(4x + 2y = -6)/(-3x -2y = 7)

Answers

Answer 1

Answer:

= 1 and = -5.

Step-by-step explanation:

To solve the system of equations:
(4 + 2 = -6)
(-3 - 2 = 7)

We can use the method of elimination or substitution. Let's solve it using the elimination method:

Step 1: Multiply the first equation by 3 and the second equation by 4 to make the coefficients of in both equations equal and opposite:

3(4 + 2) = 3(-6) => 12 + 6 = -18
4(-3 - 2) = 4(7) => -12 - 8 = 28

Step 2: Add the two new equations together to eliminate :

(12 + 6) + (-12 - 8) = -18 + 28

Simplifying, we get:
-2 = 10
= -5

Step 3: Substitute the value of = -5 back into one of the original equations, let's use the first equation:

4 + 2(-5) = -6
4 - 10 = -6
4 = -6 + 10
4 = 4
= 1

So the solution to the system of equations is = 1 and = -5.

Related Questions

You sailed 0.055 units to the left and found treasure at 0.085 units find where the ship started

Answers

To find where the ship started, we can utilize the following formula:

Starting position = Treasure location + distance sailed to the left

Since we know going in the left direction typically is a means of subtraction, we can use inverse operations to solve this. We can set up an addition problem to solve this:

Starting position = 0.085 + 0.055
Starting position = 0.03 units

Therefore, the ship started at 0.03 units.

-accurately display the data collected from Question #1 in
a histogram
-at least two comments providing analysis of your data

Answers

The histogram accurately displays the data collected from Question #1 and provides useful insights into the distribution and range of opinions among the survey population.

Question 1 data:

4, 2, 3, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1

From the histogram, it can be observed that the data is approximately normally distributed with a mean of around 3. The distribution appears to be somewhat symmetrical with the majority of the data being between 2 and 4. The frequency of the value '1' and '5' is the least which implies that the occurrence of these values is very low.

The analysis of the data shows that the majority of the people surveyed chose answers that were in the middle range of the scale, between 2 and 4. This could indicate that the survey question was not highly polarizing and that the survey population had similar opinions on the subject matter.

However, it is also worth noting that there were a few outliers at both ends of the scale. This suggests that there were a few people who had very strong opinions about the topic and did not fall within the norm of the survey population.

Overall, the histogram accurately displays the data collected from Question  and provides useful insights into the distribution and range of opinions among the survey population.

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Squeeze Theorem.......​

Answers

The limit lim ₓ → ₀ f(x) is 5

How to determine the value

The squeeze theorem is used to evaluate a kind of limits. It is also known as the sandwich theorem.

To evaluate a limit lim ₓ → ₐ f(x), we usually substitute x = a into f(x) and if that leads to an indeterminate form, then we apply some algebraic methods.

But neither of them may work in evaluating some kind of limits such as lim ₓ → ∞ (sin x / x).

From the information given, we have that;

We know that lim ₓ → ₀ 5 - x² = 5 - 0²

lim ₓ → ₀ = 5

lim ₓ → ₀ 5 + x²

lim ₓ → ₀ = 5+ 0²

lim ₓ → ₀ = 5

Also, f(x) lies between 5 - x² and 5 + x².

Using the squeeze theorem, the limit for f(x) is;

lim ₓ → ₀ f(x) = 5.

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2. How many boys are there in a class of 368 students if there are 5 boys for every 3 girls?

Answers

Using ratio, the number of boys in the class would be 230

Calculating using Ratio

If there are 5 boys for every 3 girls, then the ratio of boys to girls is 5:3. This means that for every 5 boys, there are 3 girls.

We can use this ratio to find the number of boys in a class of 368 students.

(5:3) × Total number of students

5/8 × 368 = 23

Therefore, there will be 230 boys in the class.

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please solve it it's urgent ​

Answers

The length of BL is approximately 7.9 units.

In triangle ABL, we are given that AL = 12, TS = 7.75, and SL = 5.1. We need to find the length of BL.

Since TS is parallel to AL, we can use the concept of similar triangles to solve this problem.

By drawing a line parallel to BL through point T, we create two similar triangles: triangle TSL and triangle ABL. The corresponding sides of similar triangles are proportional.

Let's denote the length of BL as x. Then we can set up the following proportion:

TS/AL = SL/BL

Substituting the given values:

7.75/12 = 5.1/x

To solve for x, we can cross-multiply and solve the resulting equation:

7.75 * x = 12 * 5.1

7.75x = 61.2

Dividing both sides of the equation by 7.75:

x = 61.2 / 7.75

x ≈ 7.9

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If you work a job and earn 1$ every 500 seconds within a normal work day(8 hours) hoq much money would you have earned(let x equal the amount earned)

Answers

If you earn $1 every 500 seconds and work for a normal 8-hour day, you would have Earned $57.

To calculate the amount of money earned in a normal workday, we need to determine the total number of seconds in 8 hours and then divide it by the time it takes to earn $1.

There are 60 seconds in a minute and 60 minutes in an hour. Therefore, there are 60 x 60 = 3600 seconds in an hour.

To find the total number of seconds in 8 hours, we multiply the number of seconds in an hour by 8:

8 hours x 3600 seconds/hour = 28,800 seconds.

Next, we need to determine how many times $1 can be earned in 28,800 seconds. Given that $1 is earned every 500 seconds, we divide 28,800 by 500:

28,800 seconds ÷ 500 seconds = 57.6.

Since we cannot earn a fraction of a dollar, we round down to the nearest whole number. Therefore, you would have earned 57 dollars during the 8-hour workday.

In summary, if you earn $1 every 500 seconds and work for a normal 8-hour day, you would have earned $57.

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A researcher was interested in the impact of listening to different types of music on learning. She designed an extensive maze for rats and after she taught rats how to get through the maze, she randomly assigned each rat to run the maze while (a) listening to classical music, (b) listening to heavy metal music, or (c) in a quiet room (i.e., no music). The researcher measured the amount of time it took each rat to get through the maze and the number of errors made.

a. Independent Variable ? _________________ What are the levels? ________________________________

b. Dependent Variable ? _____________________________

c. What might be an extraneous variable?: ___________________________________

d. Control group? _________________ Experimental Group(s)?____________________

Answers

a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

What is an independent and dependent variables?

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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Given: g(n) = 2n - 3 and f(n) = -n^3 - 4
Find: g(f (3) )

Answers

The function  g(f(3)) = g(-31) = -65

Given that g(n) = 2n - 3 and f(n) = -n³ - 4. We need to find g(f(3)).Step-by-step explanation:

First, we need to find f(3),

we substitute n = 3 in f(n) = -n³ - 4

to getf(3) = -3³ - 4 = -27 - 4 = -31

Now, we substitute this value of f(3) in g(n) = 2n - 3

to getg(f(3)) = g(-31)We substitute n = -31 in g(n) = 2n - 3 to getg(-31) = 2(-31) - 3 = -62 - 3 = -65.

Note: The function f(n) = -n³ - 4 is a cubic polynomial, whereas g(n) = 2n - 3 is a linear polynomial.

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Find the x and y intercepts for -3x + 6y = 18.

Question 10 options:

x-intercept = -24, y-intercept = -9


x-intercept = -9, y-intercept = 24


x-intercept = -6, y-intercept = 3


x-intercept = -3, y-intercept = 6

Answers

The correct answer is:

x-intercept = -6, y-intercept = 3To

How to determine the and y intercepts for -3x + 6y = 18.

find the x-intercept, we set y = 0 and solve for x.

-3x + 6(0) = 18

-3x = 18

x = -6

Therefore, the x-intercept is -6.

To find the y-intercept, we set x = 0 and solve for y.

-3(0) + 6y = 18

6y = 18

y = 3

Therefore, the y-intercept is 3.

The correct answer is:

x-intercept = -6, y-intercept = 3

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Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. Sienna wants to know the probability that at least 2 of the colors will be the same. Which of the following is the best simulation? Explain your reason for your answer.

A. Roll a standard number cube 5 times for each trial. Let each number represent a different color. Run 50 trials and find the fraction of times that at least two of the same number are rolled.

B. Create a spinner with 5 equal sections. Label each section with a different color. Spin the spinner 7 times to see if it lands on the same color two or more times.


C. Create a spinner with 7 equal sections. Label each section with a different color. Spin the spinner 5 times for each trial. Run 50 trials and find the fraction of times the spinner lands on the same color two or more times.


D. Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

Answers

The probability that at least 2 of the colors will be the same, the following is the best simulation is Option D Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

Given, Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. We have to find the probability that at least 2 of the colors will be the same. There are 5 colors in the pack of clay, and 7 colors are possible in total.

So, the probability of picking any color at random is

P(picking a color) = 5/7 = 0.7143Let P(X = 2) be the probability that exactly 2 of the colors are the same.

Then, the probability that at least 2 of the colors are the same can be calculated by using the formula:

P(X ≥ 2) = 1 - P(X < 2).

The simulation method that can be used to find the probability of at least 2 of the colors will be the same in the mystery pack is option D.

Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

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Suppose a normal distribution has a mean of 50 and a standard deviation of 3. What is P(x≤ 44)? A. 0.025 B. 0.975 C. 0.84 D. 0.16 ​

Answers

A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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the level of temperature of liquid in a thermometer is 26.52'c lower than the boiling poin. of water. what is the thermometer reading

Answers

The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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7. What is the y-intercept of line M?


8. What is the slope of line N?

Answers

The slope of line N is -3/4.

To find the y-intercept of line M and the slope of line N, we need to understand their equations, which are in slope-intercept form: y = mx + b,

where m represents the slope and b represents the y-intercept.Line M is given by the equation:

y = -3x + 7. Here, we can see that the slope, m, is -3, and the y-intercept, b, is 7.

Therefore, the y-intercept of line M is 7.Line N is given by the equation: 3x + 4y = 8.

To find the slope of this line, we can solve for y:4y = -3x + 8y = (-3/4)x + 2

Here, we can see that the slope, m, is -3/4.

Therefore, the slope of line N is -3/4.

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An(B-C)=(AnB)-(AnC) If a,b c are the subsets of universal set u then prove the following

Answers

We can conclude that `An(B-C) = AnB - AnC` using double inclusion proofs.

Given a universal set `U` and subsets `A`, `B` and `C`.To prove: `An(B-C) = AnB - AnC`.

Now, we can prove this statement by double inclusion proofs. Let `x` be an arbitrary element of `U`.

Proof of `An(B-C) ⊆ AnB - AnC`:

Suppose that `x ∈ An(B-C)`, then `x ∈ A` and `x ∈ B-C`.

By definition of `B-C`, we have `x ∈ B and x ∉ C`.

Therefore, `x ∈ B` and `x ∉ C` implies that `x ∈ B` and `x ∉ AnC`.

Therefore, `x ∈ AnB` and `x ∉ AnC` implies that `x ∈ AnB - AnC`.

Hence, we have shown that `An(B-C) ⊆ AnB - AnC`.

Proof of `AnB - AnC ⊆ An(B-C)`:


Suppose that `x ∈ AnB - AnC`, then `x ∈ AnB` and `x ∉ AnC`.

By definition of intersection, we have `x ∈ A and x ∈ B`.Now, since `x ∈ AnC`, we have `x ∈ A and x ∈ C`.Since `x ∈ A` is a common element, we can combine both sets `B` and `C` to get `B ∪ C`.

Now, since `x ∈ B ∪ C`, we can write this as `x ∈ B ∪ (U-C)` or `x ∈ B - C or x ∈ A ∩ (U-C)`.

Thus, `x ∈ An(B-C)`.Hence, we have shown that `AnB - AnC ⊆ An(B-C)`.

Therefore, we can conclude that `An(B-C) = AnB - AnC` using double inclusion proofs.

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how would I find the equation of this graph

Answers

Answer:

y = sec(x-2) - 1

Step-by-step explanation:

We can determine the graph is of a secant by the repeating parabolas. From there, graph sec(x) and add the transformations necessary to replicate the graph.

Ik its 16 but which inequality sign

Answers

Answer:

None of the answer choices

Step-by-step explanation:

Answer:

x ≥ 4

Step-by-step explanation:

The given statement is "The difference of 10 and a number is at most six".

Let "x" be the unknown number.

"The difference of 10 and a number" can be represented as either "10 - x" or "x - 10", depending on whether x < 10 or x > 10.

"Is at most six" means it is less than or equal to six.

Therefore, we have two potential cases:

[tex]\begin{minipage}{3 cm}\underline{\sf Case\;1}:\;\textsf{If $x < 10$}\\\\\boxed{10 - x \leq 6}\end{minipage} \qquad \qquad\begin{minipage}{3 cm}\underline{\sf Case\;2}:\;\textsf{If $x > 10$}\\\\\boxed{x-10 \leq 6}\end{minipage}[/tex]

Solving the inequalities:

[tex]\boxed{\begin{aligned}\underline{\sf Case\;1}\\\\10 - x &\leq 6\\10 - x-10 &\leq 6-10\\-x &\leq -4\\x &\geq 4\end{aligned}}[/tex]      [tex]\boxed{\begin{aligned}\underline{\sf Case\;2}\\\\x-10&\leq 6\\x-10+10 &\leq 6+10\\x &\leq 16\\\\\end{aligned}}[/tex]

[Remember that when dividing both sides of an inequality by a negative number, we have to reverse the inequality sign.]

Therefore, the two possible solutions are:

x ≥ 4x ≤ 16

If we take the statement "the difference between 10 and a number" as "10 - x" then the solution is x ≥ 4.

what is the property of 3x(5x7)=(3x5)7

Answers

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

what is the reciprocal for 4/9

Answers

Answer: 9/4

Step-by-step explanation:

Reciprocal means flip the fraction

The reciprocal of 4/9  is  9/4

Answer: the rciprocal is 9/4

Step-by-step explanation:

Graph makes no sense to me​

Answers

Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

The area of a rectangle is 33 square inches. The width of the rectangle is 5 inches. What is the length of the rectangle?

Answers

Answer:

6.6 inches

Step-by-step explanation:

Area of rectangle = L x W

A = 33 in²

W = 5 inches

L = ?

We Take

33 ÷ 5 = 6.6 inches

So, the length of the rectangle is 6.6 inches

There are 1 purple cube, 2 blue cubes, 2 red cubes, 4 orange cubes, 1 green cube and 2
yellow cubes. Calculate the number of possible arrangements when all the cubes are
arranged in a line.

Answers

The total number of possible arrangements when all the cubes are arranged in a line is 96.

To calculate the number of possible arrangements when all the cubes are arranged in a line.

we need to consider the total number of cubes and their quantities.

In this case, we have:

- 1 purple cube

- 2 blue cubes

- 2 red cubes

- 4 orange cubes

- 1 green cube

- 2 yellow cubes

To find the number of arrangements, we can use the concept of permutations. The formula for permutations is given by:

P(n) = n!

Where P(n) represents the number of permutations of n objects and n! denotes the factorial of n.

First, let's calculate the factorial of the total number of cubes:

[tex]n! = 1! * 2! * 2! * 4! * 1! * 2![/tex]

Calculating the factorials:

[tex]1! = 12! = 2 * 1 = 24! = 4 * 3 * 2 * 1 = 24[/tex]

Substituting the values back into the equation:

[tex]n! = 1 * 2 * 2 * 24 * 1 * 2 = 96[/tex]

Therefore, the total number of possible arrangements when all the cubes are arranged in a line is 96.

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13
ph
28 is increased by 25%
40 is decreased by 15%
Which answer is bigger?
Show how you decide.

Answers

Answer:

To determine which answer is bigger, let's calculate the values after the given changes and compare them.

Increasing 28 by 25%:

To calculate the increase, we need to find 25% of 28 and add it to 28.

25% of 28 = (25/100) * 28 = 7

Increased value = 28 + 7 = 35

Decreasing 40 by 15%:

To calculate the decrease, we need to find 15% of 40 and subtract it from 40.

15% of 40 = (15/100) * 40 = 6

Decreased value = 40 - 6 = 34

Comparing the results:

The increased value of 28 by 25% is 35, while the decreased value of 40 by 15% is 34.

Therefore, 35 is bigger than 34.

Find y.
Round to the nearest tenth:

Answers

no sorry its way to hard to answer this

A statistically significant test result (P ≤ 0.05) means that the test hypothesis is false or should be rejected. A P value greater than 0.05 means that no effect was observed

Answers

A statistically significant test result (p-value ≤ 0.05) supports the rejection of the null hypothesis, while a p-value greater than 0.05 suggests that there is not enough evidence to reject the null hypothesis.


The statement provided is not entirely accurate. A statistically significant test result with a p-value ≤ 0.05 indicates that the observed effect is unlikely to have occurred by chance alone, and it provides evidence to reject the null hypothesis. It does not necessarily mean that the test hypothesis is false, but rather that the data collected supports an alternative hypothesis.

The p-value represents the probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true. When the p-value is smaller than the predetermined significance level (often set at 0.05), it suggests that the observed effect is statistically significant and not likely due to random chance.

Conversely, a p-value greater than 0.05 does not necessarily mean that no effect was observed. It simply means that the observed effect is not statistically significant at the chosen significance level, and there is insufficient evidence to reject the null hypothesis. However, it is important to consider the specific context and limitations of the study when interpreting the results.

In summary, a statistically significant test result (p-value ≤ 0.05) supports the rejection of the null hypothesis, while a p-value greater than 0.05 suggests that there is not enough evidence to reject the null hypothesis.

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Calculate the insurance costs. a. What would be the premium for a twenty-one-year-old single man who owns his car, purchasing insurance in the amount of 50/100/10? b. How much would it cost him to purchase insurance in the amount of 100/300/25? c. What is the difference in cost?

Answers

a. The premium for this coverage will depend on the  individual's age, location, driving record, and the insurance company's rates.

b.   It will cost higher because the insurance company provides more coverage in the event of an accident.

c.  The difference in cost between the two coverage amounts depends on factors such as the insurance provider's rates and the person's specific circumstances.

How do we calculate?

a. Insurance coverage of 50/100/10:

The coverage limits 50/100/10 is a representation of  the minimum liability coverage required by state laws.

$50,000 = coverage for bodily injury liability per person.

$100,000  = coverage for bodily injury liability per accident.

$10,000 = coverage for property damage liability per accident.

b. Insurance coverage of 100/300/25:

The coverage limits 100/300/25 represent higher liability coverage limits:

$100,000  = coverage for bodily injury liability per person.

$300,000  = coverage for bodily injury liability per accident.

$25,000  = coverage for property damage liability per accident.

c. Difference in cost:

The difference in cost between the two coverage levels is influenced by a number of variables, including the insurance company's rates and the individual's unique situation.

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Unit 7, Lesson 13 - Classwork (Time and Temperature) The temperature in Princeton was recorded at various times during the day. The times a temperatures are shown in the table. 1. time (hours before or after midnight) -5 -2 0 8 Label axes and plot points that represent the data. temperature (degrees C) 1.2 -1.6 -3.5 -6.7​

Answers

A graph that represent the data is shown below, with the x-axis labeled time and the y-axis labeled temperature.

What is a graph?

In Mathematics and Geometry, a graph is a type of chart that is typically used for the graphical representation of data points, end points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

In this scenario, we would use an online graphing calculator to label the x-axis of the cartesian coordinate with time (measured as hours before or after midnight) while the y-axis of the cartesian coordinate would be labeled temperature (measured in degree Celsius), and then plot the data points as shown in the image attached below.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Which figure correctly demonstrates using a straight line to determine that the graphed equation is not a function of x?
Mark this and return
3
2
4
Save and Exit
Next
Submit

Answers

Answer:

2 is really answer it is this question bro than ka for good point

Step-by-step explanation:

hello shreekant thanks 886A bubs 2 is answr

Please help me!! A ray has been lined up with the baseline and origin on the protractor. What is the next step in drawing a 40° angle?

A protractor showing a ray lined up with the base line.

Line up the ray with the baseline and origin on the protractor.
Draw a ray.
Draw a ray connecting the vertex and the mark.
Draw a mark on the paper at 40°.

Answers

The next step in drawing a 40° angle would be to: D. draw a mark on the paper at 40°

How to Draw an Angle Using a Protractor?

A protractor is a geometric tool used to measure and draw angles. It typically has a semi-circular shape with markings along the curved edge representing degrees or angles.

The next step in drawing a 40° angle after lining up the ray with the baseline and origin on the protractor is to draw a ray connecting the vertex (starting point) of the angle and the mark on the protractor corresponding to the 40° angle.

This ray will form the desired 40° angle with the baseline, completing the construction of the angle.

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Select the correct answer.
Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been transformed to produce figure 2.

A four-quadrant graph of the x-axis and y-axis. Has a semi cube formed by joining points (2, 3), (2, 6), (6, 6), (6, 4), (4, 4) as 1 and (minus 2, minus 2), (minus 6, minus 2), (minus 6, minus 5), (minus 4, minus 4) and (minus 2, minus 4) as 2
Which notation describes this transformation?


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Answers

The Transformation notation for transforming figure 1 to figure 2 is R y-axis T(-3, -2) R 180° T(2, -2).

The notation that describes the transformation of figure 1 to figure 2 is a combination of translation, reflection and rotation.To begin with, figure 2 is a mirror image of figure 1.

The mirror reflection transformation is represented by an ‘R’ in notation, followed by the line of reflection. In this case, the line of reflection is the y-axis. Therefore, the mirror reflection transformation notation is R y-axis.Next, the figure is translated or moved. The vertices (2, 3), (2, 6), (6, 6), (6, 4), (4, 4)

which forms the semi-cube have moved three units left and two units down. While the vertices (minus 2, minus 2), (minus 6, minus 2), (minus 6, minus 5), (minus 4, minus 4) and (minus 2, minus 4)

which forms the second semi-cube have moved two units right and two units down. Thus, the notation for this transformation is T(-3, -2) and T(2, -2).

Lastly, the figure is rotated 180 degrees counterclockwise around the origin. This transformation is represented by the notation R 180°.

Therefore, the transformation notation for transforming figure 1 to figure 2 is R y-axis T(-3, -2) R 180° T(2, -2).

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enter the number that belongs in the green box 7 4 10

Answers

The value of the missing angle using Cosine rule is 128.68°

Using Cosine rule

Let :

a = 7

b = 10

c = 4

Missing angle = B

From Cosine rule :

CosB = (a² + c² - b²)/2ac

Substituting the values into the formula :

CosB = (7² + 4² - 10²)/2×7×4

CosB = -35/56

CosB = -0.625

Taking the cosine inverse of 0.625

B = 128.68

Therefore, the value of the missing angle is 128.68

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