Agrocery store bought milk for $2.20 perhalf gallon and stored it in two refrigerators. During the night one refrigerator malfunctioned and ruined 13 half gallons. If the remaining milk is sold for $3.96 per half gallon, how many half gallons did the store buy if they made a profit of $121.00

To start, we need write the polynomials:

Now we gonna find the difference between first polynomial and second, like this:

tip: Special care with operate signs.

That is the final solution, you can solve that polynomial if you need.

Solution

The function is written in factored form

Using vertical asymptote at x = 3 opposite end behaviour

vert asymp at x=2 same end behavior, bounce off x axis at x=1, y int at -1/2

Therefore the numerator is : -6(x-1)²

The denominator is : (x+3)(x-2)²

1. replace f(x) with y:

2. Replace every x with a y and replace every y with an x:

3. Solve for y:

4. replace y with f-1(x):

Given function:

The minimum value of the function can be found by setting the first derivative of the function to zero.

Solving for x:

Substituting the value of x into the original function:

Hence, the minimum value in the given range is (-1, -0.368)

The area of a parallelogram is given by the equation:

Where b is the base of the parallelogram and h is the height.

In this case, b=1/2 in and h=8in, then:

Therefore, the area of the described parallelogram, is:

Answer:

Subtract 4

Explanation:

In the number pattern:

We subtract the next term from the previous term below:

We see that each one gives a subtraction of 4.

Therefore, the rule of the pattern is 'Subtract 4'.

The are of the octsagon is given by:

where a is the lenght of its side.

Since the second octagon has sile lengths equal to 18.03, its area is:

Therefore the area is 1563.6 squared centimeters

6The mean number of children each team member will bring

Here, we want to get the mean number of students that each team member willl bring

From the histogram, we can deduce the following;

a) 4 team members will bring no (0) children

b) 3 team members will bring 1 children each

c) 5 team members will bring 2 children each

d) 2 team members will bring 3 children each

e) 1 team member will bring 5 children

So the totla number of children at the party will be;

4(0) + 3(1) + 5(2) + 2(3) + 1(5)

= 0 + 3 + 10 + 6 + 5 = 24 children

The number of team members is 4 + 3 + 5+2 + 1 = 15

So, the mean number each will bring is; the number of children attending the party divided by the number of team members

The initial equation is:

so we can move all term with x to the left and the constants to the right so:

Now we divide by 8 bout side of the equation so:

The slope is define as the rate of y coordinate with respect to the x coordinate.

In the line D which is parallel to x axis has the constant y coordinate i.e

y = -3

So, for the numerator of the slop for line D is ( -3) - ( -3) = 0

Thus the slope will be express as :

Thus the slope of line is 0

Now, for the line A :

The line A is parallel to y axis, that is only y coorsinates are changes x is at contant position.

i.e. x = -5

So, substitute the value in the expression for the slope :

Slope of line A is not define

In the line B and C, the coordinates of x and y aixs are changes countinously

thus thier slopes will be well define.

Answer : Slope of line A is not define.

In order to determine the amount of money Rain, Kevin and Eric have, write the given situation as an algebraic equation.

If x is the money of Raina, y the money of Kevin and z the money of Eric, you have, based on the given problem, the following equations:

x + y + z = 66 All of them have a total of $66

y = 3z Kevin has 3 times what Eric has

x = z - 9 Raina has $9 less than Eric

Replace the expressions for x and y into the first equation and solve for z, as follow:

(z - 9) + (3z) + z = 66

z - 9 + 3z + z = 66

3z = 66 + 9

3z = 75

z = 75/3

z = 25

Next, replace the previous value of z into the expressions for x and y:

y = 3(25)

y = 75

x = 25 - 9

x = 16

Hence, the amount of money each of them has is:

Raina: $16

Kevin: $75

Eric: $75

The required value of the x is given as 8.66 for the given triangle.

Given that,
A figure of the triangle is shown, with the help of trigonometric operators we have to determine x.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
Tan60 = x/ 5
x = tan60 × 5
x = 1.732 × 5
x = 8.66

Thus, the required value of the x is given as 8.66 for the given triangle.

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the initial function is:

now we replace the values in x that gives the table so:

for -2:

for 0:

for 2:

for 4:

Part A)

2.7 --- 60%

Therefore in order to know what is the 100% we will do the next operation

2.7 is 60% of 4.5

Part B)

4.2 --- 10%

In order to know the 100% we will do the next operation

4.2 is 10% of 42

Part C)

58 --- 100%

214.6 --- ?

214.6 is 370% of 58

Answer:

Explanation:

Using the graph of both equations, we want to get the correct option

We start by making a plot of the two on same axes

We have the plot of the functions as follows:

Now, let us take a look at the options:

a) This is wrong. The functions have two intersection points

b) This is incorrect. They have equal y-intercepts at y = 2

c) This is correct. The quadratic function have a greater maximum

We have the following inequality:

x > - 0.75

This is the same as state "x is greater than -0.75". Therefore, any value greater than -0.75 is a solution to this inequality

Considering this rule, we can answer each item:

a) The statement "-0.75 is a solution to the inequality" is FALSE, because, or rule states that x must be greater than -0.75.

b) The statement "There are many solutions to this inequality" is TRUE. Actually, there is an infinite number of solutions to this inequality (some of them can be expressed by -0.74, -0.73, -0.72...)

c) The statement "All the solutions to the inequality are negative" is FALSE, since any positive (or null) number is also greater than -0.75.

d) The statement "The inequality -0.75 < x is equivalent to the given inequality" is TRUE, since this inequality is tha same as the statement "-0.75 is less than x", which is a different form of express the original statement "x is greater than -0.75".

e) The statement "-4.5 is a solution to the inequality" is FALSE, because -4.5 is less than -0.75, which contradicts or rule.

LK = 2.91m

JK = 7.99m

hypotenuse = 8.5m

angle = 20°

LK = side opposite the angle 20°

Since we know the hypotenuse and we need to find the opposite, we would apply sine ratio

sine ratio = opposite/hypotenuse

sin 20° = LK/8.5

LK = 8.5(sin 20°)

LK = 8.5(0.3420)

LK = 2.907

To the nearest hundredth, LK = 2.91m

JK = base = adjacent

We would apply cosine ratio

cos 20° = adjacent/hypotenuse

cos 20° = JK/8.5

JK = 8.5(cos20°)

JK = 8.5(0.9397)

JK = 7.98745

To the nearest hundredth, JK = 7.99m

EXPLANATION

Given the system of equations:

(1) 60x + 110y = 265

(2) 120x + 90y = 270

We can apply the substraction method as shown as follows:

Multiply 60x + 110y = 265 by 2:

----> (60x + 110y = 265)*2 -------> 120x + 220y = 530

Subtract the equations:

120x + 220y = 530

- (120x + 90y = 270)

--------------------------------

130y = 260

Divide both sides by 130:

y= 260/130

Simplifying:

y= 2

Replacing on the first equation:

60x + 110(2) = 265

Applying the distributive property:

60x + 220 = 265

Subtracting 220 to both sides:

60x = 265 - 220

Subtracting like terms:

60x = 45

Dividing both sides by 60:

x = 45/60

Simplifying:

x= 3/4

The solutions to the system of equations are:

x=3/4 y=2

Before we calculate the perpendicular line, let's rewrite our line equation in slope-intercept form. The slope-intercept form is

Where m represents the slope and b the y-intercept.

Rewritting our equation, we have

This means the slope of our line is equal to - 3.

Two perpendicular lines are related by their slope. Let's say two lines are perpendicular, this means the slope of one of the lines is equal to minus the inverse the slope of the other. If we call the slope of one of those lines as m_1, the slope of the perpendicular line m_2 is given by

Using this relation, we can find the slope of a perpendicular line. Since the slope of our line is equal to - 3, then, the slope of the perpendicular line is

In slope-intercept form, our perpendicular line has the following form

To find our y-intercept, we can use our given point that belongs to this line.

The point is (-3, 1), evaluating this point in our equation, we have

Then, our line is

Answer: y=3x+5

Step-by-step explanation:

Using midpoint of a line, the point at which E is located on the coordinates is (-4, -10)

Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.

The formula of midpoint is given as

(x, y) = (x₂ + x₁) / 2 , (y₂ + y₁) / 2

Taking x-coordinate

x = (x₂ + x₁) / 2

2 = (8 + x₁) / 2

x₁ = -4

Taking the y - coordinate

y =  (y₂ + y₁) / 2

-4 = (2 + y₁) /2

y₁ = -10

The coordinate of E is (-4, -10)

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Using the function  f(x) = 28.7 + 1.2log (x + 1) that models the salinity of the ocean to depths of 1000 meters the salinity to the nearest hundredth is 32.18 g/kg

The salinity s calculated using the logarithmic function model

f(x) = 28.7 + 1.2log (x + 1)

given that f(x) is in grams of salt per kilogram of seawater and x is the depth in meters

for x = 797 meters

f(x) = 28.7 + 1.2log (x + 1)

f(x) = 28.7 + 1.2log (797 + 1)

f(x) = 28.7 + 1.2log (798)

f(x) = 28.7 + 1.2 * 2.902

f(x) = 28.7 + 3.4824

f(x) = 32.1824

f(x) = 32.18  (to the nearest hundredth)

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ANSWER

0.1069

EXPLANATION

We have two possible outcomes for each experiment: the seed grows or the seed does not grow. So, this follows a binomial distribution, where, in this case, the probability of success is the probability that a seed does not grow - note that we want to find what is the probability that a number of seeds do not grow.

We know that the probability that a seed grows is 85%, so there is a 15% chance the seed does not grow. This experiment is repeated 9 times (9 seeds) and we want to find what is the probability that the number of successes is 3 - remember that "success" is that the seed doesn't grow.

To find this, we have to use the binomial probability formula,

For this problem:

• n = 9

• x = 3

• p = 0.15

• q = 0.85

So we have,

Hence, the probability that exactly 3 seeds don't grow is 0.1069, rounded to four decimal places.

Given: 0.6 divided by 30

We will find the result as follows:

So, the answer will be 0.02

Given:

f(x) = x^2 + 4x + 4 and g(x) = x^2 - 2x - 8.

we are to find the domain of (f/g) (x)

before we find the domain of the function, its best we know what a domain is.

The Domain of a function is the set of all possible inputs for the function. it can also be seen as the set of input or arguement values for which the function is real and defined.

recall that we have x + 2 as our the simplest form

x - 4

so the domain we wil be looking for is x + 2

x - 4

so we have to take t denominator of the above and compare to zero

x - 4 = 0

x = 4

so this is undefined

the function domain

x < 4 or x > 4

so the domain is:

(- infinity, 4) U (4, infinity)

The correct option is A.

Standard form by definition of standard form of polynomials

Solution:

Given:

From the table, the probability that Michiko will hava a quiz on Wednesday is 0.070.

This is the probability of success.

Hence, the probability that Michiko will not have a quiz on Wednesday is the probability of failure.

Thus,

Hence, the probability of failure (the probability that Michiko will not have a quiz on Wednesday is 0.93.

As a percent,

Therefore, the probability that Michiko will not have a quiz on Wednesday is 93%

EXPLANATION

The coordinate son the plane when x=-3 are y=9 ---> A= (-3,9)

The points on the parabola when y= 16 are x=4 ---> (x_1,y_1) = (4,16) and (x_2,y_2) = (-4,16)