Solve: x² + x + 1 = 0.​

Since the grade of the numerator and the denominator is the same, then the limit exists and is distinct from 0. The limit of the expression is 4/7.

In this problem we must apply some algebraic handling and some known limits to determine whether the limit exists or not. The limit exists if and only if the result exists.

[tex]\lim_{x \to \infty} \frac{4\cdot x - 1}{7\cdot x + 3}[/tex]

[tex]\lim_{x \to \infty} \frac{4\cdot x - 1}{7\cdot x + 3} \cdot \frac{x}{x}[/tex]

[tex]\lim_{x \to \infty} \frac{4 - \frac{1}{x} }{7 + \frac{3}{x} }[/tex]

[tex]\lim_{x \to \infty} \frac{4}{7}[/tex]

4/7

Since the grade of the numerator and the denominator is the same, then the limit exists and is distinct from 0. The limit of the expression is 4/7.

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

plug 1 in for t

[tex]F(t)=4(\frac{1}{2^3^t})\\ F(1)=4(\frac{1}{2^3^*^1})\\ F(1)=4(\frac{1}{2^3})\\ F(1)=4(\frac{1}{8})\\ F(1)=\frac{4}{8} \\F(1)=\frac{1}{2}[/tex]

Answer:

  (b)  (-3, 2, -5)

Step-by-step explanation:

The solution to the system of equations will satisfy every equation. If it fails to satisfy any equation, it is not a solution.

The system of equations does not seem to lend itself to simple solution by substitution or elimination. Hence, a reasonable strategy for finding the answer is to try the offered choices. Of course, a calculator can be used to find the answer almost as quickly.

Using the third equation, we can check the answer choices fairly easily. That equation involves the least number of arithmetic operations. Substituting for (x, y, z), we have ...

  a) 3(1) -(11) -(5) = -13 ≠ -6

  b) 3(-3) -(2) -(-5) = -6 . . . . . . a potential solution

  c) 3(1) -(8) -(0) = -5 ≠ -6

  d) 3(-1) -(3) -(4) = -10 ≠ -6

The only viable choice is (-3, 2, -5).

Check

In the other two equations, we have for this solution, ...

  2(-3) -2(2) +(-5) = -15 . . . . works in the first equation

  6(-3) -3(2) -(-5) = -18 . . . . works in the second equation

The ordered pairs which is the solution of the system of Inequalities is;

x > 0 and y < 2

We are given the inequalities;

x + 2y > 4    ----(1)

3x - y < 2     -----(2)

Subtract 2y from both sides in eq 1 to get;

x > 4 - 2y   ----(3)

Put 4 - 2y for x in eq 2 to get;

3(4 - 2y) - y < 2

12 - 4y - y < 2

12 - 5y < 2

Subtract 12 from both sides to get;

-5y < -10

Divide both sides by -5 to get;

y < 2

Put 2 for y in eq 3 to get;

x > 4 - 2(2)

x > 0

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Answer:

[tex]f(x)=x^3-12x^2+37x+130[/tex]

Step-by-step explanation:

So I'm assuming when you provided n=3, that means the degree is 3? So the first thing to know, is you can express a polynomial using it's factors as: [tex]f(x)=a(x\pm b)(x\pm b)(x\pm c)[/tex] where the sign of each factor depends on the sign of the factor... the point is it can be either. Notice the a? This usually will determine the stretch/compression of the polynomial, since sometimes the factors will have a coefficient for the x, but in this case I'm assuming all the coefficients of x are 1. So the next thing that is vital to know is that imaginary solutions come in conjugates. This means that if you have a zero at: [tex]a-bi \text{ then }a+bi \text{ is also a zero}[/tex]. So this means you have the 3 zeroes at x=-2, x=7+4i, x=7-4i. These are all the zeroes of the polynomial, since the Fundamental Theorem of Algebra states that a polynomial with degree n will have n solutions, which can be complex or real.

So the factor isn't going to be written as (x-2), it's going to be (x+2) since when you plug in -2 as x, it makes x+2 equal to 0.

