what is the area of a rectangle wxyz with vertces w(0,1), x(3,4), y(-1,8), z(-4,5)

Answer:

-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

-4 + (-3) is basically -4 - 3

-4 - 3 = -7

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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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

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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Answer:

216

Step-by-step explanation:

gof(6) means g(f(6))

f(6)=2(6)-6=6

g(6)=6^3=216

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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The symbol that creates a true sentence for the expression is (16 - 8) ÷ 2 < 16 – 8 ÷ 2.

It should be noted that an expression is used to show the relationship between the values or the data given. This will be illustrated as thus:

It should be noted that (16 - 8) ÷ 2 will be:

(16 - 8) ÷ 2

= 2 ÷ 2

= 1

On the other hand, 16 - 8 ÷ 2 will be;

= 16 - 8 ÷ 2

= 16 - 4

= 12

It should be noted that 1 is less than 12. The symbol will be less than.

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The value of (x + 5) * (x^3 + 6x^2 + 18x) is x^4 + 11x^3  + 48x^2 + 90x

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the polynomial expression?

The polynomial expression is given as

(x + 5) * (x^3 + 6x^2 + 18x)

Express the polynomial expression as a product of factors

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x * (x^3 + 6x^2 + 18x) + 5 * (x^3 + 6x^2 + 18x)

Open the brackets in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 18x^2 + 5x^3 + 30x^2 + 90x

Collect the like terms in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 5x^3  + 18x^2 + 30x^2 + 90x

Evaluate the like terms in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 11x^3  + 48x^2 + 90x

Hence, the solution is x^4 + 11x^3  + 48x^2 + 90x

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From the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.

As given in the question,

From the given figure:

line l is parallel to line m.

t is the transversal of line l and m

Relationship between angles for the parallel lines

∠1 and ∠2  are straight angles and are supplementary

∠3 and ∠2 are interior angles and are supplementary

⇒m(∠1 + ∠2) = m(∠3+∠2)

⇒m∠1= m∠3

Therefore, from the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.

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Answer:

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

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:

It has one line of folding symmetry

4 1/6 divided by 8/9 is 4 11/16

The first step is to change the mixed fraction (4 1/6) to a proper fraction

4 1/6

= 4 × 6

= 24 + 1

= 25

= 25/6

The Fraction can be divided as follows

25/6 ÷ 8/9

= 25/6 × 9/8

= 75/16

= 4 11/16

Hence the result of the division of 4 1/6 and 8/9 is 4 11/16

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If f(x) = 1/x, then the function representing the graph plotted will be -

y = f(x + 2) - 1.

The function f(x) = 1/x is called the multiplicative inverse function, because for each input it returns the multiplicative inverse or reciprocal of that input.

Given is function f(x) = 1/x.

The graph of the function f(x) = 1/x is plotted in the graph. If we plot the graph for f(x + 2) = 1/(x + 2), than the graph will shift towards left. If we subtract 1 from the f(x + 2), than the graph will shift downwards.

Therefore, if f(x) = 1/x, then the function representing the graph plotted will be -

y = f(x + 2) - 1

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The values of the expression h(1), h(-7) and h(9) are 6, 50 and 62

After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division.

Given the following modulus function shown below;

h(x)= |1 - 7x|, we are to find the following.

h(1)

h(-7)

h(9)

If x = 1, then;

h(x)= |1 - 7(1)|

h(1) = |1-7|

h(1) = |-6|

h(1) = 6

If x = -7, then;

h(-7)= |1 - 7(-7)|

h(-7) = |1--49)|

h(-7) = |1+49|

h(-7) = |50|

h(-7) = 50

If x = 9, then;

h(x)= |1 - 7(7)|

h(1) = |1-63|

h(1) = |-62|

h(1) = 62

This gives the equivalent values of the expression

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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:

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

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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[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]

In case whereby Soledad says 3 (2-2)-1=36 the error she made was that ​she does not perform, the calculation base  PEDMAS  rule of mathematics.

The mathematical error can be described as the error that can be made when making a calculation, and the expected rule in mathematics in solving the particular problem is not followed.

From the given mathematical expression, 3 (2-2)-1=36, if we are to solve it, we will need to open the parenthesis first which will give us 6-6-1=-1, therefore it can be concluded that she make the mistake by not following the rules required.

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The domain and range of the function f(x) = |x-1| +3 are-

For the given expression for the function;

f(x) = |x-1| +3.

Domain: Unless the expression is undefined, the domain of the representation is all real numbers. Because there is no real number in this case, the expression is undefined.

Interval Notation:(−∞,∞)

Set-Builder Notation:{x| x ∈ R}

Range: The range is indeed the collection of all possible y values. To determine the range, consult the graph.

Interval Notation:[3,∞)

Set-Builder Notation:{y| y ≥ 3}

Thus, the domain and the range of the function is estimated.

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Answer:

a

Step-by-step explanation:

Answer:

x = - 4, y = 2

Step-by-step explanation:

First equation: 4x + 3y = - 10

Second equation: 4x+y= - 14

To solve simultaneously:

Rearrange one of the equations and substitute the equation to another equation, I prefer rearranging the second equation because it is easier.

Rearranging the second equation to get y, and then substitute back to the first equation to find x:

y = - 14 - 4x ------> new second equation

Substitute y (new second equation) into the first equation to find x:

4x +3(-14 -4x) = - 10

4x - 42 - 12 x = - 10

       - 8x - 42 = -10

                -8x = - 10 + 42

               - 8x = 32

                 8x = - 32

                   x = - 4

Now we substitute x = - 4 to the second equation to find y:

4x + y = - 14

y = - 14 - 4(-4)

y = - 14 - (-16)

y = - 14 + 16

y = 2

The value of x that makes the equation shown in the model true is x = -3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The model shown can be represented by the equation:

4(-x) + 9(1) = 8(-x) + 3(-1)

-4x + 9 = -8x - 3

-4x + 8x = -3 - 9

4x = -12

x = -3

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If the Employee: Curtis R. Evan with SSN: 5 5 5-55-5 5 55 has regular earning of $421 and overtime of $78. Curtis's net pay is $499.

Net pay can be defined as the amount a person received or earn as a salary after all deduction has been substracted.

Using this formula to determine the net pay

Net pay = Regular earnings + Overtime

Where :

Regular earning  = $421

Overtime = $78

Let plug in the formula

Net pay = $421 + $78

Net pay = $499

Therefore we can conclude that the net pay or take home amount is the amount of $499.

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Answer:

9

Step-by-step explanation:

Vertical angles are congruent, so:

[tex]16y=18y-18 \\ \\ -2y=-18 \\ \\ y=9[/tex]

Answer:

y = 9

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Therefore, equate the expressions and solve for y:

[tex]\begin{aligned}(18y-18)^{\circ}&=16y^{\circ}\\18y-18&=16y\\18y-18+18&=16y+18\\18y&=16y+18\\18y-16y&=16y+18-16y\\2y&=18\\2y \div 2 &=18 \div 2 \\y&=9\end{aligned}[/tex]

Therefore, the value of y is 9.

Answer:

Is 23

Step-by-step explanation:

His name 721 6 the y 8th 7th in his 6th grade 6th class and I was

The value of the x for the given expression [tex](32)^{1/25}\times (2)^x = (8)^{1/4}[/tex] is 19/20.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is

[tex](32)^{1/25}\times (2)^x = (8)^{1/4}[/tex]

Simplify the expression,

[tex]((2)^5)^{1/25}\times (2)^x = (2^3)^{1/4}\\\\(2)^{5/25}\times(2)^x =(2)^{3/4}\\\\(2)^{1/5}\times(2)^x = (2)^{3/4}\\(2)^{1/5 + x} = (2)^{3/4}\\[/tex]

The base is same, so the expression can be written as,

1/5 + x = 3/4

x - 3/4 = 1/5

x = 1/5 + 3/4

x = (4 + 15)/20

x = 19 / 20

The required value of x is 19/20.

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