Which is an equation for the nth term of the sequence?

12, 15, 18, 21, ...

Question 1 options:

a)

= 12n + 3


b)

= 3n + 9


c)

= n + 3


d)

= 9n + 3

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 2 and (a, b) = (10, - 9), hence

y - (- 9) = - 2(x - 10), that is

y + 9 = - 2(x - 10) ← in point- slope form

Answer: [tex]y+9=-2(x-10)[/tex]

Step-by-step explanation:

We know that the equation of a line in point slope form passing through point (a,b) and having slope 'm' is given by :-

[tex](y-b)=m(x-a)[/tex]

Given : Point : (10,-9)

Slope :  m=-2

Then , the equation of a line in point slope form passing through point (10,-9) and having slope '-2' is given by :-

[tex](y-(-9))=-2(x-10)\\\\\Rightarrow\ y+9=-2(x-10)[/tex]

namely, how many times does 3/4 go into 3½?  Let's firstly convert the mixed fraction to improper fraction.

[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}\div \cfrac{3}{4}\implies \cfrac{7}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]

Answer:

Danika signed up to work for 3.5 hours at the science fair, if each work shift is 3/4 hour = 0.75 hours, the amount of shifts will be:

Shifts = 3.5/0.75 = 4,66 ≈ 5 shifts. Given that shifts have to be an integer number, we need to round the result to the nearest integrer.

Therefore, Danika will work 5 shifts.

Answer:

[tex]\large\boxed{x=-\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]f(x)=9x^2+6x+1\\\\\text{The zeros are for}\ f(x)=0\\\\9x^2+6x+1=0\\\\9x^2+3x+3x+1=0\\\\3x(3x+1)+1(3x+1)=0\\\\(3x+1)(3x+1)=0\\\\(3x+1)^2=0\iff3x+1=0\qquad\text{subtract 1 from both sides}\\\\3x=-1\qquad\text{divide both sides by 3}\\\\x=-\dfrac{1}{3}[/tex]

Answer:

Option A is correct.

Step-by-step explanation:

We need to find the quotient of the polynomials

[tex](6x^3+8x^2+16)\div(2x+4)[/tex]

The quotient is: 3x^2-2x+4

The remainder is: 0

The division is shown in the figure attached.

Option A is correct.

Answer:

your answer is A// -37

Step-by-step explanation:

1 shirt=$6

5 shirts= 5 × $6

=$30

lunch= $7

So in total she spent:

$30 + $7= $37

And from what we are given above; the balance in her account is

5(-6) + (-7)

= -30 - 7= -37

The statement which is rue about the effects of the transformations on the graph of function f to obtain the graph of function g is D. The graph of function f(x) is shifted right 3 units and up 4 units.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given is a function f(x) and the transformed function g(x) = f(x - 3) + 4.

After translation, the original figure is shifted from a place to another place without affecting it's size.

Here the transformation is both horizontal and vertical translation.

f(x) is first changed to f(x - 3).

When f(x) is changed to f(x - d), the function is shifted right d units.

So here the function is shifted right to 3 units.

Similarly when f(x) changed to f((x) + d, then the function is shifted up d units.

So the function is also shifted up 4 units.

Hence the transformation is the graph is shifted right to 3 units and up 4 units.

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Answer:

C) the value of a person's wealth or income

Step-by-step explanation:

If an economy doesn't have money nobody would be wealthy because nobody would have money.

it's r because it does not sit on the same plane as the rest of the points that are given.when looking at the diagram c,d and e are all connected to the square on the bottom of the pyramid. The same goes for points u,s and a. The point R is different by sitting on one of the triangles of the pyramid.

The point R is not coplanar with C, D, and E. This is because point R is not lying in the plane of C, D, and E.

The points which lie on the same plane are said to be coplanar points.

The given points are R, A, S, and U

The considered pane is w.r.t the points C, D, and E.

So, point A is forming a square with the points C, D, and E. So, it is coplanar with these points.

Point S is on the surface of the plane formed by ACDE. So, it is coplanar.

Point U is also in the plane w.r.t point C, D, and E. So, it is a coplanar point.

But point R does not lie in the plane w.r.t C, D, and E. So, it is not coplanar with points C, D, and E.

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The equation for [tex]\( G(F(x)) = 4x^2 - 20x + 26 \)[/tex].

