Simplify and state the restrictions on the domain:

The missing statement is the quadratic formula and the correct option therefore is the third option;

The quadratic formula is used to find the solution of a quadratic equation. The quadratic formula is; \(x = \frac{-b\pm\sqrt{b^2-4\cdot a\cdot c} }{2\cdot a}\)

The statements and reasons can be presented algebraically as follows;

Statements \({}\)                                          Reasons

\(x^2+\frac{b}{a}\cdot x+(\frac{b}{2\cdot a} )^2 = -\frac{4\cdot a\cdot c}{4\cdot a^2}+ \frac{b^2}{4\cdot a^2}\)        Find a common denominator on the

                                                            right side of the equation

\(x^2 + \frac{b}{a} \cdot x+(\frac{b}{2\cdot a} )^2 = \frac{b^2-4\cdot a \cdot c}{4\cdot a^2}\)                 Add the fractions together on the

                                                     \({}\)        right side of the equation

\((x +\frac{b}{2\cdot a} )^2 = \frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2}\)                             Rewrite the perfect squared equation

                                                      \({}\)      to the left side of the equation as a

                                                        \({}\)    binomial squared

\(x + \frac{b}{2\cdot a} = \pm\sqrt{\frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2} }\)                   Take the square root of both sides of  the

                                                    \({}\) equation

\(\underline{x = \frac{-b\pm\sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}}\)                                 Simplify the right side of the equation    

The correct option is therefore;

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Answer:

A

Step-by-step explanation:

i took the test

have a great day :) .!

Answer:

When using inverse operations with negative numbers, when you change subtraction to addition, the negative turns to a positive.

-8 - -10 can be changed to:

8 + 10

8 + 10 = 18

Step-by-step explanation:

Hope it helps! =D

Sorry took so log to answer. My internet is being slow some reason. -_-

=168.96m

that's my answer

hope it's help

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

$292.40 earned

Step-by-step explanation:

$10.75 x 27 = $290.25

$10.75 x 1/5 = $2.15

$290.25 + $2.15 = $292.40 (total earned)

I hope this helps :)

Answer:

k=44

Step-by-step explanation:

Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

Answer:

Step-by-step explanation:

1. This paragraph describes an observational study.

It is not a controlled experiment because the guidance counselors didn't plan to separate the students into 2 groups and then observe the results. They instead checked records.

2. The students who took Latin are the treatment group.

3. The fact that students decided on their own to take Latin is a confounding factor.

4. The students who did not take Latin are the placebo or control group.

Answer:

it is b

Step-by-step explanation:

The time the balls roll when the total distance is 130 cm is 10 seconds.

let

d = total distance the ball rolls

t = time in seconds

The total distance is directly proportional to the time in seconds. Therefore,

d ∝ t

d = kt

where

∝  is the proportionality sign

k = constant of proportionality

when d = 78 cm, t = 6 seconds

Therefore, let's find the constant of proportionality.

k = d / t

k = 78 / 6

k = 13

The constanst of proportionality is known . Now let's find the time(seconds) when d = 130 cm .

d = kt

make t the subject of the formula

t = d / k

t =  130 / 13

t = 10 secs

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Answer:

C

Step-by-step explanation:

A triangle always consists of it being 180 degrees. The box on the triangle on angle A depicts that it is a right angle, 90 degrees. And since Angle B is given at 45, angle C must be 45 degrees as well, since 180-45-90 (triangle angles=given angles for A and B) equal up to 45. When the angles beside the right angle is both identical and the same, the sides that correspond with that triangle is also the same. AC is given at 9 feet, and since Angle C and B both have the same angles, AB must ALSO be a 9ft.

Now, since we know the two sides, it is very easy to find BC, or the hypotenuse of the triangle, using the Pythagorean Theorem: \(a^{2} +b^{2} =c^{2}\), where a and b are sides, and c is the hypotenuse (or the long end) of a right triangle.

We can plug both 9s in for a and b since they're both the same, and it should equal to

9^2+9^2=c^2.

9^2 is 9*9, and that is 81. We have two of these so add them together to find 162. Since c^2 is equal to 162, we would need to square root both sides so we can find a number that equals c.

\(\sqrt{162} =c\)

We can either plug this into a calculator, and we should get something around 12.72, and that would be the same as C if you plug that value into a calculator.

You can also simplify the radical if you know how to. 162 is 81 times 2 (example) and 81 is 9*9, so we can add that to the outside and 2 is still under the radical. But this would only make sense if you know how to do that.

Answer: 130

Step-by-step explanation:

Scale factor = BY / TY = 72 / 45 = 1.6

So the perimeter of TZY is 208/1.6 = 130

Answer:

187.5

Step-by-step explanation:

In this sequence, you are dividing 2 each time:

Term 1: 6000

Term 2: 6000/2 = 3000

Term 3: 3000/2 = 1500

Term 4: 1500/2 = 750

Term 5: 750/2 = 375

Term 6: 375/2 = 187.5

The 6th term in the sequence is 187.5

~

Answer:

-6

Step-by-step explanation:

you multiply (3)x(-2). a negative times a positive is a negative. so you get -6

Answer:

what do u mean

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

x³ - 3 =24

x³ = 27

x = 3

Answer:

center : (-3, -1) radius : 4

Answer:

(2,-1) _______________

EXPLANATION

Given the expression √18+√2, the statement that is true about the expression is the following:

It is an irrational number an equal to 4√2

Answer:

4/8 in lowest terms is 1/2.

Step-by-step explanation:

Answer: 1/2

4/8 is equivalent to 1/2

Answer:

y=12/5 (in decimal notation y=2.4)

Step-by-step explanation:

the value of 7y-2 = 10 more than 2y

7y-2 = 10+2y

7y-2y = 10+2

5y = 12

y = 12/5

y = 2.4

Answer:

X ~ N(27, 4) ;

xbar ~ N(27, 0.1026) ;

0.5 ;

0.5

Step-by-step explanation:

Probability distribution of X : N(μ, σ²)

μ = 27 ; σ = 2

X ~ N(μ, σ²) = X ~ N(27, 2²) ;X ~ N(27, 4)

Distribution is approximately normal ; μ = xbar ; xbar = 27

(Standard Error)² = (σ/√n)²= (2/√39)² = 0.1026

xbar ~ N(μ, σ²) = xbar ~ N(27, 2²) ; xbar ~ N(27, 0.1026)

Probability that a randomly selected individual found a job in less than 27 weeks :

P(X < 27) :

Obtain the Zscore :

Z = (x - μ) / σ

Z = (27 - 27) / 2 = 0/2

Z = 0

P(Z < 0) = 0.5

D.) n = 36

P(X < 27) :

Obtain the Zscore :

Z = (x - μ) / σ/√n

Z = (27 - 27) / (2/√36) = 0/0.33333

Z = 0

P(Z < 0) = 0.5

The inequality  y < |x – 2| + 1 is shown by the plotted graph.

As an inequality is really a particular kind of relation, we may graph it just like we would any other relation. When dealing with inequalities, the trick is to darken large portions of the graph rather than using lines to link the dots.

Modulus function is given as: y = |x| and  f(x) = |x|,

For the given graph:

Thus, y < |x – 2| + 1 function is plotted.

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The complete question is attached-

The graph shows which inequality? The vertex is (2, 1).

y ≥ |x + 2| + 1

y < |x – 2| + 1

y < |x + 2| + 1

y > |x – 2| + 1

Sumando los ahorros de Juan los días lunes, martes y miércoles, los ahorros de Juan ascienden a 20 pesos.

En primer lugar, sabes que Juan ahorró 12 pesos el día lunes.

El martes Juan ahorró la mitad de lo ahorrado el lunes. La mitad de un número es un número que divida a este en dos partes iguales. Entonces la mitad de un número equivale a dividirlo entre 2 o lo que es igual multiplicarlo por \(\frac{1}{2}\).

Entonces, lo ahorrado el martes por Juan se calcula como: 12 pesos÷ 2= 6 pesos

Finalmente el miércoles Juan ahorró la tercera parte de lo que ahorró el martes.  La tercera parte de un número se obtiene al dividir un número entre tres. O  lo que es lo mismo, multiplicando por un tercio (\(\frac{1}{3}\)), dividiendo así al número en un total de tres partes iguales.

Entonces, lo ahorrado el miércoles por Juan se calcula como: 6 pesos÷ 3= 2 pesos

Entonces, sabes que los ahorros de cada día son:

Los ahorros totales de Juan es la suma de lo ahorrado el lunes, martes y miércoles:

12 pesos + 6 pesos + 2 pesos= 20 pesos

Finalmente, los ahorros de Juan ascienden a 20 pesos.

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Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

Answer:

The rate of the train on level ground is 75 mph, and the rate of the train in the mountains is 30 mph like you mentioned. If you were asking for the time it takes for the train to travel 120 miles in that speed in the mountain, then it would be 4 hours.

Answer:

3,530

Step-by-step explanation:

8474-1621=6853

6853-3323=3530