The graph of y = x^2 -2x -3
a) Write down the coordinates of the turning point on the graph of y = x² – 2x - 3
(1)
(b) Use the graph to find the roots of the equation r? - 2x - 3 = 0

g(x) as given has no inverse because there are instances of two x values giving the same value of g(x). For instance,

x = -1   ⇒   g(-1) = 4 (-1 + 3)² - 8 = 8

x = -5   ⇒   g(-5) = 4 (-5 + 3)² - 8 = 8

Only a one-to-one function can have an inverse. g(x) is not one-to-one.

However, if we restrict the domain of g(x), we can find an inverse over that domain. Let [tex]g^{-1}(x)[/tex] be the inverse of g(x). Then by definition of inverse function,

[tex]g\left(g^{-1}(x)\right) = 4 \left(g^{-1}(x) + 3\right)^2 - 8 = x[/tex]

Solve for the inverse:

[tex]4 \left(g^{-1}(x) + 3\right)^2 - 8 = x[/tex]

[tex]4 \left(g^{-1}(x) + 3\right)^2 = x + 8[/tex]

[tex]\left(g^{-1}(x) + 3\right)^2 = \dfrac{x + 8}4[/tex]

[tex]\sqrt{\left(g^{-1}(x) + 3\right)^2} = \sqrt{\dfrac{x + 8}4}[/tex]

[tex]\left| g^{-1}(x) + 3 \right| = \dfrac{\sqrt{x+8}}2[/tex]

Recall the definition of absolute value:

[tex]|x| = \begin{cases}x & \text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]

This means there are two possible solutions for the inverse of g(x) :

• if [tex]g^{-1}(x) + 3 \ge 0[/tex], then

[tex]g^{-1}(x) + 3 = \dfrac{\sqrt{x+8}}2 \implies g^{-1}(x) = -3+\dfrac{\sqrt{x+8}}2[/tex]

• otherwise, if [tex]g^{-1}(x)+3<0[/tex], then

[tex]-\left(g^{-1}(x) + 3\right) = \dfrac{\sqrt{x+8}}2 \implies g^{-1}(x) = -3-\dfrac{\sqrt{x+8}}2[/tex]

Which we choose as the inverse depends on how we restrict the domain of g(x). For example:

Remember that the inverse must satisfy

[tex]g\left(g^{-1}(x)\right) = x[/tex]

In the first case above, [tex]g^{-1}(x) + 3 \ge 0[/tex], or [tex]g^{-1}(x) \ge -3[/tex]. This suggests that we could restrict the domain of g(x) to be [tex]x \ge -3[/tex].

Then as long as [tex]x \ge -3[/tex], the inverse is

[tex]g^{-1}(x) = -3+\dfrac{\sqrt{x+8}}2[/tex]

Answer:

ABE

Step-by-step explanation:

Perpendicular means the slope of the line and the answer are reciprocal to each other.

The slope of the line is -1/2, which means the slope of the answer should be 2.

From A we got: y=2x-1

B:y=2x

C:y=-2x+1

D:y=-1/2x-2

E:y=2x-3

So the answer is ABE

Answer:

it's AAS is my opinion

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

we can eliminate two of the answer choices from the start. AA and SSA do not prove triangle congruence. we are then left with SAS and AAS. we can see that there is one pair of sides and one pair of angles marked congruent on the triangles. the triangles are formed by intersecting lines which form vertical angles. according to the vertical angles theorem, those two angles will be congruent. therefore, these triangles are proven congruent by AAS. hope this helps!

Answer:

4x-12

Step-by-step explanation:

2x-5[2x-7(5)}=2x+2x-7-5

4x-12

negative integers are added to each other

[tex]\rm{\green{Answer \: is:-}}[/tex]

[tex]3xy \sqrt[24]{ {4x}^{2} } [/tex](3xy^2 4 sqrt 4x^2)

Step-by-step explanation:

Let's see

[tex]\\ \rm\Rrightarrow \sqrt[4]{324x^6y^8}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{4}{18^2x^6y^8}[/tex]

[tex]\\ \rm\Rrightarrow 18^{2/4}x^{6/4}y^{8/4}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{18}x^{3/2}y^2[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{18}\sqrt[2]{x^3}y^2[/tex]

Answer:

h = 60˚

Step-by-step explanation:

Look at where it shows the 120˚, and its verticle angle. Verticle angles are congruent, or the same meaning it's also 120˚.

Then go to its corresponding angle, which is next to the h. Corresponding angles are also congruent, or the same. I'll call this angle m to save time and hopefully confusion.

Now, h and m are supplementary angles, meaning they add up to 180˚.

180˚ - 120˚, or 60˚ is your answer.

h = 60˚

The solution is, the value of h is, h = 60˚

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given figure, we get,

Look at where it shows the 120˚, and its vertical angle.

Vertical angles are congruent, or the same meaning it's also 120˚.

now, we have,

Then go to its corresponding angle, which is next to the h. Corresponding angles are also congruent, or the same.

We call this angle m to save time and hopefully confusion.

Now, h and m are supplementary angles,

meaning they add up to 180˚.

so, we have,

180˚ - 120˚,

or 60˚ is your answer.

i.e.

h = 60˚

Hence, The solution is, the value of h is, h = 60˚

To learn more on angle click:

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Answer:

Step-by-step explanation:

m=-2/3

b=-7

First, find the slope-intercept form.

y=mx+b

You know what the m and b values are, so simply plug them into the equation.

Slope-Intercept Form

y=-2/3x-7

From there, let's find the point-slope equation.

An easy way to find a coordinate point that the line crosses is to set one of the x or y variables equal to 0.

So let's set the x to 0.

y=-2/3x-7

y=-2/3(0)-7

y=-7

Therefore, when x is 0, y is equal to -7. We can now write our point. (0,-7)

Use the point-slope formula to write the point-slope equation.

y-y1=m(x-x1)

Point-Slope Equation

y-(-7)=-2/3(x-0)

Now, to find the standard form equation, let's find it using our slope-intercept equation. The formula to find standard form is

ax+by=c

y=-2/3x-7

Standard Form Equation

2/3x+y=-7

Answer:

Y = 10x + 20

Step-by-step explanation:

sorry if im wrong

Answer:

y = 2x - 4

Step-by-step explanation:

10x - 5y = 20

Subtract 10x both sides

-5y = 20 + (-10x)

Divide by -5

y = -4 + 2x

y = 2x + (-4)

Answer:

$49

Step-by-step explanation:

70 x 30%

70 x 0.3

21

70 - 21

49

Answer: this is a reflection across the x-axis

Answer:

a=100

b=1

Step-by-step explanation:

18a+65b=1865

23a+7b=2314

We need to make one of the variables equal to the other

So...

The LCM for 65 and 7 is 455

So multiply 7 with 18a+65b=1865

and Multiply 65 with 23a+7b=2314

7 times 18a+65b=1865 is 126a+455b=13055

65 times 23a+7b=2314 is 1495a+455b=150410

So Subtract 126a+455b=13055 and 1495a+455b=150410

So 1369a=137355

Divide:

Which is about 100 (The actual value is 100.3323594)

Thus a=100

Substitute:

b=1

Hope this helps!

(The answer is rounded)

Answer:

D

Step-by-step explanation:

Answer:

12 square units

Step-by-step explanation:

once you plot the triangle on a graph, you'll see that the height is 4 sq inches, while the base is 6. multiply those two and you get 24, and divide that by 2. thats 12

Answer:

r=0.5d

Step-by-step explanation:

Answer:

=-0.8

Step-by-step explanation:

1+2+3+4+5-6÷7×8-9

15-6÷7×8-9

15-0.85×8- 9

15-6.8-9

=-0.8

Answer:

20 (30 + d)

Step-by-step explanation:

your welcome :)

Answer:

2 and 4th one.

Step-by-step explanation:

Hopes This Helps :)

Answer:

A and F

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

45°+45°+m∆2 = 180°

m∆2 = 90°

; m∆2 = 16x-6

90 = 16x-6

96 = 16x

96/16 = x

6 = x

Answer:

[tex]\huge\color{pink}\boxed{\colorbox{black}{Answer♡}}[/tex]

The reason that a heavy body doesn't fall faster than a light body is because the greater gravitational force on the heavier body (its weight), acts on a correspondingly greater mass (inertia). The ratio of gravitational force to mass is the same for every body—hence all bodies in free fall accelerate equally.

hope helpful~

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Answer:

This is the graph of a sine function

The y-intercept of the graph is the function value y=0

The smallest positive x-intercept of the graph is located at x=pi/2

The greatest value of y is y=2

For x between x=-pi and x=pi/2, the function value y=>0

Step-by-step explanation:

Answer:

2:1 RATIO

Step-by-step explanation:

If you walked for 5 minutes, the ratio of feet to minutes would be approximately 2.1665 feet per minute.

To determine the ratio of feet to minutes, we can use the steps to minutes ratio from Task 1. Let's find the steps-to-feet ratio first:

Steps:Feet

4:10

6:15

12:30

30:40

Now, let's calculate the steps-to-feet ratio by finding the average of the steps-to-feet ratio from all the given data points:

Average Steps-to-Feet Ratio = [(10/4) + (15/6) + (30/12) + (40/30)] / 4

Average Steps-to-Feet Ratio = (2.5 + 2.5 + 2.5 + 1.333) / 4

Average Steps-to-Feet Ratio = 2.1665

Now, for the question at hand, if you walked for 5 minutes, the ratio of feet to minutes would be approximately 2.1665 feet per minute.

learn more about ratio: https://brainly.com/question/12024093

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Answer:

[tex]g(x)=\frac{1}{8} x^{3} -\frac{3}{2} x^{2} +6x-5[/tex]

Step-by-step explanation:

[tex]x=2\sqrt[3]{y-3} +4[/tex]

switch the x and y, then use order of opperations

Answer:

The answer is 75ft. Hope this helps.

Answer:

Integers

Step-by-step explanation:

Integers include both positive and negative numbers. This is the simplest answer. This set doesn't include any fractions or decimals. Integers are a subset of rational numbers, which are a subset of real numbers, which are a subset of complex numbers.

Answer:

t+c ≤ 55

Step-by-step explanation:

t+c is the total pieces of furniture and it must be at most (less than or equal to) 55 so t+c ≤ 55 is the equality that represents the possible values.

Answer:

y = -2x - 1

Step-by-step explanation:

Put y on the left and everything else on the right

Answer:

67!

Step-by-step explanation:

A way to look at it is, since the number is 387, it can be broken into 6 parts. 50x6 is about 300. That leaves 87 to be left over. So it's safe to assume each number will be around 50-60, so I started to add up six consecutive numbers together until I reached my final set of numbers to reach 387.

My numbers were 62+63+64+65+66+67=387

I hope this makes sense!