Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. Write the polynomial function for the graph. f(x) = (x – 2)(x – 3)(x – 5) Simplify the right side. What is the equation? f(x) = x3 + 31x – 30 f(x) = x3 – 10x2 + 31x – 30 f(x) = x3 – 10x2 + 19x – 30 f(x) = x3 + 19x – 30 graph

Step-by-step explanation:

we switch the like terms across the equation and when we do that we change the signs

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em}\textit{we know that} \begin{cases} y=-4\\ x=10 \end{cases}\implies -4=k(10) \\\\\\ \cfrac{-4}{10}=k\implies -\cfrac{2}{5}=k\hspace{10em}\boxed{y=-\cfrac{2}{5}x} \\\\\\ \textit{when x = 2, what is "y"?}\qquad y=-\cfrac{2}{5}(2)\implies y=-\cfrac{4}{5}[/tex]

Answer:

X = 14

Hope this helps!

Step-by-step explanation:

The small red square means the angle is 90°.

( 2x + 22 ) + ( 3x - 2 ) = 90°

2x + 22 + 3x - 2 = 90

( 2x + 3x ) + ( 22 - 2 ) = 90

5x + 20 = 90

5x + 20 - 20 = 90 - 20

5x = 70

x = 14

Answer: x = 14

Step-by-step explanation:

When you have a right angle, they add up to 90 degrees

So you add up the two angles that you have that equal a total of 90 degrees

2x+22 + 3x-2 = 90

5x+20 = 90

5x = 70

x = 14

I hope this helps :D

An equation for a line that is parallel to the y - axis, based on the options, is B.x = −8.

The y - axis is a vertical line which runs straight through the x - axis. This means that the coordinates of the y - axis are expressed in terms of 0. The y - axis intercepts the x - axis at point 0 which is why the coordinates are:

x = 0

Any line that is parallel to the y - axis will therefore be expressed in terms of x as well. The equation for a line that is parallel to the y - axis is therefore:
x = -8

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Domain of the function is,  (0, ∞).

Range of the function is, (-∞, ∞).

x - intercept of the function is, (1, 0).

Vertical asymptote of the function is,  None.

What is domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

First to find the domain of the function,

Since, all input values shown on the x-axis make up a graph's domain.

We can see that values of x values are from 0 to ∞.

Hence, the domain is (0, ∞).

Now to find the range.

Since, the y-axis on a graph represents the possible output values, or range.

The y - axis having the values from -∞ to ∞.

Hence, the range of the function is, (-∞, ∞).

x - intercept is the point where function crosses the x - axis.

Here function crosses x - axis at (1, 0).

Hence, the x - intercept is (1, 0).

A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.

So, the vertical asymptote is x = 0.

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Marlee is in short of -768.95 inches of wire for making jewelry.

Given that, Marlee is making jewelry for a class craft show. She began with 115 inches of wire.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The numerical expression for the given situation is
115-25.75+3014-(3812+60.2)

= 89.25+3014-3872.2

= 3103.25-3872.2

= -768.95 inches

Therefore, Marlee is in short of -768.95 inches of wire for making jewelry.

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The solution to the inequality 4x + 6 ∠ -6 is x ∠ -3

inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value.

4x + 6 ∠ -6

taking 6 to the right hand side of the inequality

4x < -6 -6

4x < -12

divide both sides by 4

x < -12/4

x < -3

In conclusion, x < -3 is the solution to the Algebraic expression above.

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The equation of the parabola is f(x) = 7(x-3)^2+5.

Given:

The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.

If the parabola has same shape then its a values are same.

so f(x) = 7x^2

here a = 7

so the equation with vertex (3,5) also has a value is 7.

(h,k) = (3,5)

f(x) = a(x-h)^2+k

= 7(x-3)^2 + 5.

Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.

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By using properties of triangle, it can be inferred that

The value of c lies between 5 and 21 and also 5 and 21 are not included

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles. The sum of the interior angles of a triangle is 180°

Let a = 8, b = 13 and let the third side be c

We know sum of two sides of a triangle is always greater than the third side

a < b + c

8 < 13 + c

c > 8 - 13
c > -5, which is obvious

b < c + a

13 < c  + 8

c > 13 - 8

c > 5

c < a + b

c < 8 + 13

c < 21

5 < c < 21

The value of c lies between 5 and 21 and also 5 and 21 are not included

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Answer:-10.25

Step-by-step explanation:

Just because ;) -10.25= -10.00

Answer:

-10

Step-by-step explanation:

Estimate between the two numbers?

Add them together first

Which equals -10.25

The closest would be -10

The expression that is equivalent is y(x + 2) and xy + 2y and x(x + y + 2) and  x² + xy + 2x

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

y(x + 2) and xy + 2y

xy + 2y and xy + 2y

Therefore, the expressions are equivalent.

x(x + y + 2) and  x² + xy + 2x

x² + xy + 2x and x² + xy + 2x

They are equivalent expression.

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The solution set for the pair of inequalities as given in the task content is; (-∞, -4) U (11, ∞).

It follows from the task content that the solution set of the pair of inequalities is to be determined.

Therefore, each inequality can be solved as follows;

-13 > 2x - 5;

-13 + 5 > 2x

-8 > 2x

-4 > x.

Also, the inequality 2x - 5 > 17 can be solved as follows;

2x > 17 + 5

2x > 22

x > 11.

Therefore, the solution set of the inequalities as given in the task content in interval notation is;

(-∞, -4) U (11, ∞).

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As stated in the preceding statement the point R is collinear with points A and B.

An axis is a term used to describe a line upon whatever points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points become trivially collinear.

Two lines may coincide if they have a same point and have the same slope. To put it another way, if A, B, as well as C are three points there in XY plane, they will all lie on a line, or three points will be collinear, but only if AB's slope and BC's slope are both equal.

then

m A B = m BC ( = m AC ).

The point is collinear with points A and B.

Therefore, the correct answer is option (d) R.

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The required equation for height H of the plant t months after Angel bought the plant is,

H = 15 + 3t

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

t = time in months

H = total height

H= initial height+ rate of growth * time

H = 15 + 3t

So, the required equation for height H of the plant t months after Angel bought the plant is,

H = 15 + 3t

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If you slant the height of the cylinder but keep the radius the same then the volume of an oblique cylinder is the same.      

When a cylinder "leans over," that is when its sides are not parallel to its bases, then the cylinder is said to be an oblique cylinder. The bases (ends) of an oblique cylinder stay parallel to one another, while the sides tilt outward at an angle that isn't quite 90°.

An oblique cylinder will have the same volume as a right cylinder with the same radius and height. As long as the radius and height are the same, the volume does not vary, but the height must equal the perpendicular height.  

From the above observations, we can say that If you slant the height of the cylinder but keep the radius the same then the volume of an oblique cylinder is the same.  

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Answer: The 2 Plan will have same cost of $2149 after 64 sessions.

Let the Two plan be Plan A and Plan B.

Also let the number of session be

According to given detail

Plan A =

Plan B =

We need to find the value of when both are equal.

Plan A = Plan B

=

Solving above equation we get;

Number of session are 64.

Cost after 64 session will be,

Plan A =

Plan B =

Hence The 2 Plan will have same cost of $2149 after 64 sessions.

Step-by-step explanation:

Answer:

x,y [tex]( \frac{2}{61})(\frac{91}{61} )[/tex]

To find: Equation of line parallel to 5x + 3y = -21 and passes through the point (-9, -3)

Solving the given 5x + 3y = -21 for 3y yields  3y = -5x - 21.  

Dividing all three terms by 3, we get:

y = (-5/3)x - 7, indicating that the given line has slope -5/3.

The slope of a line perpendicular to this y = (-5/3)x - 7 is 3/5, the negative reciprocal of -5/3.

Start with y = mx + b

Substitute -3 for y, -9 for x, and 3/5 for m

We get,

-3 = (3/5) (-9)  + b

∴  b   = 5/9

Thus, the equation is y = (3/5)x + 5/9 is the required equation of a line parallel to 5x+3y=−21 that passes through the point (-9,-3)

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The graph of the quadratic equation with axis of symmetry x = - 2 is shown in figure.

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = - 3 (x + 2)² + 1

Now,

We know that;

If the function is of the form y = a (x - h)² + k;

Then, The vertex = (h, k)

And, Axis of symmetry is, x = h

Here, The function is,

⇒ f (x) = - 3 (x + 2)² + 1

⇒ f (x) = - 3 (x - (- 2))² + 1

By comparing we get;

h = - 2 , k = 1

So, Vertex of the function = (- 2, 1)

And, Axis of symmetry is;

⇒ x = - 2

Thus, The graph of the quadratic equation with axis of symmetry x = - 2 is shown in figure.