The same thing applies for the two imaginary factors, so you're going to have the other two factors as (x-(7+4i)) and (x-(7-4i). You can instead think of it as ((x-7)+4i) and ((x-7)-4i) and you can use the difference of squares identity: [tex](a-b)(a+b)=a^2-b^2[/tex] where in this case a=x-7 and b=4i

So this gives you the equation: [tex]((x-7)-4i)((x-7)+4i) = (x-7)^2-(4i)^2[/tex]

Which becomes: [tex](x^2-14x+49)-16(-1) = x^2-14x+49+16 = x^2-14x+65[/tex]

So this gives us one of the factors: [tex]x^2-14x+65[/tex]

Now plug this in with the other factor and we get the equation:

[tex]f(x) = a(x+2)(x^2-14x+65)[/tex]

Now plug in 1 as x and make f(x) = 156, to solve for a

[tex]156=a(1+2)(1^2-14(1)+65)\\156=a(3)(1-14+65)\\156=a(3)(52)\\156=152a\\a=1[/tex]

So in this case, a=1, so that last step wasn't necessary, although I would check each time just in case a =/= 1.

Original equation

[tex]f(x) = (x+2)(x^2-14x+65)[/tex]

Multiply

[tex]f(x)=(x^3-14x^2+65x)+(2x^2-28x+130)\\[/tex]

Combine like terms:
[tex]f(x)=x^3+(-14x^2+2x^2)+(65x-28x)+130[/tex]

add like terms:

[tex]f(x)=x^3-12x^2+37x+130[/tex]

Answer:

[tex]f(x)=x^3-12x^2+37x+130[/tex]

Step-by-step explanation:

Complex Conjugate Theorem

For a polynomial p(x) with real coefficients, the complex zeros occur in conjugate pairs.  So if (a + bi) is a zero, then its conjugate (a - bi) is also a zero.

Given zeros:

-2 and (7 + 4i)

As one of the given zeros is a complex number, (7 - 4i) is also a zero.

Write each zero as part of a factor and multiply them together, adding a leading coefficient [tex]a[/tex]:

[tex]\begin{aligned}f(x) & = a(x+2)(x-(7+4i))(x-(7-4i))\\& = a(x+2)(x-7-4i)(x-7+4i)\\& = a(x+2)(x^2-7x+4ix-7x+49-28i-4ix+28i-16i^2)\\& = a(x+2)(x^2-14x+49-16i^2)\end{aligned}[/tex]

Remember that [tex]i^2=-1[/tex], therefore:

[tex]\begin{aligned}f(x) & = a(x+2)(x^2-14x+49-16(-1))\\& = a(x+2)(x^2-14x+49+16)\\& = a(x+2)(x^2-14x+65)\end{aligned}[/tex]

To find the value of the leading coefficient (a), use the given [tex]f(1)=156[/tex] :

[tex]\begin{aligned}f(1) & = 156\\\implies a(1+2)(1^2-14(1)+65) & = 156\\a(3)(52) & = 156\\156a & = 156\\\implies a & = 1\end{aligned}[/tex]

Therefore, the polynomial in factored form is:

[tex]f(x)=(x+2)(x^2-14x+65)[/tex]

Finally, expand the brackets:

[tex]\begin{aligned}f(x) & =(x+2)(x^2-14x+65)\\& = x^3-14x^2+65x+2x^2-28x+130\\& = x^3-14x^2+2x^2+65x-28x+130\\& = x^3-12x^2+37x+130\end{aligned}[/tex]

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Answer:

23 years old

Step-by-step explanation:

Let x = age of younger sibling.

Then, the age of the older sibling is x + 9.

x + x + 9 = 55

2x = 46

x = 23

Answer: 23 years old

Answer:

32 seats per row

Step-by-step explanation:

Total number of seats in auditorium = 288

Number of rows in which seats evenly distributed = 9

Number of seats per row = 288/9= 32

Answer: -4

Step-by-step explanation:

[tex]\frac{1}{4}x-\frac{1}{8}=\frac{7}{8}+\frac{1}{2}x[/tex]

Multiplying both sides of the equation by 8,

[tex]2x-1=7+4x\\\\-1=7+2x\\\\-8=2x\\\\x=\boxed{-4}[/tex]

Answer:

11

Step-by-step explanation:

since 30÷45 = 2/3 then

The space taken by a small book is equal to

the space taken by 2/3 a large book.

