(x^3- 5x² – 33x – 35) /(x+3)

Answer:

The explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]

Option A is correct option.

Step-by-step explanation:

Third term of sequence is 18

Sixth term of sequence is 33

We need to find the explicit equation for the sequence.

The explicit sequence is [tex]a_n=a_1+(n-1)d[/tex]

We need to find a_1 the first term and common difference d

We have a₃=18

We can write it as: [tex]a_3=a_1+(3-1)d\\[/tex]

[tex]18=a_1+2d[/tex]

a₆=33

We can write it as: [tex]a_6=a_1+(6-1)d\\33=a_1+5d[/tex]

Now, solving these equation s we can find value of d

[tex]18=a_1+2d[/tex]

[tex]33=a_1+5d[/tex]

Subtract both equations

[tex]18=a_1+2d[/tex]

[tex]33=a_1+5d[/tex]

[tex]--------\\-15=-3d\\d=\frac{-15}{-3}\\d=5[/tex]

So, we get common difference d = 5

Now finding a_1

Put value of d in equation [tex]18=a_1+2d[/tex]

[tex]18=a_1+2(5)\\18=a_1+10\\a_1=18-10\\a_1=8[/tex]

So, we get a₁ = 12

Now, the explicit equation is:

[tex]a_n=a_1+(n-1)d\\a_n=8+(n-1)5\\a_n=8+5n-5\\a_n=5n+3[/tex]

So, the explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]

Option A is correct option.

Answer:

y=13.15x+14

Step-by-step explanation:

That is the equation, if you need the graph lmk

Answer:

?=14+13.15x

14+13.15x=?

?=13.15x+14

13.15x+14=?

Answer:

Step-by-step explanation:

Given a set of elements corresponding to the domain, we obtain the range by evaluating the function at each value:

22. [tex]f(x) = x^{2}-3[/tex]

[tex]f(-2) = (-2)^{2}-3[/tex]

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

[tex]f(0) = 0^{2}-3[/tex]

[tex]f(0) = -3[/tex]

[tex]f(2) = 2^{2}-3[/tex]

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

[tex]f(4) = 4^{2}-3[/tex]

[tex]f(4) = 13[/tex]

The set of ordered pairs associated with the given function is:

[tex]S = \{(x,y)|(-2,1), (0,-3), (2,1), (4,13)\}[/tex]

23. [tex]g(x) = -5\cdot x + 2[/tex]

[tex]g(-4) = -5\cdot (-4)+2[/tex]

[tex]g(-4) = 22[/tex]

[tex]g(-1) = -5\cdot (-1) + 2[/tex]

[tex]g(-1) = 7[/tex]

[tex]g(3) = -5\cdot (3) +2[/tex]

[tex]g(3) = -13[/tex]

The set of ordered pairs associated with the given function is:

[tex]S =\{(x,y)|(-4,22),(-1,7),(3,-13)\}[/tex]

Answer:

(1)  4

Step-by-step explanation:

Isolate x.

[tex]\frac{x-2}{3}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{5}{6}[/tex]

[tex]\frac{x-2}{3}[/tex] = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex]

[tex]\frac{x-2}{3}[/tex] = [tex]\frac{2}{3}[/tex]

[tex]\frac{x-2}{3}[/tex] × 3 = [tex]\frac{2}{3}[/tex] × 3

x - 2 = 2

x = 2 + 2

x = 4

Answer:

C. n=4

Step-by-step explanation:

got it

Answer:

Area of the triangle :---

1/2×base×height

1/2×5×6

15 square unit

15 square unit is the right answer.

Answer:

3 of the DVDs were documentaries.

Step-by-step explanation:

We know that at first, there were 15 DVDs in total.

Now, we need to find how much 1/5 of 15 DVDs were equal to.

1/5 of 15 is equal to the number 3.

So, that means our answer is 3 of the DVDs are documentaries.

Hope this helps.

Answer:

I think the answer should be 3.

Answer:

Parallel

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It is D because the scuba diver was 35 m below the surface of the water at the start of the ascent. Meaning that the Y value is showing how deep the diver was in the water

Answer:

MP is approximately equal to ON because one side of a rectangle is always the same as another side of a rectangle.  

Step-by-step explanation:

Answer:

Face Value = 8

Place Value = 80

Step-by-step explanation:

What is the difference between face value and place value of 8 in the number 281 ?

First we define Place value and Face Value

Place value

Place value is defined as the digit multiplied wherever it is placed, either by tens, hundreds or thousands.

Face Value

Face value is defined as the digit itself within a number.

Now: we will find face value and place value of 8 in the number 281.

