Solve the given systems of equations:
x-y+z=1
-3x+2y+z=1
2x-3y+4z=3​

The difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).

Thus, the correct option would be:

C. (x + 12)/(x(x+2))

To find the difference of the rational expressions, we need to subtract the second expression from the first expression.

Let's simplify the expressions first:

The first expression is 6/x - 5x/(x+2).

To combine the terms, we need a common denominator, which is (x)(x+2).

Converting the first term, 6/x, to have a denominator of (x)(x+2), we get (6(x+2))/(x(x+2)).

Now, we can combine the terms:

[(6(x+2))/(x(x+2))] - [5x/(x+2)]

To subtract the fractions, we need to have a common denominator, which is (x)(x+2).

Expanding the numerators, we get:

[(6x + 12)/(x(x+2))] - [5x/(x+2)]

Now, we can subtract the fractions:

[(6x + 12 - 5x)/(x(x+2))]

Simplifying the numerator, we have:

(6x - 5x + 12)/(x(x+2))

Combining like terms, we get:

(x + 12)/(x(x+2))

Therefore, the difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).

Thus, the correct option would be:

C. (x + 12)/(x(x+2))

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Answer:

hope you get it....sorry for any mistake calculations

Answer:

80

Step-by-step explanation:

The quadrilateral is a kite.

The angle opposite to angle H is equal to angle H.

Angle F = 110 degrees

Angles in a quadrilateral add up to 360 degrees.

60 + 110 + 110 + G = 360

280 + G = 360

G = 360 - 280

G = 80

The measure of angle G is 80 degrees.

Answer: 80 degrees.

Step-by-step explanation:

In a kite, the angles formed by noncongruent sides are congruent.  Thus, <EFG is 110 degrees.  Then, because a kite is a quadrilateral, all of the angles in it add up to 360.  Thus, is <FGH = x, then 110+110+60+x=360.  Thus, x = 80.

Hope it helps <3

Answer:

[tex]-5<x<26[/tex].

Step-by-step explanation:

We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.

Angle opposite to larger side is larger.

Since, 14 < 15, therefore

[tex]2x+10<62[/tex]

[tex]2x<62-10[/tex]

[tex]2x<52[/tex]

[tex]x<26[/tex]          ...(1)

We know that, angle can not not negative.

[tex]2x+10>0[/tex]

[tex]2x>-10[/tex]

[tex]x>-5[/tex]        ...(2)

From (1) and (2), we get

[tex]-5<x<26[/tex]

Therefore, the range of values of x is [tex]-5<x<26[/tex].

Work Shown:

[tex]\sin^2 \theta + \cos^2 \theta = 1\\\\\left(\frac{3}{10}\right)^2 + \cos^2 \theta = 1\\\\\frac{9}{100} + \cos^2 \theta = 1\\\\\cos^2 \theta = 1 - \frac{9}{100}\\\\\cos^2 \theta = \frac{100}{100}-\frac{9}{100}\\\\\cos^2 \theta = \frac{91}{100}\\\\\cos \theta = \sqrt{\frac{91}{100}} \ \text{ cosine positive in Q1}\\\\\cos \theta = \frac{\sqrt{91}}{\sqrt{100}}\\\\\cos \theta = \frac{\sqrt{91}}{10}\\\\[/tex]

Answer:

√91/10

Step-by-step explanation:

sin 0.3 is equal to 18(approximate value)

cos18°=0.951

which is √91/10

Answer:

2.25

Step-by-step explanation:

The computation of the number c that satisfied is shown below:

Given that

[tex]f(x) = \sqrt{x}[/tex]

Interval = (0,9)

According to the Rolle's mean value theorem,

If f(x) is continuous in {a,b) and it is distinct also

And, f(a) ≠ f(b) so its existance should be at least one value

i.e

[tex]f^i(c) = \frac{f(b) - f(a)}{b -a }[/tex]

After this,

[tex]f(x) = \sqrt{x} \\\\ f^i(x) = \frac{1}{2}x ^{\frac{1}{2} - 1} \\\\ = \frac{1}{2}x ^{\frac{-1}{2}[/tex]

[tex]f^i(x) = \frac{1}{{2}\sqrt{x} } = f^i(c) = \frac{1}{{2}\sqrt{c} } \\\\\a = 0, f (a) = f(o) = \sqrt{0} = 0 \\\\\ b = 9 , f (b) = f(a) = \sqrt{9} = 3\\[/tex]

After this,

Put the values of a and b to the above equation

[tex]f^i(c) = \frac{f(b) - f(a)}{b - a} \\\\ \frac{1}{{2}\sqrt{c} } = \frac{3 -0}{9-0} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{3}{9} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{1}{3} \\\\ \sqrt[2]{c} = 3\\\\\sqrt{c} = \frac{3}{2} \\\\ c = \frac{9}{4}[/tex]

= 2.25

Answer:

a) rCn = 1176

b) 2352

Step-by-step explanation:

a)Each committee should be formed with 3 members ( no two members could be of the same state) then

Let´s  fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then

rCn =  n! / (n - r )! *r!

rCn =  49!/ (49 - 2)!*2!

rCn =  49*48*47! / 47!*2!

rCn = 49*48 /2

rCn = 1176

So we can choose in 1176 different ways a senator for a given state

b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.

1176*2 = 2352

Answer:

n = 13

Step-by-step explanation:

24 = 3 (n-5)

3n  - 15 = 24

3n = 24 +15

3n = 39

n = 39/3

n = 13

Answer:

[tex]\boxed{\sf n=13}[/tex]

Step-by-step explanation:

[tex]\sf 24=3(n-5)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]\sf 24=3n-15[/tex]

[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]

[tex]\sf 24+15=3n-15+15[/tex]

[tex]\sf 39=3n[/tex]

[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]

[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]

[tex]\sf 13=n[/tex]

Answer: 189 mg.

Step-by-step explanation:

Let x be the weight of the body( in pounds) and y be the amount of medicine( in mg).

Given: A certain medicine is given in an amount proportional to patient’s body weight.

i.e. [tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]

Let [tex]x_1=116\ \ \ ,\ y_1=126[/tex] ,  [tex]x_2=174[/tex]

then,

[tex]\dfrac{116}{126}=\dfrac{174}{y_2}[/tex]

[tex]\Rightarrow\ y_2=\dfrac{174\times126}{116}\\\\\Rightarrow\ y_2=189[/tex]

Hence, he amount of medicine required by patient weighing 174 pounds = 189 mg.

Answer:

B.77.4%

Step-by-step explanation:

Mean wage (μ) = $4.50

Standard deviation (σ) = $0.50

For nay given salary X, the z-score is given by:

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

For X = $3.75, the z-score is:

[tex]z=\frac{3.75-4.50}{0.50}\\z=-1.5[/tex]

For X = $5.00, the z-score is:

[tex]z=\frac{5.00-4.50}{0.50}\\z=1[/tex]

A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:

[tex]P=84.13-6.68\\P=77.45\%[/tex]

The answer is alternative B.77.4%

Answer:

Option D is the correct option.

Step-by-step explanation:

Given: 3 boxes with volumes 1331 , 1331 , 729

To find : Height of stacked boxes

[tex]h {1}^{3} = 1331 = h1 = \sqrt[3]{1331} = 11[/tex]

[tex]h {2}^{3} = 1331 = h2 = \sqrt[3]{1331} = 11[/tex]

[tex]h {3}^{3} = 729 = h3 = \sqrt[3]{729} = 9[/tex]

Now,

[tex]h = h1 + h2 + h3[/tex]

[tex] = 11 + 11 + 9[/tex]

[tex] = 31[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Sample size

Step-by-step explanation:

Central Limit Theorem states that population with mean and standard deviation and if the sample size is large then the distribution of sample mean will be will be normally distributed. The central limit theorem holds assumptions that the factors to be considered when assessing central limit theorem is sample size.

The CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.

It is given that the objective that central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds.

It is required to describe the above theorem.

It is defined as the in statistics the assumption holds that the sample means distribution of arbitrary variables follows a normal distribution or close to normal distribution if the sample size is big.

We have an objective:

The CLT is the factor to be considered when assessing if the CLT holds a large sample size.

If we draw the random sample data and its measures, the Central limit theorem explains the distribution will explain the normal bell curve, the mean of the parameters and the distribution will be the same.

Thus, the CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.

Learn more about the Central limit theorem here:

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Answer:

x=-3/5 and y=-38/5

Step-by-step explanation:

y=6x-4  

y= x -7 substitute y=6x-4

6x-4=x-7

6x-x=-7+4

5x=-3

x=-3/5 ( substitute for x in y=6x-4)

y=6(-3/5)-4

y=-18/5-4

y=(-18-20)/5= -38/5

Answer:  D. y = (x - 3)² + 2

Step-by-step explanation:

Inverse is when you swap the x's and y's and solve for y.

               y = [tex]\sqrt{x-2}[/tex] + 3

Swap:      x = [tex]\sqrt{y-2}[/tex] + 3

Solve:  x - 3 = [tex]\sqrt{y-2}[/tex]

           (x - 3)² = [tex](\sqrt{y-2})^2[/tex]

           (x - 3)² = y - 2

    (x - 3)² + 2 = y

Answer:

B

Step-by-step explanation:

Answer:

the 2nd one

Step-by-step explanation:

because the Minimum is 20

the Maximum is 31

the median is 23

20, 21, 22, 23, 25, 27,  31,

21, 22, 23, 25, 27

22, 23, 25,

23

Answer:

D. 6

Step-by-step explanation:

here, as given set Q consists { 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36}

and set Z contains {3, 6, 9, 12, 15, 18, 21,24, 27, 30, 33, 36, .... }

so be comparing both, we can see that the numbers 6, 12, 18, 24, 30 and 36 is repeated.

Answer:

B. 168 students

Step-by-step explanation:

Given that there are a total of 600 students.

28% of the students pack their lunch.

To find:

Total number of students who pack their lunch = ?

Solution:

Percentage of a given number is calculated using the following method.

[tex]y\%[/tex] of a number [tex]x[/tex] is given by:

[tex]x \times \dfrac{y}{100}[/tex]

i.e. multiply the number by percentage to be found and divide by 100.

So, we have to find 28% of 600 here, to find the answer to the question.

[tex]\therefore[/tex] Number of students who pack their lunch is given as: (Multiply the given number 600 with 28 and divide by 100.)

[tex]600 \times \dfrac{28}{100}\\\Rightarrow 6 \times 28\\\Rightarrow \bold{168}[/tex]

So, the correct answer is:

B. 168

Answer:

Step-by-step explanation:

According to the angle sum theorem, the interior angles of a triangle add up to 180 degrees:

So, we can use the following equation to find x:

x+(x+10)+(210-3x)=180

now add like terms:

x+x+(-3x)+10+210=180

-x+220=180

now isolate the variable:

-x=180-220

-x=-40

x=-40/-1

x=40/1

x=40

The answer is that: the measure of x is 40 degrees

Answer:

ln(60)

Step-by-step explanation:

We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].

Step-by-step explanation:

Intersecting secant angles theorem: The angle between two secants is half the difference of the intersected arcs.

52 = ½ (x − 38)

x = 142

Arc angles add up to 360.

360 = 80 + 38 + z + x

z = 100

Tangent-chord theorem: The angle between a tangent and a chord is half the intercepted arc angle.

y = x/2

y = 71

Answer:

18.8 cubic inches

Step-by-step explanation:

1. Solve for the volume of Cup A. (volume of a cone = 1/3πr² · h)

1/3 · 3.14 · 1² · 3 = 3.14 in³

2. Solve for the volume of Cup B (volume of a cylinder = πr² · h)

3.14 · 1² · 7 = 21.98 in³

3. Subtract the volume of Cup A from Cup B

21.98 - 3.14 = 18.84

4. Round 18.84 to the nearest tenth

18.84 → 18.8 in.³

Answer:

18 .8

Step-by-step explanation:

got it right on test

Answer:

Step-by-step explanation:

[tex]A=\pi r^2\\Area = 36\pi\\r = ?\\36\pi = \pi r^2\\Divide \:both \:sides \:of\: the \:equation\: by\: \pi\\\frac{36\pi}{\pi} = \frac{\pi r^2}{\pi} \\r^2 = 36\\Find\: the\: square\: root\: of\: both\: sides\: \\\sqrt{r^2} =\sqrt{36} \\\\r = 6\: feet\\[/tex]

Answer:

The greatest possible value of [tex]y^3=216[/tex]

Step-by-step explanation:

We have the statement [tex]y^2=36[/tex], and we have to find the greatest possible value of [tex]y^3[/tex], first we need to find the value of y.

[tex]y^2=36[/tex], to get the y by itself on the left side, we need to take the square root of both sides. [tex]\sqrt{y^2} =\sqrt{36}[/tex] The square root of [tex]y^2[/tex] is y, because y*y = [tex]y^2[/tex], and the square root of 36 is 6 or -6.

We now need to find the greatest value of [tex]y^3[/tex]. When we plug in 6 to [tex]y^3[/tex], we get positive 216, and when we plug in -6, we get -216. We need to find the greatest possible value, so in this case we compare 216 and -216, 216 is greater than -216, so the answer would be positive 216.

Answer:

216

Step-by-step explanation:

If y² = 36, then y is 6 or -6. When y = 6, we have y³ = 6³ = 216. When y = -6, we have y³ = (-6)³ = -216. The greatest possible value of y³ is 216.

Answer:

(a) 3:5

(b) 15

Step-by-step explanation:

Well first we need to create a ratio for the 5 shades squares and 3 non+shaded squares.

It is asking for unshaded first so our ratio will be,

3:5

(a) 3:5

So if there is 9 unshaded how many shaded is there.

Well we can just make the following ratio 9:x

So 9/3 = 3

Meaning 3*5 = 15

So x = 15

(b) 15

Answer:

a) 3/5

b) 15

Step-by-step explanation:

(a)

unshaded: 3

shaded: 5

unshaded to shaded: 3/5

(b)

There are now 3 unshaded squares. You need 9 unshaded squares, so you need to have three times as many total squares as you have now.

Add two more lines just like the given line.

Each new line will have 5 shaded and 3 unshaded squares.

Now you have a total of 9 unshaded and 15 shaded squares.

Answer:

31 adults, 62 children, and 86 students.

Step-by-step explanation:

The seating capacity of the movie theatre = 179

Children's(c) Ticket = $5.00

Student's(s) Tickets = $7.00

Adult's(a) Tickets = $12.00

There are half as many adults as there are children.

The total ticket sales was $1284

We then solve the three resulting equations simultaneously.

c+s+a=179

c=2a

5c+7s+12a=1284

We substitute c=2a into the first and third equation

[tex]2a+s+a=179 \implies s=179-3a\\5(2a)+7s+12a=1284 \implies 22a+7s=1284[/tex]

Substitute s=179-3a into 22a+7s=1284

[tex]22a+7(179-3a)=1284\\22a+1253-21a=1284\\a=1284-1253\\a=31[/tex]

Recall:

c=2a

c=2*31

c=62

Finally:

c+s+a=179

62+s+31=179

s=179-62-31

s=86.

Therefore:

31 adults, 62 children, and 86 students attended the movie theatre.

Answer:

B. (1,7)

Step-by-step explanation:

We can substitute the x and y values of each coordinate into the inequality and test if they work.

Let's start with A, 5 being y and 0 being x .

[tex]5 > |0|+5\\5> 0+5\\5 > 5[/tex]

5 IS NOT greater than 5, they are the exact same, so A is out.

Let's try B, 1 being x and 7 being y.

[tex]7 > |1| + 5\\7 > 1 + 5\\7 > 6[/tex]

7 IS greater than 6, so B. (1,7) does work for this inequality!

Let's do C for fun, when 7 is x and 1 is y.

[tex]1 > |7| + 5\\1>7+5\\1>12[/tex]

1 IS NOT greater than 12, it is quite less than 12, so C doesn't work.

Therefore B. (1,7) works for the inequality of [tex]y > |x|+5[/tex].

Hope this helped!

Answer:

(a) 5/7 chance

(b) 2/7 chance

(c) 5/7 chance

Step-by-step explanation:

Event X: There are 3 letters that come before "D". A, B, and C. There is a 3 out of 7 chance of picking one of those letters. (3/7)

Event Y: There are 4 letters in "C A G E". Those 4 letters are in the 7 first letters of the alphabet meaning that they are in our pile of tiles. There is a 4 out of 7 chance of picking one of those letters. (4/7)

(a) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 5/7 chance of either Event X or Event Y happening since tiles "A" and "C" are included in both events.

(b) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 2/7 chance of both X and Y happening since there are only 2 tiles that are the same in both events, "A" and "C". (We are only allowed to pick one tile)

(c) The complement of Event Y is 1-4/7=5/7 chance.

Answer:

a) 5/7 chance

(b) 2/7 chance

(c) 5/7 chance

Step-by-step explanation:

Event X: There are 3 letters that come before "D". A, B, and C. There is a 3 out of 7 chance of picking one of those letters. (3/7)

Event Y: There are 4 letters in "C A G E". Those 4 letters are in the 7 first letters of the alphabet meaning that they are in our pile of tiles. There is a 4 out of 7 chance of picking one of those letters. (4/7)

(a) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 5/7 chance of either Event X or Event Y happening since tiles "A" and "C" are included in both events.

(b) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 2/7 chance of both X and Y happening since there are only 2 tiles that are the same in both events, "A" and "C". (We are only allowed to pick one tile)

(c) The complement of Event Y is 1-4/7=5/7 chance.

Answer:

23

Step-by-step explanation:

since the number is relatively prime to the product of the first 20 positive numbers

It number must not have factor of (1-20)

Therefore the smallest possible number is the next prime after 20

Answer is 23

The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,

⇒ 23

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Since, The number is relatively prime to the product of the first 20 positive numbers means a number which must not have factor of (1 - 20).

Hence, The smallest possible number is the next prime after 20 is, 23

Therefore, The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,

⇒ 23

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