Which system of equations can be graphed to find the solution(s) to x^2 = 2x + 3?

Answer: The answer is [tex]1\dfrac{28}{99}.[/tex] .

Step-by-step explanation: The given rational number is

[tex]R=1.\bar{28}.[/tex]

We are to select the correct expression from the options  that is equivalent to the given rational number.

Let us consider that

[tex]x=1.\bar{28}\\\\\Rightarrow x=1.28\bar{28}\\\\\Rightarrow 100\times x=100\times 1.28\bar{28}\\\\\Rightarrow 100x=128.\bar{28}\\\\\Rightarrow 100x=128+.\bar{28}\\\\\Rightarrow 100x=127+x\\\\\Rightarrow 100x-x=127\\\\\Rightarrow 99x=127\\\\\Rightarrow x=\dfrac{127}{99}\\\\\Rightarrow x=1\dfrac{28}{99}.[/tex]

Thus, the correct option is [tex]1\dfrac{28}{99}.[/tex]

We will see that the exact value is √2/2 = 0.707, and the reference angle is 45°.

We know that for any angle θ we have that:

sin(θ) = sin(θ + n*360°)

Where n is an integer value.

To find the reference angle of a given angle θ, we just need to find a value of n such that:

0 ≤  θ + n*360° ≤ 360°

So we can write our angle in the normal range.

in this case, our angle is -135°

Then we can write:

0 ≤  -135° + n*360° ≤ 360°

Is immediate to notice that we must take n = 1

0 ≤  -135° + 1*360° ≤ 360°

0 ≤  -135° + 1*360° ≤ 360°

0 ≤  225° ≤ 360°

Now we know that θ = 225°.

Ok, this lies on the third quadrant, when an angle lies on the third quadrant, to get the reference angle you just need to subtract 180°.

We will get:

225° - 180° = 45°

So the reference angle is 45°.

Finally, to get the exact value we use:

sin (-135°) = sin(225°) = cos(45°) = √2/2 = 0.707

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Final answer:

In art, vertical lines suggest stability and structure, contrasting with calming horizontal lines and dynamic diagonal lines. These lines help define shapes, indicate motion, and guide the viewer through the composition.

Explanation:

The term vertical lines in the context of art and design, refers to lines that run up and down the canvas or design space, perpendicular to the horizon. These lines can convey a variety of meanings and emotions in visual compositions. According to a description by Oliver Harrison, vertical lines are seen as visually stable and can be associated with structures like tree trunks or classical columns, suggesting strength and stability.

The probability that 3 randomly selected people all have the same birthday is 1 in 48,627,125.

In order to find the probability that 3 randomly selected people all have the same birthday, we need to consider the total number of possible outcomes and the number of favorable outcomes. There are 365 days in a year (excluding leap years) and each person's birthday is independent of the others. Therefore, the probability of each person having the same birthday as the previous person is 1/365. To calculate the probability that all 3 people have the same birthday, we multiply the probabilities together:

P(3 people have the same birthday) = (1/365) * (1/365) * (1/365) = 1/48,627,125

Thus, the probability that 3 randomly selected people all have the same birthday is approximately 0.0000000206, rounded to eight decimal places.

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Answer:

The required form of the given expression is : (a + 4)(b + 1)

Step-by-step explanation:

The given expression is : ab + 4 + a + 4b

We need to factor he given expression and arrange the factors in the alphabetic order.

To find the factors of the given expression, we need to use the concept of algebra :

ab + 4 + a+ 4b

First rearranging the terms in order to form the factors :

= ab + 4b + 4 + a

= b(a + 4) + 1(4 + a)

= b(a + 4) + 1(a + 4)

= (b + 1)(a + 4)

Now, the factors in the alphabetic order :

= (a + 4)(b + 1)

Hence, the required form of the given expression is : (a + 4)(b + 1)

The value of the digit 4 in the number 943,268 is 40,000 because it is in the ten thousand place.

The value of the digit 4 in the number 943,268 depends on its place value in the number.

In 943,268:

- The digit 4 is in the ten-thousands place.

So, the value of the digit 4 in 943,268 is:

4 × 10,000 = 40,000

Therefore, the value of the digit 4 in 943,268 is 40,000.

Answer:

Step-by-step explanation:

Givens:

So, the problem is asking how many more bears than cougars were in the given region. From the table, we know that there where 790 cougar when the study started.

Now, we have to calculate the initial condition of the function, because it's modelling bear population. Initial condition means when the study started, which is when [tex]x=0[/tex].

So, we have:

[tex]f(0)=830(0.8)^{0}=830(1)=830[/tex]

So, there were 830 bears when the study started.

If we compare, we find that there were 40 more bears than cougars when the study started, because 830-790 = 40.

Answer:

Option 4th is correct

the domain of the following relation R is:

[tex]\{-3, 1, 6\}[/tex]

Step-by-step explanation:

Domain is the set of all values of x-coordinates where function is defined.

Given the Relation:

[tex]R = \{(6, -2), (1, 2), (-3, -4), (-3, 2)\}[/tex]

The ordered pairs are in the form of (x, y)

Domain = Set of all values of x.

In the given relation:

x-values = { 6, 1, -3}

⇒[tex]\text{Domain} = \{-3, 1, 6\}[/tex]

therefore, the domain of the following relation R is:

[tex]\{-3, 1, 6\}[/tex]

so use a basic formula here:

area of a circle = πr²

and the circumference of a circle = πd

a)

therefore the area of the pool cover is π multiplied by the radius² (which is the diameter of the pool cover plus the extra 12 inches divided by two, so the radius is 21/2 or 10.5) is 346.36(to two decimal places.)

b)

Using the same diameter, we can work out the length of the rope by multiplying the diameter (10.5) by π, which is 32.99 (to two decimal places).

Linear pair Postulate. Two angles are a linear pair if the angles are adjacent and the two unshared rays form a line. Below is an example of a linear pair: The linear pair postulate states that two angles that form a linear pair are supplementary.

Answer:

B. Square

D. Rhombus

Step-by-step explanation:

If you take a rhombus ABCD, its all sides are congruent. Lets take E as the point where the diagonals of a rhombus meet. Now it is known fact that the point where diagonals meet, they bisect each other.

Since, for sides, AB , CD,AD and CB are congruent

For diagonals, AC = BD

As E is the bisecting point for diagonals,

AE = EC and ED = EB

Now by SSS postulate, we can prove that all four triangles formed by rhombus are congruent

ΔAED , ΔBEC , ΔEDC and ΔAEB are congruent

Now the angles

∠AED, ∠AEB, ∠CED and ∠CEB are congruent as well,

So, we know that sum of interior angles of any quadrilateral is 360°

So each angle is 360/4 = 90°

This calculation is valid for square as well.

Answer:

B and D

Step-by-step explanation:

cya

Answer with explanation:

It is given that ,

  In two triangles, ΔWAS and ΔNOT

1. WA = NO

2. W S = NT

3. ∠W=∠N

≡ΔWAS ≅ ΔNOT

The Angle is included between two sides .

So,these two triangles are congruent by ,SAS.

Option B:→ S AS

The solution of the expression will be;

⇒ x = 126

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ √(2x + 4) = 16

Now,

Solve the expression as;

The expression is,

⇒ √(2x + 4) = 16

Square both side, we get;

⇒ 2x + 4 = 16²

⇒ 2x + 4 = 256

⇒ 2x = 256 - 4

⇒ 2x = 252

⇒ x = 126

Thus, The solution of the expression will be;

⇒ x = 126

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Answer:

[tex]x^2-4[/tex]

Step-by-step explanation:

Sally found that a solution of x = 2 was extraneous for her function.

Extraneous solution is a solution that makes the denominator 0

Possible denominator are given . LEts plug in 2 for x and check which option gives us 0

[tex]4x+8=4(2)+8= 16[/tex]  

[tex]2x+12=2(2)+12=4+12= 16[/tex]

[tex]x^2-4= (2)^2-4= 4-4=0[/tex]

[tex]x^2-16= (2)^2-16= 4-16= 12[/tex]

[tex]x^2-4[/tex] gives us 0 when we plug in 2 for x.

So x=2 was extraneous solution for [tex]x^2-4[/tex]