Face Value = 8

Place Value = 8 x 10 (because 8 is at tens place) = 80

So, the answer is:

Face Value = 8

Place Value = 80

Answer:poop

Step-by-step explanation:

ineed points

Answer:

WHat is your question I don't see one I just see a whole bunch of answers

Step-by-step explanation:

Answer:

B) [3, 5]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, the line's y-values span from 3 to 5. Since both are closed dot, they are inclusive in the range:

[3, 5] or 3 ≤ y ≤ 5

Answer:

t=8/3+4/3u  

Step-by-step explanation:

4u=3t+8

-3t+8-4u

t=8/3+4/3u

hope it helps

Answer:

40 ounces ;

2.5 pounds

Step-by-step explanation:

Given that:

Number of ounces of food per day = 4 ounces

Number of days for which cats were fed = 10

The smallest bag that has enough food to feed the cats should be :

(ounces of food per day * Number of days)

(4 ounces * 10)

= 40 ounces

1 pound = 16 ounces

40 ounces = 40/16 = 2.5 pounds

Answer:

40 divided by 16 = 2.5 pounds .

Given:

The equation of a circle is

[tex]10y+x^2=-18+5x-y^2[/tex]

To find:

The center and radius of the given equation by completing the square.

Solution:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]            ...(i)

where, (h,k) is center and r is radius of the circle.

We have,

[tex]10y+x^2=-18+5x-y^2[/tex]

It can be written as

[tex](x^2-5x)+(y^2+10y)=-18[/tex]

[tex]\left(x^2-5x+\left(\dfrac{5}{2}\right)^2\right)+\left(y^2+10y+\left(\dfrac{10}{2}\right)^2\right)=-18+\left(\dfrac{5}{2}\right)^2+\left(\dfrac{10}{2}\right)^2[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+\left(y^2+10y+5^2\right)=-18+\dfrac{25}{4}+5^2[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=-18+\dfrac{25}{4}+25[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{-72+25+100}{4}[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{53}{4}[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\left(\dfrac{\sqrt{53}}{2}\right)^2[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]h=\dfrac{5}{2},k=-5,r=\dfrac{\sqrt{53}}{2}[/tex]

Therefore, the center is [tex]\left(\dfrac{5}{2},-5\right)[/tex] and the radius is [tex]\dfrac{\sqrt{53}}{2}[/tex] units.

Answer:

In vertex form the parabola can be expressed as:

y = (x - 2.5)² + 0.75

Step-by-step explanation:

To complete the square, all you need to do is take the term 5x, divide the coefficient in two, and square it.  That is what you need for the third term:

[tex]y = x^2 - 5x + 7\\y = x^2 - 5x + 6.25 + 0.75\\y = (x - 2.5)^2 + 0.75[/tex]

Answer:

$5.60

Step-by-step explanation:

So each pound equals to $1.75 which means that we need to multiply by 3.2 because we're trying to find the number of money we'll spend on a certain amount of coffee. So if we multiply, we get 5.6. Though in context with the problem, it should be $5.60.

Answer: [tex]\frac{7x-6}{6x}[/tex]

Step-by-step explanation:

The value of the equation is ( 7/6 ) - ( 1/x )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be = A

Now , the equation is

A = ( 5/3 ) - ( x + 2 ) / 2x

On simplifying the equation , we get

A = [ ( 5/3 ) ( 2x ) - ( 3 )( x + 2 ) ] / 2x ( 3 )

A = [ ( 10x) - 3x - 6 ] / 6x

A = ( 7x - 6 ) / 6x

On simplifying the equation , we get

A = ( 7/6 ) - ( 1/x )

Therefore , the value of A is ( 7/6 ) - ( 1/x )

Hence , The value of the equation is ( 7/6 ) - ( 1/x )

To learn more about equations click :

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Answer:

Step-by-step explanation:

15

it would take 9 minutes to fill a 15-gallon container using the same garden hose.

If a garden hose can fill up a 5-gallon container in 3 minutes, we can use this information to calculate how long it would take to fill a 15-gallon container. The time it takes to fill a container is directly proportional to the volume of the container. In this case, the ratio of volumes is 15 gallons (larger container) to 5 gallons (smaller container). Since the volumes are in the ratio of 15:5, which simplifies to 3:1, the time it takes to fill the larger container will also be in the same ratio.

So, if it takes 3 minutes to fill a 5-gallon container, it will take 3 times longer to fill a 15-gallon container.

3 minutes (to fill 5 gallons) x 3 = 9 minutes

Therefore, it would take 9 minutes to fill a 15-gallon container using the same garden hose.

To know more about volumes

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Answer:

[tex](81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8[/tex]

Step-by-step explanation:

Given

[tex](81x^4y^{16})^{\frac{1}{2}}[/tex]

Required

Determine an equivalent expression

Express 81 as [tex]9^2[/tex]

[tex](9^2x^4y^{16})^{\frac{1}{2}}[/tex]

Apply law of indices

[tex]9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}[/tex]

[tex]9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}[/tex]

[tex]9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}[/tex]

[tex]9^1 * x^2 * y^8[/tex]

[tex]9 * x^2 * y^8[/tex]

[tex]9 x^2 y^8[/tex]

Hence:

[tex](81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8[/tex]

Answer:

69 more pages

Step-by-step explanation:

Answer:

1 is 10

2 is 6

3 is -15

Step-by-step explanation: