What is the vertex form of y=x^2-6x+6

Answer:

All real numbers less than or equal to 7

Step-by-step explanation:

we have

f(x)=-(x+3)^2+7

we know that

The function is a vertical parabola open downward

The vertex is the point ( -3,7 )

The vertex is a maximum

The range is the interval-----------> (-∞,7]

That means

All real numbers less than or equal to

The range of the function is all real numbers less than or equal to 7. The correct option is A.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The given function is f(x)=-(x+3)² + 7. draw the graph of the function. It is observed that the function is a vertical parabola open downward.

The vertex is the point ( -3,7 ). The vertex is a maximum and the range is the interval is (-∞,7).

Therefore, the range of the function is all real numbers less than or equal to 7. The correct option is A.

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Answer:

5

Step-by-step explanation:

f(x)= 3х^2

g(x) = 4х^3 + 1

(f•g)(x) = (3x^2) * (4x^3+1)

           = 12x^(2+3) + 3x^3

          = 12 x^5 + 3x^2

The degree is the highest power of x, which is 5

It would be any number with a - inside the sqrt, since taking the square root of a negative number gives a multiple of i. Using, this, we see that the second one, fourth, fifth, and sixth ones are correct.

Hope this helps!

Plz Brainliest

Answer:

Option C (The mean would decrease).

Step-by-step explanation:

In this question, there are 16 observations and their mean is 80. There is an outlier which has the value 91. This means that the outlier is on the greater side of the mean. The formula for mean is:

Mean = Sum of observations/Number of Observations.

Sum of observations can be calculated by substituting the values in the above formula.

80 = Sum/16.

Sum = 80*16 = 1280.

Subtracting 91 from the total sum will give the sum of rest of the 15 non-outlier values. Therefore 1280 - 91 = 1189.

Calculating the mean of the 15 values:

Mean = 1189/15 = 79.267 (correct to 3 decimal places).

It can be seen that removing the outlier decreases the mean. Therefore C is the correct answer. The information regarding the median cannot be determined since actual values are not present, which are required to calculate the median. Therefore, C is the correct choice!!!

Answer: The mean would decrease

Step-by-step explanation:

Answer:

Fourth graph

Step-by-step explanation:

First:  some important housekeeping:

Please use " ^ " to denote exponentiation:  f(x) = (1/4)(4)^x, and enclose fractional coefficients such as 1/4 inside parentheses:  (1/4).

f(x) = (1/4)(4)^x is an exponential growth function; we know that because the base is greater than 1.  The graph is vertically compressed by a factor of 1/4.

You have four graphs from which to choose.

Eliminate the first and second graphs; they are of expo decay functions.

Evaluate f(x) = (1/4)(4)^x at x = 0 to find the y-intercept:

f(0) = (1/4)(4)^0 = 1/4

Both the 3rd and the 4th graphs go through (0, 1/4).  Good.

The 3rd graph shows the curve going through (3, 2).  Let's determine whether or not this point lies on f(x) = (1/4)(4)^x:

f(3) = (1/4)(4)^2  =  (1/4)(16) = 4.  No.

The 4th graph shows the curve going through (1, 1).  Does this point satisfy f(x) = (1/4)(4)^x?  f(1) = (1/4)(4)^1 = 1.  Yes.

The fourth graph is the correct choice.

The graph of the function is given below.

The graph will have the coordinates: (1, 1) and (2, 4).

Option D is the correct answer.

We have,

The graph of the function f(x) = [tex](1/4)4^x[/tex] is an exponential function.

The base of the exponential function is 4, and the function is raised to the power of x.

The coefficient (1/4) affects the rate of growth or decay of the function.

Here are some characteristics of the graph:

- As x approaches negative infinity, the function approaches 0, but it never reaches exactly 0.

- As x approaches positive infinity, the function grows without bound, becoming larger and larger.

- The graph is always positive, as the base 4 raised to any power is positive.

And,

When x = 1, f(x) = 1/4 x [tex]4^1[/tex] = 1/4 x 4 = 1

When x = 2, f(x) = 1/4 x 4² = 1/4 x 16 = 4

Thus,

The graph of the function is given below.

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To find the volume of a container in liters, knowing it holds 5.5 gallons, we use the conversion factor that 1 gallon is approximately 3.85 liters. Multiplying this conversion factor with the gallon, we obtain approximately 21.175 liters. Rounded to the nearest hundredth, the volume is 21.18 liters.

The subject of this question falls under Mathematics, particularly volume conversions. Given that 1 liter is approximately equal to 0.26 gallons, you want to find out the volume of a container, to the nearest hundredth of a liter, that holds 5.5 gallons.

To help you understand the process, here is a step-by-step explanation:

Remember, all conversions rely on the accuracy of the conversion factor. In this case, the conversion factor of 1 liter being approximately equal to 0.26 gallons was provided, and we took the inverse of it to convert gallons to liters.

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Answer:

$1279.25

Step-by-step explanation:

The first $6800 is multiplied by .085 to get the 8.5% they earned. This equals $570. After that, the remaining money is multiplied by .1275 to get the 8.5%+4.25%. This leaves you with $5500x.1275. This equals 701.25. $701.25+$570=$1279.25. Hope this helps :)

Answer:

-34

Step-by-step explanation:

a + b = -6

x + y + z = -2

We want 8a so multiply the first equation by 8

8( a + b) = -6*8

8a+8b = -48

We also want -7x so multiply the second equation by -7

-7(x + y + z) = -2*-7

-7x-7y-7z = 14

Add the two equations together

8a+8b = -48

-7x-7y-7z = 14

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

8a+8b-7x-7y-7z = -34

Rearranging the order

8a - 7x - 7z - 7y + 8b = -34

By substituting the provided equations into the final equation, we find that 8a-7x-7y-7z+8b equals -34.

The given equations are a + b = -6 and x + y + z = -2. The equation that we are asked to solve is 8a - 7x - 7z - 7y + 8b. We can rearrange this as 8(a+b) -7(x+y+z). By substituting the given equations into this we get, 8(-6)-7(-2) which equals -48+14=-34. Thus the answer to the equation 8a-7x-7y-7z+8b is -34.

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Answer:

D

Step-by-step explanation:

Trust me I did t on edge

The vertex form of the given parabola is  [tex]f(x) = 3(x + 4)^2 - 6[/tex], option A is correct.

The vertex form of a quadratic function is given by [tex]f(x) = a(x - h)^2 + k[/tex] where (h, k) represents the vertex of the parabola.

We have a = 3, which determines the steepness or "stretching" factor of the parabola.

If a is positive, the parabola opens upwards, and if a is negative, it opens downwards.

The vertex form tells us that the vertex of the parabola is at the point (-4, -6).

The value -4 represents the horizontal shift of the parabola, moving it 4 units to the left, while -6 represents the vertical shift, moving it 6 units downwards.

The vertex form is [tex]f(x) = 3(x + 4)^2 - 6[/tex].

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Answer:

B. 30.47.

Step-by-step explanation:

E(X) = 23*0.16 + 25*0.09 + 26*0.18 + 31*0.12+ 34*0.24+38*0.21

=  30.47.

Answer:

B. 30.47

Step-by-step explanation:

The mean for a discrete random variable when the probability distribution is given is calculated by the formula:

E(X) = ∑(x_i)*P(x_i)

So, from the values given in the table

[tex]E(X) = (23)(0.16) + (25)(0.09)+(26)(0.18)+(31)(0.12)+(34)(0.24)+(38)(0.21)\\= 3.68+2.25+4.68+3.72+8.16+7.98\\= 30.47[/tex]

Hence, the correct answer is:

B. 30.47 ..

The missing value in your ratio equation /60 = 85/100 is determined by cross-multiplying and solving the resulting equation. By doing this, we find that the missing value is 51.

This is a Mathematics question about ratios and finding missing values in ratios. Let’s solve the equation /60 = 85/100. The missing value in your ratio equation represents a fraction that is equivalent to 85/100. To find the missing value, start by cross-multiplying:

missing value * 100 = 60 * 85

missing value * 100 = 5100

Finally, divide both sides by 100 to isolate the missing value:

missing value = 5100 / 100 = 51.

Therefore, the missing value in your ratio equation is 51.

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Answer:

137 km/h and 151 km/h

Step-by-step explanation:

Let x km/h be the rate of slower train, then (x+14) km/h is the rate of faster train.

In 4 hours:

Since they meet in 4 hours, then they cover in total the whole distance between two cities, so

4x+4(x+14)=1152

Solve this equation for x:

4x+4x+56-1152

8x=1152-56

8x=1096

x=1096/8

x=137 km/h

x+14=137+14=151 km/h

Answer:

Domain will be x>0 or x<0 and x≠0

Step-by-step explanation:

f(x) = 3x

g(x) = 1/x

(gof)(x) = ?

(gof)(x) = g(f(x))

(gof)(x) = 1/(3x)

The domain of a function is a set of values for which the function is defined.

Find the points for which the function (gof)(x) = 1/(3x) is undefined.

if x=0 then the function is undefined.

So, domain will be x>0 or x<0 and x≠0

Answer:

He should turn 60° to head straight towards island B.

Step-by-step explanation:

Let us assume a Triangle ABC. Where side AB is the distance of the island A and island B and is 210 miles. AC is the wrong Course that a ship took and is 230 miles. CB is the course straight towards island B from C and equals 180 miles.

Finding angle C:

Now that the three sides of the triangle are known, we can find the angle that the ship should turn to using the law of cosines:

Cos C = (a²+b²-c²)/2ab   where c = AB, b = AC, a = BC

Cos C = (180² + 230² - 210²)/2*180*230

C = cos⁻¹ (41200/82800)

C = cos⁻¹ (0.4976)

angle C = 60.15

angle C = 60° approx

Answer:

119.84

Step-by-step explanation:

Side a = 180

Side b = 230

Side c = 210

Angle ∠A = 48.03° = 48°1'49" = 0.83829 rad

Angle ∠B = 71.81° = 71°48'36" = 1.25332 rad

Angle ∠C = 60.16° = 60°9'35" = 1.04998 rad

180-60.16=119.84

Answer:

The  solution is (7, 1).

Step-by-step explanation:

2x - 6y = 8    Multiply this by  -5.

5x - 4y = 31   Multiply this by 2.

-10x + 30y = -40  ...(1)

10x   - 8y = 62.........(2)

Adding (1) and (2):

22y =  22

y = 1.

Substitute for y in the first equation:

2x - 6(1) = 8

2x = 14

x = 7.

Final answer:

The system of equations 2x - 6y = 8 and 5x - 4y = 31 can be solved using the elimination method, yielding the solution (7, 1).

Explanation:

To solve the system of equations given by 2x - 6y = 8 and 5x - 4y = 31, we can use the substitution or elimination method.

Let's use the elimination method for efficiency:

The solution to the system of equations is the ordered pair (x, y) = (7, 1).

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

12.5 is a percent and percent's are always taken out of the 100. This means that one proportion will have 12.5 as the part and 100 as the whole

We want to know out of what number is 6 12.5% of. This means 6 is the part and the unknown (let's make this x) is the whole.

Here is your proportion:

[tex]\frac{6}{x} =\frac{12.5}{100}[/tex]

Now you must cross multiply

6*100 = 12.5*x

600 = 12.5x

To isolate x divide 12.5 to both sides

600/12.5 = 12.5x/12.5

48 = x

This means that 12.5% of 48 is 6

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The distance between Point S and Point T is 6.1 unit.

Step-by-step explanation:

Given : The coordinates of Point S are [tex](\frac{2}{5} , 9\frac{1}{8} )[/tex]. The coordinates of Point T are [tex](-5\frac{7}{10},9\frac{1}{8})[/tex].

To find : What is the distance between Point S and Point T?​

Solution :

The distance formula between two point is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The point S is [tex](x_1,y_1)=(\frac{2}{5} , 9\frac{1}{8} )=(\frac{2}{5} ,\frac{73}{8} )[/tex]

The point T is [tex](x_2,y_2)=(-5\frac{7}{10},9\frac{1}{8})=(-\frac{57}{10},\frac{73}{8})[/tex]

Substitute the value,

[tex]d=\sqrt{(-\frac{57}{10}-\frac{2}{5})^2+(\frac{73}{8}-\frac{73}{8})^2}[/tex]

[tex]d=\sqrt{(\frac{-57-4}{10})^2+(0)^2}[/tex]

[tex]d=\sqrt{(\frac{-61}{10})^2+0}[/tex]

[tex]d=\frac{61}{10}[/tex]

[tex]d=6.1[/tex]

Therefore, the distance between Point S and Point T is 6.1 unit.

Final answer:

The distance between Point S (2/5, 9 1/8) and Point T (-5 7/10, 9 1/8) is 6.1 units.

Explanation:

The distance between two points in a Cartesian coordinate system is calculated using the distance formula, which is derived from the Pythagorean theorem.

In this case, the y-coordinates of Points S and T are the same, so the distance is simply the difference in the x-coordinates.

To find the distance, subtract the x-coordinate of Point S from the x-coordinate of Point T and take the absolute value:

Distance = |(2/5) - (-5 7/10)|

To simplify, first convert -5 7/10 to an improper fraction: -5 7/10 = -57/10

Distance = |(2/5) - (-57/10)|

Next, find a common denominator and subtract the fractions:

Distance = |(4/10) - (-57/10)|

Distance = |61/10|

Distance = 6 1/10 or 6.1 units

The distance between Point S and Point T is 6.1 units.

Answer:I said B(please don't come for me)Step-by-step explanation:I selected my answer because Canada is apart North America and Chicago, Miami,Tokyo and Mexico are cities and India is a country

Answer:

it would be 30

Step-by-step explanation:

Answer:

4/5 or -4/5

Step-by-step explanation:

We are going to use the Pythagorean Identity:

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

We are given the value of [tex]\sin(\theta)[/tex] which is 3/5 so plug that in:

[tex](\frac{3}{5})^2+\cos^2(\theta)=1[/tex]

Simplify:

[tex]\frac{9}{25}+\cos^2(theta)=1[/tex]

Subtract 9/25 on both sides:

[tex]\cos^2(\theta)=1-\frac{9}{25}[/tex]

[tex]\cos^2(\theta)=\frac{16}{25}[/tex]

Take the square root of both sides:

[tex]\cos(\theta)=\pm \sqrt{\frac{16}{25}}[/tex]

[tex]\cos(\theta)=\pm \frac{4}{5}[/tex]

Answer:

Step-by-step explanation:

87.5% is the answer . hope this helps.

Answer:

87.5

7=x%(8)

7/8=x%

87.5=x

Answer:

The answer is C: He graphed the function y=cot(2x-pi/4)+1 correctly but it was not the right function to graph. He should have graphed y=cot(2x-pi/2)+1.

Step-by-step explanation:

The reason why it is C is because we want a period of pi/2, which would mean that b must be equal to 2 (if you use the period equation for tan and cot, pi/b, in order for pi/b to be equal to pi/2, b must be 2). The form for a trigonometric function is: y = acotb(x-h)+k. And if you notice, the equation he uses has the b already distributed inside the parenthesis, which means that both x and h were already multiplied. If we divide 2x and pi/4 by two, we get x, but h becomes pi/8, which is not equal to pi/4 as required by the problem. The correct equation would be: y = cot(2x-pi/2)+1 because when you divide out the two from inside the parenthesis, you get: y = cot2(x-pi/4)+1, which is the equation that he should've graphed.

I hope this helped you out!

If you have any further questions don't be afraid to ask.

Chris made a mistake by multiplying the x variable by 2 instead of π/2 for the horizontal compression and by not correctly adjusting the phase shift for the horizontal translation. The correct transformed function to meet the desired criteria should be y = cot((π/2)x - π/4) + 1.

Chris wanted to alter the graph of the parent function Y = cot(x) to achieve a certain transformation: a horizontal compression for a new period of 2/π units, a horizontal translation of π/4 units to the right, and a vertical translation of 1 unit up. He graphed the function y = cot(2x - π/4) + 1. However, there was a mistake in his transformation.

The correct transformation for a horizontal compression to adjust the period to 2/π units would be by multiplying the x variable by π/2. However, Chris multiplied by 2, which would give the transformed function a period of π units, not 2/π units as intended. Moreover, for a horizontal translation of π/4 units to the right, the correct function would include (x - π/4) inside the cotangent function, not (2x - π/4) as Chris graphed . The correct transformation of the parent function thus should have been y = cot((π/2)x - π/4) + 1 .    

Answer:

minimum (3,7)

Step-by-step explanation:

y = x^2 - 6x + 16

Take the coefficient of the x term  -6

Divide it by 2   -6/2 =-3

Then square it  ( -3)^2 =9

Add that to the equation (remember if we add it we must subtract it)

y = x^2 - 6x +9  -9+ 16

y = (x^2 - 6x +9)  -9+ 16

The term inside the parentheses is x+b/2 which is x+ -3  or x-3 quantity squared

y = (x-3)^2 +7

This is in vertex form

y = a(x-h)^2 +k  where (h,k) is the vertex

(3,7) is the vertex

Since a=1, it is positive, so it opens upward and the vertex is a minimum

Final answer:-

The quadratic equation y = x ²- 6x 16 can be rewritten in vertex form as y = ( x- 3) ² 7, with the vertex at the point( 3, 7), which is a minimum.

Explanation:-

To complete the square and rewrite the quadratic equation y = x2- 6x 16 in vertex form, we need to produce a perfect square trinomial on the right- hand side. The measure of x is-6, so we take half of that, which is-3, and square it to get 9. Adding and abating this inside the equation gives us y = ( x2- 6x 9)- 9 16.

Factoring the trinomial we also have y = ( x- 3) 2 7. This is the vertex form, where the vertex is the point( 3, 7). Since the measure of the x2 term is positive, the parabola opens overhead, which means the vertex represents a minimum.

