Which polynomial function has a leading coefficient of 2, root -4 with multiplicity 3, and root 10 with multiplicity 1?

O f(x) = 2(x-4)(x-4)(x - 4)(x + 10)

O fx) = 2(x + 4)(« + 4)(« + 4)(-10)

O f) =3K – 4)(«-4)0x + 10)

O f()= 3(x + 4)(x + 4)(K- 10)

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3} \times \sqrt{2 \times {5}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 5 \times 2 \sqrt{5 \times 3 \times 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 10 \sqrt{30} [/tex]

The standard equation of the circle will be (x+5)²+(y+5)²= 145

The center of the circle, which is the midpoint between those two locations, may be found first since you know the diameter endpoints.

formula for the midpoint

= ((x1+x2)/2, (y1+y2)/2)

Given points are - (3, 4), (−13, −14)

The circle's center is at (-5,-5)

Therefore, the circle's equation will take the form (x+5)²+(y+5)²=R², where R is the circle's radius.

The distance between a point on the circle and the circle's center in order to get the radius.

Therefore, let's calculate the distance between (-5, -5) and (-13,-14)

Radius R = √((-13+5)²+(-14+5)²) using the distance formula.

= 12.04

equation will be -

(x+5)²+(y+5)²= 145

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Answer:

2/27

Step-by-step explanation:

i think this is the answer.

Answer:

subtract 6 from 3 and a is -3

Step-by-step explanation:

Answer:

a= -3

Step-by-step explanation:

a=3-6

a=-3

The correct solution of Laurie's inequality expression is y ≥ 2x – 4

Given,

The inequality expression wrote by Laurie = y > 2x - 4

The graph of the inequality expression that completes this question is added as an attachment

From the attached graph, we can see that the line of the inequality is a thick or closed line

Thick and closed line are represented by the inequality signs ≤ and ≥

Since the upper region is shaded, we make use of ≥ inequality sign

Hence, the correct solution of Laurie's inequality expression is y ≥ 2x - 4

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Another way to write the absolute value inequality |p|<12 is

-12 < p < 12

This is a term in mathematics that refers to numbers considered regardless of the sign. The concept of absolute values is well appreciated in a number line.  In a case where the signs helps on to position the number but do not have influence in the magnitude or size of the number.

Since absolute values considers the magnitude of the number and not the sign. We can see the equation given to represent values from zero to a point just less than 12 as this will have same magnitude to the point from zero to a point just less than negative 12. The sign just gives the direction.

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The description and definition and values of the sequence are;

a. Each term of sequence A is produced from the previous term by multiplying the previous term by 2

b. Each term of sequence B is produced from the previous term by adding 10 to the previous term

c. [tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]

d. B(n) = 2 + (n-1) × 10

e. B(9) > A(9)

A sequence is series of objects that follow each other in a particular order.

a. The terms of sequence A are;

1/4, 1/2, 1, 2, 4

Therefore, each term is produced from the previous term by multiplying the previous term by 2 as follows;

1/4 × 2 = 1/2,

1/2 × 2 = 1

1 × 2 = 2

2 × 2 = 4

b. The values in sequence B are;

2, 12, 22, 32, and 42

Therefore, each term is produced from the previous term by adding 10 to the previous term as follows;

c. The definition of the nth term of sequence A is found using the formula for a geometric progression as follows;

nth term of a GP is; A(n) = a•r^(n-1)

Where;

a = The first term = 1/4

r = The common ratio = 1/2/(1/4) = 2

The nth term of sequence A is therefore;

d. The definition of the nth term of sequence B is found using the formula for a arithmetic progression as follows;

nth term of a AP is; B(n) = a + (n-1)•d

Where;

a = The first term = 2

d = The common difference = 12 - 2 = 10

The nth term is therefore

B(n) = 2 + (n-1) × 10

e. The value of A(9) is therefore;

[tex] A(9) = \frac{1}{2} \times 2^{(9-1)} = 64 [/tex]

Which gives; A(9) = 64

The value of B(9) = 2 + (9-1) × 10 = 82

B(9) = 82

Which gives;

B(9) = 82 > A(9) = 64

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Answer:

Question 1:

Question 2:

Step-by-step explanation:

Question 1:

options

Solving notes:

As x decreases without bound, f(x) does NOT approach zero.

As x decreases without bound, f(x) does NOT approaches the line y = 4.

_________________________________________________

Question 2:

options

Solving notes:

As x increases without bound, f(x) does NOT approach the line y = 6.

As x decreases without bound, f(x) does NOT increase without bound.

Answer: Because the initial value is $26.40, the line must pass through this when x is 0. Thus, the answer is either the first or the second equation.

Next, we calculate the difference between the year 2019 and 1998 and substitute it into the value of x.

2019 - 1998 = 21.

Substituting this into the equation:

y = 1.006(21) + 26.40

y = $47.52

Thus, the first option is correct.

The minimum perimeter is 23.24m and dimensions of the fenced area is 15.5m x 3.8m.​

Let us assume the length of the fenced area to be L and breadth of the fenced area to be W. As we know, only three sides are to be fenced,

So, the perimeter  P of the fenced would be,

P = L + 2W

Also, it is given that, area of the fence is 60m²,

So, the are should be,

60m² = LW

60m²/L = W

Now, to minimize the perimeter,

P = L + 2W

P = L + 120/L

Differentiating both sides with respect to "L",

d(p)/dL = 1 - 240/L²

To find the value of "L", putting dp/dL equal to 0,

d(P)/dL = 0

1 - 240/L² = 0

L = √240m

Now, from the first derivative test, we know that, the perimeter will be maximum or minimum if value of L>√240 or L<√240 respectively,

For minimum, L should be,

L = √240m

L = 15.5m

Now we know from area,

area = LW

60 = 15.5 x W

W = 60/15.5

W = 3.8m

Hence, the minimum perimeter will be,

L + 2W = 23.24m

The dimensions are,

L = 15.5m

W = 3.8m

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Answer: 2(a-9)

Step-by-step explanation:

2a-18

then factor

which leads to 2(a-9)

Answer: 2(a-9)

Step-by-step explanation: Factor out 2 from the expression 2(a-9)

Using relations in a right triangle, we have that the height of the tree is of 91.6 meters.

The relations in a right triangle are given as follows:

The graph for this problem is given at the end of the answer, and using it and the relations, we can build two equations involving x and the height h, and solve the system of equations for h.

From the triangle involving point G(angle of 43º), we can build the following relation:

tan(43º) = h/x

0.9325 = h/x

x = (1/0.9325)h.

x = 1.0724h (because we want to find h, hence we write x as a function of h).

From the larger triangle, that has the angle of 38º, we have the following relation.

tan(38º) = h/(x + 19).

tan(38º) = h/(1.0724h + 19). (considering that x is a function of h, as we found above).

0.7813 = h/(1.0724h + 19).

Hence, we apply cross multiplication to solve for h, as follows:

h = 0.7813(1.0724h + 19).

h = 0.8379h + 14.8447.

0.1621h = 14.8447

h = 14.8447/0.1621

h = 91.6 meters.

Hence:

The height of the tree is of 91.6 meters.

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Answer: 2.2 miles per hour

Step-by-step explanation:

Since we are given his speed in one third of an hour, we can simply triple his speed to get his miles per hour.

[tex]\frac{11}{15} * 3\\= \frac{33}{15}\\\\= 2 \frac{1}{5}[/tex]

or, 2.2 miles per hour

Answer:

2.2mph!

Step-by-step explanation:

The  measures are possible for the other two angles are 70 degrees respectively

An isosceles triangle is a triangle that has 2 of its sides and angles to be equal.

Let the measure of the other possible angles be x and y such that x = y

Since the sum of angle in a triangle is 180 degrees, hence;

x+y +40 = 180

x+x+40=180

2x+40=180

2x=180-40

2x = 140

x = 70

x = y = 70 degrees

Hence the  measures are possible for the other two angles are 70 degrees respectively

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Question :-  Daisy is making solid spikes for her Halloween costume. the spikes are shaped like right circular cones with base radius of 2 inches and height of 6 inches. if daisy has 360 cubic inches of material for making the spikes, what is the maximum number of spikes she can make ?

Answer:- She can only create a maximum of 14 spikes.

Step-by-step explanation:

Given that :-

To find :-

According to Question,

We have,

For finding the maximum number of spikes,

We have to divide the volume of the material by the volume of the cone, for producing a maximum number of spikes.

So,

        Maximum spikes = Volume of the material / volume of the cone

Now,

      Volume of the material = 360 cubic inches

       Volume of the cone  = [tex]\frac{1}{3}[/tex] πr²h

Where:

       r = radius = 2 in

      h = height = 6 in

      π = pi = 22/7

         =  [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × [tex]2^{2}[/tex] ×6

         = 3.14 × 4 × 2

         = 25.12

So,

        Maximum spikes = Volume of the material / volume of the cone

                                      = [tex]\frac{360}{25.12}[/tex]

                                      = 14.33

∴ The number of spikes must be an integer.

∵          Maximum spikes = 14.

Answer:- She can only create a maximum of 14 spikes.

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Answer:

24

Step-by-step explanation:

140/6 = 23.3333333333333

You can’t have .3 of a car, so you would need to round up.

23.333333333333333 rounds up to 24

According to the given statements:

a. If the integers x and y are, respectively, even and odd, then xy is even.

b. When x is odd, x2 is also odd.

c. If p is a prime number, p2 is not a prime number.

d. If the integers a and b are negative, then ab is also a negative number.

e. If AC and BD are diagonally arranged in a rhombus, then AC is perpendicular to BD.

A numeral system, also known as a mathematical notation, is a way of writing numbers that uses digits or even other symbols to represent the numbers in a given set in a standardized way. The same set of symbols can represent various numbers in various numeral systems.

A. if a, then b the product of an odd integer and an even integer is even.

If the integers x and y are, respectively, even and odd, then xy is even.

B. if a, then b  the square of an odd integer is odd.

When x is odd, x2 is also odd.

C.  if a, then b  the square of a prime number is not prime.

 If p is a prime number, p2 is not a prime number.

D. the product of two negative integers is negative. (this, of course, is false.)

If the integers a and b are negative, then ab is also a negative number.

E.  the diagonals of a rhombus are perpendicular.

If AC and BD are diagonally arranged in a rhombus, then AC is perpendicular to BD.

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I understand that the question you are looking for is:

Each of the following statements can be recast in the if-then form. please rewrite each of the following sentences in the form "if a, then b."

a. the product of an odd integer and an even integer is even.

b. the square of an odd integer is odd.

c. the square of a prime number is not prime.

d. the product of two negative integers is negative. (this, of course, is false.)

e. the diagonals of a rhombus are perpendicular

the correct option is:

"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"

Here we have the exponential function:

g(x) = (2/3)^x - 2

Now, remember that for any real number different than zero, we have that:

x^0 = 1

So if we evaluate our function in x= 0 we will get:

g(0) = (2/3)^0 - 2 = 1 - 2 = -1

Then the function passes through the point (0, -1)

With this in mind, we conclude that the correct option is:

"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"

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Answer:

C: The third graph

Step-by-step explanation:

on edge

The inequality that shows the possible distances of house A from house C is x ≥ 5

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.

We are given that;

Distance= 4miles

Let x be the distance of house A from house C. Since house B is 4 miles from house A, and house C is at least 1 mile from house B, we can write an inequality that relates x, 4, and 1:

x ≥ 4 + 1

This inequality means that the distance of house A from house C is greater than or equal to the sum of the distances of house A from house B and house B from house C.

To solve this inequality, we need to simplify it by adding 4 and 1:

x ≥ 5

Therefore, by inequality the answer will be x ≥ 5.

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Answer:

This is also known as "Derivative"." in mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus."! hope this helps!

To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).

The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.

Given that,

To one decimal place, round.

Points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).

We have to find the distance between two points that are AB and EF.

1. The distance between 2 points A and B.

A(-4, 6) and B(3, -7).

Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Here, x₁=-1,x₂=3 and y₁=6,y₂=-7

After substituting we get,

[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]

[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]

[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]

[tex]\sqrt{16 +163}\\[/tex]

[tex]\sqrt{185}[/tex]

13.601

Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.

2.The distance between 2 points E and F.

E(-6, -5) and F (2, 0).

Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Here, x₁=-6,x₂=2 and y₁=-5,y₂=0

After substituting we get,

[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]

[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]

[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]

[tex]\sqrt{64 +25}\\[/tex]

[tex]\sqrt{89}[/tex]

9.433

Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.

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Answer:

x=9

Step-by-step explanation:

Simplify  7+3x−67+3x−6  to  3x+13x+1.

Subtract 11 from both sides

Simplify  2x+10−12x+10−1  to  2x+92x+9.

Subtract 2x2x from both sides.

Simplify  3x−2x3x−2x  to  xx.

Answer: x=9

Step-by-step explanation:

7+3(x-2)=2x+10

7+3x-6=2x+10

1+3x=2x+10

1+3x-2x=2x-2x+10

1+1x=10

1x=9

x=9

Answer:

2 and 12

Step-by-step explanation:

2x3=6

12 x 6=72

6 and 72 is 78

Answer:

2 and 12

Step-by-step explanation:

After 8 chairs have been bought in there are now 216 chairs in the theater.

A unitary method is a mathematical technique for first finding the value of a single unit and then deriving the required units by multiplying with it.

According to the given question, a small theater had 8 rows of 26 chairs each.

∴ The total number of chairs in the theater is (8×26) chairs = 208 chairs.

Later an extra 8 chairs have bought in.

∴ The total no. of chairs in the theater now is (208+8) = 216 chairs.

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From the given Alex and Joey  hats equation we got Alex has 24 hats Joey has 11 hats.

Given that,

Joey only has 2 times more hats than Alex, who has 2 more. The difference between the amount of hats Alex has and the 5 that Joey has is also 4 times the number of hats Alex has.

We have to discover how many hats each one of them has.

Let Alex has x hats Joey has y hats.

From the given

We get

x=2y+2 ------> equation (1)

x=4(y-5) --------> equation (2)

Equating equation (1) and equation (2)

2y+2=4(y-5)

2y+2=4y-20

2y-4y=-20-2

-2y=-22

y=-22/-2

y=11

Take y=11 in equation (1)

x=2(11)+2

x=22+2

x=24

Therefore,  Alex has 24 hats Joey has 11 hats.

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The expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.

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

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

WE have been given that Juilan divided his savings equally between two charities. then Julian's savings as 's' =$125

First, we will write the expression;

s/2

Second, substitute the value 125 in for the variable s.

Then simplify by dividing 125 and 2.

=$125 / 2

= $62.50

Hence the  expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.

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The value of A is 31.5.

The square root of any number is the factor that we can be multiplied by itself to get that given number. The symbol for square root is √.

Here, we are given an equation as follows-

A=√[15.5(15.5-14) (15.5-11) (15.5-6)]

Let us simplify it step by step. Firstly, we will perform the operations inside the brackets as follows-

A = √[15.5(1.5) (4.5) (9.5)]

Now, multiplying the terms we get-

A = √[15.5(1.5) (4.5) (9.5)]

A = √[(23.25) (42.75)]

A = √[(993.9375)]

Now, we calculate the square root of the number obtained above-

A = 31.5

Thus, the value of A in the equation A=√15.5(15.5-14) (15.5-11) (15.5-6) comes out to be 31.5.

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Answer:

A.2

explanation:

the equation to find circumference is [tex]2\pi (radius)[/tex]

the circumference of A is [tex]2\pi 8 = 50.27[/tex]

the circumference of B is [tex]2\pi 4 = 25.13[/tex]

50.27/25.13 = 2/1

Answer: 3/4

Step-by-step explanation: