A company's sales increased 20% this year, to $6740. What were their sales last year?

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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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:

9

Step-by-step explanation:

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

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: [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]

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:

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:

x = − 6

Step-by-step explanation:

I have my work

Step-by-step explanation:

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

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \:6 = 2(y + 2)[/tex]

[tex] \qquad❖ \: \sf \:(y + 2) = \cfrac{6}{2} [/tex]

[tex] \qquad❖ \: \sf \:y + 2 = 3[/tex]

[tex] \qquad❖ \: \sf \:y = 3 - 2[/tex]

[tex] \qquad❖ \: \sf \:y = 1[/tex]

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

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.

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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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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The volume of the cylinder in discuss in which case, the radius of the cylinder is 3 inches and the height is inches is; V = 141.3in³.

The cylinder in discuss according to the task content has radius, 3 inches and height, 5 inches.

Since the volume of a cylinder by convention is given as; V = πr²h

Therefore, the volume of the cylinder in discuss is;

V = π (3²)×5

V = 3.14 × 45

V = 141.3in³

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Considering the definition of mass volume percent, the percent composition of lactose in skim milk is 28%.

The concentration of solutions is the amount of solute contained in a given amount of solvent or solution. In other words, the relationship between the amount of solute and the amount of solvent is called concentration.

Mass volume percent (% m/V) is a measure of concentration that indicates the number of grams of solute in each 100 mL of solution.

In other words, mass-volume percent is an intensive property that is defined as the mass of solute (in grams) that there are in 100 mL of solution and it is calculated by applying the following equation:

[tex]Mass volume percent=\frac{mass solute (grams)}{volume solution (mL)}x100[/tex]

This is, mass volume percent is defined as the ratio of the mass of solute that is present in a solution, relative to the volume of the solution, as a whole.

In this case, you know:

Replacing in the definition of mass volume percent:

[tex]Mass volume percent=\frac{0.28 grams}{1 mL}x100[/tex]

Solving:

mass volume percent= 28 %

Finally, the percent composition of lactose in skim milk is 28%.

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Answer:

b

Step-by-step explanation:

b

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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Based on the total number of people who want the steakhouse option, the probability that a student will not want the seafoodbuffet if they want the steakhouse option is 24%

The probability that a student does not want the seafood buffet given that they want the steakhouse option is:

= Number of people who want steakhouse but not seafood / Total surveyed

Solving gives:

= 9 / (16 + 8 + 9 + 4)

= 9 / 37

= 24%

Full question is:

If a student wants the steakhouse option, what is the probability that they will not want the seafoodbuffet?

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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)

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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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:

8 ^-11

Step-by-step explanation:

It should be noted that in this case, since it's the product that we want to get, it's important to add the power together. This will be:

8^-2 × 8^-9

= 8^(-2 + -9)

= 8^-11

Answer:

12 and 14

Step-by-step explanation:

12 * 14 = 168

Answer:

12 & 14

Step-by-step explanation:

the work: x = first even number, (x+2) = second even number

The equation

[tex]x(x+2)=168[/tex]

[tex]x^{2} +2x=168[/tex]

[tex]x^{2} +2x-168=0[/tex]

Factoring

[tex](x-12)(x+14)=0[/tex]

first factor

[tex]x-12=0\\x=12[/tex]

Second factor

[tex]x+14=0\\x=-14[/tex]

The solution is the positive number

x = 12     is the first even number

x + 2 = 12 + 2 = 14    is the second even number

Hope this helps

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]

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:

The file contains the solution to the question

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