When a circle is inside of another circle and touch each other as shown there is 1 common tangent ( where they touch).

The answer is C. 1

Answer:

only 1 tangent can drawn to the circle .

Step-by-step explanation:

Given  : Two circle with common one point.

To find : What is the total number of common tangents that can be drawn to the circles

Solution : We have given two circle

A tangent to a circle is a straight line which touches the circle at only one point.

We can see both circle are touching at s single point.

By the definition of tangent: A tangent to a circle is a straight line which touches the circle at only one point.

So, only one common point hence only one tangent can be drawn to the circles.

Therefore, only 1 tangent can drawn to the circle .

Answer:

x=121

Step-by-step explanation:

The exterior angle is equal to the sum of the two opposite interior angles

x = 74+47

x = 121

Answer:

Option C. [tex]31\ units[/tex]

Step-by-step explanation:

Observing the figure

The point E is the midpoint segment FA and the point B is the midpoint segment CD

therefore

[tex](1/2)(AD+FC)=EB[/tex]

substitute the given values and solve for x

[tex](1/2)(38+6x-6)=7x-4[/tex]

[tex](32+6x)=14x-8[/tex]

[tex]14x-6x=32+8[/tex]

[tex]8x=40[/tex]

[tex]x=5[/tex]

Find the value of EB

[tex]EB=7x-4[/tex]

substitute the value of x

[tex]EB=7(5)-4=31\ units[/tex]

Answer:

They traveled 800 km by train.

Step-by-step explanation:

We assign variables and write two equations. Then we solve the system of 2 equations in 2 unknowns.

Assign variables:

let x = kilometers traveled by bus

let y = kilometers traveled by train

Write first equation:

"they traveled a total of 1450 km"

x + y = 1450

Write second equation:

"riding on the train 150 more kilometers than on the bus"

The distance on the train, y, is 150 km greater than the distance on the bus, x.

y = x + 150

We have a system of 2 equations:

x + y = 1450

y = x + 150

Since the second equation is already solved for y, we can use the substitution method. Substitute y of the first equation with x + 150.

x + y = 1450

x + x + 150 = 1450

2x + 150 = 1450

2x = 1300

x = 650

y = x + 150

y = 650 + 150

y = 800

They traveled 800 km by train.

[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} x=3\\ y=8 \end{cases}\implies 8=\cfrac{k}{3}\implies 24=k~\hfill \boxed{\stackrel{therefore}{y=\cfrac{24}{x}}} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad y=\cfrac{24}{8}\implies y=3[/tex]

Y is inversely proportional to X. When X = 8, Y = 3.

To solve this inverse proportion problem, we can use the formula:

Y = k/X

Where k is a constant. Since we know that Y = 8 when X = 3, we can plug these values into the formula and solve for k:

8 = k/3

Multiplying both sides by 3, we get:

24 = k

Now that we have the value of k, we can use it to find Y when X = 8:

Y = 24/8

Therefore, when X = 8, Y = 3.

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The difference between the two possible  lengths of the third side of the triangle is:

                            3.2 inches

The lengths of two sides of a right triangle are 5 inches and 8 inches.

This means that the third side could be the hypotenuse of the triangle or it could be a leg of a triangle with hypotenuse as: 8 inches.

Let the third side be denoted by c.

Then by using the Pythagorean Theorem we have:

[tex]c^2=5^2+8^2\\\\i.e.\\\\c^2=25+64\\\\i.e.\\\\c^2=89\\\\i.e.\\\\c=9.434\ inches[/tex]

[tex]8^2=c^2+5^2\\\\i.e.\\\\64=c^2+25\\\\i.e.\\\\c^2=64-25\\\\i.e.\\\\c^2=39\\\\i.e.\\\\c=\sqrt{39}\\\\i.e.\\\\c=6.245\ inches[/tex]

Hence, the difference between the two possible lengths of the third side is:

[tex]=9.434-6.245\\\\=3.189\ inches[/tex]

which to the nearest tenth is: 3.2 inches

Answer:

B) 3.2 inches

Step-by-step explanation:

did it on edge

Answer:

Step-by-step explanation:

Please have in mind that sin(A - B) = sin(A)cos(B) - cos(A)sin(B) 

So what we do is:

sin(3x)cos(x) - sin(x)cos(3x) = 0 => sin(3x - x) = 0 

sin(2x) = 0 

2x = 0, π, 2π, 3π, 4π 

x = 0, π/2, π, 3π/2, 2π