Tyrone wrote an equivalent expression for 28 + x - 2n + 7 - n - 5x + 4. His equivalent expression was -3n - 5x + 39 + x. What error did Tyrone make?


A. Tyrone neglected to combine the x terms.

B. Tyrone added the constants instead of subtracting them.

C. Tyrone neglected to add the coefficients of the n terms.

D. Tyrone made an error when he added the constants.

Answer:

A) μ = 91.2; σ = 9.3

B) No

Step-by-step explanation:

To find the mean, μ, we use the formula

μ = np, where n is the sample size and p is the probability of success (percentage of times the letter is used).

This gives us

μ = 0.057(1600) = 91.2

To find the standard deviation, we use the formula

σ = √(np(1-p)

This gives us

σ = √(1600×0.057×(1-0.057))

= √(1600×0.057×0.943) = √86.0016 = 9.2737 ≈ 9.3≈

Any value that is more than two standard deviations from the mean is considered unusual.  The value 102 is

(102-91.2)/9.3 = 10.8/9.3 = 1.16 standard deviations from the mean.  This is not statistically unusual.

Calculations were made based on standard English language letter frequencies to establish a mean and a standard deviation for a set number of letters. In this example, an occurrence was not considered unusual as it was within one standard deviation of the mean.

The subject revolves around probability and statistics and involves the calculation of the mean and standard deviation, and understanding of what might be considered an unusual result in a statistical sense.

In standard English text, a particular letter is used at a rate of 5.7%. This means on average, the letter will appear approximately 5.7% of the time. If each page consists of 1600 characters, then the mean (Μ) number of times that this letter will appear on a page can be calculated by multiplying the total characters by the usage rate (1600 * 0.057 = 91.2).

The standard deviation (sigma) is given as 9.3. This measure shows the dispersion or how spread out the numbers are from the mean.

In the intercepted message, the letter occurred 102 times. To determine if this is unusual, we look at how many standard deviations away from the mean this number falls. If it falls within 2 standard deviations (2 * 9.3 = 18.6) of the mean, it is not unusual. 102 is approximately one standard deviation above the mean (102 - 91.2 = 10.8), therefore, it is not considered an unusual occurrence.

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Answer:

(3y + 4)(y + 1)

Step-by-step explanation:

3y^2 +7y + 4

a = 3, b = 7 and c = 4

ac = 3 x 4 = 12

The products of 12 = 3 and 4 and sum of 3 and 4 = 7

So

3y^2 +7y + 4

= 3y^2 + 3y + 4y + 4

= 3y(y + 1) + 4(y + 1)

= (3y + 4)(y + 1)

Answer

(3y + 4)(y + 1)

Answer:

So the factors are (y + 1)(y + 4/3)

Step-by-step explanation:

Given in the question an equation

3y² + 7y + 4

To find it's factor we will use quadratic formula

y = -b ± √(b²-4(a)(c)) / 2a

here a = 3

        b = 7

        c = 4

y1 = -7 + √(7²- 4(3)(4)) / 2(3)

   = -7 + √49 - 48 / 6

   = -7 + 1 /6

   = -6/6

   = -1

y2 = -7 - √(7²- 4(3)(4)) / 2(3)

   = -7 - √49 - 48 / 6

   = -7 - 1 /6

   = -8/6

   = -4/3

So the factors are (y + 1) and (y + 4/3)

Answer:

P(A') = 0.75

Step-by-step explanation:

We are given that the probability P(A) = 0.25 and we are to determine the probability of the complement of A.

According to the Complement Rule of any probability, the sum of the probabilities of an event and its complement must be equal to 1.

So for for the event A,

P(A) + P(A') = 1

0.25 + P(A') = 1

P(A') = 1 - 0.25

P(A') = 0.75

The probability of an event and its complement add up to 1. Therefore, if P(A) = 0.25, the probability of the complement of A is 0.75.

In the field of probability theory, the probability of an event and its complement always add up to 1. Therefore, if P(A) = 0.25, then the probability of the complement of A is 1 - 0.25 = 0.75.

This is because the complement of A, denoted by A', includes all outcomes that are not in A. So, all probabilities in the sample space (which has a total probability of 1) must either be in A or in A'. Therefore, P(A) + P(A') = 1.

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3x+3=6x-57

60=3x

3x=60

60÷3=20

x=20

Answer: third option.

Step-by-step explanation:

By definition we know tht the geometric sequences has a common ratio, which is represented with r.

This ratio can be calculated by dividing a term by the previous term.

Therefore, keeping the information above on mind, you have that the ratio r  of the geometric sequence given in the problem, is the shown below:

[tex]r=\frac{-\frac{1}{2}}{\frac{1}{10}}\\\\r=-5[/tex]

Answer:

The ratio of the sequence is -5

Step-by-step explanation:

The given geometric series is ;

[tex]\frac{1}{10},-\frac{1}{2},\frac{5}{2},...[/tex]

The ratio of the geometric sequence is given by;

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

[tex]r=\frac{\frac{5}{2}}{-\frac{1}{2}}[/tex]

We simplify to get;

[tex]r=-5[/tex]

Answer:

The value that separates the bottom 4% is -1.75; the 40th percentile is D. -0.25 degrees; Q3 is A. 0.67 degrees.

Step-by-step explanation:

The bottom 4% has a probability of 4% = 4/100 = 0.04.  Using a z-table, we find the value closest to 0.04 in the cells of the chart; this is 0.0401.  This corresponds to a z value of -1.75.  

The formula for a z score is

[tex]z=\frac{X-\mu}{\sigma}[/tex]

Substituting our values for z, the mean and the standard deviation, we have

-1.75 = (X-0)/1

X-0 = X, and X/1 = X; this gives us

-1.75 = X.

The 40th percentile is the value that is greater than 40% of the other data values.  This means it has a probability of 0.40.  Using a z-table, we find the value closest to 0.40 in the cells of the chart; this is 0.4013.  This corresponds to a z value of -0.25.

Substituting this into our formula for a z score along with our values for the mean and the standard deviation,

-0.25 = (X-0)/1

X-0 = X, and X/1 = X; this gives us

-0.25 = X.

Q3 is the same as the 75th percentile.  This means it has a probability of 0.75.  Using a z-table, we find the value closest to 0.75 in the cells of the chart; this is 0.7486.  This corresponds to a z value of 0.67.

Substituting this into our z score formula along with our values for the mean and the standard deviation,

0.67 = (X-0)/1

X-0 = X and X/1 = X; this gives us

0.67 = X.

Using the normal distribution, it is found that:

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The temperature reading that separates the bottom​ 4% from the others is the 4th percentile, which is X when Z has a p-value of 0.04, so X when Z = -1.75.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.75 = \frac{X - 0}{1}[/tex]

[tex]X = -1.75[/tex]

The temperature reading that separates the bottom​ 4% from the others is -1.75 ºC.

The 40th percentile is X when Z has a p-value of 0.4, so X when Z = -0.25.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.25 = \frac{X - 0}{1}[/tex]

[tex]X = -0.25[/tex]

The 40th percentile is of -0.25 ºC, option D.

The third quartile is the 75th percentile, as [tex]\frac{3}{4}100 = 75[/tex], which is X when Z has a p-value of 0.75, so X when Z = 0.67.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.67 = \frac{X - 0}{1}[/tex]

[tex]X = 0.67[/tex]

The third quartile is of 0.67 ºC, option A.

A similar problem is given at https://brainly.com/question/12403139

Answer:

The area of the triangle is 43.5 cm².

Step-by-step explanation:

Since,  the area of a triangle is,

[tex]A=\frac{1}{2}\times s_1\times s_2\times sin \theta[/tex]

Where, [tex]s_1[/tex] and [tex]s_2[/tex] are adjacent sides and [tex]\theta[/tex] is the included angle of these sides,

Given,

[tex]s_1=12\text{ cm}[/tex]

[tex]s_2=8\text{ cm}[/tex]

[tex]\theta = 65^{\circ}[/tex]

Hence, the area of the given triangle is,

[tex]A=\frac{1}{2}\times 12\times 8\times sin 65^{\circ}[/tex]

[tex]=\frac{96\times 0.90630778703}{2}[/tex]

[tex]=\frac{87.0055475555}2}=43.5027737778\approx 43.5\text{ square cm}[/tex]

Answer:

Two parallel lines never intersect.

Step-by-step explanation:

The definition of a parallel line is: 2 lines that are exactly the same, but will not touch each other.

Answer with explanation:

~p means other line is Similar to p.

If there are two parallel lines , it means Perpendicular distance between the two lines is always constant, if measured by taking a point anywhere on the line.

⇒Two Parallel lines never intersect.

