Please Help me turn vertex form to standard form!!

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3 {x}^{2} + 9x - 30[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x where a parabola cuts the x - axis (y = 0) are the roots of the quadratic equation.

I.e -5 and 2 for the given problem.

and the equation can be represented as :

[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x - x1)(x- x2)[/tex]

where, x1 and x2 are the roots of the quadratic equation, a is a constant value (depicting strech in curve)

Now, plug in the values :

[tex]\qquad\displaystyle \tt \rightarrow \: y= a(x- 2)(x - ( - 5))[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x- 2)(x+ 5)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = a( {x}^{2} + 5x - 2x - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= a( {x}^{2} + 3x - 10)[/tex]

Now, we need to find the value of a, for that let's use the coordinates of a point lying on the curve (1 , -18)

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a( {1}^{2} + 3(1) - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a(1 + 3 - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a( - 6)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: a = ( - 18) \div ( - 6)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: a = 3[/tex]

Now, we got all required values. let's plug the value of a in equation, and we will get the required equation of parabola.

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3( {x}^{2} + 3x - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3 {x}^{2} + 9x - 30[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]\textsf{Factored form}: \quad f(x)=3(x-2)(x+5)[/tex]

[tex]\textsf{Standard form}: \quad f(x)=3x^2+9x-30[/tex]

Step-by-step explanation:

Factored form of a quadratic function

[tex]f(x)=a(x-p)(x-q)[/tex]

where:

Given x-intercepts:

Substitute the given x-intercepts into the formula:

[tex]\implies f(x)=a(x-2)(x+5)[/tex]

To find a, substitute the given point (1, -18) into the equation and solve for a:

[tex]\implies -18=a(1-2)(1+5)[/tex]

[tex]\implies -18=a(-1)(6)[/tex]

[tex]\implies -6a=-18[/tex]

[tex]\implies a=3[/tex]

Therefore, the equation of the function in factored form is:

[tex]\boxed{ f(x)=3(x-2)(x+5)}[/tex]

Expand the brackets:

[tex]\implies f(x)=3(x^2+3x-10)[/tex]

[tex]\implies f(x)=3x^2+9x-30[/tex]

Therefore, the equation of the function in standard form is:

[tex]\boxed{f(x)=3x^2+9x-30}[/tex]

Answer:

  (d)  h(x) = 1/4x

Step-by-step explanation:

You want to know the inverse of the function f(x) = 4x.

The inverse of y = f(x) will be the solution to x = f(y).

  x = f(y)

  x = 4y . . . . . . substitute the argument in the function definition

  x/4 = y . . . . . divide by 4 to solve for y

The inverse function is ...

  h(x) = (1/4)x

Answer:

x = 8

Step-by-step explanation:

The angles shown are vertical angles

Vertical angles are congruent (equal to each other)

This means that 8x + 36 = 5x + 60

Using this equation we can solve for x

8x + 36 = 5x + 60  

==> subtract 36 from both sides

8x = 5x + 24

==> subtract 5x from both sides

3x = 24

==> divide both sides by 3

x = 8

Answer:

8x + 36 = 5x + 60

8x = 5x + 24

3x = 24

x = 8

Answer:

w = 20

Step-by-step explanation:

a) Flip the equation.

-3/4 w = -15

b) Multiply both sides by 4/(-3).

(4/-3) * (-3/4 w) = (4/-3) * (-15)

w = 20

10 pounds of less expensive tea should be used in the mixture.

Inferior tea price = $2.00

Superior tea price = $5.00

Blended tea price = $4.25

Solution:

Price of 40 pounds of a custom blended tea = $4.25 * 40 = $170

Let x be the inferior tea quantity and

(40 - x) be the superior tea quantity.

2x + 5(40 - x) = 4.25 * 40

2x + 200 -5x = 170

-3x = -30

x = 10

Therefore, 10 pounds of less expensive tea should be used in the mixture.

To learn more about mixture allegations, refer

https://brainly.in/question/1139725

#SPJ13

The most appropriate choice for Distance will be given by:

The ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].

What is Distance?

The length of the path an object takes without taking into account the direction of motion of the object is known as distance.

If [tex]s[/tex] is the speed of the object and [tex]t[/tex] is the time, then

Distance = [tex]s \times t[/tex]

Here,

[tex]H(t) = 30t - 5t^2[/tex], [tex]t[/tex] is the time in seconds

For finding the time taken by the ball to reach a height of [tex]45[/tex][tex]m[/tex], we need to substitute [tex]H(t) = 45[/tex]

Now putting [tex]H(t) = 45[/tex]

[tex]45 = 30t - 5t^2\\5t^2 - 30t+45 = 0\\ 5(t^2 -6t + 9)=0\\t^2 -6t+9=0\\t^2-3t-3t+9=0\\t(t-3)-3(t-3)=0\\(t-3)(t-3)=0\\t-3 = 0\\t = 3s[/tex]

So the ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].

To learn more about Distance, refer to the link:

https://brainly.com/question/26046491

#SPJ10

Answer:

g(-3) = 16

Step-by-step explanation:

To find g(-3), we need to plus -3 into the given function. So, g(-3) = |2(-3) - 10|. Now we solve using PEMDAS. Two times -3 is -6, then we have g(-3) = |-6-10| which is essentially g(-3) = |-16|. Lastly, we take the absolute value of |-16| which is just 16, therefore g(-3) = 16.

Answer:

g = 2

Step-by-step explanation:

11- (15g - 13) = - 6 ( subtract 11 from both sides )

- (15g - 13) = - 17 ( multiply both sides by - 1 )

15g - 13 = 17 ( add 13 to both sides )

15g = 30 ( divide both sides by 15 )

g = 2

The solution of the given inequality would be x = 4. the graph of the given inequality is attached below.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

Given the inequality as |8x−8|≤24.

For solving the given expression,

|8x−8|≤24

We can consider the expression as;

8x−8 = 24

8x = 24 + 8

8x = 32

x = 32/8

x = 4

Hence, the solution of the given inequality would be x = 4.

Learn more about inequalities here:

https://brainly.com/question/27425770

#SPJ1

Answer:

185

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

250

244

18

10

are one of the answers

give this 5 stars if correct

The height of the plane PA is given as; 1591 ft

There are different trigonometric ratios such as;

cos θ = adjacent/hypotenuse

sin θ = opposite/hypotenuse

tan θ = opposite/adjacent

Now, looking at the given image showing plane and bridge indicated by lines, we can use one of the trigonometric ratios to get the height of the plane PA as;

PA/3000 = tan B

now angle B = 28 degrees from alternate angles postulate. Thus;

PA/3000 = tan 28

PA = 3000 * tan 28

PA = 3000 * 0.5317

PA = 1591 ft

Read more about trigonometric ratios at; https://brainly.com/question/13276558

#SPJ1

[tex]tan 28^o = \frac{PA}{3000}[/tex]

tan 28° · 3000= PA

(use a scientific calculator)

1595.128= PA

height = 1595

The false statement about the statement is (a) If you subtract 6 from b, it will be less than or equal to a.

From the question, the inequality is given as

y > x - 6

The ordered pair is given as

(a, b)

The above ordered pair implies that

(x, y) = (a, b)

So, we have

x = a and y = b

This means that

b > a - 6

Subtract 6 from both sides

b - 6 > a - 6 - 6

Evaluate

b - 6 > a - 12

Using the above as a guide, we cannot determine the direct relationship between variables a and b.

However, it is false that b is less than a

Hence, the false statement is (a)

Read more about inequalities at

https://brainly.com/question/25275758

#SPJ1

Complete question

The ordered pair (a,b) satisfies the inequality y > x - 6

Which statement is NOT true?

A. If you subtract 6 from b, it will be less than or equal to a.

B. If you add 6 to a, it will be greater than b.

C. a is greater than b.

D. If you add 6 to a, it will be less than b.

Answer:

42%

Tell me if you need expalining!

Step-by-step explanation:

The inequality that represents, the number of shirts he needs to remove to meet the flight requirements is 0.75p + 50ibs  ≤ 49

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Let the weight of Rodney suitcase be p

First the contents inside must weigh less than 50lbs.

x < 50

The suitcase weighs 4 pounds and the contents he wants to pack weigh 49 pounds.

0.75p < 49

Therefore, 0.75p + 50ibs  ≤ 49

The inequality that represents, the number of shirts he needs to remove to meet the flight requirements is 0.75p + 50ibs  ≤ 49

Learn more about inequalities here:

https://brainly.com/question/27425770

#SPJ1

The number of strawberry they picked is about 4050.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

89 kg = 89000 g conversion

89000=22=4045.45 ≈4045

{unit conversion}

≈4050

The number of strawberry {nearest lo} is about 4050

To learn more about division from given link

https://brainly.com/question/24662212

#SPJ9

The remainder of f(x) is 385.

What are the 5 steps of long division?

The five steps of long division are given by:

Step 1: Divide

Step 2: Multiply

Step 3: Subtract

Step 4: Bring down

Step 5: Repeat

Given,

f(x) = x3 + 5x2 –32x – 7 is divided by x – 4

To find the Remainder

Now, The solution is:

             [tex]x^{2} -9x+98[/tex]

[tex]x-4\sqrt{x^3+5x^2-32x-7}\\[/tex]

         [tex]x^{3} - 4x^2[/tex]

        -     +

      -----------------------------

                [tex]9x^{2} -32x[/tex]

                [tex]9x^{2} +36x[/tex]

              -        -

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

                       98x -7

                       98x - 392

                       -       +

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

             Remainder  385

Hence, The remainder of f(x) is 385.

Learn more about Long division Method at:

https://brainly.com/question/3935316

#SPJ1

The two triangles are similar.

Similar triangles are triangles that have the same shape, but their sizes may vary.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The side lengths of two similar triangles are proportional. That is, if ΔABC is similar to ΔDEF , then the following equation holds:

AB / DE  = AC / DF = BC / EF

Hence,

6 / 3 = 10 / 5 = 8 / 4 = 2 / 1

This common ratio is called the scale factor .

The symbol ∼ is used to indicate similarity.

Therefore, the triangles are similar.

learn more on similar triangle here: https://brainly.com/question/22411257

#SPJ1

The possible change in volume that results from the error in measuring the radius is 32. 06 millimeters

It is important to note that the formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Given that;

Based on the information given, we have the measure of the radius to be 5 mm, with a possible measurement error of 0.1 mm

The original value of radius  = 5mm

Radius after the measurement error = 5 + 0. 1 = 5. 01mm

Let's substitute the values into the formula

Volume = 4/ 3 (3.14)(5)³

We then expand the bracket

Volume = 4/ 3 (392.5)

Volume = 523. 3 cubic millimeters

For radius of the measurement error = 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

Then, expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 cubic millimeters

Change in volume = 555. 4 - 523. 3 = 32. 06 cubic millimeters

Hence, the change in volume is given as 32. 06 cubic millimeters

Learn more about volume here:

https://brainly.com/question/1972490

#SPJ1

slope of the rode is 0.015.

What is slope of line ?

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The point with coordinate having same slope as with given coordinates can be plotted on the same line.

Here, it is given that :

When driving up a certain hill, we rise 15 feet for every 1000 feet that is :

for 15 feet up = 1000 feet forward

Now,

slope = upward distance / horizontal distance covered

slope = 15/1000

slope = 0.015

slope is a unitless quantity.

Therefore, slope of the rode is 0.015.

check and know more about slope here :

https://brainly.com/question/14914699

#SPJ1

The probability that a randomly chosen battery pack lasts longer than 260 hours is 0.69.

