What is the vertex of the graph of the function below? y= x2 - 4x + 3

A. (2.-1)

B. (1,-1)

C. (1,0)

D. (2,0)​

Answer:

[tex]4(2 + y)[/tex]

Step-by-step explanation:

"4 times the sum of 2 and y".

Answer:

The answer is 4(2+y)

Explanation: No 1 is 4 times two and add 1

No 3 is 2 plus 4 and multiply y

No 4 is 2 times 4 and adds 2 y

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

[tex]\displaystyle \csc^2 x -2\csc x \cot x +\cot ^2 x = \tan^2\left(\frac{x}{2}\right)[/tex]

Note that the left-hand side is a perfect square trinomial pattern. Namely:

[tex]a^2-2ab+b^2=(a-b)^2[/tex]

If we let a = csc(x) and b = cot(x), we can factor it as such:

[tex]\displaystyle (\csc x - \cot x)^2 = \tan^2\left(\frac{x}{2}\right)[/tex]

Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):

[tex]\displaystyle \left(\frac{1}{\sin x}-\frac{\cos x }{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)[/tex]

Combine fractions:

[tex]\displaystyle \left(\frac{1-\cos x}{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)[/tex]

Square (but do not simplify yet):

[tex]\displaystyle \frac{(1-\cos x)^2}{\sin ^2x}=\tan^2\left(\frac{x}{2}\right)[/tex]

Now, we can make a substitution. Let u = x / 2. So, x = 2u. Substitute:

[tex]\displaystyle \frac{(1-\cos 2u)^2}{\sin ^22u}=\tan^2u[/tex]

Recall that cos(2u) = 1 - sin²(u). Hence:

[tex]\displaystyle \frac{(1-(1-2\sin^2u))^2}{\sin ^2 2u}=\tan^2u[/tex]

Simplify:

[tex]\displaystyle \frac{4\sin^4 u}{\sin ^2 2u}=\tan^2 u[/tex]

Recall that sin(2u) = 2sin(u)cos(u). Hence:

[tex]\displaystyle \frac{4\sin^4 u}{(2\sin u\cos u)^2}=\tan^2 u[/tex]

Square:

[tex]\displaystyle \frac{4\sin^4 u}{4\sin^2 u\cos ^2u}=\tan^2 u[/tex]

Cancel:

[tex]\displaystyle \frac{\sin ^2 u}{\cos ^2 u}=\tan ^2 u[/tex]

Since sin(u) / cos(u) = tan(u):

[tex]\displaystyle \left(\frac{\sin u}{\cos u}\right)^2=\tan^2u=\tan^2u[/tex]

We can substitute u back for x / 2:

[tex]\displaystyle \tan^2\left(\frac{x}{2}\right)= \tan^2\left(\frac{x}{2}\right)[/tex]

Hence proven.

Answer:

B

Step-by-step explanation:

We are given that Expression One is:

[tex]2\cdot 10^x[/tex]

And Expression Two is:

[tex]4\cdot 10^{x+y}[/tex]

We are given that the value of Expression Two is 20,000 times greater than the value of Expression One. And we want to find the value of y. In other words:

[tex]4\cdot 10^{x+y}=20000(2\cdot 10^x)[/tex]

We can divide both sides by four:

[tex]10^{x+y}=10000\cdot 10^x[/tex]

Recall that:

[tex]x^a\cdot x^b=x^{a+b}[/tex]

Therefore:

[tex]10^x\cdot 10^y=10000\cdot 10^x[/tex]

Divide both sides by 10ˣ:

[tex]10^y=10000[/tex]

Solve for y:

[tex]\displaystyle y = \log_{10}10000 = 4[/tex]

Our answer is B.

Answer:

Step-by-step explanation:

This answer can be found in the h value for the vertex of a parabola, (h, k). The k value is the max height and we were already given that information. We need to solve for h. There's an easy way and a really complicated way...I'll show you the easy way because it's actually quite useful to know, especially when doing a lot of work with quadratics!

The formula to find h is

[tex]h=\frac{-b}{2a}[/tex] and in our quadratic, a = -16, b = 96 and c = 6. Filling in what we need:

[tex]h=\frac{-96}{2(-16)}[/tex] so

h = 3

At 3 seconds the max height of 150 feet is reached.

Answer:

[tex]1\frac{1}{2}kg[/tex]

Step-by-step explanation:

Given

[tex]a = 6\frac{1}{2}[/tex] --- heaviest

[tex]b = 5[/tex] --- second heaviest

Required

The difference (d)

This is calculated as:

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

[tex]d = 1\frac{1}{2}[/tex]

Answer:

Option B

Step-by-step explanation:

After each round of the tournament one-fourth players are eliminated.

That means the process of elimination will represent the exponential decay.

Equation of exponential decay is given by the expression,

[tex]y=a(1-r)^n[/tex]

Here, a = Initial number of players

r = Fraction of reduction in the number of players

y = Final number of players

n = Number of rounds

In the given question,

Initial number of the players (a) = 64

Fraction of reduction in the number of players (r) = [tex]\frac{1}{4}[/tex]

                                                                             = 0.25

Number of rounds (n) = 6

By substituting these values in the expression,

[tex]y=64(1-0.25)^6[/tex]

Therefore, Option B is the answer.

Answer:

250,000 cm squared

Step-by-step explanation:

Answer:

6x+10 i think is right(sorry if its not)

Answer:

5

Step-by-step explanation:

4x-3=2x+7

-2x -2x

2x-3=7

+3 +3

2x=10

2x/2x = x

10/2=5

x=5

Answer:

I need help on this to anyone please

Answer:

it is an example of conditional statement.

hope it helps

Answer:

h(x) is the image after f(x) is horizontally stretched by a scale factor of 4

Step-by-step explanation:

Given

[tex]h(x) = \frac{1}{4}x^2[/tex]

[tex]f(x) = x^2[/tex]

Required

Compare h(x) to f(x)

We have:

[tex]h(x) = \frac{1}{4}x^2[/tex]

Substitute [tex]f(x) = x^2[/tex]

[tex]h(x) = \frac{1}{4}f(x)[/tex]

This means that f(x) is stretched horizontally by a scale factor of 4 to get h(x)

Step-by-step explanation:

y=-x+4

y=x-2

adding both the equations we get

2y=2

:. y=1

and putting the value of y in equation first we get

x=3

Answer:

-$25.84

Step-by-step explanation:

254* -0.17 = -$43.18 profit from milk

51 * .34 = $17.34 profit from OJ

-43.18 + 17.34 = -$25.84 profit total

Answer:

answer is line m........

Answer:

Option A = 1/15 cubic meters

Step-by-step explanation:

Formule to find volume of rectangular prism:

Volume = width × height × length

V = w×h×l

V = 1/3 × 1/4 × 4/5

V = 1/15 cubic meters

Answer:

(-6, 8)

Draw the point, draw the lines of reflection, reflect, find coordinates.

Answer:

7 over 2x-2

Step-by-step explanation:

Answer:

g^-1 •7

7g^-1

7•1/g

answer is 7/g

I hoped I helped!! :)

Answer:

C. (0,1)

Step-by-step explanation:

x + 1 = -2x + 1

3x = 0

x = 0

y = (0) + 1

y = 1

Answer:

70in.

Step-by-step explanation:

Since the given formula for perimeter is [tex]2l + 2w[/tex], all that's needed is to fill in the blanks with the numbers they give us.

[tex]2l + 2w[/tex]                  (Fill in for given length and width)

[tex]2(20)+2(15)[/tex]         (Multiply)

[tex]40 + 30[/tex]                  (Add)

[tex]70[/tex]

It tells us that length ([tex]l[/tex]) is 20 and that width ([tex]w[/tex]) is 15. So all that we have to do is use the equation it gave us to solve the equation.

I hope this helped :)

Step-by-step explanation:

Hey there!

Here;

Length (l) = 20 in

Width (w) = 15 in

Perimeter(p) = ?

We have;

Perimeter of rectangle (p) = 2l + 2w

= 2(l+w)

= 2(20+15)

= 2*35

= 70 inches

Therefore, perimeter of rectangular picture is 70 inches.

Hope it helps!

Answer:

B

Step-by-step explanation:  6 21  9 45

49 × 17 + 49 × 3

49 × (17 + 3)

49 × 20

Answer:

Triangle KLM

Step-by-step explanation:

Firstly, we need to write the coordinates of triangle NPQ

We have this as;

(-7,-6) for N

(-4,-3) for P

(-4,-6) for Q

Now, we are going to use the given translation formula;

(x + 8, y + 1)

N’ will be (-7+ 8, -6 + 1) = (1,-5)

P’ will be (-4+ 8, -3+1) = (4,-2)

Q’ will be (-4+ 8, -6+1) = (4,-5)

Now, we need to find the triangle with the exact given transformation coordinates calculated above;

We have the triangle as;

KLM

With K as (1,-5) ; L as (4,-2) and ; M as (4,-5)

Answer:

39,810,717.06

Step-by-step explanation:

Question:

What is the value of x when the richter scale rating is 7.6? Round your answer to the nearest hundreth.

Mathematically, the rating of an earthquake typically refers to its magnitude on the Richter scale.

The Richter scale is a logarithmic scale that measures the amplitude of seismic waves produced by an earthquake. Each increase of one unit on the Richter scale represents a tenfold increase in the amplitude of the seismic waves and approximately 31.6 times more energy released.

A rating of 7.6 on the Richter scale indicates a significant and powerful earthquake. It is considered a "great" earthquake and can cause widespread damage over an extensive area. The extent of the damage can depend on various factors, including the depth of the earthquake, the distance from populated areas, and the local building infrastructure.

It's important to note that while the magnitude of an earthquake provides a measure of its energy release, it doesn't directly indicate the extent of the damage or the specific geographical area affected. The effects of an earthquake can vary depending on factors such as local geology, distance from the epicenter, and the population density of the area.

Mathematically, the Richter scale provides a standardized way to quantify and compare the magnitude of earthquakes, aiding in the understanding and analysis of seismic events.

To know more about Richter scale. here

https://brainly.com/question/24037139

#SPJ2

Answer:

since these triangles are the same these angle must be the same

A=D

B=E

C=F

so the answer is C

Hope This Helps!!!

Answer:

Write function:

y = 3x+4

The slope is what we time x by, 3!

Answer:

The new slope is 1 and the line is shifted flatter.

Step-by-step explanation:

Line A slope is 4.

Line B slope is 1.

The y-intercept rose up 3

As far as slope, it became flatter because the line only rises 1 'square' for every 1 'square' it travels to the right. It was rising 4 'squares' for every 1 to the right.  

Answer:

there are no functions her pls add them for an answer:)

Step-by-step explanation:

Answer:

x+3?

Step-by-step explanation:

honestly, there is not alot of information present here. so when a hear "a number" i think variable.... which would be set up as x+3

Answer:

In this case, we have a linear equation:

y = 3*x - 2

And we want to graph this in the interval  –3 ≤ x ≤ 3

Because this is a linear equation, to graph it we can just evaluate the equation in both extremes of the interval to find the two extremes of the graph.

Then we just need to connect these points with a segment, and that will be the graph of our equation.

Because the symbols used are: ≤

We need to graph the extremes with a black dot, which means that the point is included in the graph (would be different if we had -3 < x < 3)

The first extreme is when we have x = -3

y = 3*(-3) - 2 = -9 - 2 = -11

Then we have one extreme at (-3, -11)

The other is when x = 3

y = 3*3 - 2 = 9 - 2 = 7

Then the other extreme is at (3, 7)

Now we just need to draw these two points and connect them, an example of this can be seen in the image below: