which of the following functions is graphed below?

Answer:

Step-by-step explanation:

233 322

Answer:

y=n^2+3n+4

Step-by-step explanation:

Sequence,S: 8,14,22,32 ,44, 58, 74...

First differences of S: 6,8,10,12,14,16,...

Second differences of S: 2,2,2,2,2,2,....

It is indeed a quadratic since the 1st differences that are the same are the second differences.

So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.

This means our quadratic it is in the form

y=an^2+bn+c where c=4.

So we have y=an^2+bn+4.

Now we can find a and b using two points from our sequence to form a system of equations to solve.

(1,8) gives us 8=a(1)^2+b(1)+4

Simplifying gives 8=a+b+4

Subtracting 4 on both sides gives: 4=a+b

(2,14) gives us 14=a(2)^2+b(2)+4

Simplifying gives 14=4a+2b+4

Subtracting 4 on both sides gives 10=4a+2b

So we have the following system to solve:

4=a+b

10=4a+2b

I'm going to solve using elimination/linear combination style.

Dividing second equation by 2 gives the system as:

4=a+b

5=2a+b

Subtract the 2nd equation from the first gives:

-1=-1a

This implies a=1 since -1=-1(1) is true.

If a+b=4 and a=1, then b=3. Because 3+1=4.

So the equation is y=1n^2+3n+4 or y=n^2+3n+4.

Answer:

See explanation

Step-by-step explanation:

the length of a rectangle is 7 feet less than three times it’s width. if the area of the rectangle is 180 ft, find the dimensions of the rectangle.

Width = x

Length = 3x - 7

Area of a rectangle = length × width

180 = (3x - 7) * x

180 = 3x² - 7x

3x² - 7x - 180 = 0

Using quadratic formula

a = 3

b = -7

c = -180

x = -b ± √b² - 4ac / 2a

x = -(-7) ± √(-7)² - 4(3)(-180) / 2(3)

x = 7 ± √49 - (-2160) / 6

= 7 ± √49 + 2160 / 6

x = 7 ± √2209/6

= 7 ± 47 / 6

= (7 + 47)/6 or ( 7 - 47)/6

= 54/6 or -40/6

x = 9 or -6.67

x cannot be negative

Therefore,

x = 9 ft

Width = x = 9 ft

Length = 3x - 7

=3(9) - 7

= 27 - 7

= 20 ft

Step-by-step explanation:

First, we put the expressions in multiplication form:

(7x2y3)×(3x5y8)(7x2y3)×(3x5y8)

We multiply like terms:

(7x2×3x5)(y3×y8)(7x2×3x5)(y3×y8)

We multiply the coefficients and add the exponents:

21x2+5y3+821x2+5y3+8

Solving, we obtain:

21x7y11

Hello!

[tex]\large\boxed{21x^7y^{11}}}[/tex]

(7x²y³)(3x⁵y⁸)

Multiply by ADDING exponents with the same base:

(7 * 3) (x² * x⁵) (y³ * y⁸)

21 * x² ⁺ ⁵ * y³ ⁺ ⁸

Simplify:

21 * x⁷ * y¹¹

21x⁷y¹¹

Answer:

shift

Step-by-step explanation:

shift

Answer:

magnitude is 4.5 lb, and the direction is given by the angle 250°.

Step-by-step explanation:

We can see that the magnitude is 4.5lb (it is already written in the graph, the "distance" between R and T).

To find the angle, remember that the angle is measured counterclockwise from the positive x-axis.

We can see that the angle, measured clockwise, is 110°

And the angle of a complete revolution is 360°

The sum of the angle measured clockwise and the angle measured counterclockwise should be equal to 360°

Then the angle, measured counterclockwise is given by:

360° - 110° = 250°

Then the magnitude is 4.5lb, and the direction is given by the angle 250°.

Answer:

[tex]\frac{6}{5}[/tex] of an hour = 1 1/5 hour = 72 minutes

Step-by-step explanation:

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

it would take Ted and Jacob 1.2 hours, or 1 hour and 12 minutes, to clear the field together.

Two or more expressions with an Equal sign is called as Equation.

Let's start by using the formula for the combined work of two people:

1/t = 1/3 + 1/2

Here, t represents the number of hours it would take to clear the field together.

To solve for t, we can first find a common denominator for the fractions on the right-hand side of the equation:

1/t = (2/6) + (3/6)

1/t = 5/6

To isolate t on one side of the equation, we can take the reciprocal of both sides:

t/1 = 6/5

t = 1.2

Therefore, it would take Ted and Jacob 1.2 hours, or 1 hour and 12 minutes, to clear the field together.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Answer:  90,  and 1600 degrees.2500

Step-by-step explanation:

If the angles are proportional to 3, 4, 5,Then the angle measures are 3x, 4X and 5X

Step-by-step explanation:

Answer:

45  60  75

Step-by-step explanation:

Let's call the angles 3 x , 4 x and 5 x

They must add up to 180 o in a triangle, so:

3 x + 4 x + 5 x = 12 x = 180 → x = 180 / 12 = 15 So the angles are:

3 ⋅ 15 = 45 o 4 ⋅ 15 = 60 o 5 ⋅ 15 = 75 o Check answer:

45 + 60 + 75 = 180

Answer:

Step-by-step explanation:

Slope is the rate of change. For us, this rate of change is inches of water per minute. If this rate of change is 2/1, that means that the rate is changing 2 inches every minute (aka The height of the water increases 2 inches per minute, first choice in your list of possibilities).

Answer:

50.265

Step-by-step explanation:

Area is radius square times pi. Radius is half of diameter .Diameter is 8 inches. Radius is 4 inches. 4 squared is 16. 16 times pi is 50.265

Answer:

I believe the question is incorrect

Step-by-step explanation:   7  1  17  02

take the english statement and convert it to math

sum of the squares of two positive integers is 183      x² + y² = 183

one integer is 3 less than the other     x = y - 3      x is three less than y  

find the larger integer   use the two equations to solve for y the larger number

x² + y² = 183 and x = y - 3

(y - 3)² + y² = 183

y² - 6y + 9 + y² = 183

2y² - 6y = 182 - 9

2y² - 6y = 173  

2y² - 6y - 173  = 0  

this equation does not result in an integer

2y² - 6y - 173 = 0

According to the question

b= 35 and (8,21) lies on the ellipse

After calculation we get a= 10

equation for the ellipse.

[tex] \frac{ {x}^{2} }{100} + \frac{ {y}^{2} }{1225} = 1[/tex]

Answer:

1.12 Units

Step-by-step explanation:

1. Use cos(56°) = x/2

Make sure your calculator mode is in deg (degree) not rad(radians)

2.  2(cos(56°)) = x

3. x = 1.118385807

4. Round up to get 1.12 Units

Answer:

15 x 150 = 2250

2250 + 1000 = 3250

you make $3250,00

Answer:

17

Step-by-step explanation:

Answer:

5n² + 8bnv² + 3b²v^4

Step-by-step explanation:

(n+bv²) (5n+3bv²)

5n² + 3bnv² + 5bnv² + 3b²v^4

5n² + 8bnv² + 3b²v^4

Answer:

Hi there!

Recall that slope-intercept form is:

y = mx + b

Where m = slope

In this instance, we are given a slope of 4,

therefore:

y = 4x + b

Substitute in the x and y coordinates of the point given:

0 = 4(3) + b

0 = 12 + b

Substract 12 from both side:

-12 = b

Therefore, the equation would be:

y = 4x - 12

Graph the equation by finding x and y values or using a calculator:

x = 0, y = 4(0) - 12 = 12 (0, 12)

x = 1, y = 4(1) - 12 = - 8 (1, -8)

x = 2, y = 4(2) - 12 = - 4 (2, -4)

x = 3, y = 4(3) - 12 = 0 (3, 0)

And so forth:

Thanks<8

Answer:

x = .464

Step-by-step explanation:

Assumptions: Equation is [tex]-2x^3+20[/tex]. Thus having an asymptote at the value x=0.

Answer:

2/6 chance the dice be rolled to the total of 12

Answer:Steve age will be 15 y.o

Step-by-step explanation:

Answer:

[tex]\frac{8}{5}[/tex]

Step-by-step explanation:

The constant of direction variation givens a proportion that is maintained by both x and y values for all points of a line that it passes through.

Usually represented with the variable [tex]k[/tex], it is given by:

[tex]\frac{y}{x}=k[/tex] for coordinates (x, y).

This relationship can be written as [tex]y=kx[/tex] which is also the layout for a proportional relationship.

Since coordinates are written (x, y), for point (5, 8), substitute [tex]x=5, y=8[/tex] to get the constant of variation:

[tex]8=5k,\\k=\boxed{\frac{8}{5}}[/tex]

Answer:

8/5

Step-by-step explanation:

Given that y varies directly with x , therefore ,

[tex]\implies y \propto x[/tex]

Let k be the constant . Therefore ,

[tex]\implies y = k x[/tex]

When the point is (5,8) ,

[tex]\implies 8 = k * 5 \\\\\implies \underline{\underline{\boxed{ k =\dfrac{8}{5}}}}[/tex]

Hence the constant of variation is 8/5.

Answer:

20 Lines

Step-by-step explanation:

According to the Question,

Now,  the total pairs of points which can be formed is 9

And, the line passing through 2 such points 9c2 = 9! / (2! x 7!) = 9x4 ⇒ 36

Here, We have overcounted all of the lines which pass through three points.

And, each line that passes through three points will have been counted 3c2 = 3! / 2! ⇒ 3 times

Now, the sides of the square consist of 3 points. We have counted each side thrice, so 4*2 are repeated.

Answer:

80 degrees

Step-by-step explanation:

First find the the angles N and L:

5x=3x+40

2x=40

x=20

m<N= 100 m<L=100

Now we know that the sum os all Interior angles of a parallelogram is 360

and you know that opposite sides are equal

hence,

2y= 360-2(100)   y being angle M (or o)

2y= 160

y=80

Answer:

1/6 of the bread

Step-by-step explanation:

Given data

Let the amount of the loaf of bread be 1

But they are expected to share half

hence the amount to be shared is= 1/2 bread

The number of children is 3

Hence

=1/2/3

=1/2*1/3

=1/6 bread

Hence each child will get 1/6 of the bread

Answer:

The equation of line which is parallel to the given line is y =  3 x + k.

Step-by-step explanation:

The equation of the line is

y = 3 x - 8

Compare with the standard equation

y = mx + c

The slope of line is

m = 3

So, the line parallel to the given line is

y = 3 x + k

where, k is any real number.

Answer:

40%

Step-by-step explanation:

2 / 5 = 0.40

0.40 x 100 = 40%