4.5,3,1.5,0 fin the difference in the following sequence

well now, let's recall the remainder theorem, check your textbook since we know you're Da Bomb and love to check that theorem.

well, we know a factor is (x-2) for the polynomial f(x), that means that f(2) =  0, so let's use that

[tex]f(x)=x^3+x^2-5ax+2a^2\hspace{5em}\stackrel{\textit{a factor of f(x)}}{(x-2)}\qquad thus\qquad f(2)=0 \\\\\\ 0=(2)^3+(2)^2-5a(2)+2a^2\implies 0=8+4-10a+2a^2 \\\\\\ 0=2a^2-10a+12\implies 0=2(a^2-5a+6) \\\\\\ 0=a^2-5a+6\implies 0=(a-2)(a-3)\implies a= \begin{cases} 2\\ 3 \end{cases}[/tex]

For given equation y = ln(3 - 4 cos(x))​,

dy/dx =  4sin(x) / (3 - 4 cos(x))

In this question, we have been given an equation y = ln(3 - 4 cos(x))​

We need to differentiate y = ln(3-4cosx)​

dy/dx

= d/dx(ln(3 - 4 cos(x))​)

= 1/(3 - 4 cos(x))​ * d/dx(3 - 4cos(x))               .......(by Chain rule)

= 1/(3 - 4 cos(x))​ * [4 sin(x)]

= 4sin(x) / (3 - 4cos(x))

Therefore, for given equation y = ln(3 - 4 cos(x))​,

dy/dx =  4sin(x) / (3 - 4 cos(x))

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Answer:

150 adult tickets where sold

Step-by-step explanation:

If we multiply 150 times 3 that gives us 450, which acounts for all the students. And 150 is the number thats left of adults that adds up to 600.

The pressure of the gas is 7kg/cm^2.

Joint Variation is a situation in which the value of one variable depends on two, or more, other variables when the other variables are held constant

Given that: The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. This can be written as:

VαT and Vα 1/P

Combining the two relations gives:

Thus Vα T/P  

V = kT/P        (where k is a constant)

PV=kT

k = PV/T

P =kT/V

Given: V = 70 cm^3

when T = 420 kelvin

P = 18 kg/cm^2

k = 18×70 / 420

k = 1260/420

k = 3

Given: T = 140 kelvin and

V = 60 cm^3.

Find the pressure

P = kT/V

P = 3×140/60

= 420/60

= 7kg/cm^2

Therefore, the pressure when T = 140 kelvin and V = 60 cm^3 is 7kg/cm^2.

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The five number from the box plot is presented as follows:

A box and whisker plot shows five things of a distribution, listed as follows:

The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.

The data set's maximum value.

These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.

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Answer:

give me the question dude......

Step-by-step explanation:

The probability that the sum is 5/9.The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa).

The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa). Given that this is feasible 4 times out of 36, the probability calculated by adding the two dice is 4/36, or 1/9.

I am assuming that you are rolling two dice.

Probability of even: 18 "evens" out of 36 total outcomes = 18/36

→(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5),(4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)

Probability of greater than 9: 6 ">9s" out of 36 total outcomes = 6/36

→(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)

Probability of both evens and >9s: 4 "both" out of 36 total outcomes = 4/36

→(4,6), (5,5), (6,4), (6,6)

evens   OR    >9s    NOT both

18/36 + 6/8 - 4/36 = 20/36 = 5/9.

The probability that the sum is 5/9.  

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Answer:

150% = 132 cm, 25%= 22 cm, 100%= 88 cm

Given:

Height of Odalis = 132 cm

This height is 150%

Divided into 6 parts.

To find: Different percentages of Dallas's Height

Solution:

Dalia's Height = Odalis height * (100/150)

= 132 cm * (2/3)

= 88 cm.

150% of Dallas's Height is 132 cm.

25% of Dalia's Height =  1/4 * 88 = 22 cm

100% of Dalia's Height = 88 cm.

This can also be taken by parts.

6 parts =  150%

1 part =  150/6 = 25%

And 6 parts = 132 cm,

so, 1 part = 132/6 = 22cm.

so , 25% = 1 part= 22cm.

100% = 4 parts = 22*4 = 88 cm.

150% = 6 parts = 22*6 = 132 cm.

Hence, 150% = 132 cm

25%= 22 cm

100%= 88 cm

Step-by-step explanation:

Answer:The tape diagram shows that Odalis is 132 cm tall, which is 150% of their sister Dalia's height.

132

Height (cm)

150%

Complete the table to show different percentages of Dalia's height.

Percentage

150% of Dalia's height

25% of Dalia's height

100% of Dalia's height

Step-by-step explanation: Just look at the awnser

Answer:

Slope = 0.75

Step-by-step explanation:

Slope Formula: y2-y1/x2-x1

4-1/5-1=3/4=0.75

The statement that is correct regarding their solutions is A. Salina combined the x squared y terms correctly but then left the Plus x squared y term in her answer.

From the information, Salina and Nessa combined like terms using the same expression.

The expression given is illustrated as.

6x²y - 3 + x²y + 2xy² + 2xy - 6

It should be noted that the like terms are:

6x²y and x²y as well as -3 and -6.

Combine the like terms

6x²y + x²y = 7x²y

Also, -3 + (-6) = -9

Therefore, the value will be 7x²y + 2xy² + 2xy - 9

The correct option is A as it illustrated the mistake Salina made.

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Answer:

A is the answer

Step-by-step explanation:

Answer:0.8

Step-by-step explanation:

0.8 can be used for 1 student and 40. :)

The values are;

i, For 1 student, it would take = 1 1/5 days

ii. For 40 students, 48 days

First, we need to know that proportion is an equation made equal to another.

From the information given, we have that;

50 students in a hostel had provisions for 60 days.

This is represented as;

50 students = 60 days

Then, we get that;

i, If 50 students = 60 days

1 students = x days

cross multiply the values

x = 60/50

x = 1 1/5 days

ii.  If 50 students = 60 days

40 students = x days

x = 60(40)/50

divide the values

x = 48 days

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An equation of this line shown in the graph in slope-intercept form is y = 0.75x + 5 or 3x/4 + 5.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

From the graph of this line, we have the following parameters:

Point (x, y) = (60, 50)

Point (x, y) = (20, 80)

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (80 - 50)/(20 - 60)

Slope, m = 30/40

Slope, m = 3/4 or 0.75

At point (60, 50), the intercept is given by:

y = mx + c

50 = 0.75(60) + c

50 = 45 + c

Intercept, c = 50 - 45

Intercept, c = 5.

Now, we can write the equation of this line in slope-intercept form as follows:

y = 0.75x + 5 or 3x/4 + 5.

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Answer: resource - trust me bro

Step-by-step explanation: Let x = the smaller numberLet 2x + 10 = the larger numberx(2x + 10) = 1002x^2 + 10x - 100 = 0Divide both sides of the equation by 2.x^2 + 5x - 50 = 0(x - 5)(x + 10) = 0x - 5 = 0 or x + 10 = 0x = 5 or x = -10, not a positive number2x + 10 = 2(5) + 10 = 20

The constant of proportionality in the equation y = 11x is  11 , the correct option is (a) .

in the question ,

it is given that

the equation is y = 11x

also given that the equation is proportional relationship ,

we need to find constant of proportionality .

we know that the proportional equation is written as y = k*x

where k is the constant of proportionality , on comparing it with the equation y = 11x

, we get k = 11 ,

So , the constant of proportionality is = 11 .

Therefore , The constant of proportionality in the equation y = 11x is  11 .

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Answer:

162.4$

Step-by-step explanation:

mark me on brainliest please follow me to

The largest multiple of 30 that is less than the number, 520, can be found to be 510.

To find the largest multiple that 30 has, which is also less than 520, first find the number of times that 30 can go into 520:

= 520 / 30

= 17.333

Then use this number to find the largest multiple below 520 by rounding 17.33 downwards to 17.

The multiple of 30 that is the largest and below 520 is then:

= 30 x Rounded down result of division of 520

= 30 x 17

= 510

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Answer:

Account A is incorrect the interest that you would earn is $8.60, not $860.00

Step-by-step explanation:

The margin of error tells you how many percentage points your results differ from the true population value.

The margin of error is a close guess at a given level of probability about the confidence interval. It is denoted as a tiny percentage that is allowed for in the event of an error.

The amount of uncertainty associated with a survey result is referred to as the margin of error. It indicates how confident you can be in the outcome's accuracy. A smaller margin of error indicates that your survey is more precise. A confidence level is the probability that a survey will yield the same results if repeated.

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Answer:

y = x^2 + 6       given equation

y = m x + b        equation of straight line required

dy/dx = 2 x       tangent to given curve

dy/dx = slope = 2 * 5 = 10

Thus our line must be of the form

y = 10 x + b

31 = 10 * 5 + b       at the point required

b = 31 - 50 = -19

Then our final equation becomes

y = 10 x - 19

The final solution of the inequality –2(5 – 4x) < 6x – 4 is x < 3.

Inequalities are expressions that have the <, >, ≤ and ≥ signs.

Therefore, let's solve the given inequality as follows:

–2(5 – 4x) < 6x – 4

open the brackets on the left side

–2(5 – 4x) < 6x – 4

-10 + 8x < 6x - 4

add 10 to both sides of the inequality

-10 + 8x < 6x - 4

-10 + 10 + 8x < 6x - 4 + 10

8x < 6x + 6

subtract 6x from both sides of the inequality

8x < 6x + 6

8x - 6x < 6x - 6x + 6

2x < 6

divide both sides of the inequality by 2

2x < 6

2x / 2 < 6 / 2

x < 3

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Proved that if a quadrilateral is a square then the quadrilateral is also a rectangle.

A quadrilateral is a closed shape created by uniting four points, any three of which cannot be collinear. Four sides, four angles, and four vertices make up a quadrilateral.

Quadrilaterals have a few characteristics. The list is as follows.

Each side has four sides.

Each of them has four vertices.

Two diagonals are present.

360 degrees is the sum of all interior angles.

Given, to prove if a quadrilateral is a square, then the quadrilateral is a rectangle.

The Square has four equal sides, and all four angles are right-angled.

Rectangle has equal opposite sides, and all four angles are the right angle.

Here, the two sides of the square can be increased to form a rectangle.

Hence, proved that if a quadrilateral is a square then the quadrilateral is also a rectangle.

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The equation of the parabola whose focus is at (3, 0) and directrix at x = - 3 is y² = 12 · x. (Correct choice: D)

In this problem we need to determine the equation of a parabola based on the information of the focus and the directrix. The vertex form of the parabola is described below:

4 · p · (x - h) = (y - k)²

Where p is the distance from the vertex to the focus. The coordinates of the vertex is the midpoint of the line segment of the least distance between the directrix and the focus.

First, determine the coordinates of the vertex:

(h, k) = 0.5 · (- 3, 0) + 0.5 · (3, 0)

(h, k) = (0, 0)

Second, calculate the distance from the vertex to the focus:

p = 3 - 0

p = 3

Third, write the vertex form of the parabola:

y² = 12 · x

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Answer:

21 gallons

Step-by-step explanation:

[tex]\frac{9}{198} \times 462 \\ \\ =\frac{462}{22} \\ \\ =21[/tex]

Answer:

x = 5

Step-by-step explanation:

2(x+5) =20  Distribute the 2

2(x) + 2(5) = 20

2x + 10 = 20  Subtract 10 from both sides of the equation

2x = 10  Divide both sides by 2

x = 5

Answer:

5

Step-by-step explanation:

2(x + 5) = 20 Divide both sides by 2

x + 5 = 10

x = 10 - 5

x = 5

Answer:

New: $44,840 Original: 47,200

Step-by-step explanation:

You have to multiply 47,200 by 95% or 0.95

For the linear function built from the scatter plot, it is found that:

The slope-intercept representation of a linear function is the rule presented as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:

b = 500.

When the input increases by 200, the output increases by 1000, hence the slope is:

m = 1000/2 = 5.

Thus the equation is:

y = 5x + 500.

The graph is given by the image at the end of the answer.

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