7, 9, 13 are the first three terms of a sequence with
nth term = an² + bn + c.
(i) By substituting n = 1, 2 and 3 set up three simultaneous equations in
a, b and c.
(ii) Solve your simultaneous equations and hence write down an
expression for the nth term.

The answers to the question have been written below

1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.

2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0

Hence the value of the exterior would move towards 0 as its sides increases.

4. As the total sum of the of the polygon changes, it would tend towards infinity.

5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.

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cos and sec can be found

The requried simplified expression is 1 / cosØ, which is equivalent to secØ. The correct option is secØ.

Let's simplify the given expression and see which of the provided options match:

We are given the expression √(1 + tan²Ø).

Now, recall the trigonometric identity: tan²Ø = sin²Ø / cos²Ø.

Substitute this identity into the expression:

√(1 + sin²Ø / cos²Ø)

Next, find a common denominator for the fraction inside the square root:

√((cos²Ø + sin²Ø) / cos²Ø)

Since cos²Ø + sin²Ø = 1 (as per the Pythagorean trigonometric identity), the expression becomes:

√(1 / cos²Ø)

Now, we can take the square root of 1 and cos²Ø separately:

√1 / √cos²Ø

Simplify:

1 / cosØ

The simplified expression is 1 / cosØ, which is equivalent to secØ.

Therefore, the correct option is: secØ.

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Answer:8.8 pounds a day

Step-by-step explanation:

7 days in a week

28/7=4 kg a day

2.2*4=8.8

8.8 pounds

The number of answers that were incorrect will be 7.

From the information given, every correct answer will be +1 while and incorrect answer will be -1. The equation to represent the information will be:

3 - x = -4

where x = incorrect answer

3 - x = -4

-x - 4 - 3

-x = -7

x = 7

In conclusion, the number of answers that were incorrect will be 7.

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The best estimate to the nearest one percent of the fraction; 7/15 is; 47%.

From the task content, it follows that the fraction given whose estimate is to be determined is; 7/15.

The fraction expressed as a percentage is;

(7/15) × 100 %

= 46.667%.

Hence, when rounded to the nearest one percent; = 47%.

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Answer:

im not too sure about that sorry!

Step-by-step explanation:

uiwgorihvncjkdnskv

It takes 15 seconds for the first cyclist to overtake the second cyclist.

First, identify the two phases of the first cyclist's motion.

Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.

Phase 2: The cyclist travels at a constant speed of 8 m/s.

Find the equations of the two straight-line sections of the graph.

The equations of the two straight-line sections of the graph are as follows:

Phase 1:

s = [tex]2t^2[/tex]

Phase 2:

s = 8t

where s is the distance traveled by the cyclist and t is the time

Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist

The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.

Let t be the time it takes the first cyclist to overtake the second cyclist.

The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).

Setting these two expressions equal to each other, we get:

8t = 8(t - 5)

Solving for t, we get:

t = 15

Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist

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Answer:

c=6p

Step-by-step explanation:

you multiply

6 dollars per pound by p pounds

pounds cancel out and you are left with dollars

that is the cost

Equations are separated by an equal sign. The value of x is given as -6/5

Given the equations below;

5(3x + 4) = 2

Expand

5(3x) + 5(4) = 2

15x +20 = 2

Subtract 2 from both sides

15x = 2 - 20

15x = -18

x = -18/15

x = -6/5

Hence the value of x is given as -6/5

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Answer: Table 1: Answer = 1. 404

Table 3 Answer = 1.66

Step-by-step explanation: i hope it's right if not, tell me

The remainder represented by synthetic division is -5.

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Given

A vertical line and a horizontal line combine to make an L shape.

There are two rows of entries within the shape.

Row 1 has entries 2, 10, 1, 5.

Row 2 has entries blank, -10, 0, -5.

Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;

x + 5 = 0

x = -5

Hence, the divisor of the synthetic division is -5.

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Answer:

its a) -5

Step-by-step explanation:

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]

Find:  [tex]\textsf{The equation in point-slope form}[/tex]

Solution: We need to take the values that were given to us and plug them into the point-slope form.  It doesn't seem like the problem is asking for anything more than that so we will leave it at that.

Plug in the values

Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).

Answer:

[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

Step-by-step explanation:

[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]

We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).

Then, we substitute these values into the Point-Slope Form to find the equation.

Here are both forms for future reference:

⇒ Slope-Intercept Form: y = mx + b

[ Where: m is the slope, and b is the y-intercept (when x = 0). ]

⇒ Point-Slope Form: y - y₁ = m(x - x₁)

[ Where: m is the slope, and (x₁, y₁) is a given point. ]

Substitute the values into the Point-Slope Form:

[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

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[tex] \sf \blue{True✅}[/tex]

Given,

[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]

Solution:

[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]

Answer:

x = -5

Step-by-step explanation:

9x - 7 = -52

we want to single out x,

add 7 to both sides to be one step closer to getting x alone

9x - 7 + 7 = -52 + 7

9x = -45

divided both sides by 9 to get x alone

9x / 9 = -45 / 9

x = -5

Let me know if you need any clarification!

[tex] 9x - 7 = - 52[/tex]

Firstly rearrange the variable on the left side of the equation...

[tex]9x = - 52 + 7[/tex]

Calculate the sum or differences

[tex]9x = - 45[/tex]

[tex]x = - \frac{45}{9} \\ [/tex]

[tex]x = - 5[/tex]

:)

..

Answer:

A=30

B=35

C=44

Step-by-step explanation:

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

Graphically speaking, linear functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). Linear functions are characterized by slope and intercept:

y = m · x + b     (1)

Slope

m = (7 - 0)/[9 - (- 6)]

m = 7/15

Intercept

b = 4

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

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Answer:

Step-by-step explanation:

số nữ là 65- 35= 30

vậy tỷ lệ số tv nữ trên tổng số thành viên của phòng tập là 30/65 = 6/13

Answer:if we start with 26 letters in the English/Latin alphabet: 26*25*24*23*

and modern Arabic numerals 0–9,

10*9 do the math by multiplying all

Number of dispositions of 4 letters without repetitions of the alphabet (26 letters): 26*25*24*23=358800. 2-digit numbers without repetitions:10*9=90. Number of passwords with 4 letters and 2-digit number without repetitions:

a) if the 2-digit numbers must be in one single position (examples:….XB73DY……..GZ57FE): 358800*90 = 32,292,000.

b) if the 2-digit numbers can be in each of the 5 possible positions (ex.:…73XBDY…X73BDY..XB73DY..XBD73Y..XBDY73…) 5*358800*90=161,460,000.

c) if both digits can be in (C6;2) = 6*5/2= 15 positions (ex.: 7XB3DY…X73BDY…..) 15*358800*90=484,380,000.26*25*24*23*10*9 = 32,292,000

Step-by-step explanation:

Answer:

1274

it is 1274

Step-by-step explanation:

mark as brainlest for the answer thankyou

Answer:

x = 3

y = -1

z = 2

Step-by-step explanation:

if x+y = 2, and x+y-z = 0, then we can substitute 2 for x+y. this means 2-z=0, meaning z=2.  if y-z=-3, then y-2=-3, and y=-1. x+y=2 which means x-1=2 so x=3. plug in the values to check your answer.

The question is incomplete. Below you will find the missing content and figure

Which value of x would make triangle ΔSUV is congruent to triangle ΔTUM by HL? Options are 2 3 4 5

The figure is shown below.

The correct option is Option D: the value of x is 5.

Triangles are congruent if the triangles are of the same size and shape. If triangles are congruent the corresponding length of the sides is the same.

Here given that triangle ΔSUV is congruent to triangle ΔTUM.

By the property of the congruent triangle, as triangle ΔSUV and ΔTUM are congruent the corresponding sides are also same.

ΔSUV ≅ΔTUM

⇒ VS≅WT

Given in the question

VS= 2x+9

WT= 4x-1

from above it is clear that

VS=WT

⇒ 2x+9=4x-1

⇒4x-2x=9+1

⇒2x=10

⇒x=10/2

⇒x=5

Therefore the correct option is Option D: the value of x is 5.

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Answer:

It will be 5 on EDG 2022 Your welcome :)

Step-by-step explanation:

Answer: c

Step-by-step explanation:

It has been given that the point (3,1) is on the graph.

And in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option C

The more appropriate measure of center is mean.

The more appropriate measure of spread is standard deviation.

Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.

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Multiply -1/4 by -7/9 ((To do this, multiply the numerator by the numerator and the denominator by the denominator.)

[tex]\bf{\dfrac{-1(-7)}{4\times9)} \ \ \to \ \ \ Multiply }[/tex]

Do the multiplications in the fraction -1(-7) / 4 x 9.

[tex]\bf{\dfrac{7}{36} \ \ \Rightarrow \ \ \ Answer }[/tex]

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines and the lines that never intersect are known as parallel lines.

We have:

You are given AB and point C. Construct a line parallel to AB that passes through point C

The correct way to draw a parallel line to AB that passes through point C is:

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Thus, the steps of student B are in the correct order but the steps of student A are in the incorrect order.

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Answer: x²-59x+114=0

explanation:

If the roots are 2 and 57, then:-

sum of roots = 2+57 = 59

and, product of roots = 2×57 = 114

the quadratic equation is given by,

x²-(sum of roots)x+(product of roots)=0

so, x²-59x+114=0 will be the desired quadratic equation.

so, none of the options are correct.

the correct answer is x²-59x+114=0.

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If the function is f(x) = √(7x – 21). Then the inverse function of the function will be f⁻¹(x) = (1/7) x² + 3.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = √(7x – 21)

Then the inverse function will be

x = √[7{f⁻¹(x)} – 21]

x² = 7f⁻¹(x) – 21

7f⁻¹(x) = x² + 21

f⁻¹(x) = (1/7) x² + 3

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Answer:

14.3%

Step-by-step explanation:

5 students got an A out of 35 total students. This means that the probability of students getting an A is 5/35 = 0.1428