write an equation of the line that passes through the point P(2, 5 ) that is parallel to y=4x+1

Given:

The function \(g(x)\) doubles the square of the input and then subtracts 13.

To find:

The value of \(g(3)\).

Solution:

Let \(x\) be the input value.

The square of the input is \(x^2\).

Doubles the square of the input \(2x^2\).

Doubles the square of the input and then subtracts 13, i.e., \(2x^2-13\).

So, the function is:

\(g(x)=2x^2-13\)

Putting \(x=3\) in the above function, we get

\(g(3)=2(3)^2-13\)

\(g(3)=2(9)-13\)

\(g(3)=18-13\)

\(g(3)=5\)

Therefore, the value of \(g(3)\) is 5.

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Step-by-step explanation:

A= πr^2

A = 8^2×π=64π= 201.06 ft^2

Answer:

7776

Step-by-step explanation:

you divide 5 by 2 to get 2.5 then put 36 to the power of 2.5 to get 7,776

Answer:

rtshsrst6hteshyrjhryjy

Step-by-step explanation:

fgjyryrjutkj

Answer:

a plane figure with three straight sides and three angles.

Step-by-step explanation:

The simplified form of the given expression is 9b

From the question, we are to simplify the given expression

The given expression is 3√b^2

This expression can be properly written as

(3√b)²

To simplify the expression,

First, we will expand the expression by applying one of the rules of exponents

(3√b)²

Applying the rule of exponent

3² × (√b)²

9 × b

= 9b

Hence,

The simplified expression is 9b

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Answer: 30 meters

Step-by-step explanation:

50/12=4.1666

4.1666x7=29.162 round it to 30

Answer:

29.19

Step-by-step explanation:

50/12=4.17

4.17= how far she ran in 1 second

4.17*7=29.19

Answer:

0.4476

Step-by-step explanation:

Answer:

ture

Step-by-step explanation:

Answer:

y = -3x + 13

Step-by-step explanation:

Assuming the line is linear, you can use the point-slope equation of a line.

(y - y) = m (x - x)

The y and x variables come from the points on the line. Points are written in the form (x, y). In the point (2,7), 2 is x and 7 is y.

1. Plug your points in.

(7 - - 2) = m (2 - 5)

2. Solve for m (the slope)

(7 + 2) = m (2 - 5)

(9) = m (-3)

9 = -3m

m = -3

3. Write an equation of the line with the slope you found.

You can write this equation in different forms, but I'll use the slope-intercept form.

y = mx + b

You'll have to find b, the y-intercept. You can plug one of your points in for x and y as well as your slope, m, and solve for b.

7 = -3(2) + b

7 = -6 + b

b = 13

Therefore, the equation is y = -3x + 13

The solution is Option B.

The angle ∠AEC is a right angle by definition of perpendicular bisector

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as AB

Let the second line be represented as CD

Now , AB is perpendicular to the line CD

where , the measure of ∠CEB = 90°

And , angles on a straight line has a sum of 180°

So , the measure of ∠AEC is a right angle by perpendicular bisector theorem

Hence , the measure of the perpendicular angle ∠AEC is 90°

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Answer: Definition of Perpendicular Bisector

Step-by-step explanation:

Took the test!

The absolute value inequality that models the cost x, in dollars, of a ticket is given by the following option:

C. |80 − 5x| ≤ 4.

The absolute value function y = |f(x)| gives the distance of any point of the function f(x) from the origin.

Jamie is buying 5 concert tickets, each for a cost of x dollars, hence the total amount that he plans to spend is given as follows:

5x.

The difference between 80 and the amount spent of 5x must be of at least 4, either above or below 80, hence the inequality that describes the situation is given as follows:

|80 - 5x| ≤ 4

This means that the correct option in the context of this problem is given by option C.

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The value of x that satisfies the equation is x = 15/8, which is equivalent to 1.875.

To solve the equation (2/3)x - (1/5)x = x - 1 and find the value of x, we can follow these steps:

Combine like terms on the left side of the equation:

(2/3 - 1/5)x = x - 1

Find a common denominator for the fractions on the left side. The common denominator for 3 and 5 is 15, so we rewrite the equation as:

(10/15 - 3/15)x = x - 1

Simplify the left side of the equation:

(7/15)x = x - 1

To eliminate the fraction, we can multiply both sides of the equation by the denominator of the fraction, which is 15:

15 * (7/15)x = 15 * (x - 1)

This simplifies to:

7x = 15x - 15

Subtract 15x from both sides of the equation to isolate the x term:

7x - 15x = -15

Simplifying further:

-8x = -15

Divide both sides of the equation by -8 to solve for x:

x = (-15) / (-8)

Simplifying the division:

x = 15/8

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The x-axis is the horizontal center line on the coordinate plane (left to right). The y-axis is the vertical center line on the coordinate plane. The point where the x and y axis interact, identified by 0, is called the origin.

This point is located at coordinates (0,0). The x-axis is usually associated with the horizontal axis in a two-dimensional graph and is typically used to represent different categories of data. The y-axis is associated with the vertical axis and is used to represent a range of values from high to low.

The formula for determining the coordinates of a point is (x,y). The x-coordinate is the distance from the origin on the x-axis and the y-coordinate is the distance from the origin on the y-axis. For example, if a point has an x-coordinate of 4 and a y-coordinate of -3, the coordinates of the point would be (4,-3). To calculate the distance between two points, you can use the distance formula, which is the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates. For example, if the coordinates of point A are (2,3) and the coordinates+ of point B are (7,1), the distance between A and B would be calculated by taking the square root of (5-2)^2+(1-3)^2, which would equal 5.

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Answer:

Your answer is 28

Step-by-step explanation:

1/2 of 4 = 2

2 (5+9)

2 (14)

28

Answer:

b

Step-by-step explanation:

BRAINIEST PLLLLLLSSSSSS

Answer:

  all positive numbers

Step-by-step explanation:

You want to know the domain of the log function.

The log function ln(x) is defined for all x > 0. A log function with any other base is similarly defined.

  log function domain: all positive numbers

A parent log function has a vertical asymptote at x=0, and an x-intercept at x=1. Its vertical scaling will depend on the base of the logarithm. Like any function, it can be translated and scaled horizontally and vertically.

__

Additional comment

In the field of complex numbers, the log function is defined for any non-zero number. For example, ln(-1) = πi.

The range is all real numbers.

The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

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Answer:

24y^3-6y^2-30

Step-by-step explanation:

6y(-5-y+4y^2)

-30y-6y^2+24y^3

Put in the correct order

24y^3-6y^2-30

{(-4, 3), (5, -1), (0, 2), (x, y)} set of ordered pairs (1, -3) could represent a linear function.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

For option A:

m=1+2/3-1=3/2

m=3/2

m=7-4/8-5=3/3=1

Slopes are not same

For option B:

m=3-6/-3+6=-3/3=-1

m=0-3/0+3=-1

m=-4/3

Slopes are same

Slopes are same at every point, so this set of ordered pairs could represent a  linear function

Hence, the correct option is B.

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Answer:

22cm

Step-by-step explanation:

Circumference of a circle = 2πr

π = 22/7

r = 3.5

Circumference of a circle = 2 × (22/7) × 3.5

Circumference of a circle = 22cm.

Answer: 1 inch = 9 yards

Step-by-step explanation:

From the question, we are informed that Rita drew a scale drawing of a picnic area near the river and that the picnic area, which is 135 yards long in real life, is 15 inches long in the drawing.

From the above, we can see that for every 1 inch, there are (135/15) = 9 yards. Therefore, the scale used Is:

1 inch = 9 yards

Answer:

153.94 in²

Step-by-step explanation:

The equation for Area is

Area = πr²

Plugging in the value for the radius into r, it will be

(note, r means radius)

Area = π(7)²= 49π ≈ 153.94

The units is -> in² so add that in the end

The scalar potential function of the vector field f=e^(-yi)-xe^(-y)j is f(x,y)=-xe^(-y)+e^(-yi)+C, where C is a constant. The line integral over any smooth path c connecting a(0,0) to b(1,1) is f(1,1)-f(0,0)=e^(-i)+1.

To find a scalar potential function f for the given vector field f = e^(-yi) - xe^(-y)j, we need to find a function F(x, y) such that the partial derivatives of F with respect to x and y are equal to the components of f:

∂F/∂x = e^(-yi)

∂F/∂y = -xe^(-y)

To find F, we can integrate the first equation with respect to x, treating y as a constant:

F = ∫e^(-yi) dx = xe^(-yi) + g(y)

where g(y) is an arbitrary function of y. Now, we can take the partial derivative of F with respect to y and set it equal to the second component of f:

∂F/∂y = -xe^(-y) + dg(y)/dy = -xe^(-y)

Solving this differential equation, we find that g(y) = e^(-y) + C, where C is a constant. Therefore, the scalar potential function for the vector field f is:

F(x, y) = xe^(-yi) + e^(-y) + C

To evaluate the line integral of f over any smooth path c connecting a(0,0) to b(1,1), we can use the fundamental theorem of line integrals, which states that if f is a conservative vector field with scalar potential function F, then the line integral of f over any smooth path from point A to point B is given by the difference in the values of F at B and A:

∫c f · dr = F(B) - F(A)

In this case, A = (0,0) and B = (1,1), so we have:

F(A) = 0e^(0i) + e^0 + C = 1 + C

F(B) = 1e^(-i) + e^(-1) + C = e^(-i) + e^(-1) + C

Thus, the line integral over c is:

∫c f · dr = F(B) - F(A) = e^(-i) + e^(-1) - 1

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11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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Answer:

MAD - mean absolute deviation is indication of the distance of data points from the mean.

Data set B shows the greater variability since has greater MAD.

It means the B data set is more spread compared to A data set.

Answer:

Step-by-step explanation:

eazy 102