On dividing x^3-3x^2+x+2 by a polynomial g(x), the quotient and remainder were x- 2 and "-2x+1" respectively, then g(x) is equal to

Answer:

70

Step-by-step explanation:

Answer:

x = - 3

Step-by-step explanation:

8x + 12 = 2(x - 3) ← distribute the parenthesis by 2

8x + 12 = 2x - 6 ( subtract 2x from both sides )

6x + 12 = - 6 ( subtract 12 from both sides )

6x = - 18 ( divide both sides by 6 )

x = - 3

Answer:

x = -3

Step-by-step explanation:

you first distribute 2(x-3) which gives you 2x-6 so 8x+12=2x-6.

next you move the terms to the correct side so you subtract 12 from the left side and subtract 2x from the right side then move them to the other side so you end up with 8x-2x=-6-12.

then you combine like terms so you will have 6x=-18.

then divide both sides by 6 which gives you x = -3.

8x+12=2(x-3)

8x+12 = 2x-6

8x-2x = 6-12

6x = -18

x = -3

Answer:

If the distance from the origin to a given point is 5, then that point lies on circle C is true.

Step-by-step explanation:

The correct statement about given circle is "If the distance from the origin to a given point is 5, then that point lies on circle C"

In mathematics, the circle is a two dimensional rounded figure which has no corner edges.

Standard form = (x - a)² + (y - b)² = r²

Given that,

The center of a circle is on origin and the radius is 5 unit.

And point p lies on the circle,

So, according to definition of circle the distance  between center and any point on the circle is always constant and which is known as radius.

Therefore, the distance between center end given point will be equal to 5 then it will lies on a circle.

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Answer:

√12×(-1)+√12×√5

-√12+√12×5

= -2√3+2√15

Answer:

Step-by-step explanation:

The formula for circumference is 2πr

First, lets find the radius

3.14 * 2 = 6.28

56.52 / 6.28 = 9

The diameter = 2r

2 * 9 = 18

The diameter is 18 feet

Hope this helps!

Answer:

The inverse of g(x) should be [tex]\sqrt{(x-3)}[/tex].

Step-by-step explanation:

The inverse means the opposite. The opposite of a term or expression squared will be the terms or expression square rooted.

The inverse of (x-3)² will be [tex]\sqrt{x-3}[/tex]

Hope this helps!

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Answer:

g(x)⁻¹ = √x + 3

Step-by-step explanation:

To find the inverse of an expression is to reverse the expression. This can be done by swapping the input and output variables. In other words, in g(x), you want to swap the places of the "x" variable the "y" variable.

Remember, g(x) = y.

y = (x - 3)²                              <----- Original function

x = (y - 3)²                              <----- Swap the variables

Now, you want to set the equation equal to "y" again. This can be done by rearranging/simplifying the expression.

x = (y - 3)²                              <----- Swapped variables

√x = √(y - 3)²                        <----- Take the square root of both sides

√x = y - 3                              <----- Eliminate parentheses from previous step

√x + 3 = y                             <----- Add 3 to both sides

If g(x)⁻¹ represents the inverse of g(x), the new function is:

g(x)⁻¹ = √x + 3

[tex]\large\boxed{y=\pm\sqrt{\frac{x+3}{5}}}[/tex]

To find the inverse, swap the [tex]y[/tex] (or [tex]f(x)[/tex] in this case) and the [tex]x[/tex], then solve for [tex]y[/tex].

[tex]\begin{aligned}y&=5x^2-3\\x&=5y^2-3\\x+3&=5y^2-3+3\\x+3&=5y^2\\\frac{x+3}{5}&=\frac{5y^2}{5}\\\frac{x+3}{5}&=y^2\\\pm\sqrt{\frac{x+3}{5}}&=\sqrt{y^2}\\\pm\sqrt{\frac{x+3}{5}}&=y\end{aligned}[/tex]

The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we can see in the picture, we have given a function:

We have a function:

g(x) = 4log(x) + 4

To find x-intercept plug g(x) = 0

0 = 4logx + 4

x = 0.1

(0.1, 0)

The vertical asymptote:

x = 0

The range of a function:

(-∞, ∞)

Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

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Answer:

310,000

Step-by-step explanation:

Since t represents time, the start would represent when no time has passed or in other words, when t=0, which is the y-intercept. You can plug in t as 0, but it's a bit redundant, since the y-intercept of a quadratic equation in the form: [tex]f(x)=ax^2+bx+c[/tex] will have a y-intercept at (0, c) where c is the constant, since whenever you plug in 0 as x, the ax^2 becomes 0 (since 0^2 = 0, and a * 0 = 0 since anything multiplied by 0... is 0) and the same thing goes for the bx, leaving the c alone. This means the y-intercept of the function is (0, 310) and since it's in the thousands there is 310,000 at the start

Answer:

310,000

Step-by-step explanation:

hope it helps!!!

Using it's concept, it is found that there is a 0.152 = 15.2% probability that they are both Democrats.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Two voters are selected, each with 39% probability of being Democrats, hence the probability of both being Democrats is given by:

p = (0.39)² = 0.152.

0.152 = 15.2% probability that they are both Democrats.

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Answer: 0.152

Step-by-step explanation:

[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{Given -}}}}}}[/tex]

Four points which lie at (0,0) ; (0,2) ; (2,2) ; (2,0)

[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{To \: Find-}}}}}}[/tex]

What is the figure formed?What is the area of the figure?

[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{Solution-}}}}}}[/tex]

The given points lie on graph as per the order given in the attachment.

Which shape?

As the points lie 2 units apart from their adjacent sides. It can be a square or rhombus.

The opposite pairs of sides are also parallel to each other. The adjacent sides of the figure formed are also perpendicular to each other.

Hence! the figure formed is a square.

What is the area?

[tex]\large{\sf{ \longmapsto Area_{(square)} = s \times s}}[/tex]

[tex]\large{\sf{ \longmapsto Area_{(square)} = {s}^{2} }}[/tex]

[tex]\large{\sf{ \longmapsto Area_{(square)} = {(2)}^{2} }}[/tex]

[tex]\large{\sf{ \longmapsto Area_{(square)} = 4 \: sq. \: units}}[/tex]

The radio station that broadcasts more news each hour based on the ratio is radio WMTH.

From the information, radio WMTH schedules 2 minutes of news for every 20 minutes or music. Radio station WILM broadcast 4 minutes of news of every 25 minutes of music.

Therefore, the ratio of radio WMTH will be:

= 10/1 = 10:1

The ratio of Radio station WILM will be:

= 25/4 = 25:4

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The correct option is D, The relationship is not proportional because the ratio of pages to days is not constant.

A linear relationship is a relationship in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.

A linear relationship with two variables, when graphed on the cartesian plane with axes of those variables, gives a straight line.

For the given relationship to be proportional, the number of pages read should be the same every day. Therefore, the ratio of the number of pages to the number of days should be equal.

85/1 = 85

170/2 = 85

249/3 = 83

340/4 = 85

435/5 = 87

Hence, the correct option is D, The relationship is not proportional because the ratio of pages to days is not constant.

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The interval for mean sale price is $582

According to statement

The given rates are 560, 468, 685, 534, 658, 593

Now,

Sample mean = X / n

Put the values in it and then

(560+ 468+ 685+ 534+ 658+ 593) / 6 = 582.1667

and use this formula S = sqrt [ X2 - n 2 / (n-1) ]

and put the values in these and

S = sqrt [ X2 - n 2 / (n-1) ] = 95.97179

So, The interval for mean sale price is $582

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Answer:

12

Step-by-step explanation:

In an equation left side = right side.

Answer: x = 4

Step-by-step explanation:

The axis of symmetry is the middle of the parabola that cuts it into two equal pieces.

Here it is fairly easy to spot, and the middle, or axis of symmetry, is x = 4.

Answer:

measure of

since

Step-by-step explanation:

[tex] < 20 = 180 - (5x - 14) = 180 - 5x + 14 = 194 - 5x[/tex]

since m

[tex] < 6 = < 20[/tex]

194-5x = 5x-2

194+2=5x+5x

196=10x

x=19.6

so

[tex] < 20 = 194 - (5 \times 19.6)[/tex]

so it's= 96

[tex] \\ [/tex]

Answer:

The width of the desk will be 38.4inches

A rectangle is a quadrilateral that has 4 sides and angles.

If a rectangular shaped desk has a length of 30 inches and a width of 24 inches and a desk with a similar shape has a length of 48 inches, the width of the desk will be calculated using this expression;

l/w = L/W

30/24 =48/W

Cross multiply

30W = 24 * 48

W = 38.4inches

Hence the width of the desk will be 38.4inches

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Answer:

Hence, 87,50,000 can be expressed as [tex]$8.75 \times 10^{6}$[/tex].

Step-by-step explanation:

- Given 87,50,000

- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .

- Then count n and write in scientific notation.

Step 1 of 1

Consider 87,50,000.

8.75

So, 8.75 lies between 1 & 10 .

Now, Decimal moved to 6 places at left.

[tex]$8.75 \times 10^{6}$[/tex]

So, [tex]$87,50,000=8.75 \times 10^{6}$[/tex].

Hello,

[tex]$$\sum_{n=0}^4$$(\frac{1}{2})^{n} =(-\frac{1}{2})^{0}+(-\frac{1}{2})^{1}+(-\frac{1}{2})^{2}+(-\frac{1}{2})^{3}+(-\frac{1}{2})^{4}=1-\frac{1}{2} +\frac{1}{4} -\frac{1}{8}+\frac{1}{16}[/tex]

See attached plots.

The top one shows all three pieces plotted simultaneously, independent of their domains.

The bottom plot takes into account the domains and removes parts of each piece (the dashed gray parts) outside their respective domains.

Answer:

Step-by-step explanation:

The x-coordinate of the point which divide the line segment is 3.

Given the coordinates in the figure are J(1,-10) and K(9,2) and the 1:3 is the ratio in which the line segment is divided.

When the ratio of the length of a point from both line segments is m:n, the Sectional Formula can be used to get the coordinate of a point that is outside the line.

To find the x-coordinate we will use the formula x=(m/(m+n))(x₂-x₁)+x₁.

Here, m:n=1:3 and x₁=1 from the point J(1,-10) and x₂=9 from the point K(9,2).

Now, we will substitute these values in the formula, we get

x=(1/(1+3))(9-1)+1

x=(1/4)(8)+(1)

x=8/4+1

x=3

Hence, the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3 is 3 units.

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Answer:

b. 3

Step-by-step explanation:

got it correct

Answer:

Can't do much without a direct question or embedded image.

Answer:

  y = (x +1)(x -3)

Step-by-step explanation:

You want the equation in factored form for the parabola shown in the graph with x-intercepts at -1 and +3, and a vertical scale factor of 1.

If p is a zero (x-intercept) of the graphed polynomial function, then (x-p) is a factor. The graph shows x-intercepts at x=-1 and x=3. This means (x-(-1)) and (x -3) are factors.

The equation of the graph may also have a vertical scale factor. That can often be determined easily from the graph by looking at the vertical distance from the vertex of points 1 unit either side of the vertex.

Here, the vertex is (1, -4) and points at x=0 and x=2 have the value -3, which differs from the vertex by 1 unit. Hence the scale factor is 1. It multiplies the other factors.

The equation of the graphed parabola is ...

  y = (x +1)(x -3)

The most economic way to purchase health insurance for the family would be to insure Patrick with his employer and Susie and the twins with her employer (Option c).

Reason behind the Choice

Patrick's employer pays for 100% of his monthly health insurance premium of $378

In this case, additional beneficiary for the twins = $280*2 = $560

Susie's employer pays 63% of her $403 monthly premium, and is ready to pay 32% of the $310 monthly premium for each additional beneficiary.

Total money to be paid in this case = 37% of $403 +2*(68% of $310)

= $570.71

Considering that Patrick's health insurance cost is lower than Susie's, it makes sense for him to get health insurance via Patrick's company.

For the twins, Susie's employer offers to pay 68% of $310 for each additional beneficiary. So, the most viable deal would be to buy Patrick's health insurance from his employer and Susie and the twin's health insurance from her employer.

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Answer:

C. Insure Patrick with his employer and Susie and the twins with her employer.

The desired linear functions are given as follows:

a) x = a.

b) y = b.

A linear function is modeled by:

y = mx + b

In which:

A vertical line has undetermined slope, hence it is defined by x = a, containing point (a,b).

A horizontal line has slope of 0, hence it is defined by y = b, containing point (a,b).

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The value of y will be equal to 4.61.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

The value of y will be calculated by using the Pythagorean theorem:-

a² + a² = (9√2)²

a = 9

Applying angle property in the triangle:-

[tex]tan26 = \dfrac{MK}{9}[/tex]

9tan26 = MK

LM = 9 - 9tan26

LM = 9 - 4.38

LM = 4.62

Therefore the value of y will be equal to 4.61.

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