Write the point-slope form of the given line that passes through the points (0, -3) and (4, 1). Identify (x1, y1) as (0, -3). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

Answer:

94.50

Step-by-step explanation:

i used a calculator

To predict the behavior of the autonomous differential equation as t -> infinity, analyze the phase portrait of the system. The behavior of X(t) as t approaches infinity depends on the initial conditions. Verify the explicit solution of the DE when k=1 and a=B. Graph the solutions and observe their behavior as t-> infinity.

To predict the behavior of the autonomous differential equation dX/dt = k(a-X)(B-X) as t -> infinity, we can analyze the phase portrait of the system. The phase portrait will show the equilibrium points and the direction of the solutions as time increases. In this case, there will be two equilibrium points, one at X = a and one at X = B, assuming a < B. The behavior of X(t) as t approaches infinity depends on the initial conditions. If X(0) < a, the solution will approach X = a, and if X(0) > a, the solution will approach X = B.

To verify the explicit solution of the differential equation when k=1 and a=B, we substitute these values into the equation: X(t) = a - 1/(t+c). For the solution that satisfies X(0) = a/2, we substitute t=0 and X(0) = a/2 into the equation and solve for c. Similarly, for the solution that satisfies X(0) = 2a, we substitute t=0 and X(0) = 2a into the equation and solve for c. We can then graph these two solutions and observe that as t approaches infinity, X(t) approaches a for both solutions, which confirms our analysis from part (b).

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we know that

[tex] 1 billion=1,000,000,000 [/tex]

In scientific notation

[tex] 1,000,000,000=1*10^{9} [/tex]

To find the value of [tex] 31 billion [/tex]

Multiply the value of one billion for [tex] 31 [/tex]

so

[tex] 31*1*10^{9} =31*10^{9}\\ =3.1*10^{10} [/tex]

therefore

the answer is

[tex] 3.1*10^{10} [/tex]

The scientific notation of [tex]31 \text{billion}[/tex] is [tex]\boxed{3.1 \times \left( {{{10}^{10}}} \right)}[/tex].

Further explanation:

Scientific notation is also called as the standard form of writing a number.

The number has two parts in the scientific notation.

First part is digits or digit with decimal and the second part is 10 to the power.

If the number is greater than 10, move the decimal point to the left.

If the number is less than 10, move the decimal point to the right.

Calculation:  

One billion is equal to [tex]1000000000[/tex].

In scientific notation one million can be expressed as,

[tex]\boxed{{\text{1}}\,{\text{billion}} = {10^9}}[/tex]

Thirty one billion is equal to [tex]31000000000[/tex].

Now find the scientific notation SN of 31 billion.

[tex]\begin{aligned}\text{SN} &= 31000000000 \\&= 31 \times \left( {{{10}^9}} \right) \\&= 3.1 \times \left( {{{10}^{10}}} \right) \\ \end{aligned}[/tex]

The first part of the scientific notation is [tex]\boxed{3.1}[/tex].

The second part of the scientific notation is [tex]\boxed{{10^{10}}}[/tex].

Hence, the scientific notation of [tex]31 \text{billion}[/tex] is [tex]\boxed{3.1 \times \left( {{{10}^{10}}} \right)}[/tex].

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Scientific notation

Keywords: scientific notation, one billion, thirty one billion, million, standard form, first part of scientific notation, second part of scientific notation, power.

Answer:- R(0, 360°) is the right answer.

Given: A parallelogram is transformed according to the rule (x, y) → (x, y).

⇒The points of the image is same as the points of the original figure.

⇒ The given mapping create an image onto itself.

We know that the mapping of all points of a figure in a plane is done by  basic rigid transformations such as translation, reflection or rotation.

In rotation to create a image that is onto itself , then the rotation must be about 360°, so that the rotation will take a complete turn to get back  the original figure with the same points.

Thus in rotation the another way to state the transformation is R(0, 360°).

To find the total cost of an item with sales tax, convert the tax rate to a decimal, multiply by the item's price, add the result to the original price, and round to the nearest cent. A $17.50 item with a 7% sales tax would cost a total of $18.73 after tax.

To calculate the total cost of an item with sales tax, you first need to determine the amount of sales tax by converting the percentage to a decimal and then multiplying by the item's cost. For an item priced at $17.50 with a 7% sales tax, you would convert 7% to a decimal (0.07) and then multiply this by $17.50. Therefore, the calculation would be:

Sales Tax = $17.50 x 0.07 = $1.225

Once you have the sales tax amount, you add it to the original price to find the total cost:

Total Cost = Original Price + Sales Tax

$17.50 + $1.225 = $18.725. After rounding to the nearest cent, the total cost would be $18.73.

Answer:

Step-by-step explanation:

The value of d that makes the lines 2dx - y = -4 and 4x - y = -6 perpendicular is -1/8, as this value makes the product of their slopes equal to -1.

To determine which value(s) of d would make the two lines perpendicular, we have to evaluate the slopes of the two lines and set their product to be -1, since perpendicular lines have slopes that are negative reciprocals of each other. Rearranging the first equation, 2dx - y = -4, we get y = 2dx + 4, which has a slope of 2d. For the second equation, 4x - y = -6, rearranging gives y = 4x + 6, with a slope of 4.

The product of the slopes of two perpendicular lines should be -1, so:

(2d) * 4 = -1

Solving for d: d = -1/8.

Thus, when the value of d is -1/8, the two lines are perpendicular.

The ratio of the perimeters of two squares with a side ratio of 3:1 is 3:1.

The ratio of the sides of two squares is 3:1. To find the ratio of their perimeters, we need to compare the lengths of their sides. Let's assume the length of the larger square is 3x and the length of the smaller square is x. The perimeter of the larger square is 4 times the length of its side, so it is 4 × 3x = 12x. The perimeter of the smaller square is 4 times the length of its side, so it is 4 × x = 4x. Therefore, the ratio of their perimeters is 12x:4x. Simplifying this ratio gives us 3:1.

The relationship between the cans of food and boxes of food that Ingrid collected can be determined by the mathematical equations involving addition/subtraction and multiplication/division.

 For addition/subtraction:

   D = x – y

Where D is difference, x is the number of cans of food, and y is the boxes. Substituting the known values,

    D = 6 – 8 = -2

 For multiplication/division:

   R = x/y

Where R is the ratio. Substituting the known values,

   R = 6/8 = ¾ = 0.75

The relationship between the number of cans of food and boxes of food collected by Ingrid is a ratio of 1 can to 3 boxes after simplification. This means there is 1 can for every 3 boxes.

Ingrid collected 6 cans of food and 18 boxes of food for the food bank. To describe the relationship between cans of food and boxes of food, we can use a mathematical ratio.

The ratio of cans to boxes is calculated by dividing the number of cans by the number of boxes. This gives us:

6 cans : 18 boxes

To simplify this ratio, we divide both numbers by their greatest common divisor, which is 6:

6 ÷ 6 = 1

18 ÷ 6 = 3

Therefore, the simplified ratio is:

1 can : 3 boxes

This means there is 1 can of food for every 3 boxes of food. This ratio helps us understand the proportional relationship between the two quantities.

After standardizing the given value using a Z-score, it is found that the probability of a person producing more than 76.7% of the cholesterol in their body is essentially zero.

The question is asking for the probability that a person produces more than 76.7% of the cholesterol in their body, given this production is normally distributed with a mean of 75% and a standard deviation of 0.5%. To calculate this, we can utilize Z-score which standardizes the deviation of a value from the mean, considering the standard deviation.

The Z-score for the value 76.7% is calculated as follows: (76.7 - 75) / 0.5 = 3.4.

Using the standard normal distribution, the probability of a Z-score being above 3.4 is extremely low, it's practically zero. Therefore, the probability that a person produces more than 76.7% of the cholesterol in their body is essentially zero.

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A fraction is a way to describe a part of a whole. The sum of the two of the given fractions is equal to 9/10.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The given fractions can be added as shown below.

(1/4) + (13/20)

Taking the LCM of the denominator which is equal to 20,

= (1×5 / 4×5) + (13/20)

= (5/20) + (13/20)

= (5 + 13)/20

= 18/20

Divide both the numerator and the denominator by 2,

= 9/10

Hence, the sum of the two of the given fractions is equal to 9/10.

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Answer:

[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to   [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]

Step-by-step explanation:

Given Parameters;

(m-4)/(m+4) and (m+2)

Required:

To divide and write out the equivalent expression.

Two or more expressions are said to equivalent if and only if they give the same result.