What is a normal distribution?

The normal distribution is a probability distribution that is symmetric about the mean and demonstrates that data that are closer to the mean are more likely to occur than data that are farther from the mean.

Since the life span of the battery pack is known to be Normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = life spans of battery packs.

µ = mean life span

σ = standard deviation

From the information given,

µ = 250 hours

σ = 20 hours

The probability that a battery pack lasts longer than 260 hours. It is expressed as

P(x > 260) = 1 - P(x ≤ 260)

For x = 260

z = (260 - 250)/20 = 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.69

To learn more about the normal distribution from the given link

https://brainly.com/question/4079902

#SPJ4

The probability that a randomly chosen battery pack lasts longer than 260 hours is 0.69.

What is a normal distribution?

The normal distribution is a probability distribution that is symmetric about the mean and demonstrates that data that are closer to the mean are more likely to occur than data that are farther from the mean.

Since the life span of the battery pack is known to be Normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = life spans of battery packs.

µ = mean life span

σ = standard deviation

From the information given,

µ = 250 hours

σ = 20 hours

The probability that a battery pack lasts longer than 260 hours. It is expressed as

P(x > 260) = 1 - P(x ≤ 260)

For x = 260

z = (260 - 250)/20 = 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.69

To learn more about the normal distribution from the given link
brainly.com/question/4079902
#SPJ4

It is said that the ratio of point B to point AC is 2: 3.

This implies;

BC/AB = 3/2

BC = 3(b - a)/2

Thus;

AB + BC Equals AC

AC equals b-a plus 3(b-a)/2.

b-a - 3b/2 - 3a/2 = AC

AC = 5b/2 - 5a/2

AC = ⁵/₂(b - a) (b - a)

Using the same vector addition law, we can state that;

OC = AC – AO

OC = ⁵/₂(b - a) - (-a) (-a)

Given that giving OA is the inverse of -a, I used -a for AO.

Thus;

OC = 5b/2 - 5a/2 + a

OC = (⁵/₂)b - (³/₂)a

OC = ¹/₂(5b - 3a) (5b - 3a)

What is vector addition law?

Objects with both direction and magnitude are referred to be vectors. When two vectors have the same magnitude and direction, they are deemed to be one and the same. A line and an arrow are used to symbolize these geometrical objects. This arrow points in the direction of the vector, and the line's length indicates the vector's magnitude. These arrows, therefore, have a starting point and an ending point. Physical quantities like velocity, displacement, and acceleration are represented by vectors.

Notation A vector is frequently written in bold letters, such as an or b.

As seen on the right side, a vector may alternatively be expressed as the letters for its head and tail with an arrow above it.

Learn more about  vector addition law  visit:

https://brainly.com/question/14454864

#SPJ1

2)

When we say that w = 4, it means that we can rewrite the expression and instead of "w", we will put "4", so

Now we have a numerical expression to solve, we can easily solve it!

Therefore, the final answer is

5)

Here we will do the same thing, the "hard" part is solving the numeric expression, it will be a little bit harder than the 2).

Again, repeat the same process, rewrite the expression, and instead of "m" you put "5"

Again, another expression to simplify, remember that we always solve what is inside ( ) first, and we have a multiplication inside ( ) so we must solve it first

Now we solve the multiplication inside ( ) we can do the subctration

The last step is just to solve another multiplication

Now we simplified everything we can have the final answer:

6)

Here we have a division, but it's similar with 5) and 2), we have

No secrets, repeat the process, but here, "a" will turn into "15", then

We can do the multiplication at the numerator of the fraction

Now we can simplify the fraction, 30 divided by 3 is 10, then

Now just do the sum and it's done!

Hence the final answer is

ANSWERS:

1) 43

2) 13

3) 67

4) 12

5) 39

6) 23

Answer:

[tex] \dfrac{7^{36}}{9^{24}} [/tex]

Step-by-step explanation:

(9^6 x7^-9)^-4=

[tex] = (9^6 \times 7^{-9})^{-4} [/tex]

[tex] = 9^{-24} \times 7^{36} [/tex]

[tex] = \dfrac{7^{36}}{9^{24}} [/tex]

Answer:

so the width is 16/35 miles

Step-by-step explanation:

Length - 7/8 miles

Area - 8/20 miles

we know from the equation that area = Length x width

we need to rearrange so the width = Area ÷Length

width = 8/20 ÷ 7/8

= 8/20 × 8/7

= 16/35

The explicit formula and the recursive formula are aₙ₋₁ +  200 and the rest is mentioned below.

A formula can be either recursive or explicit. The main difference between Recursive and Explicit is that Recursive formula gives the value of a specific term based on the previous term while Explicit formula gives the value of a specific term based on the position.

Given : a₁ =  -26, a₂ = 174, a₃ = 374, a₄= 574

The common difference that is d can be found out by

thus d = a₂ - a₁ = 174 -(- 26 ) = 174 + 26 = 200

And this is same for all the numbers of this particular sequence.

Thus aₙ = aₙ₋₁ + d

            = aₙ₋₁ +  200

Recursive formula :  aₙ₋₁ + d

That is the following sequence will have a common difference of 200 and the next 5th, 6th, 7th and nth term is going to be .

774 , 974 ... etc

To know more about arithmetic sequences visit:

https://brainly.com/question/8972906

#SPJ13

Answer:

210 days

Step-by-step explanation:

7 x 30 = 210 days

Answer:

210

Step-by-step explanation:

A Friday occurs every 7 days.

A new moon occurs (approximately) every 30 days.

We need the smallest number that is a multiple of both 7 and 30.

We need the least common multiple (LCM) of 7 and 30.

This is the same as finding the least common denominator for two fractions that have denominators 7 and 30.

First, we find the prime factorizations of the two numbers.

7 = 7

30 = 2 × 3 × 5

The LCM is the product of common and not common factors with the larger exponent.

LCM = 2 × 3 × 5 × 7 = 210

Answer: 210

P.S. This is the correct answer for this problem, but the problem is stated incorrectly since a new moon occurs approximately every 29.5 days, so in reality, the true answer is not 210 days.

Chester made 9 sales and Vickie made 16 sales this week

Base salary of Vickie = $70

Vickie's commission per sale = $24

Base salary of Chester = $142

Chester's commission per sale = $9

Both people earned the same amount this week. Let x represent the number of sales made by Vickie, then sales made by Chester is x+7

Formulating the equation we get:

Base salary of Vickie + Vickie's commission per sale*Number of sales = Base salary of Chester + Chester's commission per sale*Number of sales

= 70 + 24x = 142 + 9(x+7)

70+24x = 142+9x+63

70+24x = 205+9x

15x = 135

x = 9

Chester sales = 9

Vickies sales = 9+7 = 16

Learn more about linear equations:

https://brainly.com/question/13738061

#SPJ1

Answer:

2 dimes and 5 pennies

Step-by-step explanation:

2 dimes (d) is 10 and 5 pennies (p) is 5

75+p+d=100

75+p=80

80+d=100

Answer: 3 quarters, 2 dimes, 1 nickel.

Step-by-step explanation: 3 quarters are worth 75 cents, 2 dimes are worth 20 cents, and 1 nickel is worth 5 cents! Hope this helps

Given

Find

showing that angles H and F are supplementary.

Explanation

Let angle F , which is subtended by minor arc GHE.

so , angle F = half of angle GHE by subtended angle theorem.

similarly , angle H is the angle subtended by major arc GFE.

so , angle H = half of the angle subtended by major arc.

since , total angle around J is 360 degree.

as we know , the sum of angle subtended by minor arc and major arc is 360 degree.

so , angle F + angle H = 1/2(360) = 180 degree.

Final Answer'

Hence , H and F are supplementary angles.