{2} = c^{2} \\160 = c^{2}\\Side c is equal to 12.649 (in whatever unit given)[/tex]

A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.

In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.

Based on the information provided above, we can logically deduce the following equation:

22 . a = 242

22 × a = 242

By applying the division property of equality, we have the following:

a = 242/22

a = 11.

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Answer:

First one is a function, second one is not, since it assigns more than one y value for x values.

Step-by-step explanation:

A function means for every x value, at most 1 y value exists. This is clearly not the case for the bottom figure. You can test it with an imaginary vertical line. There should be zero or one intersections.

first the sum of all angles of in triangle is 180 degree.

x+(3x+25)+(x-5)=180

x+3x+25+x-5=180

4x+25+x-5=180

4x+x+25-5=180

5x+20=180

5x=180-20

5x=160

x=32 degree and

the angle of G is 3(32)+25=121 degree

Yield testing is a technique for figuring out the precise quantity of raw materials required to make a specific quantity of finished product.

Therefore, yield testing is a method of determining the precise amount of raw materials needed to produce a certain amount of the final product.

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Applying the midsegment theorem, the length of segment SR is: 6 units.

The Midsegment theorem states that if a segment is draw to connect the two midpoints of two sides of a triangle together, it is parallel to the third side of the triangle and also has a length measure that is half of the length of the third side of the triangle.

Segment SR is the midsegment of the triangle given and is parallel to the third side, FD.

SR = 2x - 14

FD = x + 2

Therefore:

SR = 1/2(FD) [midsegment theorem]

Substitute

2x - 14 = 1/2(x + 2)

2(2x - 14) = x + 2

4x - 28 = x + 2

4x - x = 28 + 2

3x = 30

x = 30/3

x = 10.

Length of SR = 2x - 14 = 2(10) - 14

Length of SR = 6 units

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Answer:

12 units

Step-by-step explanation:

Autumn bought 4 Donuts and 2 Cookies worth of 5 dollars.

We know two simultaneous equations have a unique solution when they intersect at a point,

when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.

Given, Autumn and her children went into a bakery and she bought $5 worth of donuts and cookies.

Each donut costs $1 and each cookie costs $0.50. She bought a total of 6 donuts and cookies altogether.

Let us denote no. of Donuts by x and no. of Cookies by y.

∴ x + y = 6...(i) and x + 0.5y = 5...(ii).

Subtracting eqn(ii) from eqn(i) we get y = 2 and substituting the value of y in eqn(i) we get x = 4.

Autumn bought 4 Donuts and 2 cookies with 5 dollars.

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As you can see in the stem-and-leaf plot, the box with the most numbers is

And in this box, the number that is repeated the most is 1. So that, the data that is repeated the most is 21.

Therefore, the mode of the data set is 21.

As x and y vary inversely as each other , if x=7 then y =  -8/7.

in the question ,

it is given that

x and y vary inversely ,

So , x * y = k

given that , when x = 4 , the value of y = -2 .

Substituting , 4 * (-2) = k

k = -8

so , the constant of variation (k) = -8 .

in order to find value of y when x = 7 ,

we substitute x=7 and k = -8 in the relation xy = k

we get , 7 * y = (-8)

Dividing both sides by 7 we get

7y/7 = -8/7

on simplifying we get ,

y = -8/7

Therefore , as x and y vary inversely as each other , if x = 7 then y = -8/7 .

The given question is incomplete , the complete question is

If y varies inversely as x, and y = -2 when x = 4 find y when x = 7  .

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The price per person attending is 104 .

If a variable's highest power is always 1, an equation is considered to be linear. As a one-degree equation, it also goes by that name. An equation with one variable that has the usual form Ax + B = 0 is a linear equation. A coefficient, B is constant, and x is a variable in this situation. An equation with two variables that has the usual form Ax + By = C is a linear equation. Both a B are factors, C is a standard, and the variables in this solution are x and y. Linear equations are defined as equations with the maximum degree of 1. A linear equation cannot have a variable with an exponent greater than 1, according to this rule. A straight line is formed on the linear equation graph.

C = 14p + 90

Here p = 1 cause per person

So,

C = 14 (1) + 90

C = 104

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The formula for calculating the total surface area of a rectangular pyramid using its length, width, and height is provided as T.S.A. = lw + l[(w/2)2 + h2] + w[(l/2)2 + h2], where l is the length of the rectangular base, w is its width, and h is its height.

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When a scale of 1 inch to 40 miles apart then distance = 112 miles .

We have been give that

If 1 inch = 25 miles,

Then 2.8 inches would be 25 miles multiplied by 2.8 since each of those 2.8 inches is 25 miles.

2.8 x 25 = 70.

70 miles.

