the graph of g(x) is the graph of f(x)=8x+20 stretched horizontally by a factor of 4.

Which equation describes the function g?

1. g(x)= 8x+5
2. g(x)= 2x+5
3. g(x)= 32x+20
4. g(x)= 2x+20

Answer:

Option D is correct .i.e., Vertical translation down 9 units

Step-by-step explanation:

Given Function is y = cosec x - 9

Here basic function or parent function is y = cosec x

1. When constant ' a ' is added to to parent function or basic function then the function is translated vertically upward by a units.

2.  When constant ' a ' is subtracted from parent function or basic function then the function is translated vertically downward by a units.

Therefore, Option D is correct .i.e., Vertical translation down 9 units

The generic form of straight line consisting of slope and y intercept  is given by

y = mx + c

Where 'm' is the slope of the straight line  and 'c' is the y-intercept

In the problem, it is given that slope of the line is 2/3 and y intercept is -2 :

m = ²/₃

c = -2

By putting these values in the equation above, we get:

y = ²/₃x - 2

Hence, the second option is correct.  

Hope it helps ..!!

Thank you :)

Answer:

only 3 lines of symmetry does an equilateral triangle have.

Explanation:

Since a triangle can have 3 or 1 or no lines of symmetry.

In a equilateral triangle:

*All sides are equal

*All angles are equal i.e each of 60 degree.

Symmetry is  when there is an exact replica or reflection of a shape or a line.    

Line of symmetry: It is an imaginary line that runs through the center of a line or shape creating two perfectly identical halves.

A line of symmetry for a given triangle must go through each vertex as shown in figure;

Therefore, the equilateral with 3 sides equal has 3 lines of symmetry.

An equilateral triangle has [tex]\fbox{\begin\\\ 3\text{lines}\\\end{minispace}}[/tex] of reflection symmetry.

Further explanation:

A triangle is a two dimensional closed figure which is formed when three non-collinear points are joined. There are three sides, three angles and three vertices of a triangle.

On the basis of sides and angles triangles are classified as follows:

1) Scalene triangle: A triangle in which all the sides and the angles have a unique value is called a scalene triangle.

2) Isosceles triangle: A triangle in which any two sides or two angles are equal then the triangle is called an isosceles triangle.

3) Equilateral triangle: A triangle in which all the sides and the angles are equal then the triangle is called an equilateral triangle.

A line of reflection is defined as a line across which the image of a figure or an object is reflected.

The reflected image is of same size as of the original image.

In case of an equilateral triangle if we drop a median from one of the vertex of the triangle to its opposite side then it is observed that the median divides the equilateral triangle into two equal halves.

From figure 1 (attached in the end) it is observed that the median AD of an equilateral trinagle [tex]\triangle \text{ABC}[/tex] divides the triangle into two equal halves.

As per the above statement it is concluded that the median AD is the line of reflection symmetry for the equilateral triangle [tex]\triangle \text{ABC}[/tex].

Now, similarly if we drop a median form the vertex B or C to its opposite side then it is observed that the triangle into two equal halves.

Figure 2 (attached in the end) shows that the median dropped from the vertex B and C divides the triangle into two equal halves.

This implies that the median BD and CD are also the line of reflection symmetry for the equilateral triangle ABC.

So, the total number of lines of reflection symmetry for an equilateral triangle is [tex]3[/tex].

Thus, an equilateral triangle has [tex]3[/tex] lines of reflection symmetry.

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1. A problem to complete the square of quadratic function https://brainly.com/question/12992613  

2. A problem to determine the slope intercept form of a line https://brainly.com/question/1473992

3. Inverse function https://brainly.com/question/1632445  

Answer details

Grade: High school

Subject: Mathematics  

Chapter: Triangles

Keywords: Triangle, isosceles, scalene, equilateral, angles, vertex, non-collinear, reflection, symmetry, line of reflection, line of symmetry, median, reflected image.

To estimate 75 x 5 you first need to round 75 to 80 and then solve the multiplication.

Estimating numbers implies rounding them if possible to simplify mathematical operations. Let's then round the numbers given:

75 = It can be rounded to 80, which is the nearest multiple of 10.

5 = It does not need to be rounded as this is already a simple number

Now after rounding each of the numbers involved, let's solve the mathematical operation, which in this case is multiplication.

80 x 5 = 400

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Answer: (-2,7)

Step-by-step explanation:

Answer:

[tex]\large\boxed{551.5\%=5\dfrac{103}{200}}[/tex]

[tex]\large\boxed{0.5\%=\dfrac{1}{200}}[/tex]

[tex]\large\boxed{350\%=3\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\27)\ 551.5\%=\dfrac{551.5}{100}=\dfrac{551.5\cdot10}{100\cdot10}=\dfrac{5515}{1000}=\dfrac{5515:5}{1000:5}=\dfrac{1103}{200}=5\dfrac{103}{200}\\\\29)\ 0.5\%=\dfrac{0.5}{100}=\dfrac{0.5\cdot10}{100\cdot10}=\dfrac{5}{1000}=\dfrac{5:5}{1000:5}=\dfrac{1}{200}\\\\31)\ 350\%=\dfrac{350}{100}=\dfrac{35}{10}=\dfrac{35:5}{10:5}=\dfrac{7}{2}=3\dfrac{1}{2}[/tex]

Let

a-------> the shorter side of the rectangle

b------> the longer side of the rectangle

we know that

[tex]b=3a[/tex]

therefore

the dimensions of the rectangle are

[tex]3a*a[/tex]

the answer is

the coordinates of the top-right vertex are [tex](3a,a)[/tex]

The numbers in decreasing order as 76.343, 76.342, 76.332, 76.232.

Descending order is defined as when numbers (or other items) are arranged from the largest numbers to the least numbers, it is said to be in descending order.

Ascending order is defined as when numbers (or other items) are arranged from the least numbers to the largest numbers, it is said to be in ascending order.

we have the given numbers as

76.342, 76.332, 76.232, 76.343

Here the largest numbers to the least numbers, it is said to be in descending order.

⇒ 76.343 > 76.342 > 76.332 > 76.232

we have to determine the descending order of given numbers

Arrange the numbers in decreasing order.

⇒ 76.343, 76.342, 76.332, 76.232

Hence, the numbers in decreasing order as 76.343, 76.342, 76.332, 76.232

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To determine how long it will take for $4000 to grow to $10000 with an interest rate of 9% compounded monthly, we can use the formula for compound interest and solve for t. The time t is approximately 7.17 years.

To find out how long it will take for $4000 to grow to $10000 at an interest rate of 9% compounded monthly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = total amount after time t
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

By plugging in the given values, we can solve for t:

$10000 = $4000(1 + 0.09/12)^(12t)

Dividing both sides by $4000, we get:

2.5 = (1 + 0.0075)^(12t)

Taking the natural logarithm of both sides, we have:

ln(2.5) = ln(1.0075)^(12t)

Using logarithmic properties, we can isolate t:

12t = ln(2.5) / ln(1.0075)

t = ln(2.5) / (12 * ln(1.0075))

Calculating the value of t, we find that it will take approximately 7.17 years for the account to reach $10000.

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Answer:

[tex]\$\,1.19[/tex]

Step-by-step explanation:

Quantity of apples bought by the student = 8.9 pounds

Amount paid by the student for apples bought by the student = [tex]\$[/tex] 10

If cost of one pound of apples is [tex]\$[/tex] 0.99  then cost of  8.9 pounds = 0.99 × Quantity of apples bought by the student = [tex]8.9\times 0.99=8.811[/tex]

Therefore,

Amount of change that the student receive if the apples are .99 per pound = Amount previously paid by the student for apples bought by the student when the student pays [tex]\$[/tex] 10 - Amount  paid by the student for apples if the apples are .99 per pound = [tex]\$ \,10-\$ \,8.811=\$\,1.19[/tex]

if the function is mirrored about the y axis, it is even

 use -x in place of x and compare the equations

lets use 2 for x

 so given formula would be 5-3(2) = 5-6 = -1

replace x with -x you would have 5-3(-2) =5-(-6) = 5+6 =11

since -1 does not = 11 the function is neither

even =f(x), odd = -f(x), neither f(x) doesn't equal -f(x)

example of odd:

f(x) = x^5 +x, replace x with -x

f(-x) = (-x)^5 +-x

=-x^5-x

=-(x^5+x)

=-f(x)

ODD

Example of even:

f(x) = 1-x^4

f(-x) = 1-(-x)^4

=1-x^4

=f(x)

EVEN

Example of Neither:

f(x) = 2x-x^2

f(-x) = 2(-x)-(-x)^2

=-(2x+x^2)

does not equal f(x)

NEITHER

Increasing the sample size by a factor of 4 or multiplying it by 4 is equal to increasing the standard error by 1/2.  Therefore, the interval will be half as varied.  This also works almost for population averages as lengthy as the multiplier from the t-curve doesn't modify much when increasing the sample size.