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Add the polynomials:

Removing the parentheses:

Collecting like terms:

Find the opposite of:

We change the signs of all terms:

Subtract:

Remove the parentheses, but the last one requires changing the signs of the second polynomial (find the opposite):

Collecting like terms:

Let's compare the given function with the model for a quadratic equation:

Since the value of a is positive, the parabola has its concavity upwards, and the function has a minimum value.

The minimum value can be found calculating the y-coordinate of the vertex:

Therefore the minimum value is -24.

For the Rhombus you know that:

The opposite sides are parallel

All sides have equal length

Its diagonals bisect each other in right angles

You can calculate the area of the Rhombus by either mutiplying its whide by its length, and sice its 4 sides are of equal lenght, the area will be equal to the square of one of it's sides (s):

Or using its diagonals (d1 and d2) you can calculate its area as:

isosceles triangle

Explanation

we have a triangle with two equal angles

An isosceles triangle, therefore, has both two equal sides and two equal angles

d = 9rt

9 and r are multiplying on the right, then they will divide on the left

You have the following equation:

9x - 5y = 6

In order to find the equation of the line, you first calculate the slope of the previous line equation:

9x - 5y = 6 subtract 9x both sides

9x - 9x - 5y = 6 - 9x simplify

-5y = -9x + 6 divide by -5 both sides

-5y/(-5) = -(9/5)x + 6/5 simplify

y = -(9/5)x + 6/5

y = -1.8x + 1.2

Then, the slope of the line is m=-1.8

Now, to find the equation of the line with the point (6,-2) you use the following formula for the slope of a line:

m=(y-yo)/(x-xo)

due to the required line is parallel to the line with slope -1.8, the slope of the required line is the same, m = -1.8. xo and yo are the given coordiantes of the given point (6,-2), that is, xo = 6 and y = -2. You replace these values into the formula for the slope and solve for y:

m = (y - (-2))/(x - 6) = (y + 2)/(x - 6) multiply both sides by (x-6)

(x-6) m= y + 2

y = mx - 6m - 2 = (-1.8)x - 6(-1.2) - 2

y = -1.8x - 5.2

This last equation is the required equation

Daniel will not going to get a bag

why?

lets read the statement, a part of it

person who donates more than $5 to charity

the key word here is more,

daniel donates exact 5 dollars,

so he will not get a bag

Courtney cant get a bag, because she donates even less,

to get a bag you need to donate, according to the statement , 5 dollars or more,

so for example, you need to donate 5.01 dollars to get a bag

Corresponding parts of the congruent triangles are congruent. This implies that the corresponding part of the triangles are equal

Also, all the four angles are congruent and they are equal to 90 degrees.

The diagonals are perpendicular to each other

The group of points (1, 2). (5,2), (5,4), (7,6). (11, 6) (11,8) is not a function as it doesn't satisfy the condition that there is one and only one value in the image space for every element in the domain.

We have the points (5, 2) and (5, 4), which shows two values (y=2 and y=4) for the same point in the domain (x=5).

It also happens for (11, 6) and (11,8).

ANSWER

The algebraic equation of the total price T is T = 3p + 2p or (6.50 = 3p + 2p)

STEP-BY-STEP EXPLANATION:

Given parameters

• Cost of still water per bottle = $p

• Cost of sparkling water per bottle = $p

• The number of sparkling water bottles purchased = 2

• The number of still water bottles purchased = 3

• The total amount of money spent altogether = $6.50

As you can see from the question, Ben and his friend spent $6.50 altogether to purchase 2 bottles of sparkling water and 3 bottles of still water. This implies that the total cost is $6.50

Total cost = (number of still water bottles x cost per bottle) + (number pf sparkling water bottles x cost per bottle)

Let the total cost be T

Mathematically, this can be written as

T = (3 * p) + (2 * p)

T = 3p + 2p

Recall that, T = $6.50

6.50 = 3p + 2p

Hence, the algebraic equation of the total price T is T = 3p + 2p or (6.50 = 3p + 2p)

Harry sold 8 smalls cars out of 11 cars.

At the end of the sale He sold 33 cars.

In order to determine how many small cars did Harry sell in the week, you take into account that the proportion of small cars for each sale is 8/11.

To find the total small cars sold in the week you multiply the proportion of small cars by the total cars sold in the week, just as follow:

(8/11)33 = 8(33/11) = 8(3) = 24

Hence, the small cars sold during the week were 24.

c. 24

The time that it took Ella to finish the race is: 37.6 minutes.

Since Miranda finished the race 9 1/10 minutes sooner, to find Miranda's time we need to subtract 9 1/10 from Ella's time of 37.6 minutes.

Miranda's time:

To solve the problem it is easier if we convert 9 1/10 to a decimal number. Since 1/10 is equal to .1, the equivalent value of 9 1/10 is:

Updating the expression to find Miranda's time:

And the result of the subtraction is:

It took Miranda 28.5 minutes to finish the race. Since this value is not one of our options, the answer is D. not here

From the given information, since AB is congruent to BC then triangle ABC is issoceles,

therefore, the base angles measure the same and they are denoted by x. Since interior angles of any triangle add up to 180, we have

which gives

Then, each base angle measure 53 degrees.

On the other hand, since DA bisects angleEAC then angle DAC measure the same as angle EAD, that is,

Therefore, angleEAB is equal to

By substituting our last result, we have

then, the answer is 141 degrees

The given expression : g(x) = -7x+4

to find the value of g(2)

Substitute x = 2 in the function of g(x)

g(x) = -7x + 4

g(2) = -7 (2) +4

g(2) = -14+4

g(2) = -10

Answer : -10

A box plot is a standardized way of displaying the distribution of data based on a five-number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”).

The points at the beginning and end of the graph show the outliers (minimum and maximum values).

The outer lines on the left and right of the box show the first quartile and third quartile respectively, while the line inside the box is the median.

From the question, the third quartile (Q3) is the outer line to the right of the box, and its value is 29.

Therefore, OPTION D (29) is correct.

Given: eighty-two million, eighty thousand, eleven

To Determine: The standard notation of the given number

Solution

Let us first write the numbers in figure

Please note Standard notation of a number is when a number is written with only number digits

Hence, the standard notation of the given is 82, 080, 011

Answer:

$375,000.

Explanation:

Let the value of the house when it was purchased = x

If its value increases by 32%, then its current value will be:

Since we are told that the current value is $495,000, then:

We solve for x.

The value of the house when it was purchased was $375,000.

lan's mom work for total 35 hours in 5-days week, so each day she worked for,

So Ian's mom worked 7 hours each, in which she work 4 hours each morning.

Determine the number of hour's Ian's mom work in afternoon in one day.

So each day Ian's mom work 3 hours in the afternoon.

Please check that the expression for the cost you typed reflects what you read in the problem.

Isn't there a "square" in one of the "x" values of the cost equation?

Great. I see now the actual equation for cost to be:

Cost = 0.3 x^2 - 66 x + 13267.

The minimum unit cost will be given by the minimum of this quadratic function (a parabola) which has a minimum at the parabola's vertex. Notice this is a parabola with branches pointing UP because the coefficient of the term in x^2 is POSITIVE.

Recall then the equation for the x position of the vertex of a pparabola with equation of the form:

y = a x^2 + b x + c

the x-position of the vertex is: x = - b / (2a)

which in our case gives:

x of the vertex = - (- 66) / (2 * 0.3) = 110

Then, since the x values represent the number of cars that are made , we now that that minimum occurs when the number of cars produced is 110.

We replace this value in the cost equation and get:

Cost = 0.3 (110)^2 - 66 (110) + 13267 = 9637

Then, the unit cost for making the 110 cars is $9637, which is in fact the minimum value we were looking for.

The translation rule that matches the transformation for congruent angles is given as follows:

(x,y) -> (x + 4, y - 5).

The translations are movements to the triangle in each of these directions:

There were two translations in this problem, listed as follows:

For the first translation, the triangle was moved down five units, hence the rule is given as follows:

y -> y - 5.

For the second translation, the triangle was moved right four units, hence the rule is given as follows:

The complete translation, obtained by the combination of each translation, is given as follows:

(x,y) -> (x + 4, y - 5).

Meaning that the first option is the correct option.

More can be learned about translations at brainly.com/question/28174785

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we have that

the aprent function

f(x)=x^2

g(x) is a reflection over x -axis of the parent function with a vertical dilation

so

g(x)=-ax^2

Find the value of the leading coefficient a

looking at the graph

For x=1

the value of g(x) is -4

therefore

We can compute the growth percentage, computing first, two consecutive values, as follows:

Then, the growth percentage is:

There are two kinds of like terms:

• Variable like terms: These are the terms that have the same variable. For example, 10x and -3x are like terms.

• Independent like terms: are the terms that don't have any variables. For example, 7 and -30 are like terms.

The important thing about like terms is that we can combine them.

The expression we have is:

The terms 8a and -3a are variable like terms because they have the same variable "a", so we combine them by subtracting 8a-3a which results in 5a:

The term 6b does not have any like term because there are no other terms that contain the variable "b", so we leave that term as is.

Now, the terms 16 and -9 are independent like terms, so we can also combine them.

To combine 16 and -9, we subtract 16-9, and the result is7, so we put 7 in the expression in the place of 16-9:

Answer:

5a+6b+7

The range of the function is the values of y

Then to find it, look for the smallest and the greatest value of y of the graph of the function

From the given figure

The lowest value of y is -1

The highest value of y is 3

Then the range of the function is [-1, 3]

Answer:

The value of the simple interest and the total value after three years is;

Explanation:

Given the following;

We want to find the simple interest and the total amount after three years.

The simple interest formula;

substituting the given values;

Therefore, the value of the simple interest and the total value after three years is;

The value of x is 9

Given the equation:

Multiply both sides by 2(x-8)

Divide both sides by 8

Finally, add 8 to both sides

The given expression is

To know the intervals where this function is increasing, we graph it

As you can see from the graph, the increasing intervals are

We have the results of a simulation that consists of 20 trials, they are the following:

5, 2, 7, 2, 3, 4, 10, 6, 4, 6, 3, 6, 6, 4, 8, 5, 7, 7, 1, 5

Each number of the results represent the number of attempts needed to make a basket.

Q) We want to know the probability to have to make at least 5 attempts to make a basket.

A) According to the question, we must compute P(# attemps ≥ 5). We can comput

Find an equation of the line parallel to the graph of y = -3x - 11 that passes through the point of (2,4). Write your equation in slope-intercept form.​

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Line parallel to the graph of y = -3x - 11

1. The slope-intercept form.

y = mx + b

m= slope

y-intercept is (0, b)

The lines parallel has the same slope (m) = -3

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Using the point-slope form

(y-y1)= m (x-x1)

2. Replacing the point and the slope

(2,4) x1= 2; y1 = 4

(y- 4)= -3 (x- 2)

3. Write your equation in slope-intercept form.​

y = -3x +6 +4

y = -3x + 10

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Answer

y = -3x + 10

we reduce the equal terms and we obtain the answer is