What is the equation in vertex form of a parabola with vertex (2, 4) that opens downward and is stretched by a factor of 3?

Hi,

x² + 8x + 12 = 0

a= 1 ; b= 8 c= 12

∆ = b² - 4ac

∆ = 8² - 4*1*12

∆ = 64 - 4*12

∆ = 64 - 48

∆ = 16

∆>0 :

x1 = (-b-√∆)/2a = (-8-4)/2 = -12/2 = -6

x2 = (-b+√∆)/2a = (-8+4)/2 = -4/2 = -2

S= { -6 ; -2 }

x = -6

or x = -2

✅(•‿•)

Answer:

Step-by-step explanation:

x² + 8x + 12 = 0

➺ x² + 2x + 6x = 0

➺ x(x + 2) + 6(x + 2) =0

➺ (x + 6)(x + 2) = 0

Whether, x + 6 = 0

⠀⠀⠀⠀⠀➺ x = -6

⠀⠀or,⠀⠀⠀⠀ x + 2 = 0

⠀⠀⠀⠀⠀⠀➺ x = -2

You do not have the options listed, but I will tell you what the line needs:

[] A parallel line will need the same slope.

- The slope is our m in y = mx + b

[] What will this be for our problem:

- [tex]y=\frac{-7}{2}x-3[/tex]

- Our slope is [tex]\frac{-7}{2}[/tex]

[] So what will the line look like:

- [tex]y=\frac{-7}{2}x +?[/tex]

- Since you do not have the options listed, I cannot tell you the answer, but I can tell you the answer will have a slope of [tex]\frac{-7}{2}[/tex]

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

The total number of students is 50

The number of students that named lacrosse as their favorite sport is given as:

[tex]Lacrosse = 19[/tex]

From the circle graph, 38% chose lacrosse.

So, the proportion of students that represent lacrosse is:

[tex]Lacrosse = 38\% \times Students[/tex]

Substitute 19 for lacrosse

[tex]19= 38\% \times Students[/tex]

Multiply both sides by 100

[tex]1900 = 38 \times Students[/tex]

Divide both sides by 38

[tex]50 = Students[/tex]

Rewrite as:

[tex]Students = 50[/tex]

Hence, the total number of students is 50

Read more about circle graphs at:

https://brainly.com/question/24461724

[tex]\huge \bf༆ Answer ༄[/tex]

Let's calculate the volume of sphere with :

[tex] \sf \: vol = \dfrac{4}{3} \pi {r}^{3} [/tex]

Now, plug the value of radius (r) and find volume ~

The value closest to it is 65.45

Therefore, that's the most appropriate choice ~

[tex] ꧁  \large \rm{kaul} \: ꧂[/tex]

Answer:

  47.2°

Step-by-step explanation:

Triangles PRQ and SRQ are congruent by HL. In these right triangles, the acute angles are complementary.

angle PRQ  = angle SRQ = 90° -42.8° = 47.2°

The measure of angle PRQ is 47.2°.

Answer:

y = - [tex]\frac{2}{5}[/tex] (x - 5)² + 7

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (5, 7 ) , then

y = a(x - 5)² + 7

To find a substitute (10, - 3 ) into the equation

- 3 = a(10 - 5)² + 7 ( subtract 7 from both sides )

- 10 = 5²a = 25a ( divide both sides by 25 )

[tex]\frac{-10}{25}[/tex] = a , that is

a = - [tex]\frac{2}{5}[/tex]

y = - [tex]\frac{2}{5}[/tex] (x - 5)² + 7 ← in vertex form

Same thing as before!

First, we can get rid of d(x) simply by looking at it because we can tell it's linear (it's a straight line). If we look at the table, we can see a(x) is also linear because it has a steady rate of growth. b(x) and c(x) both represent exponential growth. The curved shape of b(x) shows us this is exponential growth, and the exponent in c(x) tells us it's also exponential.

Answer:

[tex]\frac{5}{11}[/tex]

Step-by-step explanation:

five pears out of eleven fruit total

hope this helps!

Answer:

5 : 11

Step-by-step explanation:

total fruit = 4 + 2 + 5 = 11

Then the ratio of

pears : all fruit

= 5 : 11

Answer:

Step-by-step explanation:

For a given function f(x), we define the domain as the set of the possible inputs of the function and the range as the set of the outputs of the function.

We will see that both domain and range are the set of all real numbers.

D = (-∞, ∞)

R = (-∞, ∞)

Here we have the function:

The first thing we need to do is find the domain.

We start by assuming that the domain is the set of all real numbers and then we try to find some given values of x that cause some undefined operation, and then we remove these values of x from the domain.

Where this would be something like a zero in the denominator or something like that. We also could have specific restrictions to the domain that are applied in some specific cases (for example if x represents a length we should remove the negative values from the domain).

Here we can see that we do not have any indetermination, thus the domain is the set of all real numbers.

Now to study the range we need to see the general function, we can see that as x tends to negative infinity y will also tend to negative infinity, while when x tends to infinity y will also tend to infinity.

Then the range will also be the set of all real numbers.

Answer:

x=6+√5 or x=6−√5

Answer: I think that it's -125/27

Step-by-step explanation: Convert into a complex fraction (-5/3)^3 and then cube the 5 and 3 and don't change the negative sign.  The answer then is -125/27

Hope it helps.

