The nth term of a sequence is n2 + 5 (a) (i) Find the first two terms of this sequence. (ii) Is 126 a term of this sequence? You must show how you get your answer​

Answer:

[tex]y = (-3/2)\, x + (-2)[/tex].

Step-by-step explanation:

If [tex](x_{0},\, y_{0})[/tex] is on the equation of the line [tex]y = m\, x + b[/tex], then substituting [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex] into the equation would still give an equality: [tex]y_{0} = m\, x_{0} + b[/tex].

In this question, since [tex](-2,\, 1)[/tex] is a point on the line [tex]y = m\, x + b[/tex], equality shall still hold after substituting in [tex]x = (-2)[/tex] and [tex]y = 1[/tex]:

[tex]1 = m\times (-2) + b[/tex].

Similarly, since [tex](2,\, -5)[/tex] is a point on this line, equality shall still hold after substituting in [tex]x = 2[/tex] and [tex]y = (-5)[/tex]:

[tex](-5) = m\times 2 + b[/tex].

The unknowns of both equations are [tex]m[/tex] and [tex]b[/tex].

Solve this system of two equations and two unknowns:

[tex]\left\lbrace\begin{aligned}& (-2)\, m + b = 1\\ & 2\, m + b = (-5)\end{aligned}\right.[/tex].

[tex]\left\lbrace\begin{aligned}& m = -\frac{3}{2} \\ & b = -2\end{aligned}\right.[/tex].

Therefore, the equation of this line would be:

[tex]y = (-3/2)\, x + (-2)[/tex].

True:

   Area of trapezoid = [tex]\frac{1}{2}(b1 + b2) * h[/tex]

Hope that helps!

Answer:

A yard sale.

Step-by-step explanation:

lol

What is this question really about? Could you perhaps dive a little bit more into detail please? Ty

Applying the expression for the circumference of circle, we found the diameter as 16.86 yards

Given Data

Let us apply the expression for the circumference of a circle

Circumference = 2πr----------1

But r = d/2

hence put r = d/2 in the expression above

Circumference = 2πd/2----------2

Circumference = πd

Substitute our given data

53 = 3.142*d

Make d the subject of formula we have

d = 53/3.142

d = 16.86 yards

Learn more about mensuration of shapes here:

https://brainly.com/question/10628685

Answer:

a. 12 inches for the shorter side

b. 1050 bushels apples

c. 7/8 cups

Step-by-step explanation:

You can solve these all by the butterfly method(aka cross multiplication)

The vertices of the hyperbola are the x-intercepts of the hyperbola

The equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

The equation of a hyperbola is represented as:

[tex]\frac{(y - k)^2}{a^2} -\frac{(x - h)^2}{b^2} = 1[/tex]

The vertices are (20,0) and (-20,0).

So, the center of the hyperbola is:

(h,k) = (0,0).

Also, we have:

a = 20

This gives

[tex]\frac{(y - 0)^2}{a^2} -\frac{(x - 0)^2}{b^2} = 1[/tex]

Evaluate

[tex]\frac{y^2}{a^2} -\frac{x^2}{b^2} = 1[/tex]

Substitute 20 for a

[tex]\frac{y^2}{20^2} -\frac{x^2}{b^2} = 1[/tex]

[tex]\frac{y^2}{400} -\frac{x^2}{b^2} = 1[/tex]

The length of the conjugate axis is:

l = 18 units

So, we have:

[tex]b = \frac{18}2 = 9[/tex]

The equation becomes:

[tex]\frac{y^2}{400} -\frac{x^2}{9^2} = 1[/tex]

[tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

Read more about hyperbola at:

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Answer: Scalene Triangle

Step-by-step explanation:

Answer:

Scalene Triangle

Step-by-step explanation:

Scalene Triangle: All sides are different

Isosceles Triangle: 2 sides are the same

Equilateral Triangle: All sides are the same.

[tex] \huge\mathbb\orange{ANSWER} [/tex]

[tex] \mathsf\green{y = 6}[/tex]

[tex] \mathsf \purple{{y}^{2} - 9y + 2}[/tex]

[tex] \mathsf \pink{ {6}^{2} - 9(6) + 2}[/tex]

[tex] \mathsf \purple{36 - 54 + 2}[/tex]

[tex] \mathsf \pink{ - 16}[/tex]

[tex] \mathbb\green{Hope\:It\:Helps} [/tex]

Answer:

x = 45.

Step-by-step explanation:

The angle between the shorter line and line n is 90 degrees, so

2x must be 90 degrees for m and n to be parallel.

x = 45.

[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}[/tex]

c=9 makes the given expression a perfect square trinomial.

The given expression is:

[tex]x^{2} +6x+c[/tex]

We can rewrite it as:

[tex]x^{2} +2*x*3 + c[/tex].....(1)

The expansion of [tex](a+b)^2[/tex] is [tex]a^{2} +2ab+b^{2}[/tex]

Comparing (1) with [tex]a^{2} +2ab+b^{2}[/tex]

We get

a=x

b=3

c=b²

So, c=3² =9.

So, c=9 makes the given expression a perfect square trinomial.

Hence,  c=9 makes the given expression a perfect square trinomial.

To get more about polynomials visit:

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Answer:

choice A is correct

Step-by-step explanation:

the value of x should be 75

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the remote interior angles.

  (3x +6)° = 31° +35°

  3x +6 = 66 . . . . . . . . . . divide by °, collect terms

  3x = 60 . . . . . . . . subtract 6

  x = 20 . . . . . . . divide by 3

The value of y is the supplement of (3x+6)°, and of the sum (31 +35)°.

  y = 180° -66° = 114°

The values of x and y are 20 and 114°, respectively.

Answer:

period = 2π

Step-by-step explanation:

the period is the distance from one point on the waveform to the corresponding point on the next wave.

there is a maximum at 2π and a corresponding maximum at 4π

period = 4π - 2π = 2π

Answer: 13 [tex]\frac{1}{3}[/tex] pounds

Step-by-step explanation:

     We will set up a proportion. I will have the weight, in pounds, on the top (numerator) and the length, in inches, on the bottom (denominator).

[tex]\frac{12}{36} =\frac{x}{40}[/tex]

     Cross-multiply:

36 * x = 12 * 40

36x = 480

     Divide both sides of the equation by 36:

x = 13 [tex]\frac{1}{3}[/tex] pounds

Answer:

Step-by-step explanation:

First find unit weight.

1 foot = 12 inches

3 ft = 3*12 = 36 inches

3ft 4 inches = 36 + 4 = 40inches

Weight of 36 inches  long bar =   12  pounds

Weight of 1 inch bar = 12/36

[tex]\text{Weight of 40 inches long bar = $\dfrac{12}{36}*40$}[/tex]

                                             = 13.3 pounds

Answer:

5.025m

Step-by-step explanation:

The clothesline also creates an upside-down triangle with two sides being 5m, 0.5m, and the hypotenuse being the clothesline.

We can use the pythagorean theorem to find the length of the clothesline.

5 squared +.5 squared= the length of the clothesline squared

25+.25= the square root of 25.25

= 5.025

Answer:

Your answer would be:
5.025m

Step-by-step explanation:

5 sq + 0.5sq = the length of the clothesline sq

25 + 0.25= the square root of 25.25

= 5.025m



Have a great rest of your day
#TheWizzer

Answer: 698352.000

698352 rounded to the nearest 1000 is 698352.000

The year in which the NFL voted to create a $430 million fund to help the bottom 15 clubs was 2007.

The NFL voted by a margin of 30-2 in 2007 to create a pool of funds over 3 years that would amount to $430 million.

This money would then be used to help the bottom 15 clubs who might be struggling financially. The hope was that this would make things more competitive in the NFL.

Find out more on the NFL at https://brainly.com/question/7579515.

Answer:

2.744 cubic milimeters

Step-by-step explanation:

Here,

Length ( l ) = 1.4 mm

Base ( b ) = 1.4 mm

Height ( h ) = 1.4 mm

l = b = h = 1.4 mm = a

To find : Volume

This shape is a cube.

Formula : -

Volume of cube = a³

Volume of cube

= 1.4³

= 1.4 x 1.4 x 1.4

= 2.744 cubic milimeters

[tex] \huge\fbox\orange{ANSWER} [/tex]

[tex] \mathsf \purple{v = l \times w \times h}[/tex]

[tex] \mathsf \pink{v = 1.4 \times 1.4 \times 1.4}[/tex]

[tex] \mathsf \purple{v = 2.744 {mm}^{3} }[/tex]

2.74 cubic millimeters

Answer:

i think the answer will be = 8 × 10^2

X = 1

Explanation :

when you multiply negative 2 by negative six you get twelve. when you multiply positive one by negative six you get negative six.

Answer: X = 1

Step-by-step explanation:

give other brainliest

Answer:

Step-by-step explanation:

s to the 3rd power so S3
I hope this works

Answer:Part two is (s+2)3

Step-by-step explanation:

I got it right I hope it helps

Answer:

Mechanical

Step-by-step explanation:

Those ttype of machines build epic cars

Using the dot plot, the inference is that the number of flocks observed on the second day was less than in the first.

The dot plot shows the number of times each measure appears in the data-set.

Hence, the mean of the data-set corresponding to day 1 is given by:

M1 = (4 x 4 + 7 x 5 + 7 x 6 + 7 x 7)/25 = 5.68

And the mean of the data-set corresponding to day 2 is given by:

M2 = (2 x 8 + 3 x 7 + 4 x 6 + 5 x 4)/25 = 3.24.

M1 > M2, hence, the inference is that the number of flocks observed on the second day was less than in the first.

More can be learned about dot plots at https://brainly.com/question/24912483

Answer:

Step-by-step explanation:

Standard form: Ax + By = C

State whether each equation is in standard form.

A.) 3x + y = 8 (in standard form)

B.) x - y = 15z (not in standard form, because it has a variable(15z))

C.) x^2 + y = 11 (not in standard form, this is not a linear equation)

D.) 3xy + y^2 = 4 (not in standard form, this is not a linear equation)

E.) x + 4y = 12 (in standard form)

F.) 5x + 24y = 544 (in standard form)

Hope this helps!

Answer:

The length of river D is 2550

length of river C is 2550+500=3050

Step-by-step explanation:

Let the river D be 'x'

and the river C is (x+500)

x + x + 500 = 5600

2x + 500 = 5600

2x = 5600 - 500

2x = 5100

x = 5100/2

x = 2550

The length of river D is 2550

length of river C is 2550+500=3050

Answer:

Looking at the first two given ordered pairs (3, 5) and (4, 7), it appears that for every increase of 1 unit of x, there is an increase of 2 units of y.

Let's check by writing the next ordered pairs using this rule:

(5, 9)  (6, 11)  (7, 13)  (8, 15)

As the the ordered pair (8, 15) is in the table, then we can confirm that this is the rule.

Writing the rule as an equation:

y = 2x - 1

Therefore, n = 6

Answer:

y = 2x - 1

n = 6

Step-by-step explanation:

Hello!

This is an arithmetic sequence.

An Arithmetic sequence, also known as an arithmetic progression, is a string of numbers that follow a pattern where the difference between two terms is always the same (constant).

An Arithmetic sequence is modeled by the explicit function:[tex]\bold{t(n) = (CD)n + t(0)}[/tex]

Let's go step by step to solve these equations:

Step 1: Common Difference

The common difference of a sequence is similar to the slope of a line. The slope formula is given as [tex]\bold{\frac{y_2 - y_1}{x_2-x_1}}[/tex].

We can input values of x and y to find the common difference

We have the CD, 2!

Step 2: Starting Value

The starting value can be shown as the y-intercept of the line or the origin point of the sequence.

To find the starting value or t(0), we can input an x and y value for "n" and "t(n)"

We know have the starting value, -1!

Step 3: The Equation

We now have all the values for our equation. let's bring our attention back to the input and output variables. Since we know that "t(n)" is the same as "y" and "n" is the same as "x", we can plug that instead of t(n) and n.

Solve for n:

With our equation, we can plug in 11 as the output and solve for n.

n = 6

_______________________________________________________

Another way to solve this is to find the Recursive Equation

The Recursive Equation is only meant to find the next term, it doesn't do so well in finding the terms in the long run.

The basic form of a recursive equation is t(n + 1) = t(n) + (CD); where t(0) is ____

I'm not going to go in-depth with this, but you can see the values that we solved above can be implemented here.

Our recursive equation is t(n + 1) = t(n) + 2; where t(0) is -1

The port outside of the semi-colon represents where the sequence starts. If only t(n+1) = t(n) + 2 is given, we could start at 5, and go as 5, 7, 9...etc.

We would start by finding t(1) by doing:

We can confirm this using our explicit rule: y = 2x - 1

Answer:

E= -4,5

F=3,-2

Step-by-step explanation:

i think that's correct sorry if not

Answer:

[tex]\displaystyle 600\frac{1}{2}\%[/tex]

Explanation:

Just move the decimal mark twise to the right and you will arrive at your result.

I am joyous to assist you at any time.

Answer: 75 Degrees

Step-by-step explanation: 1. Due to the law of opposite adjacent angles, we can determine angle 1 is congruent to angle 4 and therefore is 15 degrees 2. Angle 3 is shown to be a right angle (90 degrees) 3. Since angles 1,2, and 3 are on a flat line, the sum of all 3 is 180 4. 15+90 is 105 5. 180-105 is 75 which is the measure of angle 2