Solving (m-4)/(m+4) divided by (m+2)

We have

[tex]\frac{m - 4}{m + 4}[/tex] divided by [tex]m + 2[/tex]

[tex]= \frac{m - 4}{m + 4} / (m + 2)[/tex]

Convert division to multiplication

[tex]= \frac{m - 4}{m + 4} *\frac{1}{(m + 2)}[/tex]

= [tex]\frac{(m - 4) * 1}{(m + 4) * (m + 2)}[/tex]

[tex]= \frac{(m - 4)}{(m + 4)(m + 2)}[/tex]

We can't simplify any further;

Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to   [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]

To check if this is true

Let m = 1

[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] becomes

[tex]\frac{1 - 4}{1 + 4} / (1 + 2)[/tex]

[tex]\frac{-3}{5} / (3)[/tex]

[tex]\frac{-3}{5} * \frac{1}{3}[/tex]

[tex]\frac{-1}{5}[/tex]

And

[tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex] becomes

[tex]\frac{(1 - 4)}{(1 + 4)(1 + 2)}[/tex]

[tex]\frac{(-3)}{(5)(3)}[/tex]

[tex]\frac{-1}{5}[/tex]

Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to   [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]

The answer is B) The state with the second lowest population has the lowest population density.

Answer:

Yep the answer is −3x+y=−7

Step-by-step explanation:

We want to find the equation of a cosine function after we apply some given transformations to it.

The equation of the resulting cosine curve is:

g(x) = -(1/4)*cos(x + 5) - 9/4.

Let's see how we got that equation:

First, we need to define all the transformations that we will be using:

Vertical shift:

For a given function f(x) a vertical shift of N units is written as:

g(x) = f(x) + N.

Horizontal shift:

For a given function f(x) a horizontal shift is written as:

g(x) = f(x + N).

Vertical compression.

For a function f(x) a vertical compression by a factor k is written as:

g(x) = (1/k)*f(x).

Vertical flip (or vertical reflection).

For a general function f(x) a vertical reflection is written as:

g(x) = -f(x).

So we start with:

f(x) = cos(x).

First we shift it to the left 5 units, so we get:

g(x) = f(x + 5)

Then we shift it up 9 units, then we get:

g(x) = f(x + 5) + 9

Then we compress it vertically by a factor of 4:

g(x) = (1/4)*(f(x + 5) + 9)

Then we flip it vertically:

g(x) = -(1/4)*(f(x + 5) + 9)

Replacing f by the cosine function we get:

g(x) = -(1/4)*( cos(x + 5) + 9)

g(x) = -(1/4)*cos(x + 5) - 9/4.

This is the equation of the resulting cosine curve.

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1. f(x)=1/2x-3     f(x)=1/2x-3

  f(0)=1/2(0)-3   f(6)=1/2(6)-3

  f(0)=-3             f(6)=0

m=f(b) - f(a)/b - a = 0- (-3)/6 - 0  = 3/6 = 1/2

2.  f(x) = -x         f(x) = -x

    f(-4) = -(-4)    f(2) = -2

    f(-4) = 4         f(2) = -2

m=f(b) - f(a)/b - a = -2 - 4/2 - (-4) = -6/6 = -1

3. f(x) = x^2     f(x) = x^2

   f(-2) = -2^2  f(0) = 0^2

   f(-2) = -4      f(0) = 0

m=f(b) - f(a)/b - a = 0 - (-2)/0 - (-2) = 2/2 = 1

4. f(x) = x^3     f(x) = x^3

   f(-1) = -1^3  f(1) = 1^3

   f(-1) = -1      f(1) = 1

m=f(b) - f(a)/b - a = 1 - (-1)/1 - (-1) = 2/2 = 1

5. f(x) = 2^x    f(x) = 2^x

   f(0) = 2^0    f(4) = 2^4

   f(0) = 1        f(4) = 16

m=f(b) -f(a)/b - a = 4 - 0/ 4 - 0 = 4/4 = 1

i hope this is right, have a good day

The correct inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget is $1.75x ≥ $25.

The correct inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget of $25 is b. $1.75x ≥ $25.

This inequality states that the product of the cost per box, $1.75, and the number of boxes, x, must be greater than or equal to $25 to remain within his budget.

You can solve this inequality by dividing both sides by $1.75 to find the minimum number of boxes he can buy and still stay within his budget.

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Answer:

There are total 30 students in the class.

Step-by-step explanation:

Let the total number of students in class = x

Number of males in the class = 12

Number of females in the class = 60% of Total students = 60% of x = 0.6x

So, we get that,

Number of males + Number of females = Total students

i.e. [tex]12+0.6x=x[/tex]

i.e. [tex]12=x-0.6x[/tex]

i.e. [tex]12=0.4x[/tex]

i.e. [tex]x=\frac{12}{0.4}[/tex]

i.e. x = 30

Thus, there are total 30 students in the class.

hi therrre you are an awesome person