The same two cities be on a map that has a scale of 1 inch to 40 miles

Then 1 inch= 40 miles,

then 2.8 inches would be 40 miles multiplied by 2.8 since each of those 2.8 inches is 40 miles.

2.8 x 40 = 112.

112 miles.

Hence , Distance equals 112 miles when measured on a scale of 1 inch to 40 miles apart.

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it should be 14 students i think

The step 3 follow the subtraction property of equality.

Given,

The Equation is : 1/4 (12x + 8) + 4 = 3

There is some steps:

Step                          Solution

   1                          3x + 2 + 4 = 3

   2                           3x + 6 = 3

   3                              3x = -3

   4                                 x = -1

To find the which step shows the result of applying the subtraction property of equality?

Now, According to the given steps:

From the table, we can know

From Step 2: 3x + 6 = 3

 Subtract 6 on both sides

3x + 6 - 6 = 3 - 6

3x = -3

Hence, The step 3 follow the subtraction property of equality.

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Mia, this is the solution:

4 = 2 * 2

14 = 2 * 7

Therefore, we have:

2 = two ocurrences (the higher number)

7 = one ocurrence

LCM = 2 * 2 * 7

LCM = 28

The area and the perimeter of the rectangle is found as 13.12 sq. unit and  21.77 units respectively.

For the given question;

To find the perimeter of the rectangle ABCD, first find the length of the sides.

Using the distance formula, find the length DA and DC,

DA = √(x2 - x1)² + (y2 - y1)²

Put the coordinate of the point D and A.

DA = √(8 - 1)² + (2 - 0)²

DA = √49 + 4

DA = √53 units.

Now, length DC

DC = √(3 - 1)² + (3 - 0)²

DC = √4 + 9

DC = √13 units.

For the rectangles;

DA = CB = √53 units.

DC = AB =  √13 units.

Perimeter = DA + CB + DC + AB

Perimeter = 2√53 + 2√13 units

Perimeter = 2(√53 + √13) units.

Perimeter = 21.77 units.

Area = (1/2) base × height

Area  = (1/2) CB × CD

Area  = (1/2) × √53 × √13

Area = 26.24/2

Area = 13.12 sq. unit.

Thus, the area and the perimeter of the rectangle is found as 13.12 sq. unit and  21.77 units respectively.

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Answer:

[tex]\frac{15}{2}[/tex]

Step-by-step explanation:

8 - [tex]\frac{1}{2}[/tex]

= [tex]\frac{16}{2}[/tex] - [tex]\frac{1}{2}[/tex]

= [tex]\frac{15}{2}[/tex]

Answer:

The answer is  17/2

Step-by-step explanation:

You get that by multiplying the whole number 8 by the denominator of the fraction, and that will be equal to 16 and the 1 from the numerator of the fraction 1/2, so the equation will look like 16+1=17. Your new numerator  17.

The value of x from the given function is 60.

Given that, the x value equals 7 times the y value, plus 18 more.

A function in math means a correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to outputs.

Now, the x value equals 7 times the y value, plus 18 more

x=7y+18

Put y=6 in the obtained function, that is

x=7(6)+18

⇒ x = 42+18

⇒ x = 60

Therefore, the value of x from the given function is 60.

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You have the following algebraic expression:

The previous expression can be simplified by taking into account, that for the simplification you sum or subtract (depending of signs) similar terms. Remind that similar terms are those one which has the same variable with the same exponent. In this case you have similar terms with variable x and exponent 4, furthermore you have similar terms with variable x and exponent 3. Then you sum this terms and you obtain:

where you have summed 8x^4 + 2x^4 = 10x^4, and 7x^3 + 4x^3 = 11x^3.

Hence, the simplied expression is 10x^4 + 11x^3 + 6

Any number that can be written as a fraction and in which the numerator and denominator are both integers is referred to as a rational number. In other words, p/q can be used to represent a rational number when p and q are both integers and q is 0. It will be 0.25 and 0.5.

Hence, the  rational numbers will be 0.25 and 0.5.

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The expression 2n + 1 will produce both odd and even numbers based on the choice we have made.

Expression:

An expression is a mathematical expression consisting of numbers, operations, and one or more variables.

Given,

Suppose n represents an integer. Then the next integer can be  represented by the expression n+1.

Here we need to write the linear equation for these two consecutive integers.

Then we have to use the expression to make an argument about whether the sum of any two consecutive integers is even or odd.

Let n represents the first integer and n+1 is the second integer.

Then the linear equation for these two consecutive integer is

=> n + (n + 1)

=> 2n + 1

Now we have to take the value of n and n + 1 as, 2 and 3,

Then we apply the value to the expression,

=> 2(2) + 3

=> 4 + 3

Similarly, if we take the value as 5 and 6,

Then we get,

=> 2(5) + 6

=> 10 + 6

=> 16

So, based on the given details the equation givens both odd and even number based on the number our choices.

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