Triangle DEF is rotated 60⁰ clockwise about the vertex to obtain triangle LMN. if the m

Explanation:

Step 1. We are given the graph of a line and we need to find the equation of the line parallel to it that has an x-intercept of -3.

Since the new line will be a parallel line it means that it will have the same slope. Therefore, our first step is to find the slope of the current line.

Given any line, we find the slope as shown in the following example diagram:

Step 2. Using the previous method, the slope of our line is:

The new line will have the same slope of 2/3.

Step 3. We are also told that the x-intercept of the new line is -3, which means that the new line will cross the y-axis at x=-3, that point is:

(-3,0)

We will label that point of our new line as (x1,y1):

Step 4. So far, we know that the new line will have a slope of 2/3:

And that it includes the point (-3,0) where x1=-3 and y1=0.

To find the equation, we use the point-slope equation:

Step 5. Substituting the known values into the formula:

Solving the operations:

Answer:

Given a midline of 4, an amplitude of 3 and a period of 2/3 we are asked to write a sine function.

Explanation

The equation of a sine function is given as

Where A is the amplitude, T is the period and B is the midline of the sine function.

Therefore, we will have;

Answer:

Answer:

D.

Explanation

We know that g(x) = f(1/2x)

Additionally, the graph of f(x) passes through the point (-2, 0) and (2, 0).

It means that f(-2) = 0 and f(2) = 0

Then, g(-4) = 0 and g(4) = 0 because

Therefore, the graph of g(x) will pass through the points (-4, 0) and (4, 0). Since option D. satisfies this condition, the answer is graph D.

[tex]\frac{4}{5}[/tex].

[tex]1+\frac{2}{5} -\frac{6}{10}[/tex]

A common denominator is just a number that can be used as a denominator all fractions when we convert them through multiplications. A common denominator is usually found just by multiplying all denominators of all fractions. In this case, we don't need to go that far, since 5 could be a common denominator.This is how you do it:

[tex]1=\frac{1}{1} *\frac{5}{5}=\frac{5}{5} \\ \\\frac{2}{5}= \frac{2}{5}\\\\\frac{6}{10} =\frac{6/2}{10/2}=\frac{3}{5}[/tex]

[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5} =\frac{5+2-3}{5} =\frac{4}{5}[/tex]

[tex]1+\frac{2}{5} -\frac{6}{10}=\frac{4}{5}[/tex].

[tex]\frac{4}{5}[/tex].

[tex]1+\frac{2}{5} -\frac{6}{10}[/tex]

A common denominator is just a number that can be used as a denominator all fractions when we convert them through multiplications. A common denominator is usually found just by multiplying all denominators of all fractions. In this case, we don't need to go that far, since 5 could be a common denominator.This is how you do it:

[tex]1=\frac{1}{1} *\frac{5}{5}=\frac{5}{5} \\ \\\frac{2}{5}= \frac{2}{5}\\\\\frac{6}{10} =\frac{6/2}{10/2}=\frac{3}{5}[/tex]

[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5} =\frac{5+2-3}{5} =\frac{4}{5}[/tex]

[tex]1+\frac{2}{5} -\frac{6}{10}=\frac{4}{5}[/tex].

We have the next system of equations

2x+3y=0 ...(1)

6x+9y=0 ...(2)

I order to solve this system by elimination we will multiply the first equation by -3

So we will have

-6x-9x=0

then we add the equation above with the second equation

-6x-9x=0

+6x+9y=0

As we can see we obtain 0=0 which means that we have infinity solutions

ANSWER

Infinity solutions

Given the function

The graph of the function is dhoe below

Advanced tickets(x): $15

Same day tickets(y) : $30

For one more performance there are 55 tickets sold

x+ y= 55 (a)

The total amount paid for them was 1275

15x+30y= 1275 (b)

System of equations:

x+y= 55 (a)

15x+30y = 1275 (b)

Solve for x in (a)

x=55-y

Replace x on (b)

15(55-y)+30y = 1275

82

There are different graphs of polynomial functions. In terms of shape, it can go from a straight line, slanting line, parabola, to curvy graphs especially when we are graphing polynomial functions with degrees 3 or higher.

See examples below:

However, what is similar to these graphs is that each graph is continuous or has no breaks and the domain of every polynomial function is the set of all real numbers.

hello

the question given request we write an equivalent expression as the one given which is

an equivalent expression to the one above would be

so, we can say

From the information provided we will have that the predictions will be:

*Line of best fit:

So, the extrapolation from the line of best fit is 4.9 sold.

*Curve of best fit:

So, the extrapolation for the curve of best fit is 32.2 sold.

Given function,

f(x) = 6x - 6

or

y = 6x -6

The inverse of a function is calculated by replacing the values of x and y

therefore

Inverse (y = 6x - 6)

x = 6y - 6

x + 6 = 6y

6y = x + 6

y = x/6 + 6/6

y = 1/6*x + 1

or

g(x) = 1/6*x + 1

Hence, both are inverse of each other.

Solution

- The solution steps are given below:

Final Answer

The answer is 16

Answer

Options A and C are correct.

The triangle is a Scalen triangle and it is also an Acute triangle.

Explanation

To answer this question, we first explain what these type of triangles are

According to side lengths,

- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.

- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.

- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.

According to the angles,

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

For this triangle,

We can see that all of its sides have different lengths. Hence, the triangle is a Scalene triangle.

Also, each of the angles of the triangle is less than 90 degrees. Hence, the triangle is an Acute triangle.

Hope this Helps!!!

option B

The cost of renting per hour = $2

For 1 hour = $2

For each additional hour, it is $1

For 2 hours = First hour + 1(additional hour)

For 2 hours = $2 + $1(1) = 2+1 = $3

For 3 hours = $2 + $1 (2) = 2+2 = $4

For 4 hours = $2 + $1(3) = 2+3 = $5

The graph which shows this rental cost as 2, 3, 4, 5 is option B

Given: Alfred has 12 coins in his piggy bank. Some of the coins are quarters, some are nickels, and have a total of $3.15.

Required: To determine the system of linear equations for the given situation.:

If the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.

Let the tangent function be f(z) = tan (Bz)

The period exists [tex]$P=\frac{\pi}{|B|}$[/tex]

The frequency exists [tex]$F=\frac{1}{P}=\frac{|B|}{\pi}$[/tex].

The period exists inversely proportional to B, therefore, as B increases, the period decreases.

Frequency exists inversely proportional to the period, therefore, as the period decreases, the frequency increases.

When B is negative, we get f(z) = tan -Bz = f(-z), therefore, the function exists reflected over the y-axis, as the graph at the end of the answer shows, with f(z) exists red(B positive) and f(-z) exists blue(B negative).

As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B exists negative, the graph of the function reflects over the y-axis.

To learn more about the frequency of the function refer to:

https://brainly.com/question/27195128

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The most appropriate choice for LCM of two numbers will be given by -

All the friends together can eat lunch on  14th December 2023.

What is LCM?

LCM means Lowest Common Multiple. LCM of two numbers a and b is the least number that is divisible by both a and b.

Friend 1 eats lunch together at Chipotle everyday including weekends

Friend 2 eats lunch together at Chipotle every other day including weekends

Friend 3 eats lunch together at Chipotle every third day including weekends

Friend 4 eats lunch together at Chipotle every fourth day including weekends

Friend 5 eats lunch together at Chipotle every fifth day including weekends

Friend 6 eats lunch together at Chipotle every sixth day including weekends

Friend 7 eats lunch together at Chipotle every seventh day including weekends

Number of days after which all the friends together can eat lunch

= LCM of 1, 2, 3, 4, 5, 6, 7 = 420 days

All the friends together can eat lunch after 420 days

All the friends together can eat lunch on =

(31 - 20) + 30 + 31 + 31  + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 +14 = 14th December 2023

To learn more about LCM of two numbers, refer to the link -

https://brainly.com/question/16054958

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In the expression 3/3=_/21, it can be observed that 7 is multipled by denominator 3 in order to obtain 21 in in denominator. So same number, 7 is also multiplied with the numerator also.

So, 21 is to be filled at blank space.

The parental function of the graph is,

The transformed function of the graph is,

The transformation between the parent function and the transformed function will be resolved graphically.

From the graph above, the parent function is represented with red while the transformed image is represented with green colour.

We can conclude that the parent function was shrinked horizontally by 1/2.

Hence, it shrinks the graph horizontally to 1/2 the original width.

The correct option is Option

Notice that XZ = XY + YZ

where XY = 5m

YZ = m and XZ =25

Thus,

25 = 5m + m

25 = 6m

Hence,

But YZ = m

Therefore, YZ =

Question:

Solution:

Step 1: Find the equation of a line:

Notice that the line passes through the point (x2,y2)= (4,-2) and (x1,y1)=(0,3). Then, the slope of this line would be:

now, notice that the y-intercept of this line is b=3. Then, the equation for this line is:

Step 2:

note that the shaded region is all points on the line and those above it. So, the shaded region can be represented by the following inequality:

and it is shown graphically like this:

So that, we can conclude that the correct answer is:

Problem

Which of the following equations represents a line that passes through the

points (6,-5) and (-6, -7)?

Solution

For this case the equation for a line is given by:

y= mx +b

And we can find the slope m with this formula:

And replacing we got:

Then we can find the intercept with this formula:

-5 = 1/6 (6)+b

And solving for b we got:

b= -5-1 =-6

And our equation would be:

y= 1/6 x -6

And the best option would be:

I.

Given

The graph

Two boundary points

Answer:

Step-by-step explanation:

fog(x)=3(-x+1)^2+5

         =3(x^2+2x+1)+5

        =3x^2+6x+3+5

fog(x)   =3x^2+6x+8

gof(x)=-(3x^2+5)+1

        =-3x^2-5+1

gof(x)=-3x^2-4

gof(-1)=-3(-1)^2-4

         =-3-4

gof(-1) =-7

Perpendicular line are reciprocals

slope of the original line = -1/9

slope of the perpendicular line = 9

Answer: No solutions

Step-by-step explanation:

[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]

However, as absolute value is non-negative, there are no solutions.

For this type of problems we use the formula for the volume of a pyramid:

Substituting h=12 yd and knowing that the area of a square is side*side we get that:

Let me check your question

T= the period = 6.28

_________________

Answer

L= 32

Answer:

Step 1 of 2:
-26x - 5 = x - 56

Step 2 of 2:
17/9   or 1.89

Step-by-step explanation:

1. Putting word statement in algebraic form

Step 1:
Let x be the unknown number ==> x is the unknown variable to be used in the equation and to be solved for

Step 2:
-26 times a number minus 5 ==> -26x - 5

Step 3:
is equal to 56 less than the number  ==> = x - 56

Putting it all together:
-26x - 5 = x - 56

2. Solving the equation
-26x - 5 = x - 56

1. Subtract x from both sides:
-26x - 5 - x = x - x  -56

-26x -x - 5 = -56

-27x - 5 = -56

2. Add 5 to both sides
-27x - 5 + 5 = -56+ 5

-27x = -51

x = -51/-27   (dividing both sides by -27)

x = 51/27    (negative divide by negative results in positive)

Reduce 51/27 by dividing numerator and denominator by 3

x = (51 ÷ 3)/(27 ÷ 3) = 17/9

= 1.88888.... = 1.89 rounded to two decimal places