The quotient of 12 and opposite of 3 plus the product of the opposite of 14 and 4

Answer:

Part A: The solution area is to the left of x=-2, over the right line y=2x+3 and below the right line y=-(3/2)x-4.

Part B: No, the point (-4,6) is not included in the solution area for the system.

Step-by-step explanation:

System of inequalities:

(1) y > 2x + 3

(2) y < -(3/2)x - 4

Part A

1) The first inequality represents the region over the line:

y=2x+3

This is a linear equation and its graph is a right line. We must graph the right line, and then shadow the area above this right line. To graph this right line we need two points, because through two points only goes one right line. Giving two arbitrary values to x, for example:

x=0→y=2(0)+3→y=0+3→y=3; Point=(x,y)→Point=(0,3)

x=1→y=2(1)+3→y=2+3→y=5; Point=(x,y)→Point=(1,5)

1) The second inequality represents the region below the line:

y= -(3/2)x - 4

This is a linear equation and its graph isaright line. We must graph the right line, and then shadow the area below this right line. To graph this right line we need two points, because through two points only goes one right line. Giving two arbitrary values to x, for example:

x=0→y=-(3/2)(0)-4→y=0-4→y=-4; Point=(x,y)→Point=(0,-4)

x=2→y=-(3/2)(2)-4→y=-3-4→y=-7; Point=(x,y)→Point=(2,-7)

The two lines intersect at the point (-2,-1). The solution area is to the left of x=-2, over the right line y=2x+3 and below the right line y=-(3/2)x-4.

Part B

No, the point (-4,6) is not included in the solution area for the system, because this point is not below the right line y=-(3/2)x-4

Part A: The purple region in the graph attached below is the solution to the given inequalities.

Part B: (-1,-1) is not included in the solution area for the system of inequalities.

In mathematics, inequalities specify the connection between two non-equal expressions.

Given the following information:

1) y > −4x − 1

2) y is less than 3 over 2 times x minus 1, this can be expressed in inequality as follows:

[tex]y < \dfrac{3}{2}x-1[/tex]

Part A:

Attaching image to describe the graph of the system with shaded area.

The red colored region corresponds to the solution of inequality of line 1)

The blue colored region corresponds to the solution of inequality of line 2)

Thus, purple colored region corresponds to the common region due to the 2 lines.

Part B:

To check whether (-1,-1) is included in the solution area for the system:

Mathematical justification:

Substituting (-1,-1) in eq1)

-1>-4(-1)-1

-1>3

This is false as -1 is less than 3.

Substituting (-1,-1) in eq2)

-1<3(-1)/2-1

-1<-3/2-1

-1<-5/2

-1<-2.5

This is also false as -1 is greater than -2.5

Thus, it is justified that (-1,-1) is not included in the solution.

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Tree diagrams are a helpful tool for calcuating probabilities when there are several independent events involved. They get their name because these types of diagrams resemble the shape of a tree. The branches of a tree split off from one another, which then in turn have smaller branches.  Just like a tree, tree diagrams branch out and can become quite intricate.

The solution of the given system of equations is (-4, -8).

Therefore, option A is correct.

Given equations are,

                          [tex]-3x+4y=-20..........(1)\\\\y=x-4 .........(2)[/tex]

Substituting the value of equation 2 in equation 1.

                   [tex]-3x+4(x-4)=-20\\\\-3x+4x-16=-20\\\\x=-20+16=-4[/tex]

Substituting the value of x in equation 2

We get,      [tex]y=-4-4=-8[/tex]

The solution is (-4, -8)

Therefore, option A is correct.

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The graph for the inequality y ≥ 2 - 2x is a downward sloping line with a y-intercept of 2. The area above this line, including the line itself, is shaded to denote the solutions for the inequality.

The equation y ≥ 2 - 2x is a linear inequality with a slope of -2 and a y-intercept of 2. It is represented graphically as a straight line where y is equal to or larger than 2 - 2x. As the coefficient of x is negative, the line will slope downwards towards the right based on the rule mentioned in Figure 12.4 (c).

In a two-dimensional (x-y) graph, x represents the independent variable while y is the dependent variable. Thus, for every increase of 1 unit on the x-axis (horizontally), the value of y decreases by 2 units (vertically) due to the slope of -2.

Since y is greater than or equal to 2 - 2x, the area above the line (including the line itself as it's a 'greater than or equal to' inequality) will be shaded when the inequality is graphed. This shading means that any point within this area is a solution to the inequality.

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The ratio of the amount of money Jason had to the amount of money Wilson had was 12:13, then Jason had $12x and Wilson had $13x.

Wilson spent $63, then in the end he had $(13x-63). Since in  the end Jason had 3 times as much money as Wilson, then

[tex]\dfrac{12x}{13x-63}=3.[/tex]

Solve it:

[tex]12x=3(13x-63),\\ \\12x=39x-189,\\ \\27x=189,\\ \\x=7.[/tex]

In the beginning Jason had $12·7=$84 and Wilson had $13·7=$91. In the end Jason had $84 and Wilson had $91-$63=$28.

Answer: Jason had $84, in the end altogether they had $84+$28=$112.

Answer:

I need help with this problem.

Answer:

Its  C, edge 2021

Step-by-step explanation:

No, she did not substitute the correct x and y values.

There will be 88 novels among the total of 352 books.

To find the number of novels, we can use the information that 1/4 of the books are novels.

First, we calculate the total number of books:

Total number of books = 44 books/shelf * 8 shelves

= 352 books

Then, we can find the number of novels:

Number of novels = 1/4 * 352 books

= 88 books

Therefore, there will be 88 novels.

The person who will make 40 spring rolls the fastest is required.

Eli will finish first.

Nora

[tex]10\ \text{minutes}=8\ \text{spring rolls}[/tex]

[tex]1\ \text{spring roll}=\dfrac{10}{8}\ \text{minutes}[/tex]

[tex]40\ \text{spring rolls}=40\times \dfrac{10}{8}=50\ \text{minutes}[/tex]

Eli

[tex]12\ \text{minutes}=10\ \text{spring rolls}[/tex]

[tex]1\ \text{spring rolls}=\dfrac{12}{10}\ \text{minutes}[/tex]

[tex]40\ \text{spring rolls}=40\times \dfrac{12}{10}=48\ \text{minutes}[/tex]

Eli will finish first.

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The probability of randomly selecting the 2 oldest people from the group of 8 is approximately 0.0357 or 3.57%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The total number of possible ways to select 2 people from a group of 8 is given by the combination formula:

C(8,2) = 8! / (2! x 6!) = 28

This means that there are 28 different pairs of people that can be selected from the group of 8.

To calculate the probability that the 2 oldest people are selected, we need to first determine how many ways there are to select these 2 people.

Since the order in which we select the people does not matter, we can simply choose any 2 people from the group of 8 in order to select the 2 oldest people.

There are C(8,2) = 28 ways to select any 2 people, and since there is only 1 pair that consists of the 2 oldest people, the number of ways to select the 2 oldest people is 1.

Now,

The probability of selecting the 2 oldest people is:

1/28 = 0.0357

Thus,

The probability of randomly selecting the 2 oldest people from the group of 8 is approximately 0.0357 or 3.57%.

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Final answer:

To find the probability of selecting the two oldest people from a group of 8, we calculate the number of ways to choose 2 people from 8 (28 ways) and understand that there is only 1 way to choose the two oldest. Thus, the probability is 1/28.

Explanation:

The question asks about the probability of selecting the two oldest people from a group of 8. To solve this, we can use the concept of combinations. There is only one way to pick the two oldest people. However, the total number of ways to pick 2 people out of 8 is calculated using combinations, which can be represented as 8 choose 2 or 8C2. The formula for combinations is nCk = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose.

Applying this formula, the total number of ways to choose 2 people from 8 is :

8C2 = 8! / (2!(8-2)!) = 28

Therefore, the probability that the two people selected are the oldest is :

Probability = 1 / 28

A unit rate means a rate for one of something.

The distance of the state park from their house is 42 miles.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. 

We have,

Time taken to reach state park from house = 4 hours

First two hours, speed = 12 miles per hour

This can be written as:

1 hour = 12 miles

2 hours = 2 x 12 miles = 24 miles. ______(1)

The last two hours = 9 miles per hour

This can be written as:

1 hour = 9 miles

2 hours = 2 x 9 miles

2 hours = 18 miles ______(2)

From (1) and (2) we get,

24 + 18 = 42 miles

Thus,

The distance of the state park from their house is 42 miles.

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If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.

When two lines intersect, they create angles. The properties of linear pairs and vertical angles can be used to determine these angles' measures. Linear pairs are two adjacent angles totaling 180 degrees, and vertical angles are opposite each other and are always equal.

When

two lines intersect

, they create four angles. In this formation, a couple of properties can help to determine the angle measures. The first is the concept of a

linear pair

. This is when two angles formed by intersecting lines add up to 180 degrees and are adjacent to each other. This can help when calculating one of the angle's measure if the other is known. Then, there's the principle of

vertical angles

, which are the angles across from each other when two lines intersect. Vertical angles are always equal. So if you know the measurement of one angle, you know the measurement of the angle directly across from it.

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"3x + 2y = –11 written in slope-intercept form is y = x." Not so.

To find the slope of this line, solve for y:

2y = -3x - 11 => y = (-3/2)x - 11/2. The slope of the given line is -3/2. The

graph of the new (perpendicular) line will then be the negative reciprocal of -3/2, or +2/3.

Now use the point-slope formula for the equation of a straight line to determine the equation of this new (perpendicular) line thru (-6,5):

y-5 = (2/3)(x+6) (answer)

To find the equation of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. Using the point-slope form, we can substitute the point and the new slope to get the equation of the perpendicular line.

1. To write the given equation in slope-intercept form, we need to solve for y. Rearranging the equation, we have 2y = -3x - 11, y = (-3/2)x - 11/2. Therefore, the slope of the given line is -3/2.

2. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is 2/3.

3. Using the point-slope form, we substitute the point (-6, 5) and the new slope (2/3) into the equation y - y1 = m(x - x1), where x1 and y1 are the coordinates of the given point. Plugging in the values, we get y - 5 = (2/3)(x + 6).

4. Simplifying the equation, we can distribute 2/3 to x and 6, which gives us y - 5 = (2/3)x + 4. Adding 5 to both sides, the final equation of the line passing through (-6, 5) and perpendicular to 3x + 2y = -11 is y = (2/3)x + 9.

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The indicated degree of likelihood as a probability value. "It will definitely get dark tonight." is:

                                    1

We know that in general the indicated degree of likelihood as a probability value lie between 0 and 1.

( For example-- The event of getting 7 when rolling a six-number cube.

As we know that the possible outcome on rolling a six-sided die is:

{1,2,3,4,5,6}

Hence P(getting 7)=0

( as none of the outcome is 7)  )

( i.e. P( getting a head or a tail on tossing a coin)=1

( since there are just two outcomes on tossing a coin i.e. head and tail will come up )

Here we have a outcome as:

"It will definitely get dark tonight."

It is a obvious event that it gets dark at night there is no other possibility.

               Hence, the answer is:

                          1