f(x)=x² + 6x + 2; Find f(-6)

Graph of the given function f(x) = ( 1 / 3 )x + 1 and g ( x ) = f ( 6x ) is attached for the different values of x and y.  Graph of both the function f(x) and g(x) intersect at point ( 0, 1 ).

As given in the question,

Given function are as follow:

f(x) = ( 1 / 3 )x + 1

g ( x ) = f ( 6x )

Calculate the function g(x) for f ( 6x ) is given by,

g ( x ) = f ( 6x )

⇒ g ( x ) = ( 1 / 3 )6x + 1

⇒ g ( x ) = 2x + 1

Substitute the value of x to get value of f ( x ) and g ( x ) and put it on graph.

After putting all the values of f(x) and g(x) .

Graph intersect at ( 0, 1 )

Graph is attached.

Therefore, graph of the given function f(x) = ( 1 / 3 )x + 1 and g ( x ) = f (6x ) is attached for the different values of x and y.  Graph of both the function f(x) and g(x) intersect at point ( 0, 1 ).

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a) The general equation is:

y = m*(x - h) + k

b) The slope is -3

c) the point-slope form is: y = -3*(x - 6) + 1

d) The standard form is: y + 3x = 19

We will write a linear equation that relates two variables x and y, and the slope-point form is given by:

y = m*(x - h) + k

Where m is the slope, and (h, k) is a point on the line.

Particularly, if a line passes through two points (a, b) and (c, d), then the slope of that line is:

m = (d - b)/(c - a)

In this case, the line passes through (6, 1) and (5, 4), then the slope is:

m  = (4 - 1)/(5 - 6) = 3/-1 = -3

Now  we can use one of the given points to write the line in the point-slope form, I will use (6, 1) to get:

y = -3*(x - 6) + 1

Now we want to write this in standard form.

Expanding the right side we get:

y = -3x + 18 + 1

y = -3x + 19

Adding 3x in both sides we get:

y + 3x = 19

This is the standard form.

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Answer:

a

Step-by-step explanation:

f(x) = y, so y=1-x. the slope is always infront of the x, so if there is nothing infront of x then it'll be a 1. so in this cas slope is a -1 and the y intercept is 1.

Answer:

There are 10 marbles, 2 are yellow

The probability would be 2:10 but in simplest form 1:5

The probability of picking both the same = 1:5 x 1:5 = 1:25

Step-by-step explanation:

Answer:26

Step-by-step explanation:

The measure of non reflex angle DOB in degrees is 140°

From the given information, we are to determine the measure of the non reflex angle DOB

From the given information,

m reflex ∠ DOB = 3.5y

and

m ∠ AOD = y

First, we will determine the value of y

From Linear pair theorem, we can write that

3.5y + y = 180°

4.5y = 180°

y = 180°/4.5

y = 40°

Also,

y + m ∠ DOB = 180° (Linear pair theorem)

Thus,

40° + m ∠ DOB = 180°

m ∠ DOB = 180° - 40°

m ∠ DOB = 140°

Hence, the measure of ∠ DOB is 140°

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Answer:

10,101

Step-by-step explanation:

Percent (%) means 'out of one hundred'

29.5%= 29.5/100 'out of one hundred'

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

How to increase the number 7,800

by 29.5% of it's value?

1.) Calculate the new value of the number increased by the percentage of it's initial value

The new value=

7,800+ The value of the percentage increase=

7,800 + (29.5% x 7,800) =

7,800 + 29.5% x 7,800=

(1 + 29.5%) x 7,800=

(100% + 29.5%) x 7,800=

129.5% x 7,800

129.5 ÷ 100 x 7,800=

129.5 x 7,800 ÷ 100=

1,010,100 ÷ 100=

10,101

-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-

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According to the Pythagoras theorem, the value of the other leg is, 15.7 cm

Pythagoras theorem:

Pythagoras theorem defines that  the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given,

One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.

Here we need to find the measure of the other leg and round off it to nearest tenth.

Though the given question, we know that the value of

Hypotenuse = 16 cm

one leg = 3cm,

Then let us consider the length of the other leg as x.

So, according to the Pythagoras theorem,

It can be calculated as,

=> hypotenuse² = one leg² + other leg²

=> 16² = 3² + x²

=> 256 = 9 + x²

Here we need the value of x, so it can be rewritten as,

=> 247 = x²

=> x = √247

When we take square root for 247, then we get the value of x as,

=> x = 15.716

When we round off it to the nearest tenth then we get the value of another leg as 15.7 cm.

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If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°  then the height of the flagpole will be 24.8 m .

In the question ,

it is given that ,

the length of the shadow of the flag pole = 18m

the angle of "elevation" of the sun = 54°

let the height of the flagpole be = "x" ,

The flagpole and the shadow form a right triangle ,

So , tan(54°) = (height of flag pole)/(shadow of flagpole)

Substituting the values from above ,

we get ,

tan(54°) = x/18

on cross multiplication ,

x = 18 × tan(54°)

x = 18 × 1.3763

x = 24.7734

x ≈ 24.8

Therefore , If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°  then the height of the flagpole will be 24.8 m .

The given question is incomplete , the complete question is

A flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°. What is the height of the flagpole ?

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Answer:

569.80

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

f(x) = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{8}{9}[/tex] and c = - 4 , then

f(x) = [tex]\frac{8}{9}[/tex] x - 4 ← equation of line

The value of the unknown variable in the ordered pair is 8

From the question, we have the following ordered pairs that can be used in our computation:

(r, 3), (5, 9)

Also, we have

m = 2

The meaning of the above notations are

Ordered pairs (x, y) = (r, 3), (5, 9)

Slope, m = 2

The slope of points is calculated using the following slope equation

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (r, 3), (5, 9) and m = 2

Substitute the known values in the above equation, so, we have the following representation

(9 - 3)/(r - 5) = 2

Evaluate the difference

This gives

6/(r - 5) = 2

Divide both sides by 2

So, we have

3/(r - 5) = 1

Cross multiply

r - 5 = 3

So, we have

r = 3 + 5

Evaluate the sum

r = 8

Hence, the value of r is 8

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Possible question

What is the value of r using the following points and slope

(r, 3), (5, 9), m=2

The value of 'E' in the algebraic equation is -2

Algebraic equation is a mathematical statement in which two expressions are set equal to each other.

Therefore, let solve for 'E' in the equation 0.75(8+e)=2−1.25e

Use 0.75 to open the bracket

6 + 0.75e = 2 -1.25e

Collect the like terms

0.75e+1.25e = 2-6

2e = -4

Divide both sides by 2

2e/ 2 = -4/2

e =-2

Therefore, the value of 'E' in the equation is -2

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If you work $19.50 per hour and you work 40 hours a week, you need to multiply 19.50 by 40 to get your answer

19.50 x 40 = $ 780 a week.

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The radius of the circle to the nearest 10th is 2.0537.

Given:
In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1.

we know that,

radians = arc / radius

radius = arc/radians

= 19.1/9.3

= 191/10/93/10

= 191/93

≈ 2.0537

Therefore the radius of the circle to the nearest 10th is 2.0537.

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Answer:

2m/4m = 9m/xm

2m(xm) = 4m(9m)

2xm = 36m

The population for 2015 is 1,640,000 ,so option A is correct.

Given:

The projected population in thousands for a city over the next several years can be estimated by the function P(x)=x³ + 2x² - 8x + 520.

where x is the number of years since 2005.

x = 2015 - 2005

x = 10

P(x) = x³ + 2x² - 8x + 520.

= [tex]10^{3} +2(10^{2} )-8*10+520[/tex]

= 1000 + 2*100 - 80 + 520

= 1520 + 200 - 80

= 1720 - 80

= 1640.

Given the projected population in thousands so = 1640 * 1000

= 1640000.

Therefore The population for 2015 is 1,640,000 ,so option A is correct.

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{10})\hspace{10em} \stackrel{slope}{m} ~=~ 8 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 8}(x-\stackrel{x_1}{2}) \\\\\\ y-10=8x-16\implies {\Large \begin{array}{llll} y=8x-6 \end{array}}[/tex]

Answer:

18 hours of footage.

Step-by-step explanation:

This is a LCM problem. The least common multiple of 6 and 9 is 18. The minimum amount of hours needed to see the sparrow and butterfly at the same time is 18.

The (0, 2) and (3•π, 6) minimum and maximum points on the graph of the sinusoidal function indicates that the function is as follows

[tex]y = 2\cdot sin\left(\dfrac{1}{3} \times \left(x - \dfrac{3\times \pi}{2} \right)\right) + 4[/tex]

A sinusoidal function is a function based on the trigonometric function of sine.

The points on the graph of the sinusoidal function are;

Minimum point of the function; (3•π, 6)

Maximum point of the function; (0, 2)

The general form of the equation of a sinusoidal function is presented as follows;

The sinusoidal function equation is; y = a×sin(b×(x - h)) + k

The amplitude, a, is half the distance between the maximum and minimum points, therefore;

a = (6 - 2)÷2 = 2

a = 2

From the information in the question, when x = 0, y = 2

Plugging in the values of x = 0, y = 2in the equation, y = a×sin(b×(x - h)) + k, produces;

2 = 2×sin(b×(0 - h)) + k

The point (0, 2) is a minimum point, therefore; sin(b×(0 - h)) = -1

2 = 2×sin(b×(0 - h)) + k = 2×(-1) + k = -2 + k

k = 2 + 2 = 4

At the minimum point the value of sine is -1, which indicates that the value of the argument, (b•(0 - h)) = -π/2

Therefore; -b•h = -π/2

h = π/(2·b)

At the maximum point, (b×(x - h)) = π/2

Therefore; (b×(3×π - π/(2×b))) = π/2

b = 1/3

Therefore;

h = π/(2×b) = 3×π/2

y = 2×sin((1/3)×(x - 3×π/2)) + 4

The function is; y = 2×sin((1/3)×(x - 3×π/2)) + 4

The formula of the function for the graph is therefore; y = 2×sin((1/3)×(x - 3×π/2)) + 4

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The equation of the line in slope-intercept form is y = -5x

From the question, we have the graph that can be used in our computation

On the graph, we have the following points

(0, 0) and (-1, -5)

Start by calculating the slope using

Slope = (y₂ - y₁)/(x₂ - x₁)

Where,

(x, y) = (0, 0) and (1, -5)

So, we have

Slope = (-5 - 0)/(1 - 0)

This gives

Slope = -5

The equation of the line is then calculated as

y= Slope * (x - X) + Y

So, we have

y = -5 * (x - 0) + 0

Evaluate

y = -5x

Hence, the equation is y = -5x

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Answer:

The number is 27.

Step-by-step explanation:

Since the units digit has to be 5 more than the tens digit, there are only four possible two-digit numbers which satisfy this condition. They are 16, 27, 38, and 49.

Next, the digits can be added and multiplied by three to check that the answer is the same two-digit number.

3 (1 + 6) = 21 does not work because 16 isn't the same as 21.

3 (2 + 7) = 27 does work because 3 * 9 is 27.

3 (3 + 8) = 33

3 (4 + 9) = 39

Answer:

1. $5

2. $1 per mile

3.y=x+5

Step-by-step explanation:

1. If you look at the graph you can see that the cost for 0 miles with the Green Cab is $5

2.If you look at the graph, for each mile traveled, the cost is $1

3. Since for each increase 1 increase in x, y increases by the same amount, the slope is 1

y=mx+b is the slope intercept form

m=slope

b=y intercept

since we know the slope is 1 we can put it in

y=1x+b

=y=x+b

to find the y intercept we can look at the graph and see what y equals when x is 0.

the y intercept is (0,5)

we can put that in so the equation in slope intercept form is

y=x+5

The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%.

Compound interest is applicable when there will be a change in the principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

As per the given,

Principle amount P = $2800

Rate of interest = 6% = 0.06

Compound quarterly n = 4

Time period T = 5 yeras

a)

Total amount = P(1 + R/n)^(nT)

Total amount = 2800(1 + 0.06/4)^(4 x 5)

Total amount = 2800(1.015)^20

Total amount = $3771.19

b)

Let's say the equivalent annual interest rate is r.

n = 1

3771.19 = 2800(1 + r/1)^(1 x 5)

3771.19 = 2800(1 + r)^5

1.061 = 1 + r

r = 0.06136 = 6.136%

Hence"The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%".

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Answer:

y + 8 = -3/11(x+7)

Step-by-step explanation:

What is the point-slope form formula?

y-y1=m(x-x1) -------> y+8=-3/11(x+7)

We can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:

A parabola refers to the shape that traces the equation of the form ax² + bx + c.

A parabola's directrix is a vertical or horizontal line that never contacts the parabola and is located at p distance from the vertex and 2p distance from the focus.

The parabola created when the directrix is on the y coordinate called a vertical parabola.

If the directrix value is greater than the corresponding focus or vertex, there will be a negative p and the parabola will face downhill.

If the directrix value is less than the corresponding focus or vertex, there will be positive p and the parabola will face up.

From the given definition of the directrix, we can find the value of p;

2p = y coordinate of focus - equation of the directrix

2p = 1 - (-1)

2p = 2

p = 1

Vertex, v(h, k) compared with f(h, k + p), we will get;

k + p = 1

k = 0

Therefore, the vertex is (-8, 0).

Thus, we can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:

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By evaluating The Triple Integral. Triple Integral 7x2 DV, Where T Is The Solid Tetrahedron With Verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), And (0, 0, 1) the value calculated is 7/60.

Given:

= ∫∫∫7[tex]x^{2}[/tex] dV

T(x,y,z) : 0≤x≤1; 0≤y≤1-x; 0≤z≤1-x-y]

apply limits and solving we get:

= 7/2([tex](x^{3} /3+x^{5} /5-x^{4}/2)[/tex]

= 7/2(1/3+1/5-1/2)

= 7/2(1*5+1*3/15 - 1/2)

= 7/2(8/15 - 1/2)

= 7/2(16 - 15/30)

= 7/2*1/30

= 7/60

Therefore after evaluating the value of triple integral is 7/60.

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Answer:

8

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + (4√3)^2 = c^2

16 + 48 = c^2

64 = c^2

√64 = c

8 = c