To find [tex]\( G(F(x)) \)[/tex], we first need to substitute the expression for [tex]\( F(x) \)[/tex] into the function [tex]\( G(x) \)[/tex].

Given:

[tex]\[ F(x) = 2x - 5 \]\[ G(x) = x^2 + 1 \][/tex]

Replace x in [tex]\( G(x) \)[/tex] with [tex]\( F(x) \):[/tex]

[tex]\[ G(F(x)) = (2x - 5)^2 + 1 \][/tex]

Now, expand [tex]\( (2x - 5)^2 \)[/tex] using the binomial theorem:

[tex]\[ (2x - 5)^2 = (2x - 5)(2x - 5) \]\[ = 4x^2 - 10x - 10x + 25 \]\[ = 4x^2 - 20x + 25 \][/tex]

Now, substitute this expression back into [tex]\( G(F(x)) \)[/tex]:

[tex]\[ G(F(x)) = 4x^2 - 20x + 25 + 1 \]\[ G(F(x)) = 4x^2 - 20x + 26 \][/tex]

Answer:

The 4 pack is the better deal.

Step-by-step explanation:

You need to divide the amount of cost by the number of rolls per pack to get a per roll price.

4 pack = $2.04

$2.04/4 rolls = cost $.51/roll

for the 9 pack $4.68.

$4.68/4 rolls = $.52/1 roll

The better deal is the 4 pack because $.51 is less than $.52 per roll for the 9 pack.

For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the rest.

The attached figure shows the quotient given by:

[tex]x ^ 3 + x ^ 2 + x + 1[/tex]

Answer:

Quotient: [tex]x ^ 3 + x ^ 2 + x + 1[/tex]

See attached image

Answer:

Quotient is: x^3+x^2+x+1  

Step-by-step explanation:

We need to solve (x^4-1) ÷  (x-1) using synthetic division.

In synthetic division we write the coefficients in decreasing order of their powers. We have x^4-1 that can be written as: 1x^4 + 0x^3 + 0x^2 + 0x -1

so our coefficients will be

1 0 0 0 -1

and for synthetic division, we take the constant term of divisor and change its sign.

We have x-1, constant term -1 so, our value will be 1.

The division is attached in the figure below.

Quotient is: x^3+x^2+x+1  

Answer:

d) 1⃣

Step-by-step explanation:

Multiply -5 by -2 to get , then deduct 7 to get 3. So, you now know that 3 = 3a; 1 = a.

Answer:

x is equal to 20, or the answer A

Step-by-step explanation:

They are opposite angles so they are equal to each other. When you set up the equation (x+40)=3x, you get the answer to be 20. hope this helped!

For this case we have to define by opposite angles the vertex that:

[tex]x + 40 = 3x[/tex]

Subtracting 3x on both sides of the equation:

[tex]x-3x + 40 = 0\\-2x + 40 = 0[/tex]

Subtracting 40 from both sides of the equation:

[tex]-2x = -40[/tex]

Dividing between -2 on both sides of the equation:

[tex]x = \frac {-40} {- 2}\\x = 20[/tex]

So, we have that [tex]x = 20[/tex]

ANswer:

[tex]x = 20[/tex]

Step-by-step explanation:

9.02

remember when dealing with decimals:

0.(tenth)(hundredths)(thousandths)

Nine and two hundredths as a decimal is 9.02.

The question asks for the decimal representation of nine and two hundredths. In the decimal number system, 'and' corresponds to the decimal point. So, the answer to the question is 9.02. This is because the 'nine' is in the whole number part before the decimal point and 'two hundredths' is represented by '02' after the decimal point.

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[tex](g\circ f)(x)=(2x-1)^2-2=4x^2-4x+1-2=4x^2-4x-1[/tex]

Answer:

[tex]4x^2 -4x -1[/tex]

Step-by-step explanation:

Given functions,

[tex]f(x) = 2x - 1-----(1)[/tex]

[tex]g(x) = x^2 -2-----(2)[/tex]

∵ (gof)(x) = g[f(x)]    ( Composition of functions )

[tex]\implies (gof)(x) = g(2x-1)[/tex] ( From equation (1) )

[tex]=(2x-1)^2 - 2[/tex]  ( From equation (2) )

[tex]=4x^2 + 1 - 4x - 2[/tex]

[tex]=4x^2 -4x -1[/tex]

Answer:

2.2

2.20

Explanation

You can add zeros or take them away and the number will still have the same value.

Answer:

the answers are A B AND D

Step-by-step explanation:

To find perpendicular lines you take the slope and change the sign and find the reciprocal. after doing that you set it up as a new equation that you will use to find b using the point.

in this case

y= - 2/5x +b

plug in the x and y values of the point (5, -4) to find b

b= -2

you put that together to get the equation

The equation of the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4) is y = -0.4x - 2.

The given equation is 5x - 2y = -6. First step is to convert this to the slope-intercept form (y = mx + b) to find the slope. To do this, solve for y in terms of x, which looks like y = 2.5x + 3. The perpendicular line would have a slope that is the negative reciprocal this slope (m = -1/2.5 or -0.4).

Next, apply the point-slope formula (y - y1 = m(x - x1)) where m is the slope and (x1, y1) is the point that the line passes through. In this case, (x1, y1) is (5, -4), and slope m is -0.4. Then, y - (-4) = -0.4(x - 5), results to y + 4 = -0.4x + 2, finally gives y = -0.4x - 2 as the equation of the line that is perpendicular to 5x - 2y = -6 and passes through the point (5, -4).

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Answer:

slope = [tex]\frac{7}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (2, 7)

m = [tex]\frac{7-0}{2+3}[/tex] = [tex]\frac{7}{5}[/tex]

Hello!

Hint: ⇒ Slope formula: ⇒ [tex]\frac{Y_2-Y_1}{X_2-X_1}[/tex]

[tex]Y_2=7\\ Y_1=0\\\\X_2=2\\X_1=-3[/tex]

[tex]\frac{7-0}{2-(-3)}=\frac{7}{5}[/tex]

[tex]\boxed{\frac{7}{5}}\checkmark[/tex]

[tex]\boxed{\frac{7}{5}}[/tex], which is our correct answer.

Hope this helps you!

Have a great day! :)

Answer:

Step-by-step explanation:

[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_1)-point\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\============================[/tex]

[tex]\text{We have the points:}\ (-1,\ 2)\ \text{and}\ (3,1).\\\\\text{Substitute:}\\\\m=\dfrac{1-2}{3-(-1)}=\dfrac{-1}{4}=-\dfrac{1}{4}\\\\y-2=-\dfrac{1}{4}(x-(-1))\\\\y-2=-\dfrac{1}{4}(x+1)\qquad\text{convert to the standard form}\ Ax+By=C\\\\y-2=-\dfrac{1}{4}(x+1)\qquad\text{multiply both sides by 4}\\\\4y-8=-(x+1)\\\\4y-8=-x-1\qquad\text{add 8 to both sides}\\\\4y=-x+7\qquad\text{add x to both sides}\\\\x+4y=7[/tex]

The equation of a line passing through points (-1, 2) and (3, 1) can be determined using the slope formula, which is (y2 - y1)/(x2 - x1). The resulting slope is -1/4 or -0.25. Unfortunately, none of the provided options match this description.

The subject of the question is about finding the equation of a line that passes through the points (-1,2) and (3,1). To find the correct equation, we need to use the formula for the slope of a line which is: (y2 - y1) / (x2 - x1). Plugging in the coordinates (-1,2) and (3,1) will give us a slope of -1/4 or -0.25. This slope should be the coefficient of 'x' in the correct equation. None of the provided choices A, B, C, D have a coefficient of -0.25 for x, therefore, unfortunately, none of these equations represent a line that passes through the points (-1,2) and (3,1).

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Answer:

Adjacent angles must share a vertex.

Step-by-step explanation:

we know that

Two angles are Adjacent when they have a common side and a common vertex

therefore

Adjacent angles must share a vertex.

Answer:

Adjacent angles must share a vertex.

Im so sorry I am so late on answering this question....

Hope the answer (my answer) helps!

[tex]9-(4^2-(3+20)=9-(16-23)=9-(-7)=16[/tex]

[tex]g(f(x))=5(4x^2+5x+3)-7=20x^2+25x+15-7=20x^2+25x+8[/tex]

Answer:

value of n = 2

Step-by-step explanation:

[tex]\frac{4}{5n}-\frac{1}{5}=\frac{2}{5n}[/tex]

We need to solve the above equation.

Find Least Common multiplier from 5n, 5 = 5n

Multiply both sides of the equation by 5n

[tex]\frac{4}{5n}*5n-\frac{1}{5}*5n=\frac{2}{5n}*5n\\Solving:\\4 -n = 2\\[/tex]

Now finding the value of n.

Adding -4 on both sides

[tex]4 -n-4 = 2-4\\-n= -2[/tex]

Multiplying both sides by -1

n = 2

The value of n is 2.

We can verify by putting value of n in the given question.

[tex]\frac{4}{5n}-\frac{1}{5}=\frac{2}{5n}\\n=2\\\frac{4}{5*2}-\frac{1}{5}=\frac{2}{5*2}\\\frac{4}{10}-\frac{1}{5}=\frac{2}{10}\\\frac{2}{5}-\frac{1}{5}=\frac{1}{5}\\\frac{2-1}{5}=\frac{1}{5}\\\frac{1}{5}=\frac{1}{5}[/tex]

So, value of n = 2

Answer:

It's C : n=1/2

Have a great day :)

Answer:

(x + 5 y)^2

Step-by-step explanation:

Simplify the following:

4 (x - y)^2 - 12 (x - y) (x + y) + 9 (x + y)^2

(x - y) (x - y) = (x) (x) + (x) (-y) + (-y) (x) + (-y) (-y) = x^2 - x y - x y + y^2 = x^2 - 2 x y + y^2:

4 x^2 - 2 x y + y^2 - 12 (x - y) (x + y) + 9 (x + y)^2

4 (x^2 - 2 x y + y^2) = 4 x^2 - 8 x y + 4 y^2:

4 x^2 - 8 x y + 4 y^2 - 12 (x - y) (x + y) + 9 (x + y)^2

(x + y) (x - y) = (x) (x) + (x) (-y) + (y) (x) + (y) (-y) = x^2 - x y + x y - y^2 = x^2 - y^2:

4 x^2 - 8 x y + 4 y^2 - 12 x^2 - y^2 + 9 (x + y)^2

-12 (x^2 - y^2) = 12 y^2 - 12 x^2:

4 x^2 - 8 x y + 4 y^2 + 12 y^2 - 12 x^2 + 9 (x + y)^2

(x + y) (x + y) = (x) (x) + (x) (y) + (y) (x) + (y) (y) = x^2 + x y + x y + y^2 = x^2 + 2 x y + y^2:

4 x^2 - 8 x y + 4 y^2 - 12 x^2 + 12 y^2 + 9 x^2 + 2 x y + y^2

Grouping like terms, 4 x^2 - 8 x y + 4 y^2 - 12 x^2 + 12 y^2 + 9 (x^2 + 2 x y + y^2) = 9 (x^2 + 2 x y + y^2) + (4 y^2 + 12 y^2) - 8 x y + (4 x^2 - 12 x^2):

9 (x^2 + 2 x y + y^2) + (4 y^2 + 12 y^2) - 8 x y + (4 x^2 - 12 x^2)

4 y^2 + 12 y^2 = 16 y^2:

9 (x^2 + 2 x y + y^2) + 16 y^2 - 8 x y + (4 x^2 - 12 x^2)

4 x^2 - 12 x^2 = -8 x^2:

9 (x^2 + 2 x y + y^2) + 16 y^2 - 8 x y + -8 x^2

9 (x^2 + 2 x y + y^2) = 9 x^2 + 18 x y + 9 y^2:

9 x^2 + 18 x y + 9 y^2 + 16 y^2 - 8 x y - 8 x^2

Grouping like terms, 9 x^2 + 18 x y + 9 y^2 + 16 y^2 - 8 x y - 8 x^2 = (9 y^2 + 16 y^2) + (18 x y - 8 x y) + (9 x^2 - 8 x^2):

(9 y^2 + 16 y^2) + (18 x y - 8 x y) + (9 x^2 - 8 x^2)

9 y^2 + 16 y^2 = 25 y^2:

25 y^2 + (18 x y - 8 x y) + (9 x^2 - 8 x^2)

x y 18 + x y (-8) = 10 x y:

25 y^2 + 10 x y + (9 x^2 - 8 x^2)

9 x^2 - 8 x^2 = x^2:

25 y^2 + 10 x y + x^2

The factors of 25 that sum to 10 are 5 and 5. So, 25 y^2 + 10 x y + x^2 = (x + 5 y) (x + 5 y):

(x + 5 y) (x + 5 y)

(x + 5 y) (x + 5 y) = (x + 5 y)^2:

Answer:  (x + 5 y)^2

[tex]4(x-y)^2-12(x-y)(x+y)+9(x+y)^2 =\\4(x^2-2xy+y^2)-12(x^2-y^2)+9(x^2+2xy+y^2)=\\4x^2-8xy+4y^2-12x^2+12y^2+9x^2+18xy+9y^2=\\x^2+10xy+25y^2[/tex]

which can factorised into [tex](x+5y)^2[/tex]

For this case we have that by definition, a quadratic equation is of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Its roots are given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

By definition, the discriminant is given by:

[tex]D = b ^ 2-4 (a) (c)[/tex]

According to the given equation we have to:

[tex]a = 5\\b = 3\\c = -5[/tex]

Substituting:

[tex]D = 3 ^ 2-4 (5) (- 5)\\D = 9 + 100\\D = 109[/tex]

Answer:

The discriminant is 109

Answer:

x^2 + y^2 = 5^2

or x^2 +y^2 = 25

Step-by-step explanation:

The equation of a circle is usually written in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

The center is at the origin so (h,k) = (0,0) and  the radius is 5 so r=5

x^2 + y^2 = 5^2

or x^2 +y^2 = 25

Answer:

x² + y² = 25

Step-by-step explanation:

(x - h)² + (y - k)² = r²

Center ( h⁰, k⁰)  

radius = 5/r

(x - 0)² + (y - 0)² = 5² ⇒ x² + y² = 25

This will be your answer : x² + y² = 25

Answer:

8 times

Step-by-step explanation:

We know that the radius of smaller sphere is r,

The volume of sphere is given by:

[tex]V_1=\frac{4}{3} \pi r^{3}[/tex]

where V_1 is the volume of the small sphere.

As we know that the radius of large sphere is double of the smaller sphere, the radius of large sphere will be 2r

Let V_2 be the volume of large sphere

[tex]V_2=\frac{4}{3}\pi (2r)^{3} \\ =\frac{4}{3}\pi *8r^3[/tex]

Separating 8 aside

[tex]V_2=8(\frac{4}{3}\pi r^{3})\\V_2=8V_1[/tex]

We can see that the volume of large sphere is eight times the volume of small sphere ..

Answer:

8 times

Step-by-step explanation:

Given

ratio of radii = a : b, then

ratio of volumes = a³ : b³

Here ratio of radii = 1 : 2, hence

ratio of volumes = 1³ : 2³ = 1 : 8

Thus the volume of the large sphere is 8 times the volume of the small sphere

Answer:

Step-by-step explanation:

[tex]a\ \vee\ b\ \text{is true if }\ a=T\ \text{or}\ b=T.\\\\\text{Therefore}\ p\ \vee\ (q\ \wedge\ r)\ \text{is\ true,\ if}\ p=T\ \text{or}\ (q\ \wedge\ r)=T.\\\\\text{We have}\ p=F.\ \text{Therefore}\ p\ \vee\ (q\ \wedge\ r)\ \text{is true, if}\ (q\ \wedge\ r)=T.[/tex]

Answer:

[tex]\boxed{\text{A. }\math{\left \{ x \, | \, x \in \mathbb{R}, x < -2 \right \}}}}[/tex]

Step-by-step explanation:

The open circle means that the point is not included in the solution set, and the arrow pointing left means that all numbers less than -2 are members.

In set-builder notation, each term has a special meaning. The braces enclose the members of the set.

Here's how you translate the notation,

[tex]\begin{array}{rcl}\\\left \{ & = & \text{The set of}\\x & = & \text{all x values}\\| & = &\text{such that}\\x & = & x\\\in & = &\text{is a member of}\\\mathbb{R}, & = &\text{all real numbers, and}\\x < -2 & = & \text{x is less than -2}\\\end{array}\\\text{The answer is }\boxed{\textbf{A. }\mathbf{\left \{ x \, | \, x \in \mathbb{R}, x < -2 \right \} }}}[/tex]

Answer:

Yes

Step-by-step explanation:

Think simple.

The picture has already provided us with the information that ∠EFT ≅ ∠LKM, and we also have:

∠EFT ≅ ∠GFH (opposite angles)

∠LKM ≅ ∠JKN (opposite angles as well)

Therefore ∠JKN ≅ ∠GFH