Need help with adding these!! *prob easy I’m just not good* see photo!

Answer:

A) Q(x) = (x + 3)² + 5, and the vertex is (-3, 5)

B) R(x) = (x - 3)² + 2, and the vertex is (3, 2)

C) S(x) = (x - 1)² - 5, and the vertex is (1, -5)

Step-by-step explanation:

The given function is P(x) = (x + 3)² + 2

The given function is a parabolic function in vertex form, f(x) = a·(x - h)² + k, and vertex, (h, k)

By comparison, the vertex of the function P(x) = (x + 3)² + 2 is (-3, 2)

A) A function f(x) translated α units UP gives

f(x) (translated α units UP) → f(x) + α

A translation of the function 3 units UP is given by adding 3 to the given function as follows;

Q(x) = P(x) + 3

∴ Q(x) = (x + 3)² + 2 + 3 = (x + 3)² + 5

Q(x) = (x + 3)² + 5, and the vertex by comparison to f(x) = a·(x - h)² + k, and vertex, (h, k) is (-3, 5)

B) A function f(x) translated b units RIGHT gives;

f(x) translated b units right → f(x - b)

∴ P(x) = (x + 3)² + 2 translated 6 units RIGHT gives;

P(x) = (x + 3)² + 2 (translated 6 units RIGHT) → R(x) = (x + 3 - 6)² + 2 = (x - 3)² + 2

R(x) = (x - 3)² + 2, and the vertex by comparison is (3, 2)

C) A function translated α units DOWN and b units RIGHT is given as follows;

[tex]f(x) \ translated \ by\ \dbinom{b}{a} \rightarrow f(x - b) - a[/tex]

Therefore, the given function, P(x) = (x + 3)² + 2, translated 7 units DOWN and 4 units RIGHT gives;

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow P(x - 4) - 7 = S(x)[/tex]

S(x) = P(x - 4) - 7 = (x + 3 - 4)² + 2 - 7 = (x - 1)² - 5

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow (x - 1)^2 - 5= S(x)[/tex]

S(x) = (x - 1)² - 5, and the vertex by comparison is (1, -5)

Answer:

x= -2   and x = 6

Step-by-step explanation:

The solutions are where the two graphs intersect

x=6, y= 10  is one point

x=-2 and y = -6 is the other point

The intersection points of both the equations are the solutions

From the graph the points are

Hence

x=-2 and x=6 are the solutions

Option D

Answer:  (4y-9z)( 16y^2 + 36yz + 81z^2 )

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Explanation:

We'll use the difference of cubes factoring rule

a^3 - b^3 = (a-b)(a^2+ab+b^2)

In this case,

So,

a^3 - b^3 = (a-b)(a^2+ab+b^2)

64y^3 - 729z^3 = (4y-9z)( (4y)^2 + (4y)(9z) + (9z)^2 )

64y^3 - 729z^3 = (4y-9z)( 16y^2 + 36yz + 81z^2 )

Answer:

6ft by 8ft

Step-by-step explanation:

12 / 2 is 6 and 16 / 2 is 8

Answer:

No adda doesnt get free delivery

Step-by-step explanation:

Answer: A) No, the distance from the restaurant to Ada’s house is Square Root of 41 miles, which is greater than the 6-mile maximum radius.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

In this question, we given a piece-wise function, that has different definitions depending on the domain.

Evaluate the function at x = 0.

The exercise asks for us to evaluate the function at [tex]x = 0[/tex]

We have to look at the definition, and see which definition includes [tex]x = 0[/tex]. The equal sign at [tex]x = 0[/tex] is on the second definition, that is:

[tex]f(x) = 1, 0 \leq x < 2[/tex]

Thus, at [tex]x = 0[/tex], the value of the function is 1, and the correct answer is given by option A.

For another example of evaluation of a piece-wise function, you can check https://brainly.com/question/17966003

Answer:

a=41  b=-9

Step-by-step explanation:

By expanding the brackets on the left hand side of the equation you get,35x + 40 + 6x + 3b and by simplifying you get 41x + 40 + 3b.by comparing the x and constant terms on either side you find that a = 41, and3b + 40 = 13, rearranging b = -9.

Answer from Gauth math

Answer:

Hello,

Step-by-step explanation:

We are going to use identification of terms.

[tex]5(7x+8)+3(2x+b)=ax+13\\\\35x+40+6x+3b=ax+13\\\\41x+40+3b=ax+13\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\3b+40&=&13\\\end{array}\right.\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\b&=&-9\\\end{array}\right.\\\\[/tex]

Produced by myself

Answer:

362

(8

10-7) - (-6.25 • 10-2)

Answer:

x=1

Step-by-step explanation:

3х - 6 = 6x - 9

Subtract 3x from each side

3х-3x - 6 = 6x-3x - 9

-6 = 3x-9

Add 9 to each side

-6+9 = 3x-9+9

3 =3x

Divide by 3

3/3 = 3x/3

1 =x

Answer:

3x-6=6x-9

3x-6x=-9+6

-3x=-3

-3x÷-3=-3÷-3

x=1

Answer:

hi

Step-by-step explanation:

Answer:

A. {x| –4 < x ≤ 4}

Step-by-step explanation:

Answer:

{x| –4 < x ≤ 4}

Step-by-step explanation:

Edge Quiz 2023

Answer:

Looking at the question and goin step by step

we get to know that equation formed wud be ->

product of nine and a number - 9*x = 9x

added to 6 => 9x+6

gives us 24

so

9x + 6 = 24

now 9x = 18 and x = 18/9 = 2

and now keeping x value = 9 *(2)+6 we get 18+6 = 24

so lhs = rhs = 24

9x+6=24 option a

Answer:

x+13

Step-by-step explanation:

The answer would be 1 or uh.. x+13

Answer:

16 degrees

Step-by-step explanation:

Tan(?) = perpendicular/base

Tan(?) = 13/46

?=arctan(13/46)=16

HOPE ITS HELPFUL ^_^

Answer:

y = -3x + 2

Step-by-step explanation:

y2 - y1 / x2 - x1

-1 - 8 / 1 - (-2)

-9/3

= -3

y = -3x + b

-1 = -3(1) + b

-1 = -3 + b

2 = b

The concept of greatest common factor is used to solve this question. Then, we use it to find the number of crackers and slices of cheese, and the answer is:

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

To find the greatest number of plates, you need to find the greatest common factor between 12 and 18.

Thus, factoring them, always by the same number:

12 - 18|2

6 - 9|3

2 - 3

The greatest common factor is 2x3 = 6, which means that the greatest number of plates you can prepare is 6.

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

18 crackers, so each plate has 18/6 = 3 crackers.

12 slices of cheese, so each plate has 12/6 = 2 slices of cheese.

A similar question is given at https://brainly.com/question/18454593

Answer:

45 * 3/5 = 135/5 = 27

Step-by-step explanation:

Answer:

a=6 and b=8

Step-by-step explanation:

a^2=(9/16)b^2. Substitute this in the second equation, you get b^2+b^2*(9/16)=100, b^2=100*16/25=8 and a=6

Answer:

500*2%=10

500+10=510

Step-by-step explanation:

Part (i)

We start with five dots to make the pattern in figure 1.

In figure 2, we add on 1 dot to each arm of the X shape. So that means we've added 4 dots total going from 5 to 5+4 = 9 dots.

In figure 3, there are 9+4 = 13 dots

So the pattern is simply "add 4" to get the next term. Again, this is because we add one dot per arm.

The first three terms of this arithmetic sequence are: 5, 9, 13

Your teacher wants to know what the general nth term is

We start with a = 5 and the common difference is d = 4

T(n) = nth term

T(n) = a + d(n-1)

T(n) = 5 + 4(n-1)

T(n) = 5 + 4n - 4

T(n) = 4n + 1

Let's try it out. Say we want to plug in n = 2

T(n) = 4n + 1

T(2) = 4(2) + 1

T(2) = 8 + 1

T(2) = 9

This works because the second figure indeed has 9 dots. I'll let you confirm the other figures.

============================================================

Part (ii)

Your teacher wants to know how many dots occur when n = 50

T(n) = 4n + 1

T(50) = 4(50)+1

T(50) = 200 + 1

T(50) = 201

Verifying this through drawing dots is going to be a very tedious task, and I don't recommend it unless you really want to. Hopefully the verification process of T(2) = 9, and similar (for small values of n) is enough to convince you that this equation works as intended.

Answer:

-1

Step-by-step explanation:

Remember PEMDAS! Start with distributing the parentheses -(3x+6) so you get -8x-3x-6=4-x and simplify. Then you get -11x-6=4-x and combine like terms which equals -10=10x. Simplify and you get -1.

The solution to the equation -8x - (3x + 6) = 4 - x is x = -1.

Given the equation in the question:

-8x - (3x + 6 ) = 4 - x

To solve the equation -8x - (3x + 6) = 4 - x, simplify the equation by isolating all terms with variable x:

-8x - (3x + 6 ) = 4 - x

Distribute the negative sign inside the parentheses:

-8x - 3x - 6 = 4 - x

Combine like terms on both sides of the equation:

-11x - 6 = 4 - x

Add 6 to both sides:

-11x - 6 + 6 = 4 + 6 - x

-11x = 4 + 6 - x

-11x = 10 - x

Next, add x to both sides:

-11x + x = 10 - x + x

-10x = 10

Divide both sides of the equation by -10:

x = -10/10

x = -1

Therefore, the value of x is -1.

Learn more about equations here: brainly.com/question/14686792

#SPJ6

Answer:

[tex] \sqrt{ - 147} = \sqrt{147} \times \sqrt{ - 1} = 7i \sqrt{3} [/tex]

I hope I helped you ^_^

The answer ; √ –108 = √108 × √–1 = 6i √3

Answer:

A

Step-by-step explanation:

The vertex is at (2,1) The two is the important feature to start with. That means that the point is 2 away from the y axis. That goes to the left to get to the y axis.

The get the mirror image of that 2, you have to go two to the right to get to the point that mirrors (0,4). The y value has to be the same as the y intercept. So x must be 4 and y needs to be 4.

The answer is (4,4)

In case you are interested, the graph (given below) is y = 0.75 (x - 2)^2 + 1

The y intercept is 0,4 and the vertex is 2,1

Step-by-step explanation:

If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent .

Answer:

Infinite

Step-by-step explanation:

Solution between 2 lines is considered the point of their intersection. Now, since two lines are same (not only parallel but same), it tends to have infinite solutions.

Answer:

(x - 10)(x + 8)

Step-by-step explanation:

x² - 2x - 80

Consider the factors of the constant term (- 80) which sum to give the coefficient of the x- term (- 2)

The factors are - 10 and + 8 , since

- 10 × 8 = - 80 and - 10 + 8 = - 2 , then

x² - 2x - 80 = (x - 10)(x + 8)