Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?
x squared + x + 1 + StartFraction 2 Over x + 1 EndFraction
x squared minus x + 1
x squared + x + 1 + StartFraction 2 Over x minus 1 EndFraction
x cubed minus x squared + x minus 1

[tex]9\sqrt{56 x^7 y^{12}}\qquad \begin{cases} 56=7\cdot 2\cdot 2\cdot 2\\ \qquad 7\cdot 2^2 \cdot 2\\ \qquad 2^2\cdot 14\\ x^7=x^{(3)(2)+1}\\ \qquad (x^3)^2\cdot x^1\\ y^{12}=y^{(6)(2)}\\ \qquad (y^6)^2 \end{cases}\hspace{5em} \begin{array}{llll} 9\sqrt{2^2(14)(x^3)^2 x (y^6)^2} \\\\\\ 9(2)(x^3)(y^6)\sqrt{14x} \\\\\\ {\Large \begin{array}{llll} 18x^3y^6\sqrt{14x} \end{array}} \end{array}[/tex]

Answer:

[tex]\textsf{1.} \quad 18\;x^3\;y^{6}\sqrt{14x}[/tex]

[tex]\textsf{2.} \quad -8\sqrt{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]9\sqrt{56x^7y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{56}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 56 as 4·14:

[tex]\implies 9\sqrt{4 \cdot 14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{4}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 4 as 2²:

[tex]\implies 9\sqrt{2^2}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Simplify:

[tex]\implies 9\cdot 2\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\implies 18\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]

[tex]\implies 18\sqrt{14}\;(x^7)^{\frac{1}{2}}\;(y^{12})^{\frac{1}{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^{\frac{12}{2}}[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^6[/tex]

Rewrite ⁷/₂ as 3 + ¹/₂

[tex]\implies 18\sqrt{14}\;x^{(3+\frac{1}{2})}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}= a^b \cdot a^c:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; x^{\frac{1}{2}}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; \sqrt{x}\;y^{6}[/tex]

Rearrange:

[tex]\implies 18\;x^3\;y^{6}\sqrt{14x}[/tex]

Given expression:

[tex]7\sqrt{32}-6\sqrt{72}[/tex]

Rewrite 32 as 16·2 and 72 as 36·2:

[tex]\implies 7\sqrt{16 \cdot 2}-6\sqrt{36 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 7\sqrt{16}\sqrt{2}-6\sqrt{36}\sqrt{2}[/tex]

Rewrite 16 as 4² and 36 as 6²:

[tex]\implies 7\sqrt{4^2}\sqrt{2}-6\sqrt{6^2}\sqrt{2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies 7 \cdot 4\sqrt{2}-6\cdot 6\sqrt{2}[/tex]

Simplify:

[tex]\implies 28\sqrt{2}-36\sqrt{2}[/tex]

[tex]\implies -8\sqrt{2}[/tex]

The factored form of y = x² - x + 12 will be (x + 3)(x - 4).

It should be noted that a factor simply means the number than can be multiplied by another number to get the original number. The factored form is when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form can be restated in standard form.

This will be illustrated as:

x² - x - 12

x² - 4x + 3x - 12.

x(x - 4) + 3(x - 4)

(x + 3)(x - 4)

The factored form is (x + 3)(x - 4).

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The value of the expression after simplify will be,

''negative 43 over 24 times j plus negative 1 over 12.''

Option D is true.

What is mathematical expression?

Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is;

''The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths.''

Now, We can write the expression in mathematical form as;

⇒ (- 1/8  j + 2/3) - (5/3 j + 9/12)

Solve the expression as;

⇒ - 1/8 j + 2/3 - 5/3 j - 9/12

⇒ - 1/8 j - 5/3 j + 2/3 - 9/12

⇒ j (-1/8 - 5/3) + 2/3 - 3/4

⇒ j (- 3 - 40)/24 + (8 - 9)/12

⇒ j (-43/24) + (- 1/12 )

This can be written as;

''negative 43 over 24 times j plus negative 1 over 12''

Therefore, The value of the expression after simplify will be,

''negative 43 over 24 times j plus negative 1 over 12.''

Option D is true.

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The graphic solutions for the expressions are given as follows:

10. x = 2.667 and x = 8.

13. x = 8.

15. x < -1 or x > 8.

16. x > 3.

In item 10, we are going to solve an equation graphically, hence we have to find the points of intersection of the two curves given by:

From the first graph given at the end of the answer, the x-coordinates of these points are given as follows:

x = 2.667 and x = 8.

Now we have to find the point of intersection of these two equations:

They have only one intersection point, at x = 8, which is the solution to the system.

The inequality is:

x² - 7x- 8 > 0.

Hence we have to find the intervals for which the function x² - 7x - 8 is above the x-axis, and from the third graph, these intervals are described as follows:

x < -1 or x > 8.

The inequality is:

x - 5 > -2x + 4.

Combining the like terms, it can be written as;

3x > 9

x > 3.

The interval for which the increasing line is above the decreasing line is x > 3, and is shown in the fourth graph.

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The answer is A 90 degrees

EXPLANATION

Let's see the facts:

We can use the Law of Cosines to calculate the unknown value:

Replacing terms:

Isolating x:

Answer is x=6.

Answer:

y + 4 = -6 (x - 8)

Step-by-step explanation:

Change the equation to the slope intercept form for a line

x - 6y 5 = 0  Add 5 to both sides

x - 6y = 5  Subtract x from both sides

-6y = -x + 5  Divide both sides by -6

y = [tex]\frac{1}{6}[/tex] c  - [tex]\frac{5}{-6}[/tex]  Your slope is [tex]\frac{1}{6}[/tex]

A perpendicular slope is the opposite reciprocal of [tex]\frac{1}{6}[/tex], that would be -6

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])  Plug is -4 for [tex]y_{1}[/tex] and 8 for [tex]y_{1}[/tex]

y - -4) -6(x-8)

y + 4= -6 (x -8)

Answer:  Choice A)   [tex]\boldsymbol{78.67\% \ \pm \ 9.46\%}[/tex]

======================================================

Explanation:

phat = 59/75 = 0.7867 = 78.67% approximately is the sample proportion

n = 75 is the sample size

Your teacher doesn't mention a confidence level, so I'll assume it's the default 95%.

Let's compute the margin of error at 95% confidence

E = z*sqrt(phat*(1-phat)/n)

E = 1.96*sqrt(0.7867*(1-0.7867)/75)

E = 0.0927 approximately

E = 9.27% approximately

Unfortunately the margin of error 9.27% isn't listed among the four answer choices, but let's change the z = 1.96 to z = 2 instead.

Recalculate the margin of error.

E = z*sqrt(phat*(1-phat)/n)

E = 2*sqrt(0.7867*(1-0.7867)/75)

E = 0.0946 approximately

E = 9.46% approximately

This margin of error is listed among the four answer choices.

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

We found that

The confidence interval in the format [tex]\text{phat} \ \pm \ \text{E}[/tex] is approximately [tex]78.67\% \ \pm \ 9.46\%[/tex] which points us to choice A as the answer.

Answer:

[tex]\textsf{a)} \quad 78.67\% \pm 9.46\%[/tex]

or d) None of the answers are correct.  (Please see notes below).

Step-by-step explanation:

P-hat is the probability that a given outcome will occur given a specified sample size.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{P-hat formula}\\\\$\hat{p}=\dfrac{X}{n}$\\\\where:\\\phantom{ww}$\bullet$ $\hat{p}$ is the probability. \\ \phantom{ww}$\bullet$ $X$ is the number of occurrences of an event. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula to find p-hat:

[tex]\implies \hat{p}=\dfrac{59}{75} =0.78666666...[/tex]

The critical value for a 95% confidence level using normal distribution is:

[tex]z=1.9600\;\;\sf (4\;d.p.)[/tex]

[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Margin of error}\\\\$ME=z \cdot \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$\\\\where:\\\phantom{ww}$\bullet$ $z$ is the critical value. \\ \phantom{ww}$\bullet$ $\hat{p}$ is the sample proportion. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]

Substitute the given values into the margin of error formula:

[tex]\implies ME=1.9600 \cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]

[tex]\implies ME=0.092715036...[/tex]

Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) is:

[tex]\implies \hat{p}\pm ME[/tex]

[tex]\implies 0.7867\pm 0.0927[/tex]

[tex]\implies 78.67\% \pm 9.27\%[/tex]

This result if not given in the list of answer options.  However, the final result depends on the accuracy of the z-score and p-hat used in the calculations.  

