30 POINTS!!!!
Please turn this into an EQUATION
One-half times the difference of twenty and a variable is two thirds
Here are the possible answers

An easy way to estimate would be to choose numbers close such as 90x400, which equals 36,000.

The true answer is 87*403 = 35,061.

3 600

Step-by-step explanation:

First multiply 87 to the nearest ten then multiply 403 to the nearest hundred which will give you 90 and 400. Multiply the two to get your answer

Answer:

y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((-2 x - 1/4))

x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((-2 i) y + 1/4))

Step-by-step explanation:

Solve for y:

(x + (0 + i) y)^2 = x + (0 - i) y

Subtract -i y + x from both sides:

-x + (i y + x)^2 + i y = 0

Expand and collect in terms of y:

-x + x^2 + y (2 i x + i) - y^2 = 0

Multiply both sides by -1:

x - x^2 + y (-2 i x - i) + y^2 = 0

Subtract -x^2 + x from both sides:

y (-2 i x - i) + y^2 = x^2 - x

Add 1/4 (-2 i x - i)^2 to both sides:

1/4 (-2 i x - i)^2 + y (-2 i x - i) + y^2 = 1/4 (-2 i x - i)^2 - x + x^2

Write the left hand side as a square:

(1/2 (-2 i x - i) + y)^2 = 1/4 (-2 i x - i)^2 - x + x^2

Take the square root of both sides:

1/2 (-2 i x - i) + y = sqrt(1/4 (-2 i x - i)^2 - x + x^2) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

Subtract 1/2 (-2 i x - i) from both sides:

y = 1/2 (2 i x + i) + sqrt((((-2 i) x - i)^2)/4 - x + x^2) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

1/4 (-2 i x - i)^2 - x + x^2 = -2 x - 1/4:

y = 1/2 (2 i x + i) + sqrt((-2 x - 1/4)) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

Subtract 1/2 (-2 i x - i) from both sides:

y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((((-2 i) x - i)^2)/4 - x + x^2)

1/4 (-2 i x - i)^2 - x + x^2 = -2 x - 1/4:

Answer: y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((-2 x - 1/4))

________________________

Solve for x:

(x + (0 + i) y)^2 = x + (0 - i) y

Subtract -i y + x from both sides:

-x + (i y + x)^2 + i y = 0

Expand and collect in terms of x:

x^2 + x (2 i y - 1) + i y - y^2 = 0

Subtract -y^2 + i y from both sides:

x^2 + x (2 i y - 1) = y^2 - i y

Add 1/4 (2 i y - 1)^2 to both sides:

x^2 + x (2 i y - 1) + 1/4 (2 i y - 1)^2 = 1/4 (2 i y - 1)^2 - i y + y^2

Write the left hand side as a square:

(x + 1/2 (2 i y - 1))^2 = 1/4 (2 i y - 1)^2 - i y + y^2

Take the square root of both sides:

x + 1/2 (2 i y - 1) = sqrt(1/4 (2 i y - 1)^2 - i y + y^2) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

Subtract 1/2 (2 i y - 1) from both sides:

x = 1/2 (-2 i y + 1) + sqrt((((2 i) y - 1)^2)/4 - i y + y^2) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

1/4 (2 i y - 1)^2 - i y + y^2 = -2 i y + 1/4:

x = 1/2 (-2 i y + 1) + sqrt(((-2 i) y + 1/4)) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

Subtract 1/2 (2 i y - 1) from both sides:

x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((2 i y - 1)^2)/4 - i y + y^2)

1/4 (2 i y - 1)^2 - i y + y^2 = -2 i y + 1/4:

Answer: x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((-2 i) y + 1/4))

Answer:

Step-by-step explanation:

According to the geometric diagram and the definition of the area for a rectangle, the area of the rectangle is 16√3 + 32 square milimeters.

In this problem we find a geometric system formed by a rectangle and three inscribed triangles. The detailed geometric diagram is introduced in the image attached below, in which we find that the triangle formed by the centers of the three circles is equilateral.

The area of the rectangle is equal to the product of its height and its width, whose dimensions are:

Height: h = 2 · 0.5√3 · (2 mm) + 2 · (2 mm) = 2√3 + 4 mm

Width: w = 4 · (2 mm) = 8 mm

A = h · w

A = (2√3 + 4 mm) · (8 mm)

A = 16√3 + 32 mm²

The area of the rectangle is 16√3 + 32 square milimeters.

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The features of the triangle are summarized below:

In this problem we find the case of a triangle whose three sides (AB, AC, BC) are known. First, we rationalize the expression for AC, that is, eliminate the irrational denominator by algebraic means:

AC = 1 / (√7 - √6)

AC = [1 / (√7 - √6)] · [(√7 + √6) / (√7 + √6)]

AC = (√7 + √6) / [(√7 - √6) · (√7 + √6)]

AC = (√7 + √6) / (7 - 6)

AC = √7 + √6

Second, we determine the square of each side:

AB² = (√7 + √6)²

AB² = 7 + 2√42 + 6

AB² = 13 + 2√42

AC² = (√7 + √6)

AC² = 13 + 2√42

BC² = (√14 + 2√3)²

BC² = 14 + 4√42 + 12

BC² = 26 + 4√42

BC² = 2 · (13 + 2√42)

BC² = 2 · AB² = 2 · AC²

Third, deduce the nature of the triangle:

Since BC = √2 · AB = √2 · AC, then the triangle ABC is a right triangle with internal angles 45° - 45° - 90°.

Fourth, calculate the area of the triangle by Heron's formula:

s = 0.5 · (AB + AC + BC)

s = 0.5 · (√7 + √6 + √7 + √6 + √14 + 2√3)

s = 0.5 · (2√7 + 2√6 + √14 + 2√3)

s = √7 + √6 + 0.5√14 + √3

A = √[s · (s - AB) · (s - AC) · (s - BC)]

A = √[(√7 + √6 + 0.5√14 + √3) · (√7 + √6 + 0.5√14 + √3 - √7 - √6) · (√7 + √6 + 0.5√14 + √3 - √7 - √6) · (√7 + √6 + 0.5√14 + √3 - √14 - 2√3)]

A = √[(√7 + √6 + 0.5√14 + √3) · (0.5√14 + √3) · (0.5√14 + √3) · (√7 + √6 - 0.5√14 - √3)]

A = √[8.698 · (8.698 - 5.095) · (8.698 - 5.095) · (8.698 - 7.206)]

A = √(8.698 · 3.603² · 1.492)

A ≈ 12.980

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Answer:

the fraction is 2/5

Step-by-step explanation:

4/5 + 1/2

=2/5

Duncan's height is the closest to the mean for the given normal distribution.

We learn from the question that

Given that 3-year-old boys' heights are roughly normally distributed, the mean will be the 50th.

Thus, comparing Duncan's height in the 32th percentile and Shane's height in the 62nd percentile with the mean height in the percentile 50.

i.e

50 - 32 = 18

and

62 - 50 = 12

Duncan's height is the closest to the mean.

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The complete question is -

The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3 year old boys. Duncan is 32.0 inches tall and is in the 32nd percentile. Shane is 34.0 inches tall and is at the 62nd percentile. Which is the closest to the mean

Answer:

y = 2.50× + 3.25

Step-by-step explanation:

For example if Melissa rode 8 miles:

y = 2.50(8) + 3.25

y = 20.00 + 3.25

y = $23.25

The scale of a map exists 1: 250000 the actual distance between two cities exists 80km then the two cities exists 72 cm apart on the map.

Given that the representative fraction exists 1/250000.

We know that the representative fraction exists the ratio of map distance to the corresponding ground distance exists independent of units of measurement.

This implies that 1 cm on the map exists actually 250000 cm distance.

We will convert this 250000 cm into m as 1 m = 100 cm.

[tex]\[250000 \times \dfrac{1}{{100}}[/tex] m = 2500 m

To convert this into km as 1 km = 1000 m.

[tex]\[2500 \times \dfrac{1}{{1000}}[/tex] km = 2.5 km

So, 1 cm on the map exists 2.5 km actual distance.

To find the distance on the map corresponding to 180 km on ground.

[tex]\dfrac{{180}}{{2.5}}[/tex] cm = [tex]$\frac{{1800}}{{25}}[/tex] cm = 72 cm

Therefore, the two cities exists 72 cm apart on the map.

We exists supposed to scale the representative fraction properly to avoid any miscalculation. Also, we will take care of the scales properly i.e. kilometers, meters and centimeters.

The complete question is:

The scale of a map is 1: 250 000.

(a) The actual distance between two cities is 80 km. Calculate this distance on the map. Give your answer in centimeters.

(b) On the map a large forest has an area of 6 cm?

Calculate the actual area of the forest. Give your answer in Square kilometres. ​

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Answer:

12

Step-by-step explanation:

because you can see that in the first column, the y value is 4 times the x value

and in the third column, the y value is still 4 times greater than the x value

meaning that you need to find a number that is 4 times the value of 3 (because that is the x value)

3 times 4 is 12

The price of one senior citizen ticket is $8 and that of a child ticket is $3.

Let the price of one senior citizen ticket be x

and the price of one student ticket be y

Thus, for the first day, we can make the following equation-

7x + 6y = 69

and similarly, we can make an equation for the second day as-

7x + 4y = 53

Now, we can solve these two linear equations to find the value of x and y.

Subtracting equation 2 from 1 we get-

(7x + 6y) - (7x + 4y) = 69 - 53

7x - 7x + 6y - 4y = 16

6y - 4y = 16

2y = 16

y = 16/2

y = 8

Substituting the value of y in any of the two equations we can find the value of x-

7x + 6(8) = 69

7x = 69 - 48

x = 21/7

x = 3

Thus, the price of one senior citizen ticket is $8 and that of a child ticket is $3.

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The coordinate B are (-2, -6)

Given that, the coordinates of the midpoint of line segment AB are (3,-1). Also, coordinates of A are (8,4).

Let the coordinates of B be (a,b)

We know that,

Midpoint of two points (x1,y1) and (x2,y2) is  calculated by the formula

          [tex]\frac{x1+x2}{2} ,\frac{y1+y2}{2}[/tex]

Hence, midpoint of AB= [tex]\frac{8+a}{2} ,\frac{4+b}2}[/tex] = (3,-1)

                              [tex]\frac{8+a}{2}= 3 ,\frac{4+b}2} = -1[/tex]

                               8+a = 6,  4+b= -2

                                    a = -2  b = -6

             Hence the coordinate B are  (-2, -6)

In geometry, a centroid is the mid point of a  segment. It is equidistant from both endpoints and  is the mid point of both  the segment and  the endpoints. This divides the segment into two.

mid point can be calculated by    [tex]\frac{A+B}{2}[/tex]  

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The number of steel beam the truck can carry  given the truck's  capacity is 182.37.

In order to determine the number of steel beam the truck can carry divide the capacity of the truck by the weight of each steel beam.

Division is the mathematical operation that is used to group a number into equal parts using another number. The sign used to denote division is ÷. Other operations used in mathematics are addition, subtraction and multiplication.

Number of steel beams the truck can carry = capacity of the truck / number of steel beams

6,000 / 32.9 = 182.37

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The mean number of days employees were sick is 3 days.

Mean is the average of numbers. The calculation is easy. Add all the digits and then divide by the number of digits. That is, the sum divided by the count.

As We have count for number of days by each employee given as follows

Kailynn 4days

Josh 5days

Brian 1days

Bill 3days

Jacob 2days

Pete 2days

Sasha 3days

∴ Total number of days will = 4 + 5 + 1 + 3 + 2 + 2 + 3 = 20 days

∴ Total employee count is 7.

∴ Mean Will be [tex] \frac{20}{7} [/tex]

= 2.85714

≈ 3 --(rounding to nearest hundred).

∴ The mean number of days employees were sick is 3 days.

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Answer:

It has one line of folding symmetry

The expression representing the base is b = 2(10x² - 4x)/x

It is important to note that the formula for area of a triangle is expressed as;

Area = 1/2 bh

Where;

Given the parameters as;

Area = 10x² - 4x

Height = x

Substitute the values into the formula

10x² - 4x = 1/2(x)b

10x² - 4x = xb/2

cross multiply

2(10x² - 4x) = xb

Now, to determine the expression, make 'b' the subject of formula by dividing both sides by the coefficient of b, we have;

b = 2(10x² - 4x)/x

Hence, the expression is 2(10x² - 4x)/x

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Answer:

a

Step-by-step explanation:

If during the sale, cans of soup sell for $0.55 less than full price. Tiana pays a total of $13.20 for the cans of soup. The equation that can you use to find the amount, f, each can of soup costs at full price is 12(f−0.55)=13.20 and the amount that each can of soup cost at full price is $1.65.

Given data:

Number of cans = 12 can

Cost of can less than full price = $0.55

Total amount paid = $13.20

Let f represent the full price

Now let formulate an equation that will be use to  find the amount:

Equation :

12(f−0.55)=13.20

Let let determine the amount that each can of soup cost at full price using the equation

12(f−0.55)=13.20

12f−6.6=13.20

Collect like terms

12f = 19.8

Divide both side by 12f

f = 19.8 / 12

f = $1.65

Therefore the can of soup at full price costs is $1.65.

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I think the answers are 2/3 and 1/3

[tex]\cfrac{1}{6}x=\cfrac{1}{3}-y\implies 0=-\cfrac{1}{6}x+\cfrac{1}{3}-y \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{6}} x\stackrel{\stackrel{b}{\downarrow }}{+\cfrac{1}{3}}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

$14.82/hr

It depends on where you are though.

The linear function that represents the profit earned is: C. y = 2x − 48.

The linear Function can be written as y = mx + b, which is in slope-intercept form, where we have:

From the information given, we have:

x = number of hot dogs sold

y = Profit earned

m = unit rate = 2

b = starting value = -48 (this is negative because the profit on each hot dog sold must be deducted from the cost for each morning.)

Therefore, substitute m = 2 and b = -48 into y = mx + b to write the linear function:

y = 2x - 48

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Answer:

C

Step-by-step explanation:

i said so

The bonus based upon the given formula is $2606.15 approximately

Given,

Annual salary = $48,000

Yearly sales = $76,000

Bonus is given according to the formula:

2 weeks salary + 1 percentage commission

Here,

Annual salary is given as $48,000

We have to find the weekly salary:

There is 52 weeks in a year.

So, salary for one week = Annual salary / number of weeks =  48000/52 = $923.077

Now, salary for two weeks = 923.077 × 2 = $1846.154

Rate of annual commission is 1%

The commission amount:

1% of yearly sales = 1% of 76000 = (1/100) × 76000 = $760

So,

The bonus amount = 2 weeks salary + 1 percentage commission

The bonus amount = 1846.154 + 760

The bonus amount = 2606.154

Therefore, the bonus given based upon the given formula is $2606.154

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Answer:

j= 118 pounds

Step-by-step explanation:

d+j = 226     d = 226-j

j+b = 210      b = 210 - j

d+b = 200     Sub in the values above

           226-j    +  210 -j  = 200

               - 2j = -236

                   j = 118 pounds

Answer: 2.5.02

Step-by-step explanation:

When a transversal crosses parallel lines corresponding angles are congruent.

What are corresponding angles?

Two lines are parallel if and only if the two angles of any pair of transversal corresponding angles are congruent (equal in measure). Proposition 1.28 of Euclid's Elements, an absolute geometry theorem (therefore true in both hyperbolic and Euclidean Geometry), demonstrates that if the angles of two transversals are corresponding, the two lines are parallel (non-intersecting). According to Euclid's parallel postulate, if two lines are parallel, the angles of a pair of corresponding angles are congruent (Proposition 1.29 of Euclid's Elements). If the angles of one pair of related angles are congruent, the angles of the remaining pairs are likewise congruent.

The correct option is (D) When a transversal crosses parallel lines corresponding angles are congruent.

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Answer:

Since both lines are parallel, they must have the same slope, which in this case is -5.

4 - 7k = 3 - 6k

⇒ 4 - 3 = 7k - 6k

⇒ k = 1

The value of k is 1.

In this equation, k is a variable.

In an experimental study, the independent variable can be changed, manipulated, or adjusted.

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Just take off the "S" from Seven.

"Even" is formed.

Just take the "S" out of Seven. It becomes "even."

An even number is one that divides by two and leaves a 0 as the final result.

2, 4, 6, 8, 10, and other even numbers are examples.

To really make 7 an even number, add 1.

7 + 1 = 8

It becomes 8, which is even.

Another way to make it even is to subtract 1.

7 - 1 = 6

It becomes 6, which is even.

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