Answer:

y=3x+8

Step-by-step explanation:

Answer:

y=1.5x+11

Step-by-step explanation:

Given monomials are 3x⁷ , 4x² and -5x³

On multiplying them then

⇛ (3x⁷)×(4x²)×(-5x³)

⇛(3×4×-5) × (x⁷×x²×x³)

⇛ -60×x^(7+2+3)

Since , a^m × a^n = a^(m+n)

⇛-60 × x¹²

⇛ -60x¹² Ans.

also read similar questions: Multiplying Polynomials by Monomials: 2x (5x-2) = 10x-4x...

https://brainly.com/question/21877934?referrer

Find the product of the monomial and the polynomial: 4x^3y^3*(3x^3-7xy^2+2xy-y)..

https://brainly.com/question/20695867?referrer

[tex]3x^7 .4x^2.(-5)x^3=3.4.(-5).x^{7+2+3}=-60x^{12}[/tex]

ok done. Thank to me :>

Answer:

1/2 of a bale

Step-by-step explanation:

1/4 times 2 equals 1/2

z²-2i=0

Answer:

Solution given:

z⁴=-4

doing square root on both side

[tex]\sqrt{z⁴}=\sqrt{2²*-1}[/tex]

we know i²=-1

substituting i² we get

z²=[tex]\sqrt{2²*i²}[/tex]

z²=2i

z²-2i=0 is a required answer. where

z² and 2 is real number.

Answer:

  z = {-1 -i, -1 +i, 1 -i, 1 +i}

Step-by-step explanation:

Using Euler's formula, we can write the equation as ...

  z^4 = 4e^(i(π +2πn)) . . . . . . where n is any integer

Then the 4th root is ...

  z = (√2)e^(i(π +2πn)/4 = (√2)e^(i(π/4 +nπ/2)) . . . . . for n = 0–3

  z = √2(cos(π/4+nπ/2) +i·sin(π/4 +nπ/2)) . . . . . for n = 0–3

  z = ±1 ±i

  z = {1 +i, -1 +i, -1 -i, 1 -i}

_____

Additional comment

Values of n are only needed in the range 0–3, because the answers repeat for values other than those.

Answer:

Two non co-linear segments with a slope of 3 in a coordinate plane would mean that the two segments are parallel to each other and not attached to each other. Having the same slope is the definition of being parallel in the same plane.

Step-by-step explanation:

Answer:

244140625

5¹²

it is a sequence of numbers in which each term is obtained by multiplying the preceding term by a constant. In other words, the ratio between a term and its preceding term is constant. And that constant is common ratio. Therefore, 12th term is 244140625.

Answer:

A. is the type of potential energy

Step-by-step explanation:

examples of gravitational potential energy : a raised in weight , a yoyo,water in a dam,a car parked on a hill

Answer:

4 pieces of fruit

Step-by-step explanation:

48 divided by 12 = 4

28 divided by 7 = 4

did i hear help i will help you soooooooo oooooooooo

Answer:

the domain is -11,10 but i didnt know if you wanted that or not

Step-by-step explanation:

Answer:

j>3

Step-by-step explanation:

hope this helps sorry if it doesn't have a great rest of your night :)❤

Answer:

47

Step-by-step explanation:

20*47= 940

940*5=4,700

47*100=4,700

Answer:

y = 4/3x + 4

Step-by-step explanation:

-4 - 8 / -6 - 3

-12 / -9

4/3 is slope

y = 4/3 x + b so we need to find b

Put one of the points in for y and x.

-4 = 4/3 (-6) + b

-4 = -8 + b

4 = b

y = 4/3x + 4

The time it will take the pereson to leave their money in the bank until it reaches $20,100 is 3 years

Given the exponential equation expressed as:

[tex]A=6500(1.0175)^{4t}\\[/tex]

Given that A = 20100, Substituting into the expression will give;'

20100 = 6500(1.0175)^4t

20100/6500 = (1.0175)^4t

3.0923 =  (1.0175)^4t

Taking the ln of both sides

ln3.0923  = 4tln(1.1075)

4t = ln3.0923 /ln(1.1075)

4t = 1.12891/0.1021

4t = 11.05690

t = 11.05690/4

t = 2.76

t ≈ 3 years

Hence the time it will take the pereson to leave their money in the bank until it reaches $20,100 is 3 years

Learn more on compound interest here: https://brainly.com/question/24274034

Answer: 75%

Step-by-step explanation:

Since there are 3 even numbers on each die and 3 odd, each dice has a 50% chance of showing an even number.

An easier way to think about this might be what are the chances that both dice show odd, because that is the only scenario where neither show an even number.

To do this, simply multiply the chances together:

[tex]0.5 * 0.5 = .25[/tex]

Therefore, there is a 25% chance that both die will be odd, meaning there is a 75% chance that one or both of the dice show an even number

Answer:

P = 342 ft

General Formulas and Concepts:

Pre-Algebra

Evaluations

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Equality Properties

Terms/Coefficients

Quadratics

Geometry

Area of a Rectangle Formula: A = lw

Perimeter of a Rectangle Formula: P = 2w + 2l

Step-by-step explanation:

Step 1: Define

Identify variables.

A = 5670 ft²

"Length that is 9 feet less than 3 times its width" → l = 3w - 9

Step 2: Find w

Since length/width cannot be negative, we know that w = 45 ft.

Step 3: Find l

Step 4: Find Perimeter

∴ The perimeter of Janice's fence is 342 ft.

Let width be x ft

Length be 3x-9ft

Now

On solving we wI'll get x=-42,45

Take it positive

Now

Perimeter

Answer:

yes your math seems about right but wait for someone else to respond also because im not completely sure

Step-by-step explanation:

[tex]\text{Given that,}\\\\\text{Width,}~ w = 3x-2\\\\\text{Length,}~ l = x+5 \\\\\\\text{Perimeter} =2(w+l) = 2(3x-2+x+5) = 2(4x +3) = 8x +6[/tex]