Given f(x)=3(2−x), what is the value of f(−4)?

The zeros of the given polynomial equation are {-1, -2, -3}.

The given polynomial equation is g(a)=4a³+24a²+44a+24.

The rational root theorem is also known as the rational zero theorems (or) the rational zero tests (or) rational test theorem and is used to determine the rational roots of a polynomial function. The general form of a polynomial function is [tex]f(x) = a_nx^n+a_{n-1}x^{n-1}+.......+a_2x^2+a_1x+a_0[/tex]. Here, the value(s) of x that satisfy the equation f(x) = 0 are known as the roots (or) zeros of the polynomial.

Now, g(a)=4a³+24a²+44a+24

⇒ 4a³+24a²+44a+24=0

⇒ 4(a³+6a²+11a+6)=0

⇒ a³+6a²+11a+6=0

Now, put ....-3, -2, -1, 0, 1, 2, 3,....in a³+6a²+11a+6=0 and simplify and check they are equal to 0.

Put a=-3 and check.

That is, (-3)³+6(-3)²+11(-3)+6=0

⇒-27+54-33+6=0

⇒0=0

So, -3 is the zero of the given equation.

Put a=-2 and check.

That is, (-2)³+6(-2)²+11(-2)+6=0

⇒-8+24-22+6=0

⇒0=0

So, -2 is the zero of the given equation.

Put a=-1 and check.

That is, (-1)³+6(-1)²+11(-1)+6=0

⇒-1+6-11+6=0

⇒0=0

So, -1 is the zero of the given equation.

Therefore, the zeros of the given polynomial equation are {-1, -2, -3}.

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Answer:

-9

Step-by-step explanation:

her error was that -9 can't add up to -4

Answer:

  she needs to find factors of -45 that add to -4

Step-by-step explanation:

You want to know the error involved when looking for factors of 5x²-4x-9 by considering only factors of -9.

Consider the product of factors (ax +b)(x +d):

  (ax+b)(x +d) = ax² +adx +bx +bd = ax² +(ad+b)x +bd

You will notice the two parts of the sum that is the middle term coefficient have the product abd, which is also the product of the first and last coefficients.

Sarah needs to be looking for factors of (5)(-9) = -45 that have a sum of -4.

__

Additional comment

The factors Sarah needs are -9 and 5. These will give Sarah the equation ...

  5x² -9x +5x -9

which can be factored pairwise to ...

  x(5x -9) +1(5x -9) = (x +1)(5x -9)

The solution of the given linera equation in one variable 12=2-k is at k = 10.

According to the given question.

We have a linear equation in one variable 12 = 2 - k.

As we know that, linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Therefore, the solution of the linear equation in one variable 12 = 2 - k is given by

12 = 2 - k

⇒ 12 - 2 = -k         (subtracting 2 from both the sides)

⇒ 10 = -k

⇒ k = 10  

Hence, the solution of the given linera equation in one variable 12=2-k is at k = 10.

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This is equivalent to 8.75 feet

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

Explanation:

3 & 1/2 inches = 3.5 inches since 1/2 = 0.5

30 boards of this width total to 30*3.5 = 105 inches

This is equivalent to 105/12 = 8.75 feet. I'll leave the answer in inches since the original unit is inches. I would ask your teacher for further clarification.

The average rate of change of a function [tex]f(x)[/tex] as [tex]x[/tex] varies from [tex]x=a[/tex] to [tex]x=b[/tex] is given by the so-called difference quotient

[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]

If we plot [tex]f(x)[/tex], this difference quotient would correspond to the slope of the line through two points [tex](a,f(a))[/tex] and [tex](b,f(b))[/tex] and intersecting with the curve [tex]y=f(x)[/tex].

(a) The average rate of change of height from 0 to 6.6 seconds is

[tex]\dfrac{H(6.6) - H(0)}{6.6 - 0}[/tex]

and is measured in m/s.

Consult the table for the values of [tex]H(t)[/tex] - it tells us [tex]H(0)=0[/tex] and [tex]H(6.6)=198[/tex]. So the average rate of change of height in this time is

[tex]\dfrac{198 - 0}{6.6 - 0} \dfrac{\rm m}{\rm s} = \boxed{30\dfrac{\rm m}{\rm s}}[/tex]

(b) Similarly, the average rate of change of height from 8.8 to 13.2 seconds is

[tex]\dfrac{H(13.2) - H(8.8)}{13.2-8.8} \dfrac{\rm m}{\rm s} = \dfrac{0 - 44)}{4.4} \dfrac{\rm m}{\rm s}= \boxed{-10 \dfrac{\rm m}{\rm s}}[/tex]

In linear equations,   x = 5 is value of x .

What are instances of linear equations?

-7x-3x+2=-8x-8

-7x -3x + 8x = -8 - 2

 -10x + 8x = -10

  -2x = -10

   x = 5

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Distance between parallel lines y=2x-3 and 2x-y=-4 is [tex]\frac{7\sqrt{5} }{5}[/tex] .

Two lines a₁x+b₁y+c₁=0   and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.

Distance between two two parallel lines is given by [tex]\frac{|c1-c2|}{\sqrt{a^{2} +b^{2} } }[/tex].

In the given question

2x-y-3=0   and 2x-y+4=0

Given the coefficient of x and y is same in both the line therefore they are parallel.

given, a(coefficient of x)=2 , b(coefficient of y= -1  , c₁=-3 , c₂=4.

Substituting the values in the distance formula we get

[tex]d=\frac{|-3-4|}{\sqrt{2^{2}+(-1)^{2} } }[/tex]

[tex]=\frac{7}{\sqrt{4+1} } =\frac{7}{\sqrt{5} }[/tex]

on rationalizing we get

[tex]d=\frac{7\sqrt{5} }{5}[/tex]

Therefore , the distance  between parallel lines y=2x-3 and 2x-y=-4 is [tex]\frac{7\sqrt{5} }{5}[/tex].

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Answer:

Step-by-step explanation:

y = x², y = 0, x = 2 are region enclosed by the given equations is revolved about the x -axis.

What exactly is a closed area?

All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.

What do you mean by the region that a closed curve encloses?

The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.

Whether contained or not?

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Step-by-step explanation:

5p − q − p; use p = 3, and q = 4

5*3-4-3

=15-7

=8

The orthocenter is the point where a triangle's three altitudes intersect, and the centroid is the point where the three medians intersect.

The coordinates of the orthocenter of Δ RST is (–4, –4).

An orthocenter of a triangle is the point at which altitudes drawn perpendicular from the vertex to the opposite sides of a triangle intersect. A triangle typically has three altitudes, and the intersection of all three altitudes is known as the orthocenter.

The orthocenter is the point where a triangle's three altitudes intersect, and the centroid is the point where the three medians intersect.

The slope of RS is (5-8)/(-1+4)  or –1. So, the slope of the altitude, which is perpendicular to RS is 1.

Now, the equation of the altitude from T to RS is:

y - 5 = 1(x - 5)

y  = x

Use the same way to find the equation of the altitude from R to ST. That is,

Y - 8 = -1/0 (X + 4 ) or x = -4

x = -4 and y = -4

Solve the equations to find the intersection point of the altitudes. So, the coordinates of the orthocenter of Δ RST is (–4, –4).

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Answer:

Step-by-step explanation:

3t + 4 = 12 + 3t

4 = 12  (subtract 3t from both sides)

0 = 8   (subtract 4 from both sides)

The midpoint is at (11/2, 15/2, 1/2)

In the given statement is

To find the midpoint of the line segment joining the pair of points

A(4,7,9) and B(-3,8,-8)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =(  [tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} ,\frac{z_{1}+z_{2} }{2}[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points A(4,7,9) and B(-3,8,-8)

Solving for the midpoint , we have,

m = ([tex]\frac{4+7}{2} ,\frac{7+8}{2} , \frac{9+(-8) }{2}[/tex])

m = (11/2, 15/2, 1/2)

Therefore, the midpoint is at ( 11/2, 15/2, 1/2)

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Answer:

there would be three hundred and fifty.

When Pablo bought a sweater on sale for 25% off the original price and another 40% off the discounted price, if the sweater originally cost 48 then the final price of the sweater is $21.6

Given,

The Original cost of the sweater = $48

First,

Pablo bought a sweater on sale for 25% off the original price

Then,

[tex]48-48(\frac{25}{100} )[/tex]= $36

Then another 40% off the discounted price

Final price = [tex]36-36(\frac{40}{100} )[/tex]

=$21.6

Hence, when Pablo bought a sweater on sale for 25% off the original price and another 40% off the discounted price, if the sweater originally cost 48 then the final price of the sweater is $21.6.

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The third quartile of the given data set is 42.

The third quartile (Q3, or the upper quartile) is the 75th percentile, meaning that 75% of the data falls below the third quartile.

Given is a data set, 20, 21, 24, 25, 28, 29, 35, 37, 42, 43, 44 we need to find the third quartile of the data set,

To find the third quartile we will use the given below formula,

Q3 = 3/4 (n+1)th term,

n = 11

Q3 = 3/4 (11+1)

Q3 = 3/4 x 12

Q3 = 9th term

= 42

Hence, the third quartile of the given data set is 42.

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a) 4, associative property

      - This is the associative property of multiplication. When everything is multiplied, you can rearrange the parentheses.

b) 8, commutative property

      - This is the commutative property. It means that when multiplying two numbers together, the order doesn't matter.

c) 0, zero property

      - This is the zero property of multiplication. This states that anything times 0 is equal to 0. In this case, 0 times 3 is 0.

d) 8, identity property

      - This is the identity property of multiplication. This means that any number times 1 is itself. In this case, 9 times 1 is 8.

Please note how a property is worded may differ per class.

Yes, the product of an integer and a natural number will always be an integer.

         A natural number refers to a whole number that does not have any kind of fraction or decimal. Some examples of natural numbers are 1, 2, 3, 4, and so on. Zero is not a natural number.

        Integers refer to all numbers that can be positive and negative. It should not have a fractional part or a decimal part in the number. Integers can be depicted by the positive or the negative sign. Zero is an integer.

       Whenever we are multiplying a natural number with an integer, we are ultimately getting the result as a positive number, negative number, or zero. Thus, it will become an integer.

       Example 1: We can take the natural number 10 and the integer -5. Its product will be -50. Thus, it is an integer.

       Example 2: We can take the natural number 16 and the integer 0. Its product will be 0. Thus, it is an integer.

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Answer:

[tex]2x + 9 = y \\ - 4x - 3 = y \\ so \: both \: equation \: is \: equal \\ 2x + 9 = - 4x - 3 \\ 2x + 4x = - 3 - 9 \\ 6x = - 12 \\ x = \frac{ - 12}{6} \\ x = - 2[/tex]

The coordinates of the other vertices are (2a, 2b) and (2a. 0) after using the mid-point theorem.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

From the data, we can draw a triangle as shown in the attached picture.

Let the coordination of B is at (0, 0)

The coordinate of point A:

A(x, y):

a = (x + 0)/2

x = 2a

y = 2b

A(x, y): (2a, 2b)

The coordinate of point C:

C(X, Y):

2a = (X + 2a)/2

4a = X + 2a

X = 2a

b = (Y + 2b)/2

Y = 0

Thus, the coordinates of the other vertices are (2a, 2b) and (2a. 0) after using the mid-point theorem.

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Using translation concepts, the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE are given by: (3,4).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

The rule for a 90º clockwise rotation is given by:

(x,y) -> (y, -x).

From the figure given for the problem, the coordinates of G are given as follows:

G(-4,3).

Applying the rule, we have that:

(-4,3) -> (3, 4), as y = 3, -x = -(-4) = 4.

Hence the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE are given by: (3,4).

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Answer:

f(2) = sqrt(4 - 2 ^ 2)

f(2) = sqrt(4 - 4)

f(2) = sqrt(0)

f(2) = 0

Answer: 0

Step-by-step explanation:

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Each assertion is supported by a property. The transitive feature of equality justifies this.

If x, y, and z are the three quantities, and then if x is connected to y by some rule and y is related to z through the same rule, we are able to say x is related to z by the same rule.

m∠1+m ∠2=90

m ∠2=m ∠3

m∠ 1+m∠ 3=90 .

The property that justifies each statement is This is justified by the transitive property of equality.

because :

Transitive Property of Equality  show  If a = b and b = c, then a = c.

so in the given statement the  m∠1+m ∠2=90 and ∠2=m ∠3 so m∠ 1+m∠ 3=90.

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The number of significant digits the product should have = 2

The given numbers are:

[tex]4.5160 \times 10^{-3}\\ 2.09 \times 10^7\\ 5.8 \times 10^3[/tex]

We first multiply them.

[tex]4.5160 \times 10^{-3}\times 2.09 \times 10^7\times 5.8 \times 10^3 = 54.743\times10^7[/tex]

In measurement problems, we usually write it as [tex]5.474\times10^7[/tex]

Significant digits are the numbers which decide the precision and accuracy in measurement problems.

The fewest number of significant digits in each factor of multiplication is considered as the significant digits of the product.

So number of significant digits in [tex]4.5160\times10^{-3}[/tex] = 5

Number significant digits in [tex]2.09\times10^7[/tex] = 3

Number of significant digits in [tex]5.8\times10^3[/tex] = 2

So the product should be rounded into 2 significant digits.

So the product,  [tex]5.474\times10^7[/tex]= [tex]5.5\times10^7[/tex] with 2 significant figures.

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1/13 is probability of a second king is drawn.

In statistics, what does a probability mean?

Total cards = 52

a complete pack without jokers, then it is 4/52 = 1/13.

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Answer:

2(v-3) = 5

Step-by-step explanation:

2(v-3) = 5

Answer:

$240

Step-by-step explanation:

30% of 800 is 240

.30*800

The difference between $10,000 invested at 1.33% compounded daily and 4.33% compounded semi annually is $11,188.99.

When an amount earns interest that is compounded daily, it means that both the amount invested and the interest accrued increases in value every day over the 3 year period.

If an interest is compounded semi-annually, it means that both the amount invested and the interest accrued increases in value two times in a year.

The formula that can be used to determine the future value when the amount is compounded is:

FV = P (1 + r)^nm

Where:

10,000 x [1.133^(3 x 365) ] - [1.0433^(2x3)]

10,000 x (2.4085 - 1.29)

10,000 x 1.119 = $11,188.99

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Answer: 200

Step-by-step explanation: hope this helps!!!

hey don't ask it in this way

ask a easy real question

so mods won't take it down

thanks btw <3

456.25 male lion weigh for the zoo to obtain the male lion.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Given:

A male lion grows to weight about 420 lbs with a standard deviation of 35 lbs.

A zoo would like to have a lion that is in the largest 25% of male lions based on weight.

So,

z= (x- [tex]\mu[/tex])/[tex]\sigma[/tex]

Now substituting the value

1.036 = X-420/35

36.25= X- 420

X= 36.25 + 420

X= 456.25

Hence, 456.25 male lion weigh for the zoo to obtain the male lion.

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here for the solution We have here, that jet is equal to 0.52. Their score corresponding to 30 area under standard normal distribution. By using jet table to the right up ahead here, X is equal to zero multiplied by sigma plus mu. Here by substituting the value for the next step, we get 0.52 dataset, multiply by sigma. That is 35 plus mu, That is four 20. By simplifying this, we get the value is 4 83.2, which is approximately equal to 4 38.4. Which is our Answy for the answer is 4:38.4 is the correct choice for the answer. So here is the solution. The answer. Please go through this.