Which choices are equivalent to the expression below check all that apply

The length of one side of the square is x+6

The formula for calculating the area of a square is expressed as:

A = L^2

where

L is the side length of the square

Given the following parameters

A = x^2 + 12x + 36  square feet

A = (x+6)^2

(x+6)^2 = L^2

L = x + 6

Hence the length of one side of the square is x+6

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Answer:

Step-by-step explanation:

Given function:

[tex]y=\dfrac{x-3}{x^2-2x-3}[/tex]

The domain is the set of all possible input values (x-values).

Factor the denominator of the function:

[tex]\implies y=\dfrac{x-3}{(x-3)(x+1)}[/tex]

The domain of the given function is restricted as the function is undefined when the denominator equals zero, and when both the numerator and denominator equal zero.  

Therefore, the function is undefined when x = -1 and x = 3.

Therefore, the domain is (-∞, -1) ∪ (-1, 3) ∪ (3, ∞).

The range is the set of all possible output values (y-values).

As the domain is restricted, the range is also restricted.

Therefore, the range is (-∞, 0) ∪ (0, ¹/₄) ∪ (¹/₄, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Point Discontinuity (holes): When a rational function has a factor with an x that is in both the numerator and the denominator.

Therefore, there is a point discontinuity at x = 3.

Infinite Discontinuity: A vertical asymptote occurs when the denominator of a rational function is zero. This is considered an infinite discontinuity when the graph exists on both sides of the asymptote.

Therefore, there is an infinite discontinuity at x = -1.

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & =\dfrac{x-3}{x^2-2x-3}\\\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{(x^2-2x-3)(1) - (x-3)(2x-2)}{\left(x^2-2x-3\right)^2}\\\\ & = \dfrac{(x-3)(x+1)-(x-3)(2x-2)}{\left((x-3)(x+1)\right)^2}\\\\& = \dfrac{(x-3)[(x+1)-(2x-2)]}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{(x-3)(-x+3)}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{-(x-3)^2}{(x-3)^2(x+1)^2}\\\\& = \dfrac{-1}{(x+1)^2}\end{aligned}[/tex]

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{-1}{(x+1)^2} & = 0\\ -1 & \neq 0\end{aligned}[/tex]

Therefore, there are no stationary points and no minimum/maximum points.

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0\\\implies \dfrac{-1}{(x+1)^2} & > 0\\ \dfrac{1}{(x+1)^2} & < 0\\ \textsf{If $\dfrac{1}{a} < 0$ then $a < 0$}:\\(x+1)^2 & < 0\\ \textsf{As $(x+1)^2\geq 0$, no solution.}\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0\\\implies \dfrac{-1}{(x+1)^2} & < 0\\ \dfrac{1}{(x+1)^2} & > 0\\ \textsf{If $\dfrac{1}{a} > 0$ then $a > 0$}:\\(x+1)^2 & > 0\\ \end{aligned}[/tex]

[tex]\textsf{For $a^n > 0$, if $n$ is even then $a < 0$ or $a > 0$}[/tex]

[tex]\implies x+1 < 0 \implies x < -1[/tex]

[tex]\implies x+1 > 0 \implies x > -1[/tex]

Combine the intervals:

(-∞, -1) ∪ (-1, ∞)

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)

Range: [0, ∞)

Continuity: Point discontinuity (hole) at x = 3.

Infinite discontinuity (vertical asymptote) at x = -1.

None

Decreasing function: (-∞, -1) ∪ (-1, ∞)

Symmetry: Neither

The additive inverse of the numbers given as -7/8 and 7/8  are 7/8 and -7/8

The numbers are given as:

-7/8 and 7/8

As a general rule, the additive inverse of a number x is -x

This means that the additive inverse of the numbers given as -7/8 and 7/8  are 7/8 and -7/8

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Answer:

the answer is

Step-by-step explanation:

A is more likely to be 12 and B could be 3

so 12/3=4

and

3/12= 0.25

Answer:

The school should buy 39 packages.

Step-by-step explanation:

3198 notebooks

82 notebooks = 1 package

3198÷82 = 39

(Eg: you have 4 notebooks and there are 2 in each package. How many packages are there?  4÷2 = 2   So 2 packages)

Option E:

This graph is not a function because the value of y is the same for every value of x

Solution :

Domain:

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.

For example, when we use the function notation f:R→R, we mean that f is a function from the real numbers to the real numbers. In other words, the domain of f is the set of real number R (and its set of possible outputs or codomain is also the set of real numbers R).

relation represents y as a function of x

1) is NOT a function of if there are two or more points with the same − , but

− .

2) is a function of if each has a different

There is a technique called the vertical line test that is often used to determine if a graph represents y

as a function of x

In this question only a horizontal line is present.

Option E:

This graph is not a function because the value of y is the same for every value of x

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L = 10 and w= 5 are  the dimensions of the rectangular garden.

What is a rectangle, exactly?

Let the width of the garden be a

Length of the garden = a + 5

Area = l * w

66 = ( a+ 5 ) * a

66 =  a² + 5a

a² + 5a -66 = 0

a² + 11a - 5a - 66 = 0

a( a + 11 ) -5 ( a + 11) = 0

( a + 11 ) ( a - 5) = 0

so  a + 11 = 0 ⇒  a = -11

      a - 5 = 0 ⇒ a = 5

Width cannot be negative.

l = a + 5 = 10

w = 5

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The number of vanilla and chocolate flavoured cupcakes sold every day is 1250 and 3750, respectively.

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Answer:

631

Step-by-step explanation:

This problem can be expressed as:

0.05x + 15 = 21.55
0.05x + 15 - 15 = 21.55 - 15
0.05x = 6.55
0.05x/0.05 = 6.55/0.05
x = 131

We also know that:

0.05x + 15 = x + 500

If x = 131:

x + 500
131 + 500
631

The Shorter route as per the bearing calculations is taken up by Julia.

What is a bearing?

Bearing calculations are illustrated below:

Route Taken up by Anna

360-330= 30°

First angle =90-30= 60°

Second angle= 60+(90-40) =110°

Third angle= 180-(110+30)= 40°

Route taken up by Julia:

First angle =20°

Second angle= 300-(180+20)=100°

Third angle=180-(20+100)=60°

Hence, the Shorter route as per the bearing calculations is taken up by Julia and bearing diagram is attached with the solution as an image.

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Answer: 8 kitkats

Step-by-step explanation:

40+24= 64

72-64=8

Answer:

Total candy bars to snickers = 72:40 or simplified 9:5

Ratio of kit kats to milky ways = 8:24 or simplified 1:3

Ratio for kit kats to total candy bars = 8:72 or simplified 1:9

Step-by-step explanation:

72 = 40 + 24 + x

x = 8

hi

f(a+7)

f(x) =x²+5

by remplacing X by (a+7) :

then  f(a+7) = (a+7)²+5

                  =   a² +2*a*7 +49 +5

                  = a² +14a +54

3√5

The distance between two points on an XY plane is calculated using the distance formula, which is employed in coordinate geometry or Euclidean geometry. The x-coordinate, often known as the abscissa, is a point's separation from the y-axis. The y-coordinate, often known as the ordinate, refers to a point's separation from the x-axis. A point on the x-axis has coordinates of the form (x, 0), and a point on the y-axis has coordinates of the form (0, y). We utilize the Pythagoras theorem in this case to determine the separation between any two points in a plane.

Distance formula = √ ( x₁ - x₂)² + ( y₁ - y₂)²

                                = √ 6² + 3²

                                =3√5

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[tex] \: \: \: \: \large\bf\implies \: 4.32[/tex]

[tex] \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32[/tex]

First of all we know that to do this type of question that is ↓

Answer:

Anna is correct.

Step-by-step explanation:

Using PEMDAS, you need to add the terms in the parentheses first.

After adding, you get 8×6 = 48

Jojo made the mistake of multiplying 6 and 5 first, and then adding 3.

The 34 feet perimeter and width, x, of the window which is in the shape of a rectangle surmounted by a semicircle is, A = 17•x - x²•(1/2 - π/8)

The shape of the window = A rectangle surmounted by a semicircle

Perimeter of the window, P = 34 feet

Width of the window = x

Required; The area, A, of the window as a function of x

Solution:

Diameter of the semicircle = x

Length of the semicircular arc = π•x/2

Let y represent the height of the window, we have;

P = 2•y + x + π•x/2 = 34

Therefore;

y = (34 - (x + π•x/2))/2 = 17 - x•(1 + π/2)/2

Area of the window, A = x × y + π•x²/8

Which gives;

A = x × (17 - x•(1 + π/2)/2) + π•x²/8 = 17•x - x²/2 - x²•π/8

A = 17•x - x²/2 - x²•π/8 = 17•x - x²•(1/2 - π/8)

Therefore;

Window area, A = 17•x - x²•(1/2 - π/8)

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Answer:

2.5

Step-by-step explanation:

By Using s = d/ t

So t = d / s

The conversion of 100 kilometers to meters would be,

100 kilometers = 100,000 meters

The correct answer is an option (a)

In this question we need to convert the metric units of length.

We need to convert 100 kilometers to meters.

We know that, 1 kilometer = 1000 meters

Let 100 kilometers = p meters

So, we get an expression,

p × 1 = 100 × 1000

From this expression we get,

p = 100,000 meters

This means, 100 kilometers = 100,000 meters

Therefore, the conversion of 100 kilometers to meters would be,

100 kilometers = 100,000 meters

The correct answer is an option (a)

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The answer is 27 for your math

Step-by-step explanation:

The state income tax owed on a $30,000 per year salary is $1,524

What are the applicable tax rates?

The applicable tax rates are that the first $2,000 of taxable income is taxed  at 2%, such that $9000 minus the earlier $2000, is taxed at 5% and any taxable income beyond $9,000 is taxed at 5.4%, in essence, the income tax owed by a taxpayer whose taxable income is $30,000 is computed thus:

income tax on first threshold=$2000*2%=$40

income tax on second threshold=($9000-$2000)*5%=$350

income tax on the last threshold=($30,000-$9,000)*5.4%=$1,134

total state income tax owed=$40+$350+$1,134

total state income tax owed=$1,524

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Answer: -3

Step-by-step explanation:

turn mixed numbers into improper fractions, simplify, and solve- see attached

Answer:

-3

Step-by-step explanation:

to find the answer first turn both numbers into improper fractions

-1 13/14 becomes -27/14

1 5/9 becomes 14/9

now multiply them

[tex]\frac{-27}{14} * \frac{14}{9}[/tex]

you can cancel out the 14s

[tex]\frac{-27}{1} * \frac{1}{9}[/tex]

now divide 9 to the top of the first fraction and to the bottom of the second one

[tex]\frac{-3}{1} * \frac{1}{1}[/tex]

now multiply

-3/1 is your answer

that is basically -3

The original cost of the dress is $14.45

The dresses were sold for $17 each

This price was 85% of the original price

Therefore the original cost of the dress can be calculated as follows

85/100= 0.85

The first step is to calculate the original pre sale price

17= 0.85x

x= 17/0.85

= 20

The original cost of the cloth is

= 0.85 × 17

= 14.45

Hence the original cost of the cloth is $14.45

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Greetings from Brasil...

The perimeter is the sum of all sides of the triangle. In this case

P = (2X) + (X) + (4X - 9)

as P = 89

89 = (2X) + (X) + (4X - 9)

89 = 7X - 9

7X = 98

X = 98/7

X:

X meters = X = 14

---------------------------------------------

2X:

2X meters = 2 · X = 2 · 14 = 28

---------------------------------------------

(4X - 9):

(4X - 9) meters = (4 · X - 9) = (4 · 14 - 9) = (56 - 9) = 47

54 grams of aluminium is present in aluminium sulphate Al₂(SO₄)₃.

A substance's molecular mass is the sum of the atomic masses of all of the atoms in the molecule of a substance.

For the given question, the expression is;

aluminium sulphate Al₂(SO₄)₃

As three of aluminium is present in the aluminium sulphate.

And, molecular mass of one aluminium atom is 27 grams;

Thus, for 2 aluminium atoms = 2×27 = 54  grams.

Therefore, the compound aluminium sulphate contains 54 gram of aluminium in it.

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Answer:

spam

Step-by-step explanation:

spam spam spam

450c > 900 + 250c;

For business to be profitable;

Selling price of daycare services > Cost price;

Payment for daycare of 1 child =  $450

Payment for daycare of 'c' children = $450 × c;

                                                       = $450c;

Operating cost for 1 child = $250;

Operating cost for 'c' children = $250c;

Total daily operating cost = $900 + $250c;

Therefore;

450c > 900 + 250c;

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The correct answer is option D.

The polygon ABCD can be mapped on to WXYZ but first it must be enlarged and then it must be mirrored along BC.

The mirror image of ABCD along BC must be enlarged with a scale factor of 2 to map ABCD to WXYZ.

The scale factor is the ratio of the the object to be transformed to the object with which it is to be compared.

Here, the scale factor is 2 and we must enlarge the image of ABCD along BC to get the desired mapping.

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Answer:

x is 4 and y is 1

So we put 3 x 4 + 1

if it's equal 1 (since y is 1)

but in this case it equals 13 so it's wrong

Answer:

see explanation

Step-by-step explanation:

to determine if (4, 1 ) is a solution of the equation, substitute the x and y coordinates into the equation and if both sides are equal then it is a solution.

y = 3(4) + 1 = 12 + 1 = 13 ≠ 1

since y ≠ 13 then (4, 1 ) is not a solution to the equation

Answer:

Step-by-step explanation: