If using the method of completing the square to solve the quadratic equation
X^2 −5x−27=0, which number would have to be added to "complete the square"?

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

To learn more about Fraction here,

https://brainly.com/question/10354322

9514 1404 393

Answer:

  (d) ±√15/4

Step-by-step explanation:

Useful trig identities are ...

  cos(x) = 1/sec(x)

  sin(x) = ±√(1 -cos²(x))

__

Using these, we see that ...

  sin(θ) = ±√(1 -(1/sec²(θ))) = ±√(sec²(θ) -1)/sec(θ)

  sin(θ) = ±√(4² -1)/4 = ±√15/4

The inverse of the function f(x) = 9x²- 12 is p(x) = √(x + 12)/9

Given that the domain of a function f is restricted to x ≥ 0, we need to find the inverse of the function

f(x) = 9x²- 12 for x ≥ 0.

To find the inverse of the function, we proceed as follows.

f(x) = 9x²- 12

Let f(x) = y

So, we have that

y = 9x²- 12

Adding 12 to both sides of the equation, we have that

y + 12 = 9x²- 12 + 12

y + 12 = 9x²

Dividing both sides by 9, we have that

(y + 12)/9 = 9x²/9

(y + 12)/9 = x²

Taking square root of both sides, we have that

√x² = √(y + 12)/9

x = √(y + 12)/9

Now, replacing x with y, we have that

x = √(y + 12)/9

y = √(x + 12)/9

Replacing y with f⁻¹(x), we have that

f⁻¹(x) = √(x + 12)/9

So, the inverse is p(x) = √(x + 12)/9

Learn more about inverse of a function here:

https://brainly.com/question/29497740

#SPJ1

Answer:

P= 80, A= 160000

Step-by-step explanation:

P= 20+20+20+20

A= 20x20x20x20

Answer:

|4| = 4

|-4| = 4

Step-by-step explanation:

Answer:

its 4

Step-by-step explanation:

absolute value of 4 is 4 you get rid of any signs co efficients etc.

Answer : 11 and 13

Step-by-step explanation:

Let the numbers be X and Y then,

By question

X= Y - 2 .....................(i)

2Y = 3X - 7 ...............(ii)

putting the value of X from (i) on equation (ii) we get,

2Y = 3(Y - 2) - 7

2Y = 3Y - 6 - 7

2Y - 3y = - 13

-Y = - 13

Y = 13

now putting value of Y in equation (i)

X = 13 - 2= 11

hence those numbers are 11 and 13 respectively

Answer:

is there a picture?

Step-by-step explanation:

Answer:

Step-by-step explanation:

itd B

Answer:

1 (3.66)

2(3.5)

3(5.25)

Answer:

$13.35 is in Carla's piggy bank

The value of each variable is:

x = 11 units

y = 11√2 units

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We can find the value of each variable using trigonometric ratios:

tan 45° = x/11 (tan = opposite/adjacent)

1 = x/11

x = 11 units

sin 45° =  9/y (sine = opposite/hypotenuse)

(√2)/2 = 11/y

y = 11/ (√2)/2

y = 11√2 units

Learn more about Trigonometry on:

brainly.com/question/11967894

#SPJ1

Answer:

10 ; 22

Step-by-step explanation:

Ghana = G

Cameroon = C

Cameron only = 8

Ghana only = 12

Total sampled = 40

Both Ghana and Cameroon = x

Not traveled to either = 10

Ghana only + Cameroon only + both Ghana and Cameroon + not traveled to either  = total sampled

12 + 8 + x + 10 = 40

30 + x = 40

x = 40 - 30

x = 10

Number that had gone to Ghana before :

Ghana only + both

12 + x

12 + 10

= 22

Answer:

Step-by-step explanation:

Answer:

it's C

the square root of 10 is 3.162277

Answer:

11 books = 33 Pounds

Step-by-step explanation:

24 divided by 8 = 3 pounds per book.

3 x 11 = 33 pounds

Hope this helps

Answer:

38.5

Step-by-step explanation:

28÷8=3.5

3.5×11=38.5

Answer: each 1/3 would be 4 brownies.

Step-by-step explanation: 12 divided by 3 is 4.

Answer:

Estimation and Confidence Intervals

Step-by-step explanation:

Just found it on a math website basically.

The second derivative of the function is -6x

Derivative of a function f(x) signifies the rate of change of the function f(x) with respect to x at a point lying in its domain. For a function to be differentiable at any point x = a in its domain, it must be continuous at that particular point but vice-versa is necessarily not always true.

The derivative of a function f(x) is given as; d/dx(fx)

f(x) = -x³

d/dx = 3(-x)³⁻¹

d/dx = -3x²

For the second derivative, we would derivate the function the second time.

d²/dx² = d/dx(-3x²)

d²/dx² = 2 * (-3x)

d²/dx² = -6x

Learn more on derivative of a function here;

https://brainly.com/question/28527987

#SPJ1

\(A-x=\cfrac{xr}{t}\implies At-xt=xr\implies At=xt+xr \\\\\\ At=x(t+r)\implies \cfrac{At}{t+r}=x\)

make x the subject means write all terms in terms of x

look at attachment.

1.8 0ver 1 is the answer :)

EXPLANATION:

First we must know what data the exercise gives us and thus replace them correctly in the two formulas; in the formula for the area of ​​the arc and in the formula to find the length.The data is as follows:

-Radius(r)=5.3

-angle theta(θ)=140 degrees.

To find the area of ​​the circular sector in degrees we must use the following formula:

To find the length of the arc we must use the following formula:

IMPORTANT NOTE:

The formulas that were used to find the longitude and area of ​​the arc were in degrees since the exercise indicated that the angle theta is in degrees

The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

Read more on proportional relationship:

https://brainly.com/question/12242745

#SPJ1

The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

Learn more about equations:

https://brainly.com/question/22688504

#SPJ1

The expression "7 + 4c + 2d + 3" is already in its simplest form, which means that the terms cannot be combined any further.

What is the standard form of the equation?

A standard form is a method of writing mathematical concepts like an equation, expressions, or numbers in standard form. Example: 2.5 billion years is written as 2,500,000,000 years.

This is because the like terms in the expression, which are the terms that have the same variable and exponent, have already been combined.

In this case, there are no like terms with different coefficients that can be combined.

For example, there are no two terms with the variable "c" that have different coefficients that can be combined to simplify the expression further.

Similarly, there are no two terms with the variable "d" that have different coefficients that can be combined.

Therefore, the equivalent expression is "7 + 4c + 2d + 3 = 7 + 4c + 2d + 3".

To learn more about the standard form of the equation visit,

https://brainly.com/question/28871326

#SPJ1

Answer:

Cinthia studied 2/3 of her time on Tuesday

Answer:

first term (a)=-2

common difference (d)=8

Now,

87th term=a+(n-1)d

=-2+(87-1)×8

=-2+86×8

=-2+688

=686

Answer:

Step-by-step explanation:

10(a)+5(c)=310

a= number of adult

c= number children

Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

Read more on parallel lines here: https://brainly.com/question/12783631

#SPJ1