If we round the critical value to the nearest integer then:

[tex]\implies z=2[/tex]

Substitute the rounded z-value into the margin of error formula:

[tex]\implies ME=2\cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]

[tex]\implies ME=0.094607180...[/tex]

Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) using z = 2 is:

[tex]\implies 78.67\% \pm 9.46\%[/tex]

Note:  It is likely that this question required the critical value to be rounded to the nearest integer, however please note that this is not normal practice as it produces a different result, as evidenced above.

1)

Consider P to be at the same vertical distance between the maximum and minimum height the blades can reach. Therefore, at t=0, P has to be at h=0 (the maximum height is 1 and the minimum one is -1).

Then, since the fan blades rotate counterclockwise, after t=0, h has to increase until it reaches a value of 1.

Finally, a revolution is completed after 1 second; therefore, at t=1, the h has to be equal to 0 (the same height as at t=0).

2)

Approximately, every year the Earth reaches its maximum distance from the sun and its minimum distance once a year, and that is a cycle that repeats almost without alteration. Furthermore, since the position of the Earth around the sun is given by an ellipse, the position of the Earth around the Sun can be expressed using trigonometric functions (because of polar coordinates).

Similarly, a rotating wheel will reach its maximum and minimum height eventually; therefore, it can be modeled using trigonometric functions which are periodic.

Finally, as for the area of a sheet of paper. Notice that the more we fold it, the less its area becomes, it does not reach its maximum anymore.

Given x inches, the number of centimeters is 2.54x, this is not a periodic function.

Due to the effects of gravity, the height of a pendulum can be expressed using a periodic function given that no energy is lost.

The trajectory of a tossed ball is given by a parabola, unless one tosses the ball again at the same initial height, option F cannot be modeled using a periodic function.

Solution

Using Z score calculator

P(x>Z) = 0.04093

y + 5x = 0 is the line's equation in point-slope form.

Given is a line with a slope of 0 and a point at (0, -10) on it. We must determine the line's point slope form equation.

The line's point-slope shape is  ( y -[tex]Y_{1}[/tex]  ) = m ( x - [tex]X_{1}[/tex]  ).

According to the query, slope (m) = 0 and

the line is going through ( [tex]X_{1}[/tex] , [tex]Y_{1}[/tex] ) = ( 0 , -10 )

∴ ( y - [tex]Y_{1}[/tex] ) = m ( x - [tex]X_{1}[/tex] )

y + 10 = 0 ( x - 0 )

y + 10 = 0

y + 5x = 0

As a result, the equation for the line in point-slope form will be

y + 5x = 0.

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Slope is 1/4 (0.25) while y-intercept is 5.

Here, we are interested in getting the y intercept and slope of the line joining the given points.

We can get the slope by using any two points

Let’s say (4,6) and (12,8)

Mathematically; slope

= (y2-y1)/(x2-x1) = (8-6)/(12-4) = 2/8 = 1/4 = 0.25

To get the y-intercept, we proceed

kindly recall that the equation of a straight line is;

y = mx + c

where m is the slope and c is the y-intercept

Let’s take any of the points (28,12)

Thus:

12 = 0.25(28) + c

12 = 7 + c

c = 12-7

c = 5

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According to the solving the  Polynomial  Standard Form of the given equation is :

3x^2-7x-17.

When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on. When x is the variable and ai are coefficients, the polynomial has the conventional form f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.

f(x)= x-7

g(x)= 3x^2-7x-10

f(x)= x-7 by substituting in the value of  g into f.

f(3x^2-7x-10) =  (3x^2-7x-10)-7

                     = 3x^2-7x-17

According to the solving the slandered form of the given equation is :

3x^2-7x-17

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Given

Find

Simplify

Explanation

as we know , any number divided by zero is infinity because division by zero is undefined and infinity does not really exist.

so , the solution is undefined.

Final Answer

Hence , the solution is undefined. so , the answer is

let x is the random variable that represents the speed of car.

probability that x is higher than 100 :

for x=100:

so,

probability =total area - area of the left of (z=1)

and the area of the left of z=1 is 0.8413 (from normal distribution)

The graph that shows the relationship between the height of the bamboo and months planted is given as h = 5t + 10

Given that the graph shows the relationship between the height (h) of a bamboo plant after months it has been planted.

Let us assume that h is plotted on the vertical axis and months (t) is planted on the horizontal axis.

If the graph passes through the points (0, 0) and (2, 10), hence:

h - 10 = [(10 - 0)/(2 - 0)](t - 0)

h - 10 = 5(t)

h = 5t + 10

The graph is given as h = 5t + 10

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The The 3 ratios are;

A=60: 84

F=90:126

H=5:7

The ways to translate the figure include:

It doesn't change its orientation.

It also doesn't change its size or shape.

When a geometric figure glides up, down, left, or right on the coordinate plane, this is referred to as translation. The figure changes its location but not its orientation. It also retains its size and shape. When you translate a figure, you slide it left or right, up or down.

When you translate a figure, you slide it left or right, up or down. This indicates that the coordinates for the figure's vertices will vary on the coordinate plane. To graph a, make the same modification at each point. The variations in coordinates of a reflection can be used to identify it.

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Answer:

A car travels at average speed of 4m/s and covers a distance of 2.4km calculate the time take help me

Concept

To solve the question you will use the associative property.

a . ( b + c ) = a . b + a . c

The expressions that is equivalent to 5 .(3 + 7) = 5 . 3 + 5 . 7 , ( 3 + 7 ) 5 , 5 . (

Fi

Answer:

what graph?

Step-by-step explanation:

By the knowledge on absolute values, functional theory and rigid transformations and given that the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, {\displaystyle |x|=x} if x is a positive number, and {\displaystyle |x|=-x} if x is negative, and {\displaystyle |0|=0}.

here, we have,

According to the image attached herein,

the function f(x) is an absolute value and the function g(x) results from translating f(x) in +x direction, representing a kind of rigid transformation as Pythagorean distance at every point of the function is conserved.

There, we can define the function g(x) as follows:

g(x) = f(x - k), for k > 0     (1)

By the knowledge on absolute values, functional theory and rigid transformations

and given that

the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

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What is the solution of the equation [tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1[/tex] ?

x=4

How is the given equation solved?

[tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1\\\\\frac{2}{3} x-\frac{2}{3} -\frac{2}{5} x+\frac{3}{5}=1\\\\\frac{2}{3} x-\frac{2}{5}x =1+\frac{2}{3}- \frac{3}{5}\\\\\text{Taking LCM},\\\\\frac{10x-6x}{15} =\frac{15+10-9}{15} \\\\4x= 16\\\\x=4[/tex]

What is solving an equation?

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The arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The equation:

h = −8t(2t−6)

To find the total number of seconds the arrow will be in the air:

Plug h = 0

−8t(2t−6) = 0

t(2t−6) = 0

t = 0   or    t = 6/2

t = 0  or   t = 3 seconds

Thus, the arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.

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The domain will be x ≥ 3 for f(x)=√x-3 and g(x)=1-x².

In case a function f gives a way to effectively create a single value y utilizing for that reason a value for x at that point that chosen x-value is said to have a place to the domain of f. there are some conditions to be checked such as denominators cannot equal 0, radicands of even roots can't have a negative value, logarithms can as it was being taken of positive values. Since we are given that f[tex]\sqrt{x-3}[/tex] and g(x)=1-x², for g(x)  since it's a polynomial function its domain had to be real numbers, whereas for f(x) is all positive and real numbers.

for the given  condition (f•g)(x)

=> (f•g)(x)= f(x)*g(x)

=> (f•g)(x) = √(x-3) * (1 - x²)

=>(f•g)(x) = √(x-3)-x²(√x-3)

So the domain for (f•g)(x) will be all positive real numbers x≥3 x ∈ [3,∞)

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ANSWER

EXPLANATION

We want to write the sentence as an inequality.

We have:

The sum of 3 times a number n and 8 is at most 16.

3 times a number n is 3 * n i.e. 3n

Adding that to 8 would yield:

3n + 8

That is at most 16.

This means that it is less than or equal to 16.

That is:

Answer:

B. radio stations stopped advertising

Answer:

As televisions became more affordable and advertisers flocked to the new medium, radio stations had to quickly adapt to the changing field. Stations stopped using live in-studio performances, instead playing less expensive recordings.

Step-by-step explanation:

In the 1950s, television surpassed radio as the most popular broadcast medium, and commercial radio programming shifted to narrower formats of news, talk, sports and music. Religious broadcasters, listener-supported public radio and college stations provide their own distinctive formats.

The function is given by:

The three quantities are zero then it follows:

Option D is correct.