Simplify each sum or difference. State any restrictions on the variables.
1 / x² - 4 + 6 / x+2

ΔJKL has sides that measure 17.07 units.

So,

The formula of perimeter: √(x₂−x₁)²+(y₂−y₁)²

Filling the values in the formula, we obtain:

Then, each side of the triangle will be: 17.07 units

Therefore, ΔJKL has sides that measure 17.07 units.

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Answer:

56.1

Step-by-step explanation:

Answer:

The answer is in the attached screenshot!!! :)

Step-by-step explanation:

Please let me know if you have any questions!!! :)

The result of the given expression is negative fifth sixth

The interpretation of the statement as a linear function is expressed as;

-1/6(3) - 3(1/3)²

Expand the fraction in parenthesis

-1/6(3) = -1/2

3(1/3)² = 3(1/9) = 1/3

Substitute

-1/6(3) - 3(1/3)²

-1/2 - 1/3

-3-2/6
-5/6

Hence the result of the given expression is negative fifth sixth

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The side of the square inscribed in a square be a units then the required ratio is π : 2.

A square is inscribed in a circle or a polygon if its four vertices are on the circle's circumference or the polygon's sides.

Inscribed in the circle is a square that fits snugly inside a circle. The square's corners will touch but not intersect the circle's boundary, and the diagonal of the square will equal the diameter of the circle. Furthermore, as with any square's diagonal, it equals the hypotenuse of a 45°-45°-90° triangle.

Let the side of the square inscribed in a square be a units.

Hence, the required ratio is 2 : 1.

Let ABCD be a square inscribed in a circle of radius 'r'.

Now, the diameter of the circle is the diagonal of the square.

Therefore, BD = 2r.

In △BDC, using Pythagoras theorem

[tex]BC^2+CD^2=BD^2[/tex]

⇒ [tex]a^2+a^2=(2r)^2[/tex]

⇒ [tex]2a^2=4r^2[/tex]

⇒ [tex]a^2=2r^2[/tex]

Area of square=[tex]2r^2[/tex]

Area of circle =[tex]$$\pi r^2[/tex]

Required ration = [tex]$\pi r^2:2r^2[/tex] = π : 2

Therefore, the required ration is π : 2.

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Answer: y=-4x/9 + 1/3

Step-by-step explanation:

y=mx + c

**Substitute known variables into the equation**

-1=3m + 1/3

(-1=3m + 1/3)*3      ==> Multiply equation by 3 to get rid of fractions

-3=9m+1

9m=-4

m=-4/9

y=-4x/9 + 1/3

Answer:

Answers on attached image

Step-by-step explanation:

The closing price of the stock is 131.82 dollars.

A stock is an equity or share that represents the ownership of a fraction of a issuing corporation.If someone holds a stock more than 50% that person decides or in charge of most of the things in that co-corporation.

According to the given question The value of a stock opens at 130.48 on monday.

Given it change throughout the day as follow: -0.47, +2.89 , +3 .39 , -4. 47.

∴ The closing price of the stock will be

130.40 + ( -0.47 +2.89  +3 .39  -4. 47 )

= 130.48 + 1.34.

= 131.82 dollars.

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Answer:

X = √2 R , where X is the length of the legs as R is the length of the radius .

Step-by-step explanation:

The opposite sides of two same angled triangle is also same . So in this case we can say two legs are in same length as their opposite angles are same (45°)

Now , suppose the given radius is R (look at the diagram) then total diameter  is 2R ( DIAMETER = 2 × RADIUS )

Now , we will consider the length of the legs are X ( as the are same ).

Now, we will apply Pythagoras theorem ( The squares on the legs of a right triangle is equal to the square on the hypotenuse . )

∵  X² + X² = (2R)²

or , 2X² = 4R²

or, X² = 2R²

We will root both side

X = √2R

So , X is the length of the legs as R is the length of the radius .

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Answer: y=4x/3 + 1/3

Step-by-step explanation:

y=mx+c

**Substitute already known variables**

3=2m+1/3=

(3=2m+1/3)*3=      ==> Multiply the equation by 3 to get rid of fractions

9=6m+1

6m=8

m=8/6

m=4/3

y=4x/3 + 1/3

The sequence is in an arithmetic sequence, common difference is 2, next two term is 9 and 11.

The arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Here the sequence is 1, 3, 5, 7....

Here the sequence is in arithmetic sequence, so the common difference(d) is 3-1 = 5-3 = 2

So the common difference is 2

Now we need to find the next two terms, and for this, we have the formula to find the nth term of the sequence,

[tex]a_{n}[/tex] = a + (n-1)d

We have to find the 5th and 6th terms.

[tex]a_{5}[/tex] = 1 + 4×2

   = 1 + 8

   = 9

[tex]a_{6}[/tex] = 1 + 5×2

   = 1 + 10

   = 11

Therefore the sequence is in an arithmetic sequence, the common difference is 2 and the next two terms of the sequence are 9 and 11.

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According to the question, the given data is as shown below:

A hose with a larger diameter working alone is [tex]9[/tex] hours

A hose with a smaller diameter working alone is [tex]18[/tex] hours

Now, the time taken by the larger hose to fill the pool is [tex]\frac{1}{9}[/tex]

Similarly, the time taken by the smaller hose to fill the pool is [tex]\frac{1}{18}[/tex]

When they are working together, the expression can be written as:

[tex]\frac{1}{9} +\frac{1}{18} =\frac{1}{a}[/tex]

[tex]\frac{1}{a} =\frac{27}{9X18} =\frac{1}{6}[/tex]

The total time taken by the two hoses to fill the swimming pool is [tex]6[/tex] hours.

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Answer:

The rate of the hose with the large diameter is : 1/9

What is the unknown in the problem? : C. The time it takes for the hoses working together to fill the pool

What part of the job does the hose with the large diameter do? : x/9

Answer:

2 days: 1 week

Step-by-step explanation:

4 days : 2 weeks

2 2

2:1

Answer:

Step-by-step explanation:

So we Have 4 days to 2 weeks

In order to simplify this, we need to turn weeks into days

2 x 7 = 14

so 4 days to 14 days

Now we divide and fnd a common multiple

4/2 = 2

and 14/2 = 7

so, 2 days to 7 days, or 2/7

We can leave it at that, or turn it into a decimal

4/14 =0.2857

Hope this helps!^^

Answer: Lord Farquaad

Step-by-step explanation: E

Answer:

x>18

Step-by-step explanation:

45+0.45x>50.40+0.15x

-0.15 -0.15

45+0.3>50.40

-45 -45

5.4>0.3

X>18

Just search it up online

Answer:

10

Step-by-step explanation:

:D

Using algebraic expression and equation, an executive assistant invested $14,000 and $7,000 at the rate of 8% and 5% annual interest, respectively.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Given that an executive invest a total of $21,000, we can express this as:

x + y = 21,000     ⇒     x = 21,000 - y     (equation 1)

where x = amount invested at 8% annual interest

y = amount invested at 5% annual interest

If the annual return is $1,470, then the sum of the product of the rate and the amount is equal to the annual return.

8%x + 5%y = $1,470

0.08x + 0.05y = 1,470     (equation 2)

Substitute equation 1 to equation 2 and solve for y.

0.08(21,000 - y) + 0.05y = 1,470

1680 - 0.08y + 0.05y = 1470

-0.03y = -210

y = 7000

amount invested at 5% annual interest = $7000

x = 21,000 - y

x = 21,000 - 7000

x = 14,000

amount invested at 8% annual interest = $14000

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Answer:

Asking people at an international airport can be thought of as bias because   there might a lot of people at the airport who are old and who like to travel.

Asking people whether they’d prefer Italy or France could be bias because what if the people are Italian? Then they’d obviously choose Italy. Or maybe they’re French and they’ve lived in France and been to France too many times and they’d rather visit Italy.

If 86% of people asked took a French course, you can assume they want to learn French (obviously) and that they probably want to learn French so they can visit and be able to communicate with others in France.

Step-by-step explanation:

In linear equation, the intersection at coordinate (9, 315).

What in mathematics is a linear equation?

Gym one:

f(x) =80 x + 25

Gym two:

g(x) = 35x (+ 0 [since there was no joining fee])

The first month is easy.

Gym one's cost is just the joining fee plus the one month of membership fee. Or...

105 = 80(1) + 25

Gym two's cost is just that first month's membership fee. Or...

35 = 35(1) + 0

then  second month

[f(x) = 185 = 80(2)+25

g(x) = 70 = 35(2)],

then a tenth month [

f(x) = 825 = 80(10) + 25;

g(x) = 350 = 35(10)]

and  that gym one's cost exceeded the cost of gym two,

back one month and found the answer.

By month nine, both gyms had equalized at $315.

the intersection at coordinate (9, 315).

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A triangle's centroid is the point through which all of the mass of a triangular plate appears to act.

The centroid of a triangle is the point through which all of the mass of a triangular plate appears to act. Also known as the "center of gravity," "center of mass," or "barycenter." A fascinating fact is that the centroid is the point at which the triangle's medians intersect.

The triangle's centroid is defined as the point of convergence. Three triangle medians intersect at the figure's centroid "G." The center of gravity is another name for a centroid.

The triangle is divided into two equal-area triangles by each median. The centroid is the intersection of the three medians The centroid is the intersection of the three medians. The three medians divide the triangle into six triangles, each with the same area.

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The regular polygon with an interior angle of measure 135 is an octagon.

A regular polygon is a polygon that has equal side lengths and equal interior angle measures.

Interior angle of a polygon is the angle inside it that is formed by two adjacent sides. The number of interior angles formed inside a polygon is the same as the number of its sides. Meanwhile, the sum of all the interior angles of any polygon is constant to that polygon and depends on the number of sides.

sum = 180(n - 2)

Let n = number of sides of the polygon = number of interior angles

sum = measure of interior angle x n

Using the formula,

sum = 180(n - 2)

135n = 180(n - 2)

135n = 180n - 360

180n - 135n = 360

45n = 360

n = 8

If the polygon has 8 sides and 8 interior angles, then the regular polygon is an octagon.

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Answer:

14 1/3

Step-by-step explanation:

You have to divide 86 by 6, which gives you 14 with a remainder of 2. This would result in 14 2/6, or simplified: 14 1/3

Answer:

14 2/6

Step-by-step explanation:

We want to transform 86/6 into a mixed number. We can achieve this by following these steps:

Step 1: Divide the numerator (86) by the denominator (6):

86 / 6 = 14 remainder 2

Step 2: Build your answer using the quotient (14) as the whole number and the remainder (2) as the numerator, keeping the same denominator (6). Thus,

The improper fraction 86/6

is equivalent to 14 2/6

simplest form is 14 1/3

The solution of the given equation /x + x/2 = x+ 4/2x for x is i√2.

According to the given question.

We have an equation 1/x + x/2 = x+ 4/2x.

Since, we have to solve th egiven equation 1/x + x/2 = x+ 4/2x, for x.

Therefore, the solution of the given equation 1/x + x/2 = x+ 4/2x for x is given by

1/x + x/2 = x+ 4/2x

⇒ 1/x - 4/2x = x - x/2

⇒ 1/x -2/x  = x - x/2

⇒ (1-2)/x    = (2x -x)/2

⇒ -1/x  = x/2

⇒ -2 = x^2

⇒ x = √(-2)

⇒ x = i√2   (√-1 = i)

Hence, the solution of the given equation /x + x/2 = x+ 4/2x for x is i√2.

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Answer:

Common difference = x - 2.

Step-by-step explanation:

Differences:

-2x - 9 - (-3x - 7)

= -2x - 9 + 3x + 7

= x - 2

-x - 11 - (-2x - 9)

= - x - 11 +2x + 9

= x - 2

So, it is Arithmetic.

Answer:

Arithmetic sequence.

Common difference = -x - 11

Step-by-step explanation:

This is an arithmetic sequence.

-3x - 7, -2x - 9,  -x - 11, ...

Find the common difference.

Common difference =second term - first term.

                                 = -2x - 9 - (-3x - 7)

                                = -2x -  9 + 3x  +7

                                = -2x + 3x - 9 + 7      {Combine like terms}

                                = x - 2

If we add the common difference to the second term, we will get the third term.

Third term = second term + common difference

                  = -2x - 9 + x - 2

                  = -2x + x - 9 - 2

                  = -x - 11.

Hence this is an arithmetic sequence.

32(-5) + 0 + 160 = 0 is the line in the general form of the line the passing through (−5,0) with the slope 32.

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics. There is no obvious reason why the letter m is used to represent slope, although it first appears in English in O'Brien (1844), who wrote the equation for a straight line as "y = mx + b," and it may also be found in Todhunter (1888), who wrote it as "y = mx + c."

Let us write the given data in slope-intercept form that is

y = m(x) + b

where m = slope of the line

b = y-intercept

So substituting the values we get

0 = 32(-5) + b

-b = -160

b = 160

so we have the slope intercept form

0 = 32(-5) + 160

Converting this to General form

ax + by + c = 0

32(-5) + 0 + 160 = 0

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Translated question

Given the following conditions, determine the equation of the line in its general form Ax+By+C=0.

It passes through (−5,0) and has slope m=32.

Answer: A=n(b^2-r)

Step-by-step explanation:

r + A/n = b^2

r-r+A/n = b^2-r

A/n = b^2-r

A*n/n=n(b^2-r)

A=n(b^2-r)

Given statement 'The sum of two vectors is the resultant.' is True.

We know that in mathematics, a vector is a quantity that has both magnitude and direction but no position.

Examples : velocity, force and acceleration.

Also, the resultant vector is the vector sum of two or more vectors. We find the resultant vectors by  adding two or more vectors together. Any two vectors can be added if and only if they are the same vector quantity.

For vector P = [tex]a\vec i+b\vec j[/tex] and vector Q = [tex]m\vec i+n\vec j[/tex]

The resultant vector R would be,

R = P + Q

R = [tex](a+m)\vec i+(b+n)\vec j[/tex]

Therefore, given  statement 'The sum of two vectors is the resultant.' is True.

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Answer:yes b

Step-by-step explanation:because tou add it