…………………………………………………

Calculating the number of large book corresponding to 23 small books :

= 23×(2÷3) + 3

= 18.333333333333 (large book)

Then ,Kevin can pack the shelf with (at most) : 30 - 19 = 11 more large books

The sequences are classified, respectively, as:

Geometric, Arithmetic, Neither.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

In the first sequence, we have that:

[tex]q = \frac{45}{15} = \frac{15}{5} = \frac{5}{\frac{5}{3}} = \frac{\frac{5}{3}}{\frac{5}{9}} = 3[/tex]

Hence it is a geometric sequence.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

In the second sequence, we have that:

d = -4 - 1 = 1 - 6 = 6 - 11 = 11 - 16 = -5

Hence it is an arithmetic sequence.

[tex]\frac{4}{3} \neq \frac{3}{2}, 1 - \frac{1}{2} \neq 2 - 1[/tex]

Hence it is neither arithmetic nor geometric.

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Answer:

  d.  =SQRT(ABS(A2))

Step-by-step explanation:

A spreadsheet will not tell you the square root (or half power) of a negative number. It only performs math using real numbers.

Trying to take a square root of a negative number will result in a #NUM! error being shown in the result cell. Assuming you want the root of the magnitude of the numbers in column A, the value you want the root of is ABS(A2).

Using a dollar sign on a cell reference renders that portion of the cell reference fixed when the formula is copied. Referencing cell A$2 will mean you will get 399 copies of the square root of the contents of cell A2 in cells B2 through B400.

The formula that will give you the square root of the magnitude of the adjacent cell in column A will be

  =SQRT(ABS(A2)) . . . . . . . . . formula for cell B2, copied to cells below

Step-by-step explanation:

•a reflection and a dilation

Step-by-step explanation:

the slope of a line is always the factor of x, when the line is in the form

y = ...

so,

3x + 3y = 18

3y = -3x + 18

y = -x + 6

the slope is -1 = -1/1

as the slope is the ratio of y coordinate change / x coordinate change.

a perpendicular slope switches x and y upside-down and flips the sign.

so, in our case the perpendicular slope is

1/1 = 1

a) 32.4% probability that exactly 3 drivers text while driving if a police officer pulls over five drivers.

b)  2.76% probability the next driver texting while driving that the police officer pulls over is the fifth driver.

It is a branch of mathematics that deals with the occurrence of a random event.

Using Binomial distribution,

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

We have, p= 0.52

A) probability that exactly 3 drivers text while driving if a police officer pulls over five drivers

[tex]P(x) = C_{5 , 3} * (0.52)^{3}* (0.48)^ {2}[/tex]

P(x) = 10* 0.140608* 0.2304

P(x)= 0.3239

32.4% probability that exactly 3 drivers text while driving if a police officer pulls over five drivers.

B) probability the next driver texting while driving that the police officer pulls over is the fifth driver

[tex]P(x) = C_{4 , 0} * (0.52)^{0}* (0.48)^ {4}[/tex]

P(x) = 1 * 1 * 0.053084

P(x) = 0.053084

So, 0.0531*0.52 = 0.0276

Hence, 2.76% probability the next driver texting while driving that the police officer pulls over is the fifth driver.

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Answer:

-3 (v+4) + 6v

-3v - 12 + 6v

arranging like terms

-3v + 6v - 12

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

-3(v+4)+6v, simplify

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\multimap\bf{-3(v+4)+6v}=-3v-12+6v[/tex] | combine the like terms

[tex]\multimap\bf{3v-12}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                [tex]\bf{=3v-12}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]

Answer:

sii esa misma vaina. loa a pero aya dur 7 dar s servicio rus ser rh r rhr ser ru r de dhd HD. dhs g PG15 BIT

 Answer:

 6x + 47

Step-by-step explanation:

Given following:

While solving these function sums, start from the right then head left.

⇒ f[g(x)]

⇒ f[x + 6]

⇒ 6(x + 6) + 11

⇒ 6x + 36 + 11

⇒ 6x + 47

Answer:

f(-2) = 3, f(0, -3) = -1

The answer choice which must be true regarding the linear function is; The set must have a constant additive rate of change.

Since a linear function typically takes the slope-intercept form; f(x) = mx +c.

It therefore follows that the equation must have a constant slope m, which is the described additive constant rate of change.

It therefore follows that, the answer choice which is true regarding the linear function is therefore; The set must have a constant additive rate of change.

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Answer:

-76

Step-by-step explanation:

121 - y = 197

-121        -121

-y = 76

*-1   *-1

y = -76

Volume is a three-dimensional scalar quantity. The volume of concrete that will have to be poured into the pool deck is 6.0185 cubic yards.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Since an inch is equal to 1/12 of a foot. Therefore, the thickness of the pool deck is,

3 inches = 0.25 foot

If a pool deck of 650 square feet is to be laid with concrete 3" thick, then the volume of concrete that will be needed is,

Volume of concrete = 650 ft² × 0.25 ft = 162.5 ft³

Now, one yard is equal to 3 feet, therefore,

1 cubic foot = 1/27 cubic yards

162.5 cubic feet = 6.0185 cubic yards

Hence, the volume of concrete that will have to be poured into the pool deck is 6.0185 cubic yards.

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Answer:

330°

Step-by-step explanation:

Multiply by the conversion factor of [tex]\frac{180}{\pi }[/tex]

If graphed on the same grid, the diagrammatic representation of the parabola gives an upward curve.

The graph of the function is a diagrammatic representation of the slope, x-intercept, and y-intercept of the given function.

From the information given:

y = 2.5x²

Here,

x-intercept = (0,0)

y-intercept = (0,0)

Therefore, if graphed on the same grid, the diagrammatic representation of the parabola gives an upward curve.

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The measure of TV from the figure is 38 units

The given diagram in question is a kite. From the figure, the expression below is true;

6x - 3 = 39

Determine x

6x = 42

x= 7

TV = 2(2x+5)

TV = 2(2(7)+5)

TV = 2(19)

TV = 38 units

Hence the measure of TV from the figure is 38 units

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Answer:

a and c = 115 and b and d = 65

Step-by-step explanation:

Hope this helps :)

Answer:

180

Step-by-step explanation:

Let x be the first integer.

Let y be the 2nd integer.

Given info from the question,

x = 5% x y

x = 0.05y - equation 1

x + y = 63 - equation 2

Lets now substitute equation 1 into equation 2.

0.05y + y = 63

1.05y = 63

y = 63 / 1.05

= 60

Now we substitute y into equation 1.

x = 0.05(60)

= 3

Now since we know both x and y,

we can find the product of them.

xy = 60 * 3 = 180

Answer:

28

Step-by-step explanation:

Givens

Game 1: 30

Game 2: 18

Game 3: 28

Game 4: x

Solution

(30 + 18 + 28 + x) / 4 = 26                 Multiply both sides by 4

4* (30 + 18 + 28 + x) / 4 = 26 * 4       The 4s on the left cancel

30 + 18 + 28 + x = 104                       Add the 3 other numbers together

76 + x = 104                                       Subtract 76 from both sides.

76-76+x = 104-76                              The 76s on the left disappear.

x = 28

Answer

in the next game he must score 28 points to average 26

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{7 \dfrac{2}{3} + \dfrac{4}{7}}[/tex]

[tex]\huge\textbf{Solving:}[/tex]

[tex]\mathbf{7 \dfrac{2}{3} + \dfrac{4}{7}}[/tex]

[tex]\mathbf{= \dfrac{7\times3+2}{3} + \dfrac{4}{7}}[/tex]

[tex]\mathbf{= \dfrac{21 + 2}{3} + \dfrac{4}{7}}[/tex]

[tex]\mathbf{= \dfrac{23}{3} + \dfrac{4}{7}}[/tex]

[tex]\mathbf{= \dfrac{173}{21}}[/tex]

[tex]\mathbf{\approx 8 \dfrac{5}{21}}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathsf{8 \dfrac{5}{21}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

[tex]8\frac{5}{21}[/tex]

Step-by-step explanation:

[tex]7\frac{2}{3} +\frac{4}{7} = 7\frac{14}{21} +\frac{12}{21} = 8\frac{5}{21}[/tex]

An ordinal number is a number that specifies how something ranks in respect to other numbers. The correct option is B.

An ordinal number is a number that specifies how something ranks in respect to other numbers, such as first, second, third, and so on. This order or sequence might be determined by size, importance, or chronology.

The example that illustrates the ordinal number is "Gracie told Bradly she would be the first one to go down the slide".

Hence, the correct option is B.

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the probability of rolling 4 or a number less than 6 is P = 5/6

The standard number cube has the outcomes {1, 2, 3, 4, 5, 6}

We want to find the probability of rolling 4 or a number less than 6. (4 is a number less than 6).

The outcomes that meet that condition are:

{1, 2, 3, 4, 5}

So 5 out of 6 outcomes meet the condition, then the probability is:

P(4 or less than 6) = 5/6

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