Solve 2x^2+12=x−3 help

Answer:

Below in bold.

Step-by-step explanation:

Let (x, y) be a point on the parabola. As the graph is a parabola, the distance of this point to the focus is equal to the distance of  this point from the directrix. So:

√(( x - 2)^2 + (y - 3)^2) = y - (-1)

Squaring both sides:

(x - 2)^2 + (y - 3)^2 = (y + 1)^2

x^2 - 4x + 4 + y^2 - 6y + 9  = y^2 + 2y + 1

x^2 - 4x  + 4 + 9 - 1 = 2y + 6y

8y = x^2 - 4x + 12

y = 1/8(x^2 - 4x + 12)

or we can write it as

y = 1/8x^2 - 1/2 x + 3/2.

Answer:19.93

Step-by-step explanation:

11 x 8 x 15 = 1320

then u would simplify

The value is: angle x is approximately 103.95 degrees.

Here, we have,

To calculate the size of angle x, you can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

In this case, the sides of the triangle are given as follows:

a = 8 cm (adjacent to angle x)

b = 11 cm (opposite to angle x)

c = 15 cm (hypotenuse)

The Law of Cosines states:

c² = a²+ b² - 2ab*cos(x)

Substituting the given values:

15² = 8² + 11² - 2(8)(11)*cos(x)

225 = 64 + 121 - 176*cos(x)

Simplifying:

225 = 185 - 176*cos(x)

Rearranging the equation:

176cos(x) = 185 - 225

176cos(x) = -40

Now, divide both sides by 176 to isolate the cosine term:

cos(x) = -40/176

cos(x) ≈ -0.2273

To find the value of angle x, take the inverse cosine (cos⁻¹) of -0.2273:

x ≈ cos⁻¹(-0.2273)

x ≈ 103.95 degrees

Therefore, angle x is approximately 103.95 degrees.

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Answer:

5

12

0

range

Step-by-step explanation:

i just did it, these are the right answers.

Answer:

5,12,0, and the last answer is range

Step-by-step explanation:

Did it on Edge2021. Hope this helps!

Answer:

linear model

Step-by-step explanation:

This is a linear function.  The initial value is 20 ft, and the yearly growth is 2ft/yr.  Thus, the function is

height(t) = (20 ft) + (2 ft/yr)t, where t is the number of years.

Answer:

a(1) = 72

a(n) = a (n-1) - 18

Step-by-step explanation:

This is a simple series of multiplication of 18 . If we divide all the numbers by 18 we get

72/18, 54/18, 36/18. 18/18, 0/18

4      , 3      , 2     , 1 ,       0

So we can see that the numbers are in  decreasing order as the multiples of 18.

in other words the first term is a= 72

from which we subtract 18 and get 54 and so on.

So the general rule would be

a(1) = 72

a(n) = a (n-1) - 18

Where n and (n-1 ) are subscripts. We are just subtracting 18 from the number to get the answer.

72-18= 54

54-18= 36

36-18= 18

18-18=0

[tex] \cos(2A)=\cos^2 A-\sin^2A=(\cos A+ \sin A)(\cos A-\sin A)[/tex]

substitute the second term in LHS to get

[tex]{ (\cos A - \sin A)^2 \over \cos(2A))}[/tex]

expand the square, [tex] \frac{1-2\sin A \cos A}{\cos 2A}= \sec2A- \tan 2A[/tex]

([tex] \sin (2\theta)=2 \sin\theta\cos\theta[/tex])

Answer:

Both sides can take the same identity

Step-by-step explanation:

Sec 2A - tan 2A

Express with sin and cos

1/cos (2A) - sin (2A)/cos (2A)

= 1 - sin (2A) / cos (2A)

=

1 - sin (x) = 1-sin (x) = 1 - sin^2 ( x ) / 1 + sin (x)  

=

1 - sin ^2 (x) = cos ^2 (x)  

=cos ^2 (2A) / 1+sin (2A)/Cos (2A)

simplified

cos (2A) / 1+sin 2A

identity x used = cos 2x = cos ^2 x - sin ^2 x

= 1 + sin (2x) + (cos (x)) + (sin (x))^2

= cos ^2A - sin ^2A / (cos A - sin A) ^2

= cos A - sin A / cos A +sin A

Both sides are true.

Answer:

Every 18 miles he uses 3 gallons

divide this:

18 ÷ 3 = 6 miles per gallon

30 miles = 30 ÷ 6 = 5 gallons

7 gallons = 7 x 6 = 42 miles

48 miles = 48 ÷ 6 = 8 gallons

10 gallons = 10 x 6 = 60 miles

Hope this helps :D

Answer:

1  :2

Step-by-step explanation:

12 are yellow, 4 are pink

To find the number of red

24 -12 -4 = 8

There are 8 red balls

We want the ratio of

red: yellow or pink

8 : 12+4

8 :16

Divide each side by 8

8/8 : 16/8

1  :2

Answer:1:2

Step-by-step explanation: 12 yellow + 4 pink= 16

24 balls total minus 16 =8 red balls so 8:16=1:2

Answer:

To have maximum profit, the price must be increased by 5,

Step-by-step explanation:

Given that the price increase function is:

f(x) = -2x² + 20x + 150,

For maximum profit, then f(x) = 0.

Putting f(x) = 0, we have

-2x² + 20x + 150 = 0

Or

x² - 10x - 75 = 0

(x + 5)(x - 15) = 0

x = -5

Or

x = 15

Again, differentiating f(x) and equating to zero, we have

-4x + 20 = 0

4x = 20

x = 20/4

= 5

To have maximum profit, the price must be increased by 5,

Answer:

198

Step-by-step explanation:

Of means multiply and 22% as a decimal is 0.22, so multiply 0.22 by 900.

900*0.22=198

Answer:

198

Step-by-step explanation:

22% of 900

of means multiply

22% * 900

Change to decimal form

.22 * 900

198

Step-by-step explanation:

half life time-50%-8.4hr

so for 10%- 8.4/5=1.68 hr

now for 70%

1.68 × 7 = 11.76 hrs

to one decimal place - 11.8hrs

11.8 hours ago, there were 70% more of the substance if an isotope of lead has a half-life of 8.4 hours.

Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay.

Half-life period - 50% -8.4hours

so for 10%- 8.4/5 = 1.68 hour

now for 70%

1.68 × 7 = 11.76 hours

To one decimal place - 11.8hours

Hence, 11.8hours is the answer.

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Answer:

Hey There!! The answer to this is Correct option: 1) 2600 The letter has a total of 26 possible values (from 'a' to 'z'), and each digit has a total of 10 possible values (from 0 to 9).

So, to find the number of reserved seats possible, we just need to multiply the number of possible values of each letter and digit.

We have one letter and two digits, so we have:

26 * 10 * 10 = 2600 possible reserved seats

Thus, Correct option: 1)

Hope It Helped!~ ♡

ItsNobody~ ☆

The total number of combinations of one letter followed by two digits is 2600 option (1) 2600 is correct.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

The missing options are:

We have:

The university theater uses a combination of one letter (A - Z) and two digits (0 - 9) to identify their reserved seats

As we know, in the alphabet(A to Z) there are the 26 letters and total number of digits (0 to 9) is 10

A total number of combinations of letters followed by two digits can be calculated as follows:

As we have one letter and two digits

= 26×10×10

= 2600

, so we have:

26 * 10 * 10 = 2600 possible reserved seats

Thus, the total number of combinations of one letter followed by two digits is 2600 option (1) 2600 is correct.

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Answer:

1. duck will travel in still water paddles 4 yards = 38,7 sec

up stream speed = 0,63 mph

down stream speed = 0,68 mph

Answer:

  One-sixth d + one-eighth d = 1

Step-by-step explanation:

When they work together, their rates of completion add. They want to build one shed, so the number of sheds being built is ...

  (Kaitlyn's sheds per day)×(days Kaitlyn works) +(Mark's sheds per day)×(days Mark works) = 1 shed

  (1/6)d + (1/8)d = 1 . . . . matches the last choice

Answer:

x = -2

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask ;)

The value of the function (f+ g)(x) = 0 then x = -2.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given:

f(x) = x² - 2x and g(x) = 6x + 4

As,  (f+g)(x) = 0

x² - 2x + 6x + 4 = 0

x² + 4x + 4 =0

x² + 2x + 2x + 4 = 0

x(x+2) + 2 (x +2 )= 0

(x + 2)(x+2) = 0

(x+ 2)²= 0

x+ 2= 0

x = -2

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Problem 1.

My thinking is that the furthest you can get is have two points at each opposite corner, so the distance between them is sqrt(2). If we have two other points with this property, then all four corners are filled up. It is possible to pick two points where the distance is 1 unit.

Then a fifth point can be placed at the center such that the distance from it to any of the corners is sqrt(2)/2. We placed the fifth point at the center to try to get as far away as possible from the other four points.

Basically we're trying to find the worst case scenario (leading to the largest distance possible) and seeing how we can fill up the square. This establishes the upper bound. Any other kind of scenario will have a distance less than the upper bound.

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

Problem 2.

For this one, I'm not sure what to make of it. The terminology is a bit strange so I'm not going to be fairly helpful here. Sorry about that.

If I had to guess, I'd assume it has something to do with the fact that a plane is uniquely defined by 3 points. That fourth point is not coplanar with the other three, which helps define the semi-spherical portion. The fifth point is just extra. The points can't be all collinear or else a plane won't form. Though to be honest, I'm still not sure about problem 2. I'd get a second opinion.

Step-by-step explanation:

Let's take a look at the dimensions of the cube. Since each cube has a side length of 1, the answer to the question is 1 x the number of cubes. Counting the sides gives 2 x 3 x 4, or 24 yd^3

Answer:

Step-by-step explanation:

Since the new price is lesser than the original price the percentage change will be a decrease.

To find the percentage change use the formula

[tex]Percentage \: \: change = \frac{change}{original \: \: quantity} \times 100[/tex]

To find the change subtract the new price from the original price

new price = $199.95

original price = $246.95

Change = $246.95 - $ 199.95 = $47

[tex]Percentage \: \: change = \frac{47}{246.95} \times 100[/tex]

Hope this helps you

Answer:

33

Step-by-step explanation:

We can write an equation:

x+x+1+x+2+x+3=130

x represents the smallest number of the consecutive integers

By the way, an example of consecutive would be 2, 3, 4, 5 or 10, 11, 12, 13

We can combine like terms from our equation:

4x+6=130

4x=124

x=31

The smallest number is 31. The second number would be 31+1=32, which means the third number is 33!

Hope this helps! :) :)

Answer:

[tex]\huge\boxed{3rd\ number = 33}[/tex]

Step-by-step explanation:

Let the consecutive numbers(Coming one after another) be x, x+1, a+2 and x+3

So,

x+x+1+x+2+x+3 = 130

4x + 6 = 130

Subtracting 6 to both sides

4x = 130-6

4x = 124

Dividing both sides by 4

x = 32

So,

1st number = x = 31

2nd Number = x+1 = 31+1 = 32

3rd number = x+2 = 31+2 = 33

4th number = x+3 = 31+3 = 34

Answer:

26 units

Step-by-step explanation:

Answer:

657.88 i guess becuz by using pythagoras i got 320 for the hypotenous

Answer:

Hey there!

A "flip" can be considered a reflection.

A "spin" is a rotation.

A "slide" is a translation.

None of these transformations change the way a shape looks, or the size of the shape. They only change how the shape is oriented.

Let me know if this helps :)

In this exercise we have to differentiate three geometric terms, in this way we can say that;

So in a more in-depth way these geometric terms can be described as:

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Answer:

a i think

Step-by-step explanation:

Answer:

184

Step-by-step explanation:

Answer:

5 is the answer

............

Answer:

5

Step-by-step explanation:

What number multiplied by itself gives you 25

5*5 = 25

sqrt(25) = 5

Answer:

BCDE= 100+ 80+100+80 = 360 degree

BAC = 20 degree

DBC = 100 degree

BDE = 80 degree

Shows all is correct

We associate isosceles trapezoid in this question, this helps us prove with angle A in the triangle vertices how we can find one of the adjacent angles from the trapezoid by subtraction when all angles within one single trapezoid = 360 degrees. We can use 20 degree angle A to subtract and find each alternative angle easier.

Step-by-step explanation:

The semi circle shows 9 stones

Where angles are interior to the trapezoid

Where all 4 sided shapes add up to 360 degree

We draw a line of symmetry on BCED angle

To make midway points BC  and DE = 90 degree

The two new formed shapes are still 4 sided and add up to 360 degree.

BC + DE = 180 degree

BDE = Triangle 180 -20/2 = 160/2 = 80

BCDE = Trapezoid = 360

Trapezoid angle DBC = 360-80-80/2 = 360-160/2 = 200/2 = 100 degree  

Finding interior angle A (BAC)

BAC = 180/9 = 20 degree

BAC * (2) = 360 degree circle

BAC = 360/18 = 20 degree

Proves BAC = 20 degree

20 degree is used in BAC workings above in bold and proves all trapezoid angles are correct. We now know this is an isosceles trapezoid and that is why symmetry and midway points can help us find the angles without any given length.

Answer:

$1171.05

Step-by-step explanation:

1500 × (1-(6 / 100))⁴

Answer:

Hey there!

Each year, the computer is (100-6), or 94% of it's original value.

Thus, we have:

Original: 1500

First year: 1500(0.94)

Second year: 1500(0.94)(0.94)

Third year: 1500(0.94)(0.94)(0.94)

Fourth year: 1500(0.94)(0.94)(0.94)(0.94)

Fourth year: 1171 dollars.

Hope this helps :)

Answer:

1) Get rid of grouping symbols like square brackets and parentheses

2) Simplify both sides of the equation. Combine like terms if possible.

3) Choose where you want to keep the variable because that will help you decide where to place the constant.

4) Eliminate numbers or variables by using opposite operations. Remember that addition and subtraction are opposites and so are multiplication and division.

Step-by-step explanation:

Answer:

[tex]\boxed{x=1}[/tex]

Step-by-step explanation:

[tex]2(10-2x) = 4(3x + 1)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]20 - 4x = 12x + 4[/tex]

[tex]\sf Subtract \ 12x \ and \ 20 \ from \ both \ sides.[/tex]

[tex]20 - 4x - 12x - 20 = 12x + 4 - 12x - 20[/tex]

[tex]-16x = -16[/tex]

[tex]\sf Divide \ both \ sides \ by \ -16.[/tex]

[tex]\displaystyle \frac{-16x}{-16} =\frac{-16}{-16}[/tex]

[tex]x=1[/tex]

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▹ Answer

x = 1

▹ Step-by-Step Explanation

2(10 - 2x) = 4(3x + 1)

Simple terms are written last:

2(-2x + 10) = 4(3x + 1)

Distributive Property:

-2 * 2x + 2 * 10 = 4 * 3x + 4

x = 1

Hope this helps!

CloutAnswers ❁

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Answer:

218

Step-by-step explanation:

572/21 = 27.23

8 x 27.23 = 217.9

Answer Check:

21/8 = 2.6

572/218 =2.6

8/21 = .38

218/572 = .38