If sides BD and DC have the same length, what is the length of side BC?

Answer:

The rectangles length is 2 times as much as its width.

Step-by-step explanation:

8 x 10⁴ = 80,000

4 x 10⁴ = 40,000

40,000 x 2 = 80,000

Answer:

the fraction is 2/5

Step-by-step explanation:

4/5 + 1/2

=2/5

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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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:

[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]

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

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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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: 2.5.02

Step-by-step explanation:

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

Answer:x squared = 60

Step-by-step explanation:

x2-6=54, first you have to cancel out the 6 on the left side by adding 6 to -6 after doing that you are left with

x2-(-6+6)=54

but since you did +6 on the right side you have to do +6 on the left so after that you are left with

x2=54+6

now you just do 54+6=60 so after all of that you get

x2=60

(you can use a calculator to find the square root of 60)

Taking into account the definition of a system of linear equations, a small pizza and a regular pizza cost £7 and £11 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. This mieans thar systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

2r + 3s= 43

8r + 9s= 151

Of the several methods to solve a system of equations. it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "r" from the first equation:

2r= 43 - 3s

r= (43 -3s)÷2

r= 43/2 - 3/2s

Replacing this expression in the second equation:

8×(43/2 - 3/2s) + 9s= 151

Solving:

8×43/2 - 8×3/2s + 9s= 151

172 -12s + 9s= 151

-12s + 9s= 151 - 172

-3s= -21

s= (-21)÷ (-3)

s= 7

Remembering that r=43/2 - 3/2s you get:

r=43/2 - 3/2×7

r= 11

Finally, a small pizza cost £7 and a regular pizza cost £11.

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

An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products.

An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products. A factored form can represent any logic function, and every factored form represents some logic function.

1a)The length given as words is "3 more than 7 times x"

The width given as words is "4 times x minus 2"

The expression for length would be 7x + 3

The expression for width would be 4x - 2

1b)Area = length × width

To estimate the algebraic expressions for length and width

Area = (7x + 3)(4x - 2) = 28x² - 14x + 12x - 6 = 28x² - 2x - 6

Area = 28x² - 2x - 6

Given x = 10,

Let the equation be 28 x² - 2x - 6

substitute the value of x, in the above equation, we get

= 28(10)² - 2(10) - 6

= 2774

Area = 2774 sq . m

2. We can group the first two terms and next two terms:

xy - 4y + 7x - 28 = (xy - 4y) + (7x - 28)

simplifying the above equation, we get

y(x - 4) + 7(x - 4) = (x - 4)(y + 7)

Therefore, the equation is in factored form.

The complete question is:

1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow change. The college conducts a lottery, and whichever number is drawn, represents the x value. Your plot has a length that is three more than seven times x and the width is four times x minus 2.a.) What are the dimensions of your mowing plot? (2 points)

Length: ______________________________________

Width: ______________________________________

b.) What is the area of your plot (remember area = length x width)? (2 points)

Area: _________________________________________

c.) If x = 10 meters, how many square meters is your plot? (show steps)(2 points)

Area: _________________________________________

2.) Factor by grouping: (4 points)

xy − 4y + 7x − 28

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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 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:

$14.82/hr

It depends on where you are though.

Answer: 1665

Step-by-step explanation:

Prime factorization of the numbers:

15 = 3 × 5

45 = 3 × 3 × 5

37 = 37

LCM(15, 45, 37)

= 3 × 3 × 5 × 37

= 1665

Hope this helps!

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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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

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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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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Answer: Yes, 6.20

Step-by-step explanation:

1/5 is equal to 0.20, so 6 1/5 equals 6.20

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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Answer: r

Step-by-step explanation:

The figures are symmetrical about line r.