Find the perimeter and area of the rectangle given below.
A rectangle ABCD with vertices A(3,4), B(3,9), C(6,9), and D(6,4).
The perimeter is units.
(Simplify your answer.)
square units.
The area is
(Simplify your answer.)

Answer:

-7/3

Step-by-step explanation:

Since the lines are parallel, the slopes would have to be the same

Gene earns 2% interest after depositing $150 into his account , Option D.

A function is a law that relates an independent variable and a dependent variable with each other.

The function given is

f(x) = 0.02 x +150

Option D , Gene earns 2% interest after depositing $150 into his account

So this verbal description matches the function given as it represents , the total account balance of Gene .

Therefore Option D is the correct answer.

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Answer:

13

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

y positive

x positive

Answer; its positive negative but its mostly negative

Answer:

Step-by-step explanation:

Answer:

y = \(-\frac{1}{5}x\) - 3

OR

y = \(-\frac{x}{5}\) - 3

Step-by-step explanation:

x + 5y = -15

5y = -x - 15

y = \(-\frac{1}{5}x\) - 3

or

(it's the same thing)

y = \(-\frac{x}{5}\) - 3

They are the same because x by itself has an invisible 1 in front of it.

1x = x

\(-\frac{x}{5}\) = \(-\frac{1x}{5}\) = \(-\frac{1}{5}x\)

The system described by the given second order linear ordinary differential equation (ODE) is underdamped for values of k less than a certain critical value, critically damped when k equals the critical value, and overdamped for values of k greater than the critical value.

The given ODE represents the motion of a mass-spring system. The general solution of this ODE can be expressed as y(t) = A*e^(r1*t) + B*e^(r2*t), where A and B are constants determined by the initial conditions, and r1 and r2 are the roots of the characteristic equation r^2 + 31r + k = 0.

To determine the damping behavior, we need to analyze the roots of the characteristic equation. If the roots are complex (i.e., have an imaginary part), the system is underdamped. In this case, the mass oscillates around the equilibrium position with a decaying amplitude. The system is critically damped when the roots are real and equal, meaning there is no oscillation and the mass returns to equilibrium as quickly as possible without overshooting. Finally, if the roots are real and distinct, the system is overdamped. Here, the mass returns to equilibrium without oscillation, but the process is slower compared to critical damping.

The discriminant of the characteristic equation, D = 31^2 - 4k, helps us determine the behavior. If D < 0, the roots are complex and the system is underdamped. If D = 0, the roots are real and equal, indicating critical damping. If D > 0, the roots are real and distinct, signifying overdamping. Therefore, the system is underdamped for k < 240.5, critically damped for k = 240.5, and overdamped for k > 240.5.

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Amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

As given in the question,

Amount  invested by Nathan is principal 'P' = $3,500

Interest rate 'r' = 3.5% compounded quarterly

Number of compounding periods per year for given quarterly 'n'  = 4

Time period 't'= 19 years

Amount of money in the account after 19 years when no deposits or withdrawals are done.

Let 'A' be the amount.

Formula used:

 \(A = P \times ( 1+ \frac{r}{n} )^{nt}\)

Substitute the value in the formula we get,

A = 3500 × [ 1 + (0.035/4) ]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1 + 0.00875]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1.00875]⁷⁶

   = 6,786.06 (approximately)

   = $6800 (nearest hundred dollars)

Therefore, amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

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Answer:

35*x=280

Step-by-step explanation:

Answer:

x = 8

35 x 8 = 280

Step-by-step explanation:

Answer:

the answer is in the link

Step-by-step explanation:

https

      bxaha zshkkkvxxxkvvvvwuqgceuuuegieg   DONT KNO

Answer: Simplifying

2x + 4 + 2x + 8 + 2x + 8 = 180

Reorder the terms:

4 + 8 + 8 + 2x + 2x + 2x = 180

Combine like terms: 4 + 8 = 12

12 + 8 + 2x + 2x + 2x = 180

Combine like terms: 12 + 8 = 20

20 + 2x + 2x + 2x = 180

Combine like terms: 2x + 2x = 4x

20 + 4x + 2x = 180

Combine like terms: 4x + 2x = 6x

20 + 6x = 180

Solving

20 + 6x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-20' to each side of the equation.

20 + -20 + 6x = 180 + -20

Combine like terms: 20 + -20 = 0

0 + 6x = 180 + -20

6x = 180 + -20

Combine like terms: 180 + -20 = 160

6x = 160

Divide each side by '6'.

x = 26.66666667

Simplifying

x = 26.66666667

Step-by-step explanation:

Answer: x=

44.25

Step-by-step explanation: (2x+2x)+(4+−9+8)=180                                               4x+3−3=180−3                                                                                                           4x/4=177/4                                                                                                               x=44.25

Answer:

1.05 a minute is the answer

Answer:

C. 1.05 mi/min

Step-by-step explanation:

Use this formula to find your answer Y2-Y1/ X2-X1

=(4.2-2.1) over (4-2)

=21 over 2

=1.05 mi/min

The percentage change from the number 84 to 21 is P = -0.75 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage change be represented as P

Now , let the first number be p = 84

Let the second number be q = 21

And , P = [ ( 84 - 21 ) / 84 ] x 100

P = 63 / 84 x 100

P = 0.75 x 100

On simplifying , we get

P = 75 % decrease

Hence , the percentage change is P = -0.75 %

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Answer:

y - 7 = 6(x - 2)

Step-by-step explanation:

1. Since we're given one point and the slope of a line, we can use the point slope form: \(y-y_1=m(x-x_1)\)

2. (Plugging in values)

Therefore, one equation of the line is y - 7 = 6(x - 2).

The most appropriate choice for unitary method will be given by-

Volume of petrol consumed = 26 liters

Cost of 60 liters petrol  =  € 37.70

€ 58 is the cost of 40 liters of petrol

What is unitary method?

Unitary method is the method in which the value of single unit can be calculated from the value of multiple unit and value of multiple unit is calculated from the value of single unit.

Here,

Total volume of petrol filled by Giorgio in his car = 60 liters

Volume of petrol left = 340 deciliters

                                   = \(\frac{340}{10}\) liters

                                   = \(34\) liters

Volume of petrol consumed = (60 - 34) liters

                                               = 26 liters

Cost of 1 liter petrol = € 1.45

Cost of 60 liters petrol = € 1.45 \(\times\) 26

                                    = € 37.70

€ 1.45 is the cost of one liter of petrol

€ 1 is the cost of \(\frac{1}{1.45}\) liters of petrol

€ 58 is the cost of \(\frac{1}{1.45} \times 58\) liters of petrol

€ 58 is the cost of 40 liters of petrol

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Answer:

1,100 ounces because 20 × 30 + 10 × 50 = 1,100

Step-by-step explanation:

Answer:

On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 5, 3) to (negative 4, 3). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (2, negative 4) to (3, negative 4).

Step-by-step explanation:

Answer:

B) −2, −1, 0, 1

Hope This Helps!

The ratio of the trigonometric function of the right triangle, cos A is 3/5.

Given that,

In △ABC , ∠C is a right angle.

Then the opposite side to the right angle will be the hypotenuse.

So AB is the hypotenuse.

Sin A = BC / AB [ Since sine of an angle is opposite side / hypotenuse]

BC / AB = 4/5

BC = 4 and AB = 5

Using the Pythagoras theorem,

Third side, AC = √(5² - 4²) = 3

Cos of an angle is the ratio of adjacent side to the hypotenuse.

Cos A = 3/5

Alternatively, we can use the identity,

sin²A + cos²A = 1

to find the value of cos A.

Hence the value of cos A is 3/5.

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Answer:

The two numbers are a = 57 and b = -7

Step-by-step explanation:

Let's write the first sentence into an equation.

A) The sum of two numbers is 50

\(a+b=50\) (1)

B)The first number is 43 less than twice the second number.

\(a=43-2b\) (2)

Now, we just need to solve the system of equations (1) and (2)

Let's put (2) into the (1)

\(43-2b+b=50\)

\(43-b=50\)

\(b=43-50\)

\(b=-7\)  

Using this value in (1) we can find a

\(a-7=50\)

\(a=57\)

Therefore, the two numbers are a = 57 and b = -7

I hope it helps you!

The total profit will be maximized by using the objective function Z = 22x₁ + 53x₂ + 124x₃ + 25x₄ + 156x₅ + 37x₆ + 108x₇ + x₈

To formulate this problem mathematically, we need to define the decision variables, objective function, and constraints.

We will define a binary decision variable, \(x_i\), which indicates whether or not to invest in project i. If \(x_i\) = 1, the project i will be funded, and if \(x_i\) = 0, the project i will not be funded.

The objective is to maximize the total profit earned by investing in the selected projects. Thus, the objective function can be written as:

Maximize Z = 22x₁ + 53x₂ + 124x₃ + 25x₄ + 156x₅ + 37x₆ + 108x₇ + x₈

This objective function adds the profit of all the projects that will be funded based on the decision variable \(x_i\).

The total investment cannot exceed the available investment budget of $1 million, which can be written as:

0.50x₁ + 1.40x₂ + 1.70x₃ + 1.10x₄ + 4.00x₅ + 0.60x₆ + 2.50x₇ + 1.10x₈ <= 1

Additionally, the decision variables are binary, which means that x_i can only be either 0 or 1. Therefore, we can add binary constraints for each decision variable as follows:

x_i = 0 or 1 for i = 1,2,3,4,5,6,7,8

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Four of them have in all 504 cards.

Multiplication: In math, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

It is given that Stephanie has 126 basketball cards

and also said that her three friends have the same number of cards as she does

which gives 126 each of three friends so, three of them are having

friend 1 =126

friend 2=126

friend 3=126

=3×126 by combining three friends cards which gives,

=378

four of them will have 4×126=504 cards.

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Of them, four have all 504 cards.

What does "multiplication" mean?

Multiplication in mathematics is the addition of equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

Given her collection of 126 basketball trading cards

and added that she shares the same number of cards with her three friends.

which amounts to 126 for each of the three friends, meaning that three of them

buddy 1 = 126

friend 2=126

friend 3=126

=3×126 by combining three friends cards which gives,

=378

four of them will have 4×126=504 cards.

The value of X is 10.

To find the value of X in the similar shapes, we can set up a proportion using the corresponding sides of the two shapes.

Let's label the sides of the first shape as follows:

Side A: 16

Side B: 10

Side C: 20

Side D: 16

And label the sides of the second shape as:

Side A': 8

Side B': 5

Side C': X

Side D': 8

We can set up the proportion using the corresponding sides:

A / A' = B / B' = C / C' = D / D'

Using the given information, we have:

16 / 8 = 10 / 5 = 20 / X = 16 / 8

Now, let's solve for X:

16 / 8 = 2

10 / 5 = 2

20 / X = 2

16 / 8 = 2

Since the ratios are all equal to 2, we can set up the equation:

20 / X = 2

To solve for X, we can cross-multiply:

20 = 2X

Dividing both sides of the equation by 2:

20 / 2 = X

X = 10

Therefore, the value of X is 10.

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Answer:

Step-by-step explanation:

  YZ = Z - Y = 1 -(-3) = 4

  XW = W -X = 5 -(-7) = 12

The segments are different lengths, so are not congruent.

_____

Obviously, segment YZ is only part of segment XW, so will not be the same length.

The Area of Computer Chip is  25.776 x 10⁻¹⁶.

The Perimeter of Computer chip is 14.3272 x 10⁻⁷.

Part A: To determine the area of the computer chip, we multiply the length and width of the chip.

Length = 7.16 x 10⁻⁷ meters

Width = 3.6 x 10⁻⁹ meters

Area = Length x Width

Area = 7.16 x 10⁻⁷ x 3.6 x 10⁻⁹

= 7.16 x 3.6 x 10⁻¹⁶

= 25.776 x 10⁻¹⁶

Part B: In this case, 25.776 can be written as 2.5776 x 10¹, where 2.5776 has four significant digits.

Since we are multiplying by 10^(-16), the final scientific notation for the area is:

Area = 2.5776 x 10¹ x 10⁻¹⁶

= 2.5776 x 10⁻¹⁵ square meters

Part C: To determine the perimeter of the computer chip, we add up all the sides of the rectangle.

Perimeter = 2 x (Length + Width)

Perimeter = 2 x [(7.16 x 10^(-7)) + (3.6 x 10^(-9))]

= 2 x ( 7.16 x 10⁻⁷ + 3.6 x 10⁻⁹ )

= 14.3272 x 10⁻⁷

Part D:

In this case, 14.3272 can be written as 1.43272 x 10 where 1.43272 has five significant digits. Since we are multiplying by 10⁻⁷ the final scientific notation for the perimeter is:

Perimeter = 1.43272 x 10 x 10⁻⁷

= 1.43272 x 10⁻⁶ meters

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Answer:

The answer is option 3.

Step-by-step explanation:

You have to form an inequality expression and then solve it. Let x be the side of the square :

\(4x < 16\)

\(x < 16 \div 4\)

\(x < 4\)

Answer:

C

Step-by-step explanation:

You can't have negative values. So x should be greater than 0 and less than 4.

0<x < 4

which is the short way of writing what I just said.

The correct answer is x<4 with only positive values. C

Answer:

45

Step-by-step explanation:

10x5 is 50

so now you have to multiply 9x5 and you get 45

Answer:

b > -8

Step-by-step explanation:

Given inequality:

\(4b-3(2b-6) > 3-(5b+9)\)

To solve for b, begin by expanding the brackets on the left side of the inequality:

\(4b-3 \cdot 2b -3 \cdot (-6) > 3-(5b+9)\)

\(4b-6b +18 > 3-(5b+9)\)

Distribute the negative sign inside the parentheses on the right side:

\(4b-6b +18 > 3-5b-9\)

Combine like terms on both sides of the inequality:

\(-2b +18 > -5b-6\)

Add 5b to both sides:

\(-2b +18 +5b > -5b-6+5b\)

\(3b+18 > -6\)

Subtract 18 from both sides:

\(3b+18-18 > -6-18\)

\(3b > -24\)

Divide both sides by 3 to isolate b:

\(\dfrac{3b}{3} > \dfrac{-24}{3}\)

\(b > -8\)

Therefore, the solution to the given inequality is:

\(\large\boxed{\boxed{b > -8}}\)