Option B

Answer:

[tex]\large\boxed{x\approx0.52}[/tex]

Step-by-step explanation:

[tex]2^{5x}=6\Rightarrow\log_22^{5x}=\log_26\qquad\text{use}\ \log_ab^n=n\log_ab\\\\5x\log_22=\log_26\qquad\text{use}\ \log_aa=1\\\\5x=\log_26\qquad\text{divide both sides by 5}\\\\x=\dfrac{\log_26}{5}\\\\\log_26\approx2.585\\\\x\approx\dfrac{2.585}{5}\to\boxed{x\approx0.52}[/tex]

Answer:

72 members

Step-by-step explanation:

Total surveyed members = 40

members voting yes = 12

probability of the members voting yes = 12/40 = 3/10

It is observed that, out of every 'n' members, n*(3/10) members are expected to vote yes:

Therefore,

number of members expecting to voye yes out of 240 are = 240 * 3/10

=> 24 * 3 = 72 members

Answer:

slope = - 5

Step-by-step explanation:

given the equation of a line in the form

y = mx ← m is the slope

y = - 5x is in this form with slope m = - 5

Answer:

plane velocity (with wind) = 500 mph

plane velocity (against wind) = 420 mph

velocity difference divided by 2 = 40

plane velocity = 500 - 40 = 460 mph

Step-by-step explanation:

Answer:

Step-by-step explanation:

One number would be

9.31

The 3 in this number is 3/10

The 3 in the given number is 3/100

3/10 is 10 times bigger than 3/100

3/10 = 0.3

3/100 = 0.03

0.03 * x = 0.3                   Divide both sides by 0.03

0.03/0.03 x = 0.3/0.03

x = 10

Answer:

C

Step-by-step explanation:

A function in the form  [tex]y=a*b^x[/tex] is an exponential function. If

The given function can be written as  [tex]y=1*0.8^x[/tex], so a > 0 and 0 < b < 1, hence this is exponential decay function.

For end behavior, we take limits from -∞ and from ∞. If we do that we can see that C is the correct answer. Also, looking at the graph explains it. Attached is the graph.

From the graph, as we move towards negative infinity, the graph goes towards positive infinity and as we move towards positive infinity, the graph goes towards 0.

Answer:

0.6826

Step-by-step explanation:

To solve this, we find the z scores for both sample means.  We then us a z table to find the area under the curve to the left of (probability less than) each z score, and subtract them to find the area between them.

The formula we use, since we are using sample means, is

[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]

Our x-bar will be 116 in the first z-score and 120 in the second; our mean, μ, is 118; our standard deviation, σ, is 6.3; and our sample size, n, is 10:

[tex]z=\frac{116-118}{6.3\div \sqrt{10}}=\frac{-2}{1.9922}\approx -1.0039\\\\z=\frac{120-118}{6.3\div \sqrt{10}}=\frac{2}{1.9922}\approx 1.0039[/tex]

Using a z table, we see that the area under the curve to the left of -1.00 is 0.1587.  The area under the curve to the left of 1.00 is 0.8413.  This makes the area between them

0.8413-0.1587 = 0.6826.

To solve this statistics problem, calculate the z-scores for the lengths 116 cm and 120 cm, using the given mean, standard deviation, and sample size. Then, use a z-table to find the probabilities associated with these z-scores. The difference between these probabilities will give the likelihood of the machine producing shells between these lengths.

This problem is essentially a question about probability in statistics, specifically relating to the normal distribution. Given that the machine is operating properly, and assuming that the lengths of the shells it produces are normally distributed with a mean of 118 cm and a standard deviation of 6.3 cm, we want to find the probability that the average length of 10 randomly selected shells is between 116 and 120 cm.

First, we need to find the z-scores corresponding to the lengths of 116 cm and 120 cm. The formula for the z-score is (X - μ)/σ, where X is the measurement (in this case, the average length of the shells), μ is the mean, and σ is the standard deviation. However, in this scenario, due to the application of the Central Limit Theorem, we must use σ/sqrt(N) as the standard deviation for the distribution of sample means, where N=10. Therefore, for 116 cm we get Z1 = (116 -118) / (6.3/ sqrt(10))  and for 120 cm we get Z2 = (120 - 118) / (6.3/sqrt(10)).

Once the Z-scores are calculated, we can use Z-tables (commonly found in statistics textbooks or online) to find the probabilities associated with these z-scores. Subtract the probability of Z1 from the probability of Z2 to get the desired range probability.

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Answer:

100

Step-by-step explanation:

The total length of ten pens laid end-to-end is

10 pens × 130 mm/1 pen = 1300 mm

The number of tiles needed to stretch the same length is

1300 mm × 1 tile/13 mm = 100 tiles

Helen uses 100 tiles.

Here is your answer

[tex]\bold{107.62} inches [/tex]

Since the door will be in shape of a rectangle where,

length= 80 inches

breadth= 72 inches

So,

widht of largest mattress that can fit diagonally is diagonal of the door.

i.e.

[tex]d= \sqrt{{l}^{2}+{b}^{2}}[/tex]

[tex]d= \sqrt{{80}^{2}+{72}^{2}}[/tex]

[tex]d= \sqrt{6400+5184}[/tex]

[tex]d= \sqrt{11584}[/tex]

[tex]d= 107.62[/tex]

HOPE IT IS USEFUL

The largest mattress to fit diagonally through the french doors measuring 72 inches by 80 inches is approximately 107.6 inches, using the Pythagorean theorem to calculate it.

To find the largest mattress that can fit diagonally through french doors with dimensions of 72 inches by 80 inches, we can use the Pythagorean theorem because the door creates a right-angle triangle. The diagonal can be calculated using the formula: diagonal = \/(width² + height²).

We plug in the dimensions: diagonal = \/(72² + 80²). First, square each dimension: 72² = 5184 and 80² = 6400. Then add these together: 5184 + 6400 = 11584. Now take the square root of 11584 to find the diagonal: diagonal = \/11584 which is approximately 107.6 inches.

Therefore, the largest mattress that can fit diagonally through the french doors rounded to the nearest tenth is 107.6 inches.

Answer:

A

Step-by-step explanation:

Nature of roots is determined by using the Discriminant, D, which is:

[tex]D=b^2-4ac[/tex]

If

D > 0, there are 2 real unique solutions

D = 0, there are 2 real equal solutions

D < 0, there are no real solutions

Note: a is the coefficient of x^2, b is the coefficient of x, and c is the independent term (the constant)

Now, for our quadratic expression, a = 3, b = 12, & c = -3. Plugging it in the discriminant formula, we get:

[tex]D=b^2-4ac\\D=(12)^2-4(3)(-3)\\D=180[/tex]

Thus, D > 0 , which means there are 2 distinct real solutions. Answer choice A is right.

Answer:

a:  It is binomial because it is either on time, or it's not. There are only 2 choices

b:  0.0668

c:  0.0319

d:  0.9681

e:  0.097

Step-by-step explanation:

The formula (nCr)(p^r)(q^(n-r)) will tell us the probability of binomial events occuring.  n is the population, r is the desired number of chosen outcomes, p is the probability of success, and q is the probability of failure. nCr tells us how many different ways we can choose r items from a total of n outcomes

Here, n = 17, p = 0.85, q = 0.15 and r depends on the question.

b.  r = 12, plug in the values into the formula...

(17C12)(0.85^12)(0.15^5) = 0.0668

c.  Use the compliment: the probability of fewer than 12 means 1 - P(12 or more), so 1 - (the sum of the probabilities or 12, 13, 14, 15, 16, or 17 flights being on time).  This will save some time when calculating...we have

1 - [ (17C12)(0.85^12)(0.15^5) + (17C13)(0.85^13)(0.15^4) + (17C14)(0.85^14)(0.15^3) + (17C15)(0.85^15)(0.15^2) + (17C16)(0.85^16)(0.15^1) + (17C17)(0.85^17)(0.15^0) ]

= 1 - 0.9681 =  0.0319

d:  this is what we just calculated before subtracting from 1 in the last problem, 0.9681

e.  This is the probability of 10, 11, or 12 flights being on time

(17C10)(0.85^10)(0.15^7) + (17C11)(0.85^11)(0.15^6) + (17C12)(0.85^12)(0.15^5)

= 0.97

This question deals with the concept of binomial distribution. The situation of selecting 17 flights and recording if they are on time is a binomial experiment as it meets the required conditions. The probabilities for the various scenarios can be calculated using the binomial probability formula.

This question pertains to the topic of binomial distribution in probability statistics. A binomial experiment is defined as a statistical experiment that meets specific parameters, such as a fixed number of trials with two potential outcomes (often defined as success and failure), and each trial is independent while repeated under identical conditions.

(a) The situation described - selecting 17 flights and recording whether they are on time or not - represents a binomial experiment because it satisfies these conditions. There are a fixed number of trials (17 flights), there are two outcomes (the flight is on time, or it's not), and each flight is an independent occasion.

(b) The probability of exactly 12 flights being on time can be calculated using the binomial probability formula: P(X=k) = C(n, k) *[tex](p^k) * ((1-p)^(n-k)).[/tex]Here, n=17, k=12, p=0.85 (the probability of a flight being on time).

(c), (d), (e) The probabilities that fewer than 12 flights are on time, at least 12 flights are on time, and between 10 and 12 flights (inclusive) are on time can also be calculated using the binomial formula, varying the value of k as required.

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QUESTION 1

We want to find the slope through the points (12,-18), (11,12).

We use the slope formula,

[tex]m = \frac{y_2-y_1} {x _2-x_1} [/tex]

We substitute the points to get,

[tex]m = \frac{12 - - 18}{11 - 12} [/tex]

[tex]m = \frac{30}{ - 1} = - 30[/tex]

The slope is -30.

QUESTION 2.

We want to find the slope through the points (-18, -20), (-18, -15).

We use the slope formula again to obtain,

[tex]m = \frac{ - 15 - - 20}{ - 18 - - 18} [/tex]

We simplify to get;

[tex]m = \frac{5}{0} [/tex]

Division by zero means the slope is not defined.

QUESTION 3

The given equation is 4x + y = 5.

At x-intercept, y=0.

We put y=0 into the equation to get,

[tex]4x + 0 = 5[/tex]

[tex]4x = 5[/tex]

[tex]x = \frac{5}{4} [/tex]

The x-intercept is

[tex]( \frac{5}{4} , 0)[/tex]

To find the y-intercept,we substitute x=0 into the equation to get,

[tex]4(0) + y = 5[/tex]

[tex]y = 5[/tex]

The y-intercept is (0,5)

QUESTION 4.

The given equation is

[tex]y = 5x - 4[/tex]

To find the y-intercept put x=0 into the equation.

[tex]y = 5(0) - 4[/tex]

[tex]y = - 4[/tex]

(0,-4)

To find the x-intercept, put y=0,

[tex]0 = 5x - 4[/tex]

[tex]4 = 5x[/tex]

[tex] \frac{4}{5} = x[/tex]

[tex]( \frac{4}{5} ,0)[/tex]

QUESTION 5

To find the equation of a line given the slope m, and a point

[tex](x_1,y_1) [/tex]

we use the formula,

[tex]y-y_1=m(x-x_1)[/tex]

The given line has slope zero and passes through

(3,4)

The equation is

[tex]y - 4 = 0(x - 3)[/tex]

[tex]y - 4 = 0[/tex]

[tex]y = 4[/tex]

Question 6

The given equation is

[tex]x = 1[/tex]

This is the equation of a line that is parallel to the y-axis.

The slope of all lines parallel to the x-axis is undefined.

The slope of x=1 is not defined.

Answer:

D

Step-by-step explanation:

Exponential equation takes the form  [tex]y=a*b^x[/tex]  where

The equation given in the problem can be written as  [tex]y=-4.8*4^x[/tex], so it is an exponential equation,  where a = -4.8 and b = 4.

Thus we can say that the initial value = -4.8 and the base is 4

The correct answer is  D

Answer:

d

Step-by-step explanation:

Answer:

18.15

Step-by-step explanation:

Percent means per hundred, so we can convert 4.6% and 3.65% to equivalent decimals.

4.6%= 4.6 divided by 100 = 0.046

3.65%= 3.65 divided by 100 = 0.0365

Since both sales tax rates apply to $220, we can add the two rates.

0.046 + 0.0365= 0.0825

0.0825 x 220 = 18.15

And so, Yuki pays$18.15 in sales tax for her handbag purchase.

Answer:

1. The marked answer is correct.

2. The only equivalent equation is the 2nd one: x^2 -12x +36 = 28

Step-by-step explanation:

The square of a binomial is ...

(x -a)^2 = x^2 -2ax +a^2

This tells you the constant term in the perfect square trinomial is the square of half the x-coefficient.

1. The x-coefficient is -8, so half that is -4. The square of -4 is 16. To complete the square, the added constant term must be 16, the marked answer.

___

2. The x-coefficient is -12, so the square of half that is (-6)^2 = 36. Adding 36 to the equation gives ...

x^2 -12x +36 = 28 . . . . . . matches the 2nd choice

_____

The rule that makes algebra work is this: whatever you do on one side of the equal sign must also be done on the other side.

If you add 36 on one side of the equation, you must add 36 on the other side. Of course addition of signed numbers is done in the usual way: 36 + (-8) = 28.

To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic. For each congruence, we substitute the given values of a and b and simplify the congruences to solve for c. The possible values of c are then determined using the Chinese Remainder Theorem when appropriate.

To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic:

a) To find c such that a.c ≡ 13a (mod 19), we divide both sides of the congruence by a. This gives us c ≡ 13 (mod 19).

b) To find c such that b.c ≡ 8b (mod 19), we divide both sides of the congruence by b. This gives us c ≡ 8 (mod 19).

c) To find c such that c.c ≡ a - b (mod 19), we square both sides of the congruence. This gives us c^2 ≡ (a - b)^2 (mod 19). Since we know a ≡ 11 (mod 19) and b ≡ 3 (mod 19), we substitute these values and simplify the congruence to c^2 ≡ 8 (mod 19). To solve this quadratic congruence, we can use the Chinese Remainder Theorem to find the two square roots of 8 modulo 19, which are 7 and 12. Therefore, c ≡ 7 (mod 19) or c ≡ 12 (mod 19).

d) To find c such that c.c ≡ 7a + 3b (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 7(11) + 3(3) ≡ 4 (mod 19). Similar to part (c), we use the Chinese Remainder Theorem to find the square roots of 4 modulo 19, which are 2 and 17. Therefore, c ≡ 2 (mod 19) or c ≡ 17 (mod 19).

e) To find c such that c.c ≡ 2a^2 + 3b^2 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 2(11^2) + 3(3^2) ≡ 2(121) + 3(9) ≡ 149 ≡ 2 (mod 19). Therefore, c ≡ ±4 (mod 19).

f) To find c such that c ≡ a^3 + 4b^3 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c ≡ 11^3 + 4(3^3) ≡ 11^3 + 4(27) ≡ 11^3 + 4(8) ≡ 11 + 32 ≡ 17 (mod 19). Therefore, c ≡ 17 (mod 19).

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➷ Find the multiplier:

1 + (3.4/100) = 1.034

Use this formula:

Final = original x multiplier^n

n is the number of years

Substitute the values in:

final = 6000 x 1.034^3

Solve:

final = 6633.0438

This can be rounded to the final answer of £6633.04

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

THX THIS HELPED ME A LOT

Step-by-step explanation:

Answer:

Step-by-step explanation:

You know there is only one solution because the ratio of x- and y-coefficients is different in the two equations. That means the lines will have different slopes, so must intersect in exactly one point.

__

The y-coefficients are opposites, so you can eliminate the y-variable by adding the equations:

  (2x -y) + (3x +y) = (2) + (-6)

  5x = -4

  x = -4/5 = -0.8

Substituting this into the second equation, we have ...

  3(-0.8) +y = -6

  y = -3.6 . . . . . . . add 2.4 to both sides

The solution is (x, y) = (-0.8, -3.6).

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You can also find the solution by graphing (or using a graphing calculator).

The system of linear equations has one and only one solution, which is (x, y) = (-4/5, -18/5).

This is a question about solving a system of linear equations. To determine whether a system has one, many, or no solutions, we add or subtract the equations to eliminate one of the variables, usually y or x.

Given the system of equations:

2x - y = 2

3x + y = -6

When we add the two equations together, we get 5x = -4, so x = -4/5.

Substitute x = -4/5 into the first equation to find y:

2(-4/5) - y = 2 => -8/5 - y = 2 => -y = 2 + 8/5 => y = -18/5.

Therefore, the system of equations has one and only one solution, which is (x, y) = (-4/5, -18/5).

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If you multiply the numerator and the denominator by the same number, it will be equal to 1/3.

For example:

1/3 * 3/3 = 3/9

1/3 * 8/8 = 8/24

Answer:

2/6, 3/9, and 4/12

Step-by-step explanation:

Any fraction where you can divide both the numerator and the denominator by the same number to get 1/3 also equals 1/3.

For example: 2/6

When you divide both numbers by 2, you get 1/3. Which means they are equivalent fractions (or equal).

Answer:

Step-by-step explanation:

Answer:

75 "I think"

Step-by-step explanation: