Kelly drank .86 of her Gatorade and John drank 7/8 of his Ginger Ale. Who drank less?

The vertex form of the quadratic equation is f(x) = -3(x - 2)² + 5. The coordinates of the vertex are (2, 5).

We are given a quadratic function. The equation of the quadratic function is f(x) = -3x² + 12x - 7. We need to convert the equation to vertex form. We can convert a quadratic equation to its standard vertex form by "completing the square" method. The calculations are done below.

f(x) = -3x² + 12x - 7

f(x) = -3(x² - 4x) - 7

f(x) = -3(x² - 4x + 2² - 2²) - 7

f(x) = -3(x² - 4x + 2²) - 7 + 3*2²

f(x) = -3(x - 2)² - 7 + 12

f(x) = -3(x - 2)² + 5

The coordinates of the vertex are (2, 5).

To learn more about vertex, visit :

https://brainly.com/question/29030495

#SPJ1

Answer:

what are the instructions

Step-by-step explanation:

please repost with instructions

Answer:26

Step-by-step explanation:

Answer:

1, 2, 4, 7,  14 and 28

Step-by-step explanation:

1 x 28 = 28

2 x 14 = 28

4 x 7 = 28

Answer:

 1, 2, 4, 7, 14 and 28

Step-by-step explanation:

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

The given logarithmic equation solved for x is x = 10

From the question, we are to solve the given logarithmic equation.

The given logarithmic equation is

log((4x)/(8)) = log(x - 5)

To solve the given logarithmic equation, we will determine the value of the unknown variable.

The unknown variable in the equation is x.

From one of the rules of logarithm, we have that

If logₓY = logₓZ

Then,

Y = Z

Thus,

From log((4x)/(8)) = log(x - 5)

We can write that

(4x)/(8) = (x - 5)

Now, solve for x

(4x)/(8) = (x - 5)

Multiply both sides by 8

8 × (4x)/(8) = (x - 5) × 8

4x = 8x - 40

Subtract 8x from both sides of the equation

4x - 8x = 8x - 8x - 40

-4x = -40

Multiply both sides by -1

-1 × -4x = -1 × -40

4x =40

Divide both sides by 4

4x/4 = 40/4

x = 10

Hence, the solution of the equation is x = 10

Learn more on Solving logarithmic equation here: https://brainly.com/question/237323

#SPJ1

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.

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:

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:

To learn more about directrix of a parabola visit:

https://brainly.com/question/29321376

#SPJ1

1/2 x + 8 = 15  Grace will pay for a student ticket

the question requests the cost of a "student ticket." Because we don't know, let's assume the student ticket price is "x" dollars.

Because we know from the question that "the price of an adult ticket is half the price of a student ticket plus $8.00," we can represent the adult ticket price as follows:

1/2 x + 8

If we also get "An adult ticket costs $15.00" from the question, we can write the equation as:

1/2 x + 8 = 15

Grace will pay for a student ticket

To learn more about Cost:

https://brainly.com/question/15135554

#SPJ4

Step-by-step explanation:

so, it is

3³ × (3⁴)^(0.5) ?

remember, when multiplying exponents of the same base, we add the exponents : e.g.

a⁵ × a³ = a⁸

when we have exponents in exponents we multiply the exponents : e.g.

(a³)⁴ = a¹²

now, also remember the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

now, let's look at our expression again :

3³ × (3⁴)^(0.5)

since we only want to simplify and not to calculate, we leave (3⁴) alone, because the only thing we could do would be to actually calculate 3⁴.

so,

(3⁴)^(0.5) = 3^(4×0.5) = 3²

and then,

3³ × 3² = 3^(3+2) = 3⁵

so, the simplified expression is 3⁵.

which is 243 ...

Answer:

1. 190 degrees

2.

For the red triangle

-2,4, -4,2 -2,1

For the blue triangle

-2,-5 -5,-5 -7,-4

I don't know if this is correct but I hope this helps :)

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

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

I hope this was helpful!

Answer:

569.80

Step-by-step explanation:

The next term of the given geometric series is the fifth term which is; a₅ = 4

We are given the geometric series as;

1024, -256, 64, -16,.....

The formula to find the nth term of a geometric series is;

aₙ = ar^(n - 1)

where;

a is first term

r is common ratio

n is position of term

Thus, from the given series, we have that;

a = 1024

r = -256/1024

r = -1/4

Thus, the formula for the nth term of the series is;

aₙ = 1024(-¹/₄)^(n - 1)

Next term is the fifth term and so we have;

a₅ = 1024(-¹/₄)^(5 - 1)

a₅ = 1024(-¹/₄)^(4)

a₅ = 4

Read more about nth term of geometric series at; https://brainly.com/question/24643676

#SPJ1

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 ).

Learn more about graph here

brainly.com/question/17267403

#SPJ1

Answer: I believe y=1x+0 (or y=x)

Step-by-step explanation: if you copy the slope and make the line go through (2,2), you get this line.

Answer:

Step-by-step explanation: If the square is 30 ft on one side the other side must be too. So 30x30 = 900. Now, we know the rectangle must also be 900 in area. So, the width must be 10feet and the length must be 90ft because 10x90 is also 900. How I got the length? I did 10x2+70.

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.

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

[tex]x=1+5\sqrt{2}, 1-5\sqrt{2}[/tex]

Step-by-step explanation:

[tex](x-1)^2=50 \\ \\ x-1=\pm 5\sqrt{2} \\ \\ x=1 \pm 5\sqrt{2}[/tex]

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)

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

Learn more about the sinusoidal function in mathematics here:

https://brainly.com/question/26288131

#SPJ1

The future value of ordinary annuity $1000 a year for 10 years at 10% year compounded annually is $15937.

The value of a sum of money that will be paid on a specified date in the future is known as its future value. Since each payment is made at the end of a period, the formula for the future value of an ordinary annuity refers to the value on a specified future date of a series of periodic payments.

Given,

R=$1000, n=10, i=10%=10/100=0.1

The formula to calculate the future value is

FV=R[(1+i)^n-1]/i

[tex]FV=R(\frac{(1+i)^{n} -1}{i})[/tex]

[tex]FV=1000(\frac{(1+0.1)^{10} -1}{0.1})[/tex]

[tex]FV=1000(\frac{(1.1)^{10} -1}{0.1})[/tex]

[tex]FV=1000(\frac{1.593742}{0.1})[/tex]

[tex]FV=1000\times15.9374[/tex]

[tex]FV=15937.4[/tex]

Future Value approximately equal to $15937.

Therefore, the future value of the ordinary annuity $100 a year for 10 years at 10% compounded annually is $15937, Option c is the correct answer.

To learn more on future value here:

https://brainly.com/question/8286272#

#SPJ4

[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]

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

Read more about slopes at

https://brainly.com/question/27630604

#SPJ1

Possible question

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

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

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°

Lear more on Calculating the measure of angles here: https://brainly.com/question/28429456

#SPJ1

Answer:

the answer i think it is 432