Suppose a parabola has an axis of symmetry at x = -6, a maximum height of 6 and also passes through the point (–5, 4). Write the equation of the parabola in vertex form.

Answer:

Step-by-step explanation:

The general formula for finding the antiderivative of a polynomial function is to add one to the exponent of each term and divide by that new exponent.

To find the antiderivative of y = 5x -6x² +9x³, we need to integrate each term individually, using the general formula:

∫ (5x) dx = (5/1)x^(1+1) = 5x^2 + C

∫ (-6x²) dx = (-6/2)x^(2+1) = -3x^3 + C

∫ (9x³) dx = (9/4)x^(3+1) = (9/4)x^4 + C

So the antiderivative of y = 5x -6x² +9x³ is:

∫ y dx = 5x^2 - 3x^3 + (9/4)x^4 + C

Where C is the constant of integration, which can take any real value.

Answer:

Step-by-step explanation:

a. 47 men

b. 24 men like soda

c. 23 men do not like soda

d. 61 women

e. 26 women like soda

f. 35 women do not like soda

After transformation, the point (-1,2) in the image would be (-1,-2)

Each transformation applied to the prior image is combined into a composition of transformations. The result of a translation is identical to a composition of reflections across parallel lines (twice the distance between the parallel lines). The composite transformation is carried out by multiplying the matrix in order from the right to the left side if it is represented as a column. The output from the preceding matrix is multiplied by the new matrix that will follow.

First, we must mirror the point (-1, 2) around the line y=-x.

(X, Y) is the rule (-y,-x)

you obtain (-1,2)—>(-2,1) (-2,1)

At this point, you must rotate (-2,1) by 90 degrees.

(X, Y) is the rule ( -y,x)

so (-2,1)—> (-1,-2) (-1,-2)

After transformation, the point (-1,2) in the image would be (-1,-2)

The complete question is,

What is the image point of (-1,2) after the transformation R 90° ry=-x

To learn more about composition of transformations refer to:

https://brainly.com/question/25800331

#SPJ1

The mean number of goals for two seasons is 2.44 goals per match.

When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.

To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.

Given, Last season Rio's football team scored 50 goals in 20 matches.

This season they scored 60 goals in 25 matches.

Therefore, The mean number of goals per match for each season is,

= (50 + 60)/(20 + 25).

= 110/45.

= 2.44 goals per match.

learn more about mean here :

https://brainly.com/question/521501

#SPJ1

The slope-intercept form of the equation of the given line which passes through the point (2, 7) and has a slope of 8 is:

     y = 8x - 9

What is meant by slope-intercept form of the line equation?

The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b). One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis) are known, the slope-intercept formula can be used to determine the equation of a line. The equation of a line is the equation that each point on the line fulfils.

Given the line passes through a point  (2,7) and the slope is 8.

When a point on the line and slope are given, the equation of the line is:

y - y₁ = m ( x - x₁)

m = slope  = 8

Substituting,

y - 7 = 8 ( x - 2)

y - 7 = 8x -16

y = 8x - 9

Therefore the slope-intercept form of the equation of the given line is:

     y =  8x - 9

To learn more about slope-intercept, follow the link.

https://brainly.com/question/22057368

#SPJ1

Answer:

(g+f)(x/4) = x^2/16 + 3x/4

Step-by-step explanation:

To find (g+f)(x/4), we must first find the expressions for g(x) and f(x) and then add them together.

g(x) = x^2 + 4

f(x) = 3x - 4

So (g+f)(x) = g(x) + f(x) = x^2 + 4 + 3x - 4 = x^2 + 3x + 0

Now we can substitute x/4 for x in the expression:

(g+f)(x/4) = (x/4)^2 + 3(x/4) + 0

Multiplying it out

(g+f)(x/4) = (x^2/16) + (3x/4) + 0

so (g+f)(x/4) = x^2/16 + 3x/4

Answer: Two times a number y would be represented mathematically as 2*y. It means that a number y will be multiplied by 2 to get the result.

Answer:

y = - 3

Step-by-step explanation:

A line parallel to the x- axis is a horizontal line with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (2, - 3 ) with y- coordinate - 3 , then

y = - 3 ← equation of line

Answer:152+n

Step-by-step explanation:

152 for last year, n for this year. Add them together you get the answer for the total of pies in 2 years

Answer:

175 mins

Step-by-step explanation:

LCM of 25 and 35 is 175 which is when the next bell together will happen.

After adding the expressions (8.5+ 6.25m) and (12 +3.75m) the value is obtained as (20.5 + 10m).

What is an expression?

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

The first expression is - (8.5+ 6.25m)

The second expression is - (12 +3.75m)

Apply the addition operation on the expressions -

= (8.5+ 6.25m) + (12 +3.75m)

= 8.5 + 6.25m + 12 + 3.75m

= 8.5 + 12 + 6.25m + 3.75m

= (20.5 + 10m)

Therefore, the value is obtained as (20.5 + 10m).

To learn more about expression from the given link

https://brainly.com/question/28036586

#SPJ1

Answer:

It may

Step-by-step explanation:

Vertically shift the graph of f(x) up 7 units.

By:-"||Ziddiboy||"

Answer:

Let's use the same information as above to show how a formula can be used to quickly calculate the break-even output.

Remember contribution per unit? Here is a reminder of this crucial and really useful formula:

Contribution per unit = selling price per unit less variable cost per unit

In our example, contribution per unit = £10 less £4 = £6 per unit

Now apply the classic formula for calculating breakeven output:

Break-even output (units) = Fixed costs (£) / Contribution per unit (£)

So, break-even output = £40,000 divided by £6 = 6,666 units

Note: break-even output is always expressed in terms of units

So break-even output = 6,666 units

If the information is available, it is always quicker and easier to use this formula rather than use a table or draw a chart.

The function that is positive for the entire interval [-3, -2] is given as follows:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0).

A function is positive over an interval if the values of y of the function are above zero for the entire interval.

A function is negative over an interval if the values of y of the function are below zero for the entire interval.

For the function in this problem, we have that:

As the function is concave up, it is positive to the left of the smaller root at x = -1, that is, positive for all x < -1, hence the correct option.

More can be learned about positive and negative functions at https://brainly.com/question/1527366

#SPJ1

A system of inequalities that can be used to model the scenario is d + a ≤ 300 and 10d ≥ 1,200.

A system of inequalities is two or more inequalities that must be proved simultaneously.

A system of inequalities contains at least two linear inequalities in the same variables.

Systems of inequalities are applied when there are a range of solutions and more than one constraint.

Inequalities may include greater than, less than, not equal to, equal to but less than, and equal to but greater than.

The total capacity of people the auditorium can hold = 300

The cost per ticket at the door = $10

The cost per ticket in advance = $7.50

Tickets cannot exceed 300

Door tickets must generate at least $1,200

Let the number of tickets sold at the door = d

Let the number of tickets sold in advance = a

10d + 7.5a ≤ 300

10d ≥ 1,200

Learn more about inequalities at https://brainly.com/question/24372553

#SPJ1

The simplified expression of -7(3z + 5t - 3g) is  -21z - 35t + 21g.

An algebraic expression consists of unknown variables, numbers and arithmetic operators such as addition, subtraction, multiplication etc.

To simplify an expression means to write an equivalent expression which contains no similar terms.

Therefore, let's simplify the expression as follows:

-7(3z + 5t - 3g)

Hence, open the brackets

-7(3z + 5t - 3g) = -21z - 35t + 21g

Therefore, the simplified expression is -21z - 35t + 21g.

learn more on expression here:https://brainly.com/question/18077352

#SPJ1

From the coordinates we can see the rule for this transformation is:

It is a dilation by a scale factor of 2 and reflection in the y-axis.

It means this is a similarity transformation, since the figure has changed its size.

Answer:

Dilation of scale factor 2 centered at the origin, followed by a reflection in the y-axis.

Similarity transformation.

Step-by-step explanation:

Given vertices of ΔABC:

Given vertices of ΔA'B'C':

From observation, the series of transformations the transforms ΔABC to ΔA'B'C' are:

This is a similarity transformation as the two triangles have the same shape but different sizes.

Answer: The answer to the computation 348 + 598 is 946.

Step-by-step explanation:

To obtain an estimate for the computation 348 + 598, we can round the two numbers to the nearest ten.

348 rounded to the nearest ten is 350

598 rounded to the nearest ten is 600

So, our estimate for the sum of 348 + 598 is 350 + 600 = 950

Using a calculator, the actual computation is 348 + 598 = 946

Our estimate of 950 is 4 more than the actual answer of 946. This means that our estimate is slightly higher than the actual answer. This is not a big difference and it is reasonable as the numbers are rounded to nearest 10.

Answer:

Nose inglés lo siento xdddddddddddddddddddddd

Answer: y= 5x - 9

Hope this will help

Answer:

y=5x-9

Step-by-step explanation:

In y=mx+b, m is the slope and b is the y intercept all you have to do is replace m and b with the numbers associated in the problem this case since 5 is the slope you put it where m is, and b being the y-intercept you put the -9 there!

Answer:

a) 6a+5 b)4

Step-by-step explanation:

a) 3a+3a+5 = 6a+5

b)6a + 5 = 29

6a = 29-5

6a = 24

6 6

a = 4

Answer:

B. -0.45

Step-by-step explanation:

I'm assuming the values you have provided are pertaining to the correlation coefficient.

The correlation coefficient (r) is used to describe how strongly points are correlated and in which direction they are correlated. This correlation coefficient ranges between -1 and 1: [tex]-1\le r\le1[/tex]

If the correlation coefficient is negative, the correlation is down-sloped or in other words as the variable on the x-axis increases, the variable on the y-axis decreases.

If the correlation coefficient is positive, the correlation is upward-sloped or in other words as the variable on the x-axis increases, the variable on the y-axis also increases.

The strength of the correlation can be analyzed by the absolute value of the correlation coefficient (r). So if you want to compare two correlation coefficients and say which has a stronger correlation, you would first take the absolute value and then compare which is larger as such: [tex]|r|[/tex]

In this case the -0.45 is technically less than the 0.34, although the absolute value indicates it is a stronger correlation, just in a different direction. You can compare all the other options and -0.45 has the largest absolute value.

The annual salary of the man is Rs 780,000 and his total taxes is given by the relation T = Rs 9,000

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Since the man's monthly salary is Rs 65,000, his annual salary would be:

Annual salary = Monthly salary x 12

Annual salary = 65,000 x 12

Annual salary = 780,000

His annual salary of Rs 780,000 falls in the third tax bracket which is from 750,001 to 2,000,000.

So, the tax rate applicable to him would be 30%.

To calculate the amount of tax he would have to pay, we can use the formula:

Tax amount = Tax rate x Taxable income

where taxable income is the income above the lower limit of the tax bracket.

In this case, the taxable income would be:

Taxable income = Annual income - Lower limit of tax bracket

Taxable income = 780,000 - 750,001

Taxable income = 29,999

So, the amount of tax he would have to pay would be:

Tax amount = 30% x 29,999

Tax amount = 8,999.7

Rounding this to the nearest rupee gives us:

Tax amount = Rs 9,000

Hence , the man would have to pay Rs 9,000 in taxes on his annual salary of Rs 780,000.

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

y = 2x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (2, 6 ) and (x₂, y₂ ) = (9, 20 )

m = [tex]\frac{20-6}{9-2}[/tex] = [tex]\frac{14}{7}[/tex] = 2 , then

y = 2x + c ← is the partial equation of the line

to find c substitute either of the 2 points into the partial equation

using (2, 6 ), then

6 = 2(2) + c = 4 + c ( subtract 4 from both sides )

2 = c

y = 2x + 2 ← equation of line

The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) ,

B ' ( 28, 14 ) and C ' ( -7, -7 ) .

What is a graph ?

Graph can be defined as the visual representation which is used to represent the data.

The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.

For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.

The dilation rule can be written as (x, y) -> (7x, 7y)

As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.

Example: side AB = 7 units, side A'B' = 49 units

Hence, The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) , B ' ( 28, 14 ) and C ' ( -7, -7 ) .

To learn more about graph from the given link.

brainly.com/question/17267403

#SPJ1

The expression that describes the sequence is 3 + n.

Let's use an expression to describe the sequence as follows:

4, 5, 6, 7....

The sequence follows an arithmetic patterns. Therefore, let's use an arithmetic progression formula to express the sequence.

Hence,

a + (n - 1)d = nth term

where

Therefore,

a = 4

d = 5 - 4 = 1

Hence,

nth term = 4 + (n - 1)1

nth term = 4 + (n - 1)

nth term = 4 + n- 1

nth term = 3 + n

learn more on sequence here: https://brainly.com/question/29968383

#SPJ1

Answer:

A) The standard formula of the equation of a circle that has a center of (-4,-2) and contains the points (-1,2) is (x + 4)2 + (y + 2)2 = 25.

B) The general formula for the equation of a circle is (x - h)2 + (y - k)2 = r2, where (h,k) is the center of the circle and r is the radius.

Answer:

[tex]\boxed{y = 4x + 7}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

where m is the slope and b the y-intercept

To find the slope, take the two points, find the difference in y values and divide by the corresponding difference in x values

Two points are [tex](- 1, 3)[/tex] and [tex](- 2, -1)[/tex]

Difference in y values [tex]= -1 -3 = -4[/tex]

Difference in corresponding x values [tex]= -2 - (-1) = -2 + 1 = -1[/tex]

Slope

 [tex]m = \dfrac{-4}{-1} = 4[/tex]

So the equation of the line is of the form
[tex]y = 4x + b[/tex]

To find b, take the coordinates of any of the two points and plug the x and y values into the above equation and solve for b

Let's take point (-1, 3)

Plug in values:

[tex]3 = -4 + b\\\\3+4 = b\\ \\b = 7[/tex]

Therefore the equation of the line is
[tex]\boxed{y = 4x + 7}[/tex]

Answer: The solution of the equation is x = 48. The equation is 20 = x - 28.

Step-by-step explanation:

-20 is like having -20 dollars, and you want to know how much you have to add to it to get to 28 dollars. So we add 20 to -28 and we get the number x = 48, so 48 dollars is what we need to add to -20 dollars to get to 28 dollars.

Answer:

x=3

Step-by-step explanation: I'm not 100% if this is it because it's been awhile but I believe that you write 2x+2=4x-4 to solve for x since they're both y=mx+b equations. After solving it you would get 3

Answer:

Step-by-step explanation:

The formula for calculating the time it takes to reach a target amount with a constant periodic deposit is given by

Time = ln(Target Amount / (Periodic Deposit x (1 + Interest Rate)^0)) / ln(1 + Interest Rate)

In this case, we have Target Amount = 500,000, Periodic Deposit = 500, and Interest rate = 7.8%. Plugging the values into the formula gives

Time = ln(500,000 / (500 x (1 + 0.078)^0)) / ln(1 + 0.078)

Time = ln(500,000 / 500) / ln(1.078)

Time = ln(1,000) / ln(1.078)

Time = 8.98 years

Rounding to the nearest tenth of a year, the answer is 8.9 years.