Evaluate the equation
ƒ (n) = −n
ƒ (−6) =

The figure RSTU can represent Quadrilateral, Parallelogram and Rectangle

The figure KLMN  represents Quadrilateral and Parallelogram

The figure ABCD  represents only Quadrilateral

Given,

The figures;

RSTU, KLMN and ABCD

We have to identify the true facts about the figure.

All figure are drawn like a rectangle.

Quadrilateral;

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Parallelogram;

A quadrilateral is referred to as a parallelogram in geometry. The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.

Now here,

RSTU; This figure can represent all the options.

That is,

Quadrilateral, Parallelogram and Rectangle

KLMN; This figure represents Quadrilateral and Parallelogram

ABCD; This figure represents only Quadrilateral

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x = 9

x + 3 + x - 1 = 20

2x + 2 = 20

2x = 18

x = 9

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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Q is the set of the rational numbers

Rational numbers are all numbers that can be put in the form of a/, where b is not equal to zero.

Examples:

The given equation is

Insert log on both sides

Use the rule of power with a log

Divide both sides by log(1/5)

Since we can not put the value of x in the form of a/b, then

The equation has NO solution in Q (or empty set { } or Nul)

Answer:

shifted 5 up and 4 to the left

Step-by-step explanation:

Answer: NM = 40

Step-by-step explanation:

    First, we will label everything. See attached.

    Next, we will set up a proportion to solve. Let the missing side, ? in the picture, be equal to x.

➜ On the left side will be the "smaller top" triangle

➜ On the right side will be the larger triangle

➜ View the second attachment for a visual explanation of this if you are confused.

[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]

    Next, we will cross-multiply and solve.

[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]

48x = 30(x + 24)

48x = 30x + 720

18x = 720

x = 40

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.

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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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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The volume of the remaining solid correct to 2 decimal places is 3634.60 m³

From the question, we are to determine the volume of the remaining solid

Volume of the remaining solid = Volume of the larger prism - Volume of the rectangular prisms carved out

First, we will determine the volume of the larger prism

Volume of the larger prism = 17 × 17 × 17

Volume of the larger prism = 4913 m³

Now, we will determine the volume of one of the rectangular prism that was carved out

Volume = 4 × 9.4 × 17

Volume = 639.2 m³

∴ Volume of the two identical holes carved out = 2 × 639.2 m³

= 1278.4 m³

Thus,

Volume of the remaining solid = 4913 m³ - 1278.4 m³

Volume of the remaining solid = 3634.60 m³

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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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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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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:

8.0/0.8

=10times

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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Answer:

-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

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

-4 - 3 = -7

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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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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£1 = 99.72 rupees -> £450 = 44874 rupees.

As the post office only has 500 rupee papers, once we calculate out the result, we have to round down to the nearest whole number.

The amount of rupee papers we can change out is : 44874 : 500 = 89.748 (papers)
We round down to 89 papers.

Answer:

216

Step-by-step explanation:

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

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

g(6)=6^3=216

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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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:

<DKF IS 54° BECAUSE IT IS VERTICALLY OPPOSITE ANGLE OF THE<IKL.

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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Answer:

25

sum of the interior angles of triangle =180

101+54=155

155-180=25

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 original dimensions are 12 m and 20 m.

What is area of rectangle?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.

Let x be the width of the rectangle.

Length of the rectangle = x+8

Area of the rectangle = x(x+8)

According to question, new width= x+2

New length = x+2+8 = x+10

New area = (x+2)(x+10)

Area increased = (x+2)(x+10) – x(x+8)

x^2+12x+20-x^2-8x=68

4x-20=68

4x=48

x=12

Hence, the width = 12m and length = 12+8 = 20 m

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