Which best describes the relationship between the successive terms in the sequence shown? 9, –1, –11, –21, … The common difference is –10.  The common difference is 10.  The common ratio is –9. The common ratio is 9.

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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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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 expression 7 x 10³ is 3.5 times larger than 2 x 10³ because the power of 10 is the same in both, so we simply compare the coefficients 7 and 2.

The student is asking to compare two expressions written in scientific notation: 7 x 10³ and 2 x 10³. Scientific notation allows us to write very large or very small numbers conveniently and is commonly taught in middle school math.

To compare these two expressions, we can look at the coefficients (7 and 2) because the powers of 10 are the same in both expressions (10³). Since these powers are the same, comparing the coefficients directly will give us the relationship between the two expressions. Here, 7 is simply 3.5 times as large as 2, so we can say that 7 x 10³ is 3.5 times larger than 2 x 10³.

In terms of the answer choices provided by the student, we can thus conclude that the correct answer is:

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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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.

Answer:

Step-by-step explanation:

I find it convenient to do the problem in the reverse order: find the LCM, then distribute. That way, I'm not distributing a fraction.

The LCM of 2 and 5 is their product: 2·5 = 10. Multiplying the equation by 10 gives ...

  5(4 -k) = 4

Now, distributing, we get ...

  20 -5k = 4

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°).

The line will shift vertically down by 4 tons.

Answer:

Step-by-step explanation:

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.

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:

Yep the answer is −3x+y=−7

Step-by-step explanation:

Answer:

94.50

Step-by-step explanation:

i used a calculator

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.

The correct transformation is to reflect the graph about the y-axis and then translate it 2 units down, corresponding to option 4.

The correct transformation is therefore to reflect the graph about the y-axis to change the slope from positive to negative and then translate 2 units down to change the y-intercept from +9 to +7. This corresponds to option 4 from the question.

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]