Find the coordinates of the image point for S(−11, 2) across y = 1.

The limit of f(x) as x goes to 1 will not exist for function III.

A limit is given by the value of function f(x) as x tends to a value. For a function with different lateral limits at a point x = a, the limit will not exist at the point x = a. Additionally, the limit may not exist at a point if there is a non-removeable discontinuity.

Factoring the function 1, the limit will be given as follows:

[tex]\lim_{x \rightarrow 1} \frac{1 - x^2}{x - 1} = \lim_{x \rightarrow 1} \frac{(1 - x)(1 + x)}{x - 1} = \lim_{x \rightarrow 1} -(1 +x) = -2[/tex]

Hence the limit exists.

Factoring the function 2, the limit will be given as follows:

[tex]\lim_{x \rightarrow 1} \frac{x^2 - x^3}{x^2 - 1} = \lim_{x \rightarrow 1} \frac{x^2(1 - x)}{(x - 1)(x + 1)} = \lim_{x \rightarrow 1} -\frac{x^2}{x + 1} = -\frac{1}{2}[/tex]

Hence the limit exists.

Factoring the function 3, the limit will be given as follows:

[tex]\lim_{x \rightarrow 1} \frac{x + 1}{x^2 - 1} = \lim_{x \rightarrow 1} \frac{x + 1}{(x - 1)(x + 1)} = \lim_{x \rightarrow 1} \frac{1}{x - 1}[/tex]

Non-revemoveable discontinuity, as we can't remove x - 1 for the denominator, ence the limit does not exist for function III.

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The least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors. This can be obtained by simply giving colors to the small shapes according to the criteria.

From the question the figure, the number of colored sections with which are not colored with respect to a "touching" colored section, would not be half of the total colored sections since the sections are not alternating as they still meet at a common point.

After all, it notes no two touching sections, not adjacent sections.

There is no equation to calculate this requirement with respect to the total number of sections.

Taking one triangle or square as the starting we can give colors to each small units. This figure will be the start of sequence of other small figures.

If a square were to be this starting shape that have same color as that color of the square.

Now from the remaining given another color to the starting figure. We will get that shapes, that will have same color.

Like that the remaining figures are given colors.          

Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.

Hence the least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors.

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Answer:

2

Step-by-step explanation:

If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.

The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.

In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."

Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.

Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,

Total cost of x painting = $10 + $45(x)

Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,

Revenue generated = $50(x)

Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,

Total cost of x painting = Revenue generated

$10 + $45(x) = $50(x)

10 + 45x = 50x

10 = 50x - 45x

10 = 5x

x = 10/5

x = 2

Hence, For breakeven Lamar needs to sell 2 paintings.

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Answer:

9

Step-by-step explanation:

6 ÷ 2/3   =    6 /  (2/3 )   =  (6/1) / (2/3)  = 6/1  x  3/2 = 18/2 = 9

Step-by-step explanation:

Answer:

x = − 6

Step-by-step explanation:

I have my work

Answer:

  SAA

Step-by-step explanation:

Identify the corresponding congruent parts as either sides or angles. Look at their order of appearance around the triangle.

The sides marked with a single hash mark are identified as corresponding and congruent.

The angles marked with a single arc are identified as corresponding and congruent.

The vertical angles where the lines cross are congruent.

Working counterclockwise around the left triangle, we encounter ...

These same features appear in the same order working counterclockwise around the triangle on the right.

The "side," "angle," and "angle" are referenced in the congruence postulate as S, A, and A.

Congruence is proved by the SAA congruence postulate.

Answer:

6 gallons

Step-by-step explanation:

the total area to be painted :

= The total surface area - area of the floor

= area of the walls + area of the ceiling

area of the walls :

= [perimeter of the room] ×height

= [2 × (30+20)] × 12

= 1 200

area of the ceiling :

= length × width

= 30 × 20

= 600

the total area to be painted :

= 1200 + 600

= 1800

The number of gallon of paint needed to cover the room :

= 1800 ÷ 300

= 6

Answer: -1

Step-by-step explanation:

Evaluate 4x if x = -1/4

4(-1/4) = -1

Answer: -1

Step-by-step explanation:

4x and x = -1/4

plug x into the expression

[tex]4(-\frac{1}{4} )[/tex]

simplifies to:

[tex]-\frac{4}{4}[/tex]

4 divided by 4 is just 1, but it is negative so your final answer is

-1

Answer: a) $ 6,487.47

b) $ 1,487.47

Step-by-step explanation:

Answer:

d(t)=-10t-520

Step-by-step explanation:

First you have to find the gradient (m) using the formula [tex]m=\frac{d(t)2-d(t)1}{t2-t1}[/tex]

using the two points you have been given: 1(3,-550) and 2(8,-600)

so you substitute these points into the equation [tex]m=\frac{-600+500}{8-3}[/tex]

m=-10

Now that you have found the m-value you need to find the b-value by using one of the points you already have, I will use Point 2 (8,-600), and substitute it into the equation and solve

d(t)=-10t+b

-600=-10*8+b

-600=-80+b

-520=b

Therefore, the equation is d(t)=-10t-520

Answer:

y = 3/2x + 2

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y = 3/2x + 2

Answer:

[tex]\sf y =\dfrac{3}{2}x+2[/tex]

Step-by-step explanation:

 Pick any two points on the line.

 (0,2) and (2 , 5)

  (0,2) ⇒ x₁ = 0  & y₁ = 2

  (2,5) ; x₂ = 5 & y₂ = 5

[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

            [tex]\sf =\dfrac{5-2}{2-0}\\\\=\dfrac{3}{2}[/tex]

Equation of line in point slope form:

         [tex]\sf y - y_1 =m(x -x_1)[/tex]

        Point(0 ,2) and m = 3/2

       [tex]\sf y - 2 = \dfrac{3}{2}(x -0)\\\\ y - 2 = \dfrac{3}{2}x\\\\[/tex]

Equation of line in slope y-intercept form:

              [tex]\sf y =\dfrac{3}{2}x+2[/tex]

The factor of such equation described as having the number 3 as a root can be determined as; (x-3).

It follows from the task content that; we are required to determine a possible factor of a polynomial in the event that such polynomial has a root of 3.

The implication of a polynomial having a root of 3 is that; such a polynomial has 3 to be one of it's zeros.

Hence, a linear equation which holds for such polynomial is that; x = 3 and when expressed as a linear factor, the linear factor is; (x-3).

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Answer:

x=70

Step-by-step explanation:

when added together, verticle angles equal 180 degrees.

2x-10+x+20=180

3x-10+20=180

3x-30=180

3x=210

x=70

Answer: 15

Step-by-step explanation: Using the pythagorean theorem A^2 + B^2 = C^2 where C is the hypotenuse of the triangle and any A and B are any sides of the triangle that are not the hypotenuse; we can rewrite this as A^2 = C^2 - B^2 to find out the missing side. I picked A to be the unknown side but you could also choose B. We know the hypotenuse is 39, and side B is 36. 39^2 - 36^2, or 1521 - 1296, is 225.

Now we have A^2 = 225. To get rid of the square, we have to take the square root of both sides. The A^2 cancels to be A, and sqrt(225) is 15. Thus, side A, or the missing side is 15.

Hope this helped!

The aim of factorization to obtain the common factors that are present in the expression.

When we factorize an expression, the aim is to obtain the common factors that are present in the expression.

Now we have trinomials numbered 1 - 15. Trinomial is an expression that is made up of three terms. Quadratic expressions are mostly found to appear as trinomial

The binomial factors that are associated with each are shown in the factorized expressions below. The binomials contain two terms in each bracket.

Given the trinomials, the correct binomial factors are;

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Answer:

Step-by-step explanation:

Here's the solution

f^(-1)(x)=(\sqrt(5(x-10)))/(5), -(\sqrt(5(x-10)))/(5)

Answer:

b

Step-by-step explanation:

b

Answer: [tex]y+2=2(x-3)[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so substituting into point-slope form, the equation is

[tex]y+2=2(x-3)[/tex]

A. No, AB and BC are not congruent

B. No, AC and BD are not congruent

From the question, we are to determine if the given pairs of segments are congruent

To do this, we will determine the length of the line segments

Consider the given number line,

AB = -2 - (-5) = -2 + 5 = 3

BC = 0 - (-2) = 0 + 2 = 2

AC = 0 - (-5) = 0 + 5 = 5

BD = 5 - (-2) = 5 + 2 = 7

Now,

A. AB and BC

AB = 3 and BC =2

∴ AB and BC are not congruent.

Thus, No

A. AC and BD

AC = 5 and BD = 7

∴ AC and BD are not congruent.

Thus, No

Hence,

A. No, AB and BC are not congruent

B. No, AC and BD are not congruent

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Using the binomial distribution, there is a 0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given by:

p = 0.3, n = 6.

The probability that exactly four of them use a Motorola cell phone is given by P(X = 4), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

P(X = 4) = C(6,4) x (0.3)^4 x (0.7)² = 0.0595

0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.

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The value of the composite functions (g∘f)(x) and (f∘g)(x)   are 32x^2 + 16x + 3 and 8x^2 + 5 respectively

Composite function is also known as function of a function. They are determined by representing x with the other function.

Given the following functions

f(x)=4x+1

g(x)=2x^2+1

(f∘g)(x) = f(g(x))

(f∘g)(x) = f(2x^2+1)

(f∘g)(x) = 4(2x^2+1) + 1

(f∘g)(x)  =8x^2 + 5

For the composite function (g∘f)(x)

(g∘f)(x) = g(f(x))

(g∘f)(x) = g(4x+1)

Replace x wit 4x+1  to have:

(g∘f)(x) = 2(4x+1)^2 + 1

(g∘f)(x)= 2(16x^2+8x+1) + 1

(g∘f)(x) = 32x^2 + 16x + 3

Hence the value of the composite functions (g∘f)(x) and (f∘g)(x)   are 32x^2 + 16x + 3 and 8x^2 + 5 respectively

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Answer:

1. 2A + 3A

2. 2A - B

3. 2A

4. 2(A-B)

Step-by-step explanation:

When multiplying matrix by a number you just multiply each number in the matrix by whatever you are multiplying. When adding 2 matrices you just add the corresponding number in each matrix. Ex: You add the top left number to the top left number. The same goes with subtraction.

Answer:

Behold!

Step-by-step explanation:

Answer:

39°

Step-by-step explanation:

Opposite angles of a parallelogram are congruent.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

" The opposite angles of a Parallelogram are always equal to one another "

[tex] \qquad \large \sf {Conclusion} : [/tex][tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

x = - 4

Step-by-step explanation:

using the rule of indices

[tex]\frac{1}{a^{n} }[/tex] = [tex]a^{-n}[/tex] , then

[tex]3^{x}[/tex] = [tex]\frac{1}{81}[/tex] = [tex]\frac{1}{3^{4} }[/tex] = [tex]3^{-4}[/tex] , that is

[tex]3^{x}[/tex] = [tex]3^{-4}[/tex] , thus

x = - 4

The best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.

It should be noted that conjecture simply means a conclusion that's proffered on a tentative basis without any proof.

From the information, Charlie used construction paper, scissors and a ruler to construct an isosceles triangle with a pair of sides each 3 inches long and an acute angle on top.

Here, the best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.

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Answer:

It could be 105, 112 or 133.

Step-by-step explanation:

Having 7 as a factor means it is a multiple of 7.

The first 3 digit multiple of 7: 100 ÷ 7 = 14 2/7 → first 3 digit multiple of 7 is 15 × 7 = 105

Last 3 digit multiple of 7 less than 140: 140 ÷ 7 = 20 → last 3 digit multiple of 7 less than 140 is 19 × 7 = 133

→ The possible multiples of 7 to consider are [15..19] × 7 which gives 105, 112, 119, 126 and 133.

The sum of the digits of these number is:

105 → 1 + 0 + 5 = 6

112 → 1 + 1 + 2 = 4

119 → 1 + 1 + 9 = 11

126 → 1 + 2 + 6 = 9

133 → 1 + 3 + 3 = 7

Of these sums only 6, 4 and 7 are less than 9, thus the possible numbers are 105, 112 or 113.

Answer:

(0, -2)

Step-by-step explanation:

The equation of y axis is x = 0. So, the y intercept is located at point (0, b). Therefore we can substitute 0 into x in the given equation to find b and hence the coordinates of the y intercept.

3x - 7y = 14

3*0 - 7y = 14

-7y = 14

y = -2

Answer:

The file contains the solution to the question