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Answer:

x = 1

Step-by-step explanation:

Given exponential equation:

[tex]3^{2x}-9=0[/tex]

Add 9 to both sides of the equation:

[tex]\implies 3^{2x}-9+9=0+9[/tex]

[tex]\implies 3^{2x}=9[/tex]

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

[tex]\implies \left(3^2\right)^{x}=9[/tex]

[tex]\implies9^{x}=9[/tex]

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

[tex]\implies9^{x}=9^1[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x=1[/tex]

Answer: THE ANSWER IS 26

The standard form of  (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

The expression given is (3x10^199)+(2*10^201) we need to write it in the standard form

Take 10^199 from the equation

=10^199((3x1)+(2x10^2))

=10^199(3+(2x100))

=10^199(3+200)

=10^199(203)

=203x10^199

2.03 x 10^201

1. there are 201 zeros after 2 and 199 zeros after 3

2. difference  between  201 and 199 is 2

3. on adding both of them the 3 will come 2 spaces to the right of 2

The value of (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

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The probability that a woman has a malignant tumor in her breast is 7.5%. ie 75

Let  + = mammogram result is positive

B = tumor is benign

M = tumor is malignant.

Note that Bc = M.

given that P(M) = .01,

so P(B) = 1 − P(M) = 0.99.

We are also given the conditional probabilities

P(+ | M) = .80 and

P(− | B) = .90, where the event − is the complement of +

P(+ | B) = .10

Bayes’ formula:-

P(M | +) = P(+ | M) P(M) / (P(+ | M)P(M) + P(+ | B)P(B))

= 0.80 × 0.01 / (0.80 × 0.01 + 0.10 × 0.99)

=0.075

So the chance would be 7.5%. ie 75

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The value of x is 25

What is congruent polygons ?

A polygon is said to be congruent if it has the same shape as the polygon it is compared to, as well as the identical side lengths and interior angles. In order to meet the condition, congruent shapes must all have the same kind of shape. Because they are different shapes, a rectangle and a pentagon cannot be congruent.

Two squares or two hexagons can be considered congruent polygons since they both have equal-length sides and angles. However, it's crucial to keep in mind that the length of the sides must also be equal. A square is not congruent if it is larger than another square.

1. Pairs of congruent corresponding parts

 ∠A = ∠C     AB = CD

 ∠B = ∠D    AH = CF

 ∠H = ∠F    HG = FE

 ∠G = ∠E    GB = ED

To find the value of x

4x + 5 = 105

4x = 105 - 5

4x = 100

 x = [tex]\frac{100}{4}[/tex]

    = 25

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An equation for the nth term of the arithmetic sequence is aₙ=a+(n-1)d and a₁₀ of sequence -3,-1,1,3 is 15.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

-3,-1,1,3 is a sequence.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

We know that nth term of arithmetic sequence is aₙ=a+(n-1)d

-3,-1,1,3

First term a=-3

Common difference d=-1-(-3)=-1+3=2

We need to find the 10th term

a₁₀=-3+(10-1)(2)

a₁₀=-3+9(2)

a₁₀=-3+18

a₁₀=15

Hence,  an equation for the nth term of the arithmetic sequence is aₙ=a+(n-1)d and a₁₀ of sequence -3,-1,1,3 is 15.

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The value of angle b is 60 degrees. The reason is angle b is a supplementary angle to angle 120 degrees

angle b is equal to angle c the reason id that they form alternate internal angles

A linear pair is a situation where two adjacent angles are on a straight line, hence their sum is 180 degrees.

Linear pair is special cases of supplementary angles involving only two angles that are adjacent

How to solve for angle b

b + 120 = 180

b = 180 -120

b = 60

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Answer: Part A : it is a function

Step-by-step explanation: once its on a graph it will only cross the line once

The mean number of new subscribers per month during that year is 242000.

A mean simply means the average of the numbers given.

The number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003.

The mean number of new subscribers will be:

= Change in numbers / Number of years

= (1393000 - 1151000) / 1

= 242000 / 1

= 242000

Therefore, the mean is 242000.

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The transformation of the equation f(x) = -2|x + 1| + 5 is

Shift Left 1 units

Shift Up 5 units

Compress by a factor of 2

Reflect over x axis

Transformation involves movements of image or object usually described in a cartesian plane

starting from |x| at the origin

|x + 1| is a shift to the left 1 unit

|x + 1| + 5 is a shift on the y axis, it represents a shift up 5 units

2|x + 1| + 5 is a vertical compression by a factor of 2  

-2|x + 1| + 5 the negative sign shows reflection over x axis turning the graph over

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