Find the inequality by the graph

\(x+y=2 \implies x=2-y \\ \\ x^2 + y^2 = 9 \\ \\ (2-y)^2 + y^2 = 9 \\ \\ y^2 - 4y + 4 + y^2 = 9 \\ \\ 2y^2 - 4y-5=0 \\ \\ y=\frac{-(-4) \pm \sqrt{(-4)^2-4(2)(-5)}}{2(2)} \\ \\\)

\(=1 \pm \sqrt{7/2} \\ \\ \implies x=1 \mp \sqrt{7/2} \\ \\ \therefore x=1 \mp \sqrt{7/2} , y=1 \pm \sqrt{7/2}\)

Answer: D.

hope this helps

Answer:

37

Step-by-step explanation:

If she has 24 left, and lost 13, you add 13 and 24 to find the original amount.

Virginia's mother gave her 37 marbles for her birthday.

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

We have to given that;

Virginia's mother gave her marbles for her birthday.

Let number of marbles = x

Here, Virginia lost 13 of them and she has 24 marbles left.

So, We get;

⇒ x - 13 = 24

Solve for x;

⇒ x = 24 + 13

⇒ x = 37

Thus, Virginia's mother gave her 37 marbles for her birthday.

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Answer:

aₙ = 6 + 7n

Step-by-step explanation:

20 - 13 = 27 - 20 = 34 - 27 = 7

It is an arithmetic sequence with common difference of 7

a₁ = 13

a₂ = 20 = 13 + (2 -1 )*7

a₃ = 27 = 13 + (3 - 1)*7

a₄ = 34 = 13 + (4 - 1)*7

...

aₙ = 13 + (n - 1)*7 = 13 + 7n - 7 = 6 + 7n

ao

aₙ = 6 + 7n

Answer: 331.4

Step-by-step explanation:

33.14 x 10
Whenever you get 10x  you move a place or zero. In this case you move the decimal back one. So 33.14 x 10 = 331.4

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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Answer:

i think it's b4

Step-by-step explanation:

Answer:

7x+10

Step-by-step explanation:

2x(3x)+1x(x+10)

6x+1x+10

7x+10

The value of sin(23°) is equivalent to 0.39.

There are six major trigonometric functions as -

We can write the relation between them as -

Given is to find the value of sin 23°.

Now, we can write the value of sin(23°) as -

sin(23°) = sin(30° - 7°)

Expanding using the compound angle formula, we can write -

sin (x - y) = sin(x) cos(y) - cos(x) sin(y)

sin(30° - 7°) = sin(30°) cos(7°) - cos(30°) sin (7°)

sin(30° - 7°) = 1/2 x 0.99 - √3/2 x 0.121

sin(30° - 7°) = 1/2 x 0.99 - √3/2 x 0.121

sin(30° - 7°) = 0.495 - 0.105

sin(30° - 7°) = 0.495 - 0.105

sin(30° - 7°) = 0.39

Therefore, the value of sin(23°) is equivalent to 0.39.

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The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

Answer:

Explained below.

Step-by-step explanation:

The random variable X is defined as the number of missing pulses and follows a Poisson distribution with parameter (μ = 0.50).

The probability mass function of X is as follows:

\(P(X=x)=\frac{e^{-\mu}\ \mu^{x}}{x!};\ x=0,1,2,3...\)

(a)

Compute the probability that a disk has exactly one missing pulse as follows:

\(P(X=1)=\frac{e^{-0.50}\ 0.50^{1}}{1!}=0.3033\)

Thus, the probability that a disk has exactly one missing pulse is 0.3033.

(b)

Compute the probability that a disk has at least two missing pulses as follows:

\(P(X\geq 2)=1-P(X<2)\\\)

                \(=1-[P(X=0)+P(X=1)]\\=1-[\frac{e^{-0.50}\ 0.50^{0}}{0!}+\frac{e^{-0.50}\ 0.50^{1}}{1!}]\\=1-0.6065-0.3033\\=0.0902\)

Thus, the probability that a disk has at least two missing pulses is 0.0902.

(c)

It is provided that the two disks selected are independent of each other.

The probability that a disk has no missing pulses is:

\(P(X=0)=\frac{e^{-0.50}\ 0.50^{0}}{0!}=0.6065\)

Compute the probability that neither of the two disks contains a missing pulse as follows:

\(P(X_{1}=0,\ X_{2}=0)=P(X_{1}=0)\times P(X_{2}=0)\)

                               \(=0.6065\times 0.6065\\=0.367842\\\approx 0.3678\)

Thus, the probability that neither of the two disks contains a missing pulse is 0.3678.

As a result of answering the given question, we may state that triangle As a result, Nina substituted 13 1/3 for b.

A triangle is a closed, two-dimensional geometric object composed of three line segments, known as sides, that intersect at three locations, known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all sides equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles greater than 90 degrees). The area of a triangle can be computed using the formula A = (1/2)bh, where A is the area, b is the triangle's base, and h is the triangle's height.

The area of a triangle is calculated as A = (1/2)bh, where A is the area, b is the base, and h is the height. We know Nina computed the area of the triangle correctly as 40 square yards and that she substituted 6 for h.

Hence, using the formula, we may solve for b as follows:

A = (1/2)bh

40 = (1/2)b(6) (6)

40 = 3b

b = 40/3

b = 13 1/3

As a result, Nina substituted 13 1/3 for b.

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The divers in order from least to greatest based on the number of liters left in their oxygen tank is: D. Dante, Sofia, Alexis.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

Next, we would convert each of the volume of oxygen (in liters) that is written in words to a numerical data as follows:

Seventy nine eighths = 79/8 = 9.875.

Nine and eight fifteenths = 9 8/15 = 9.533.

Now, we can arrange the divers in order from least to greatest based on the number of liters left in their oxygen tank:

In conclusion, we can infer and logically deduce that the divers in order from least to greatest based on the number of liters left in their oxygen tank is Dante, Sofia, Alexis.

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Complete Question:

Three divers went scuba diving in the ocean for a couple of hours. The table shows how much oxygen they had left in their oxygen tanks.

Diver        Oxygen (liters)

Alexis       seventy nine eighths

Dante       9.3

Sofia         nine and eight fifteenths

Place the divers in order from least to greatest based on the number of liters left in their oxygen tank.

A. Sofia, Dante, Alexis

B. Alexis, Sofia, Dante

C. Dante, Alexis, Sofia

D. Dante, Sofia, Alexis

Answer: Sofia, Alexis Dante

Step-by-step explanation: Did the test and got all the other choices wrong. It's D.

Answer: 40

Step-by-step explanation:

Because 36 / 0.9 = 40

4,8,12,16,20,24,28,32,36,40 that equals 100 percent

Answer:  

40  i hope this helps all of you guys!                                                        

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer:

35/16

Step-by-step explanation:

Answer:

2.1875

Step-by-step explanation:

35/16=2.1875

2.1875 pounds

Answer:

a) -2, -1

b) (-3,0) and (-1,0)

From the graph of the given equation

the coordinates of the turning point is \((-2,-1)\)

The coordinates of the roots of the equation \(x^2+4x+3=0\) are \((-3,0) \; and \;( -1,0)\)

Given :

the graph of y=x^2 +4x + 3 is shown

The graph of \(y=x^2 +4x + 3\) is attached below

From the graph we can see that , the vertex is (-2,-1)

The graph changes direction at the point (-2,-1)

so we can say that there is only one turning point at \((-2,-1)\)

Now we find out the roots of the equation

roots are the points where the graph crosses or touches x axis

The graph crosses x axis at \(-3 \; and \; -1\)

The coordinates of the roots of the equation \(x^2+4x+3=0\) are \(-3 \; and \; -1\)

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The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

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Correct option will be (C) In the short run, firms may incur economic losses or earn economic profits, but in the long run they earn normal profits.

The short run is a concept that states that, within a certain period in the future, at least one input is fixed while others are variable. In economics, it expresses the idea that an economy behaves differently depending on the length of time it has to react to certain stimuli. The short run does not refer to a specific duration of time but rather is unique to the firm, industry or economic variable being studied.

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Answer: A.

Step-by-step explanation:

I just took the exam

can i get brainlyiest?

Answer:

If f(x) = +4, which of the following is the inverse of f(x)?

O A. ƒ˜¹(x) = 2(2+4)

B. ƒ˜¹(x) = 7(2-4)

C. ƒ˜¹(x) = 7(2+4)

D. f¯¹(x) = ²(2-4)

Step-by-step explanation:

Greece is different from most other countries in southern Europe because its most popular religion is not Catholicism. Option B

Catholicism refers to the traditions, beliefs, and behaviors of the Catholic Church

Greece is predominantly an Orthodox Christian country, whereas most other countries in southern Europe, such as Italy, Spain, and Portugal, are predominantly Catholic.

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The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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Answer:

It would be 1.073 you can also rojnd ot to 1.07

Answer:

$1.07 per pound

Step-by-step explanation:

$3.22/3lb is about $1.07 per lb.

Answer:

M = kwh^2/L

k = 400

Step-by-step explanation:

Given that the maximum weight M that can be supported by a beam is jointly proportional to its width w in inches and the square of its height h in inches and inversely proportional to its length L in feet

Then

M ∝ wh^2/L

M = kwh^2/L

where k is the constant of proportionality

if a beam 4 in. wide, 6 in. high, and 15 ft long can support a weight of 3840 lb then

3840 = k * 4 * 6^2/15

k = 3840 * 15 / (4 * 36)

k = 400