Explain why (4) × (-5) = 20. Use patterns, an example from the Integer Game, or the properties of operations to support your reasoning. ​

Step 1:

Write the equation of the line in the form of y = mx + c

m = slope

Step 2

Step 3

From the equation

Step 4:

Final answer

The measure of acute angle = 26.6

\(dy/dx = 2e^(2x)\)is the final answer To know the functions: a) To find the derivative of y = -x², we can apply the power rule for differentiation. The power rule states that if y = x^n, then the derivative dy/dx = n*x^(n-1).

In this case, we have y = -x², so using the power rule:

\(dy/dx = -2x^(2-1)       = -2x\)

Therefore, the derivative of \(y = -x² is dy/dx = -2x.\)

b) For y = √x, we can use the power rule along with the chain rule to differentiate it.

So, \(dy/dx = (1/2)*x^(-1/2) * (1/2)x^(-1/2)           = (1/2)*(1/2)x^(-1/2)*x^(-1/2)           = (1/4)x^(-1/2-1/2)           = (1/4)x^(-1)           = 1/(4x)\)

Therefore, the derivative of y = √x is dy/dx = 1/(4x).

c) To find the derivative of y = 2cos(x²), we can apply the chain rule.  cos(x) is -sin(x)and the inner function will be  x², and the derivatives can be derived by x², which is 2x.

So, \(dy/dx = 2(-sin(x²))*2x           = -4x*sin(x²)\)

Therefore, the derivative of \(y = 2cos(x²) is dy/dx = -4x*sin(x²).\)

d) For y = 2x, the derivative is straight forward. The coefficient 2 remains and the derivative of x concerning x is 1.

Therefore, the derivative of \(y = 2x is dy/dx = 2.\)

e) The function y = -√x does not have a derivative because the square root of a negative number is undefined in the real number system.

f) For \(y = e^(2x),\)we can use the chain rule. The derivative will be \(e^x\)is\(e^x,\) and the inner function can be 2x, we multiply the derivative by the derivative of 2x, which is 2.

So, \(dy/dx = 2e^(2x)\)

Therefore, the derivative

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The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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The coordinate point T' the reflection of T over the y-axis is (4, -5).

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given that, the point T is plotted on the coordinate grid.

The coordinate point on the grid is (-4, -5).

The reflection of point (x, y) across the y-axis is (-x, y).

Here, (-4, -5)→(4, -5)

Therefore, the coordinate point T' the reflection of T over the y-axis is (4, -5).

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132 feet²

For this question, you have to find area.

Area is length x width

so multiply 11 x 12

You will get 132 feet²

Step-by-step explanation:

13. f(x) = 6x; f(x) = -24

6x = -24

x = -4

14. g(x) = -10x; g(x) = 15

-10x = 15

x = -1.5

15. f(x) = 3x – 5; f(x) = 4

3x-5 =4

3x =9

x = 3

16. h(x) = 14 – 8x; h(x) = -2

14-8x=-2

-8x = -16

x = 2

1. -2 + 15 = 13

If the temperature is -2 and it rises 15 degrees, the new temperature is 13 degrees.

2. The temperature rose 15 degrees

-6 + 9 = 15

Answer:

1 a) 13 degrees Celsius

b) By fifteen degrees

To rank the cereals in order from least likely to be chosen to most likely to be chosen, we need to compare their probabilities. Here are the cereals ranked in order:

Bran O's (0.04): This cereal has the lowest probability of being chosen among the options provided.

Rice O's (8.9% or 0.089): This cereal has a higher probability than Bran O's but is lower than the remaining options.

Wheat O's (5/16 or 0.3125): This cereal has a higher probability than Rice O's but is lower than the remaining options.

Chocolate O's (3/10 or 0.3): This cereal has a higher probability than Wheat O's but lower than the last remaining option.

Corn O's (0.113): Among the given options, Corn O's has the highest probability and is the most likely to be chosen.

So, the cereals ranked from least likely to be chosen to most likely to be chosen are: Bran O's, Rice O's, Wheat O's, Chocolate O's, and Corn O's.

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Answer:

D is the outlier

Step-by-step explanation:

An outlier is a point that is far from the other points

We can draw a line that roughly represents an equation for the points

A,B ,C are all near the line

D is not along the line

The greatest common divisor (GCD) of two integers a and b, denoted as gcd(a, b), is defined as the largest positive integer that divides both a and b without leaving a remainder.

In Section 4.10, the concept of greatest common divisor (GCD) is introduced. The GCD of two integers a and b is a positive integer that is the largest divisor common to both a and b. It is denoted as gcd(a, b). The GCD is determined by finding the highest factor that divides both a and b without leaving a remainder. It represents the largest integer that can evenly divide both numbers.

For example, if a = 12 and b = 18, the common divisors are 1, 2, 3, and 6. However, the greatest common divisor is 6 since it is the largest factor that divides both 12 and 18 without any remainder. The GCD has various applications, such as simplifying fractions, finding common factors, and solving modular equations.

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The correct answer for the carrying capacity of the population in the logistic model with the equation dp/dt = p(12-3p) is 4.

In the logistic model, the carrying capacity represents the maximum population size that an environment can sustain in the long term. In the equation dp/dt = p(12-3p), the carrying capacity is represented by the value at which the growth rate of the population is zero.

To find this value, we set the right-hand side of the equation to zero and solve for p:

0 = p(12-3p)

0 = p(4-p)

This equation has two solutions: p = 0 and p = 4. The solution p = 0 represents the population size when the growth rate is zero, but it is not the carrying capacity since the population would not survive at this size.

The solution p = 4 represents the carrying capacity, which is the maximum population size that the environment can support in the long term.

Therefore, the carrying capacity of the population in the logistic model with the equation dp/dt = p(12-3p) is 4.

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Answer:

31.59/1.3 = 24.3

Answer:

24.3

Step-by-step explanation:

Answer:

The expression for the area is;

Explanation:

Given that the length of the rectangle is 3 and the width is (7-4x);

Recall that the area of rectangle can be calculated by multiplying its length by the width.

So, the expression for the area of the given rectangle is;

Therefore, the expression for the area is;

Answer:

(-5,-8)

Step-by-step explanation:

-3x+7y=5x+2y

Substitute -5 for x:

-3(-5)+7y=5(-5)+2y

Simplify:

15+7y=-25+2y

Add 25 to both sides of the equation:

40+7y=2y

Subtract 7y from both sides of the equation:

40=-5y

Divide both sides by -5:

40/-5=y

y=-8

The answer in simplest form is x = -3/4

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

The given equation is

3x + 3 +9 =-x-9

Collecting like terms to have

3x + x = -9+9-3

4x = -3

Making x the subject of the relation

Therefore, the value of x is x = -3/4

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Answer:

Step-by-step explanation:

Potential energy=stored energy so say when the roller coaster stops somewhere they are storing energy.

In then when they just go down there would now be using kinetic energy.

Hope this helps have a great afternoon:)

The particular solution of the differential equation, given y = 8 when x = 1, is \(y = -x^2 + 9x^3.\)

To solve the first-order linear differential equation using the integrating factor method, we follow these steps:

(a) Determine the integrating factor:
1. Start with the given differential equation: \(dy/dx - 3y/x = x^2.2. Rewrite the equation in the standard form: dy/dx + (-3/x)y = x^2.3. Identify the coefficient of y as P(x) = -3/x.4. Find the integrating factor (IF), which is given by IF = e^(∫P(x)dx). Integrating P(x), we have ∫(-3/x)dx = -3ln|x|. Therefore, the integrating factor is IF = e^(-3ln|x|) = 1/x^3.\)

(b) Solve the differential equation using the integrating factor:
1. Multiply the entire equation by the integrating factor (IF):
  \((1/x^3)dy/dx + (-3/x^4)y = (x^2/x^3). Simplifying, we get dy/dx - (3/x^4)y = x/x^3.\\\)
2. Notice that the left side of the equation is the derivative of (y/x^3):
  d/dx(y/x^3) = x/x^3.

3. Integrate both sides with respect to x:
\(∫d/dx(y/x^3)dx = ∫(x/x^3)dx.\)

4. Simplify and integrate:
  \(y/x^3 = ∫(1/x^2)dx = -1/x + C,\)where C is the constant of integration.

5. Multiply both sides by x^3 to solve for y:
  \(y = -x^2 + Cx^3.\)

(c) Find the particular solution given y = 8 when x = 1:
  Substitute the values x = 1 and y = 8 into the equation:
  \(8 = -(1)^2 + C(1)^3. 8 = -1 + C. C = 8 + 1 = 9.\\\)
The particular solution of the differential equation, given y = 8 when x = 1, is \(y = -x^2 + 9x^3.\\\)
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Therefore, the multiplication operator (*) is evaluated first.

In computer programming, an operator is a symbol or a keyword used to perform operations on one or more operands (values or variables). There are different types of operators, including arithmetic operators (such as +, -, *, /), comparison operators (such as <, >, ==, !=), logical operators (such as &&, ||, !), assignment operators (such as =, +=, -=), and more. Operators allow programmers to manipulate data and variables in various ways, enabling them to perform complex computations and make decisions based on the results.

Here,

The order of operator evaluation is determined by the rules of operator precedence in programming languages. In this case, the order of evaluation is as follows:

Multiplication operator (*)

Subtraction operator (-)

Relational operator (<)

Logical operator (<)

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Answer:

Send a proper picture, the fifth point is not visible.

Answer:

the diameter will be D=26 in.

Step-by-step explanation:

The area of a circle is given by:

\(A=\pi R^{2}\) (1)

Where:

Now, we know that A = 169 π in²

So, we just need to use equation 1 to find R.

\(169\pi = \pi R^{2}\)

\(R=\sqrt{169}\)

\(R=13 \: in\)

Therefore, the diameter will be D=2*R=26 in.

I hope it helps you!

The diameter of the circle is 26 inches

The area of the circle is given as:

\(A = 169\pi\)

The area of a circle is calculated as:

\(A = \pi r^2\)

By comparison, we have:

\(\pi r^2 = 169\pi\)

Divide both sides of the equation by pi

\(r^2 = 169\)

Take the positive square roots of both sides

\(r = 13\)

Multiply by 2, to calculate the diameter

\(d =2 * 13\)

\(d = 26\)

Hence, the diameter of the circle is 26 inches

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Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines, cake can be cut into 20 equal parts.

This is further explained below.

Generally, In spreadsheet software, gridlines are the light gray lines that divide the cells, rows, and columns. Gridlines are often used to maintain track of data. Gridlines are widely used in popular spreadsheet programs like Spreadsheet.

In conclusion, If the cuts can only be done along the gridlines, the cake may be divided into 20 equal pieces when cutting along the lines.

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Answer:

The answer is 60

Step-by-step explanation:

2x5x6

rearrange by the commutative property

(2x5)x6

Calculate

10x6

calculate the product or quotient to 60

hence the answer is 60

Hoped this helped:D

Alison has five different hats, six different bracelets, and seven cats. She wants to take a selfie with a hat, a bracelet, and two cats. So she can take 630 different selfies.

         She wants to take selfies with what she has, and the question asks how many different selfies can she take.

    Let's solve the question below:

         The total number of selfies Alison can take is 5 × 6 × ( ₇C₂ )

          As Alison wants to take a selfie with a hat, a bracelet, and two cats, there are 5 hats and 6 bracelets she can select from, and she needs to select 2 cats out of 7 available cats.

          We can use the combination formula to calculate the total number of ways:

            ₇C₂ = \((7 * 6)/2\)

                   = 21

  Hence, Alison can take \(5 * 6 * 21\) = 630 different selfies with a hat, a bracelet, and two cats.

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Answer:

its y*x+z

Step-by-step explanation:

4*4

Answer:65.6

Step-by-step explanation:

So $0.25 per yard

16.4/$0.25=65.6

Answer:

$40,788

Step-by-step explanation:

3% of 39600 = 1188

increased price = 39600 + 1188 = $40,788

There are 16 different answer combinations possible for the three questions.

For each question, there are a certain number of answer choices available. Let's analyze each question separately:

Were you born before 1990?" - This question has 2 answer choices: yes or no.

b) "What is your favorite color?" - This question has 4 answer choices: red, green, blue, or other.

c) "Do you play a musical instrument?" - This question has 2 answer choices: yes or no.

To find the total number of answer combinations, we multiply the number of choices for each question. Therefore, we have 2 * 4 * 2 = 16 different answer combinations.

For question a, there are 2 choices. For each choice in question a, there are 4 choices in question b, resulting in 2 * 4 = 8 combinations. For each of these 8 combinations, there are 2 choices in question c, resulting in a total of 8 * 2 = 16 different answer combinations.

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Answer:

A) The lower portion of the lungs has more oxygen than perfusion.

Step-by-step explanation:

Answer:

2 feet.

Step-by-step explanation:

Since the volume of cube A is 64, we can divide the edge (4) by two because cube B can only hold half as much liquid.

Thus, the edge of cube b is 2 feet.

Hope it helped!

Step-by-step explanation:

the initial Equation :

50 + 20X = 150

it could be changed to :

20X + 50 = 150

=>

20X = 150-50

20X = 100

x = 100/20

x = 5 hours

the correct answer is option A