Find the equation of the line tangent to the graph of y = cos(2x) at x = pi/4 ...?

For the function, f(x) = 2x + 1 and g(x) = x² – 7, (f – g)(x) will be D. –x² + 2x + 8

To find (f - g)(x), we need to subtract the function g(x) from the function f(x).

f(x) = 2x + 1

g(x) = x² - 7

(f - g)(x) = f(x) - g(x)

Substituting the given functions:

(f - g)(x) = (2x + 1) - (x² - 7)

Now let's simplify:

(f - g)(x) = 2x + 1 - x² + 7

Combining like terms, we have:

(f - g)(x) = -x² + 2x + 8

Therefore, the answer is D. -x² + 2x + 8.

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The inverse of a function is gotten by swapping the x and y coordinates.

The inverse of function f(x)  is[tex]h(x) = \frac x2 + 5[/tex]

Given

[tex]f(x) = 2x - 10[/tex]

Rewrite as:

[tex]y = 2x - 10[/tex]

Swap x and y

[tex]x = 2y - 10[/tex]

Solve for y

[tex]2y = x + 10[/tex]

Divide by 2

[tex]y = \frac x2 + 5[/tex]

So, we have:

[tex]h(x) = \frac x2 + 5[/tex]

Hence, the inverse function is[tex]h(x) = \frac x2 + 5[/tex]

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Answer:

Option B

Step-by-step explanation:

In the figure attached we have to find the scale factor of dilation of figure A to figure B.

Since figure A is smaller than figure B, it concludes figure A has been enlarged to form figure B.

Now we have to find the scale factor of enlargement.

Scale factor =  [tex]\frac{\text{one side of the larger figure}}{\text{one side of the smaller figure}}[/tex]

=  [tex]\frac{5}{2}[/tex]

Therefore option B is the correct answer.

I'm pretty sure the answer would be x^12

The dimensions of the triangle with a base that is 2/3 of its height and an area of 12 square centimeters are a base of 4 centimeters and the height of 6 centimeters.

The question asks for the dimensions of a triangle. We are given that the base is 2/3 of the height and the area is 12 square centimeters. The formula for the area of a triangle is 1/2 * base * height. Since we know that the base is 2/3 of the height, we can denote the height as 'h' and the base as (2/3)h. From here, we can set up the equation 12 = 1/2 * (2/3)h * h, which simplifies to 12 = 1/3 * h². Solving for 'h', we find the height is √36 or 6 centimeters. Given the base is 2/3 of the height, the base, therefore, is 4 centimeters.

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To copy a line segment and ensure it has the same length as the original, use a compass to measure and create a duplicate line segment.

To copy a line segment and ensure that the new line segment has the same length as the original, we can use a compass. Here are the steps:

By using this method, we can create a duplicate line segment with the same length as the original.

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Final answer:

The quadratic functions are: y = 2(x - 3x² + 1), y = 1/2x² - 13x + 4, and y = 1.

Explanation:

A quadratic function is a polynomial function of degree 2, which means its highest power of x is 2. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Out of the given options, the quadratic functions are:

a. y = 2(x - 3x² + 1)

c. y = 1/2x² - 13x + 4

d. y = x/x - 1 (this can be simplified to y = 1)

The options b. (y = 5 + 2x) is not a quadratic function because it only has a linear term (power of x is 1).

Missing number to complete the factorization is 3.

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.

Given expression

[tex]x^{3}+x^{2} -21x-45=(x+3) (x-5) (x+a)[/tex]

Let a be the missing number

(x + 3) (x - 5) (x + a)

= [tex](x^{2} -5x+3x-15)(x+a)[/tex]

= [tex](x^{2} -2x-15)(x+a)[/tex]

[tex]x^{3}+x^{2} -21x-45=x^{3} +x^{2} a-2x^{2} -2xa-15x-15a[/tex]

By comparing the expressions

-2xa - 15x = -21x

⇒ -2xa = -6x

⇒ a = 3

[tex]x^{2} (a-2) = 1x^{2}[/tex]

⇒ a - 2 = 1

⇒ a = 3

-15a = -45

⇒ a = 3

Hence, missing number to complete the factorization is 3.

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Answer:

12th grade data set

Step-by-step explanation:

The greatest common factor of 34n and 8n² is 2n, as both expressions share the variable n and the highest common numerical coefficient is 2.

The greatest common factor (GCF) of two algebraic expressions can be found by identifying the highest powers of common factors in the terms. For the expressions 34n and 8n², both terms have n as a common factor. Since we want the greatest common factor, we take the highest power of n that appears in both terms, which is n (not n² because n is the highest power in the least degree term, 34n). Next, we find the GCF of the numerical coefficients 34 and 8, which is 2. Therefore, the greatest common factor of 34n and 8n² is 2n.

Answer:

Proportion states that two fractions or ratios are equal.

Let x be the  closing cost amount.

As per the statement:

Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000.

Purchased Price = $275,000

then, by definition of proportion :

[tex]\frac{4}{100}=\frac{x}{275000}[/tex]

By cross multiply we have;

1,100,000 = 100x

Divide both sides by 100 we have;

11,000 = x

or

x = $ 11,000

Therefore, the closing cost amount is, 11,000