Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of f(x)=x^2-5x+1 . Write a rule for g .

Answer:

The perimeter is approximately 6.40.

Step-by-step explanation:

To find the perimeter of a triangle with vertices X (1, 3), Y (-4, -1), and Z (4, -1), we can first find the distance between each pair of points using the distance formula.The distance between points X and Y is:

$d(X,Y) = \sqrt{((1 - (-4))^2 + (3 - (-1))^2)} = \sqrt{25 + 16} = \sqrt{41}$

The distance between points Y and Z is:$d(Y,Z) =

\sqrt{((-4 - 4)^2 + ((-1) - (-1))^2)} = \sqrt{0 + 0} = 0$

The distance between points X and Z is:

$d(X,Z) = \sqrt{((1 - 4)^2 + (3 - (-1))^2)} = \sqrt{9 + 16} = \sqrt{25}$

We can then find the perimeter of the triangle by adding up the lengths of the sides. In this case, the perimeter is $d(X,Y) + d(Y,Z) + d(X,Z) = \sqrt{41} + 0 + \sqrt{25} = \sqrt{41} + \sqrt{25} = 6.40\ldots$.

Rounded to two decimal places, the perimeter is approximately 6.40.

Answer:

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.

The Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:

  c² = a² +b²

  RQ² = PQ² +PR²

  RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root

The distance between planets Q and R is 1.64×10⁷ km.

__

Additional comment

The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.

You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.

Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.

Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)

The distance QR is :

[tex] \qquad \sf \rightarrow d = \sqrt{(1.6 \times 10 {}^{7}) {}^{2} + (3.6 \times 10 {}^{6} ) {}^{2} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{2.56 \times 10 {}^{14} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{256\times 10 {}^{12} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(268.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex]\qquad \sf \rightarrow d = 16.4\times 10 {}^{6} {}^{} [/tex]

The value of x for the expression is equal to -5 and -2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the logarithmic expression is log₂ (x+4) + log₂ (x + 3) = 1. The value of x will be calculated as,

log₂ (x+4) + log₂ (x + 3) = 1

log₂ { (x+4)(x + 3) } = 1

x² + 7x + 12 = 2

x²+ 7x + 10 = 0

Solve the above quadratic equation,

x²+ 7x + 10 = 0

x² + 5x + 2x + 10 =0

x ( x + 5 ) + 2 ( x + 5 ) = 0

(x + 5 ) ( x + 2 ) = 0

x  = -5 and -2

The values of x are -5 and -2.

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The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released. is  

(a)  [tex]0.2$[/tex]

(b) [tex]1.5$[/tex]

[tex]0.2 y+1.5 \longleftarrow \text { initial value }[/tex]

[tex]when $y$ increase one. the value increase $\$ 0.2$[/tex]

Travelling to movies and television programmes. An element of a comic book being in a popular film or television programme is a major factor in its value rising. Characters' comic book appearances have become far more valuable as they are integrated into the Marvel Cinematic Universe.

Marvel's first comic book just sold for $1.26m. Movies have contributed to the enduring popularity of superheroes, bringing in new audiences. The printed comic is still big business, worth over $1bn in North America alone.

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Average rate of growth over this period is 0.4%.

Average rate of growth over a period is given by:

A=P[tex]e^{rT}[/tex] where,

A- Population at time T

P- Initial population

r-average rate of growth

T-Time period

Now, P=250,000, A=310,000 and T=21 (2000-1980+1)

therefore, putting values in the equation, we get:

310,000=250,000[tex]e^{21r}[/tex]

⇒ [tex]e^{21r}[/tex] = 1.24

⇒ 21r = log(1.24)

⇒ r = 0.0044 or 0.4%.

so, the average rate of growth over this time period is 0.4%.

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The average rate of change, in simplest form, is -2/5.

What is average rate ?

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

[tex]m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]

Using the coordinate points from the table (0,41) and (15,35)

Substitute the coordinate into the expression:

[tex]$$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$[/tex]

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The amount of margarine needed in Kg for making biscuits is  0.6kg

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

The amount of margarine needed in Kg is calculated using proportions

If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require

0.225 l  = 0.15 kg

0.9 l = ?

cross multiplying

0.225 * ? = 0.9 * 0.15

? = 0.135 / 0.225

? = 0.6

Angela will require 0.6 kg of margarine

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Answer:

(2½,1)

Step-by-step explanation:

(-1+6/2,5+-3/2)

(5/2,2/2)

(2½,1)

The required original price of the coat is given as £95.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95

Hence, the cost of the coat before the sale is £95.

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The constant amount that Carson makes every hour is $16.25.

It is important to note that this question has to do with a proportional relationship. Since Carson earns $113.75 for 7 hours of work and he makes a constant hourly wage.

The amount that he makes per hour will be:

= Amount / Number of hours

= $113.75 / 7

= $16.25

Therefore the constant amount he makes every hour is $16.25.

Note that the options weren't given but the question has been solved accordingly.

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Answer:

√192

Step-by-step explanation:

12 cos 30° + 2 tan 60°

Substitute the trig functions of the special angles.

12 (½√3) + 2 (√3)

Simplify.

6√3 + 2√3

8√3

Move under the radical.

√(8² · 3)

√192

Answer:

$9,712.12 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies A=9544\left(1+\frac{0.0525}{12}\right)^{12 \cdot \frac{1}{3}}[/tex]

[tex]\implies A=9544\left(1.004375\right)^{4}[/tex]

[tex]\implies A=9544\left(1.017615179\right)[/tex]

[tex]\implies A=9712.119269[/tex]

The balance of the account at the end of August will be $9,712.12 (nearest cent).

Answer:

A.86

is the answer will show how it's solved if necessary on comment.

hope it helps!!!

Answer:

the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Step-by-step explanation:

To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).

Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.

We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.

We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:

y = -3/17 * x + (-3 3/4)

x = (y - (-3 3/4))/(-3/17)

Substituting the coordinates of the corner we found earlier, we get:

x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3

So, the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Answer:

Step-by-step explanation:

The initial height of the rocket before it is launched can be found by evaluating the function h(t) at t=0. To do this, you can substitute 0 for t in the function:

h(0) = -5(0)² + 42(0) + 54

h(0) = 0 + 0 + 54

h(0) = 54

Therefore, the initial height of the rocket before it is launched is 54 meters.

Answer: 54 meters.

Step-by-step explanation: The initial height of the rocket before it is launched is represented by the constant term in the quadratic function, which is 54. This means that the rocket's height at time t = 0 (before it is launched) is 54 meters.

To confirm this, you can plug in t = 0 into the quadratic function to get:

h(0) = -5(0)² + 42(0) + 54 = 54 meters

This means that the initial height of the rocket before it is launched is 54 meters.

The total cost of the meal plus tip and tax was more than 122% of the cost of the bill.

What is percent?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

Indigo goes out to lunch.

The bill, before tax and tip, was $10.85.

A sales tax of 3% was added on.

Indigo tipped 18% on the amount after the sales tax was added.

The amount after adding sales tax is,

$10.85 x 3% = 0.3255

⇒ $10.85 + 0.3255 = $11.1755

Now to find the amount after tipped 18% on the amount after the sales tax was added.

$11.1755 x 18% = 2.01159

⇒ $11.1755 + 2.01159 = $13.18709

Hence, the amount  after tipped 18% on the amount after the sales tax was added is $13.18709.

Let x be the percent of more than the cost of the bill of $13.18709.

⇒

[tex]\frac{10.85(x)}{100} = 13.18709\\ x = \frac{100 (13.18709)}{10.85}\\ x = 121.54[/tex]

Hence, the total cost of the meal plus tip and tax was more than 122% of the cost of the bill.

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The value of x and y at which function P = 3x+2y becomes maximum are

(9,0), data from given graph.

What is the graph?

Graph is the pictorial representation of given data.

Graph is defined as to create a diagram that shows a relationship between two or more things. An example of graph is to create a series of bars on graphing paper.

The four most common are

1. Probably line graphs,

2. Bar graphs and histograms,

3. Pie charts, and

4. Cartesian graphs

To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.

Note: (5,4) is not a vertex.

(0,8) :

P = 3*0 + 2*8

  = 16

(5,4):
P = 3*5 + 2*4

  = 23

(9,0):

P = 3*9 + 2*0

  = 27.

So, the maximum value = 27 at (9,0).

So, the x value = 9 and

      the y value = 0.

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The trigonometric ratio, cos E of the right triangle is 5 / 13.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

A right triangle is a triangle that has one of its angles as 90 degrees.

The sides and angles of a right triangle can be found using trigonometric ratios. The sides of a right triangle base on its sides are as follows;

Therefore,

cos E = adjacent / hypotenuse

Hence,

let's find the hypotenuse side using Pythagoras theorem,

24² + 10² = c²

c = √576 + 100

c = √676

c = 26

cos E = 10 / 26

Therefore,

cos E = 5 / 13

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Answer: 27, 65, 29, 77, 37

Step-by-step explanation:

The number of diagonals of an [tex]n[/tex]-gon is [tex]\frac{n(n-3)}{2}[/tex].

The number of apothems of an [tex]n[/tex]-gon is [tex]n[/tex].

Answer:

Step-by-step explanation:

the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².

What is derivative?

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

given expression p(x)= f(x)/1-f(x)

The derivative of the given expression will be

p'(x) = f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))²

Hence the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².

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Answer:

j = 4

Step-by-step explanation:

calculate the slope of the line passing through the goven points and equate to 2

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 7, - 10 ) and (x₂, y₂ ) = (0, j )

m = [tex]\frac{j-(-10)}{0-(-7)}[/tex] = [tex]\frac{j+10}{0+7}[/tex] = [tex]\frac{j+10}{7}[/tex] then equating gives

[tex]\frac{j+10}{7}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )

j + 10 = 14 ( subtract 10 from both sides )

j = 4

0-4 can be the domain of positive real numbers but can not be the domain of whole numbers.

Numbers an arithmetical value used in counting and calculating that is expressed as a word, symbol, or figure that represents a specific quantity.

Let's understand what is positive real numbers.

That is all the real numbers that are greater than or equal to zero.

real numbers are numbers which include both rational and irrational numbers.

whole numbers are positive integers that mean only positive integers.

that means 0-4 can be the domain of positive real numbers but can not be the domain of whole numbers because 0.5 and 0.6 these numbers are not whole numbers.

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The vertex of the function f(x) = 10.25 |x - 0.75| will be at (0.75, 0).

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The absolute function is given as,

f(x) = 10.25 |x - 0.75|

Compare the function f(x) with standard equation, then we have

h = 0.75

k = 0

The vertex of the capability f(x) = 10.25 |x - 0.75| will be at (0.75, 0).

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The length of the other leg is (c) √43

From the question, we have the following parameters that can be used in our computation:

Hypotenuse = 7

One leg = √6

The length of the other leg can be calculated using

The length of the other leg = √(Hypotenuse^2 - One leg^2)

So, we have

The length of the other leg = √(7^2 - √6^2)

Evaluate

The length of the other leg = √43

Hence, the length is (c) √43

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Complete question

A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.

The equation of the line, in slope-intercept form,  that passes through the given points, (6,-4) and (6,5) is: x = 6.

An vertical line can be written in slope-intercept form as x = a, because the line has no y-intercept and the change in x values in the slope formula is equal to zero.

The value of a in the equation is the point on the x-axis where the vertical line intercept, irrespective of the change in y-values up the line.

Given the line goes through the points, (6, -4) and (6, 5), it means the line is a horizontal line because they both have the same x-value, 6.

Therefore, the value of a is 6. The equation of the line would be x = 6.

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The graphed two lines will have one solution.

Any line that isn't twisted or bent is said to be straight.

Intersecting lines are two or more lines that have exactly one point in common. The point of junction is this central location that connects all of these lines.

A system of Intersecting Lines will have one unique solution

Lines that are parallel to one another on a plane do not overlap or meet at any point. They are always parallel and equally spaced from one another.

A system of Parallel Lines will have no solution

Here we have

System of equations

Given that the two lines are not parallel line

As we can see that both lines meet at a point

So here we can conclude that both lines are Intersecting Lines

Therefore,

The graphed two lines will have one solution.

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