What is the apparent solution to the system of equations graphed above?

Choices:
(-2,2)
(2,-2)
(0,8)
(0,-2)

The golden ratio or golden mean is approximately 1.618 when calculated to the nearest thousandth using a calculator to evaluate (1 + √5) / 2.

The golden ratio or golden mean is a number often encountered in mathematics and art, and it is commonly represented by the Greek letter phi (φ). It can be expressed mathematically as (1 + √5) / 2. To find its decimal value to the nearest thousandth, we use a calculator to perform the operation.

First, calculate the square root of 5, then add 1 to the result. After this, divide the sum by 2. This will give us the golden ratio:

√5 ≈ 2.236
1 + √5 ≈ 3.236
(1 + √5) / 2 ≈ 1.618

So, to the nearest thousandth, the decimal value of the golden ratio is 1.618.

Answer and Explanation :

Given : Function [tex]f(x)=\frac{x^2}{2}+2x+1[/tex]

To find : The vertex, axis of symmetry, maximum or minimum value, and the graph of the function.

Solution :

The quadratic function is in the form, [tex]y=ax^2+bx+c[/tex]

On comparing, [tex]a=\frac{1}{2}[/tex] , b=2 and c=1

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

[tex]h=-\frac{b}{2a}[/tex]

[tex]h=-\frac{2}{2(\frac{1}{2})}[/tex]

[tex]h=-\frac{2}{1}[/tex]

[tex]h=-2[/tex]

For k, The y-coordinate of the vertex is given by,

[tex]k=f(h)[/tex]

[tex]k=\frac{h^2}{2}+2h+1[/tex]

[tex]k=\frac{(-2)^2}{2}+2(-2)+1[/tex]

[tex]k=2-4+1[/tex]

[tex]k=-1[/tex]

The vertex of the function is (h,k)=(-2,-1)

The x-coordinate of the vertex i.e. [tex]x=-\frac{b}{2a}[/tex] is the axis of symmetry,

So, [tex]x=-\frac{b}{2a}=-2[/tex] (solved above)

So, The axis of symmetry is x=-2.

The maximum or minimum point is determine by,

If a > 0 (positive), then the parabola opens upward and the graph has a minimum at its vertex.

[tex]a=\frac{1}{2} >0[/tex] so,  the parabola opens upward and the graph has a minimum at its vertex.

The Minimum value is given at (-2,-1)

Now, We plot the graph of the function

At different points,

x          y

-4        1

-2        -1

0         1

Refer the attached figure below.

Answer:

z=2

Step-by-step explanation:

im not going to explain it because the other person explained it but i will just show you a trick, might not always work but for the equation z^2 -4z+4=0 if you try putting 2 in for z it will be true 0=0... (2)^2 -4(2) +4= 0

Answer:

The factors of the  7x² - 12x - 4 = 0 are (7x + 2)(x -2) .

Option (b) is correct i.e none of the above .

Step-by-step explanation:

As the expression given in the question.

7x² - 12x - 4 = 0

7x² - 14x + 2x - 4 = 0

7x (x - 2)  + 2(x - 2) = 0

(7x + 2)(x -2) = 0

Thus the factors of the  7x² - 12x - 4 = 0 are (7x + 2)(x -2) .

Option (b) is correct i.e none of the above .

Answer:

The answer is A, 30

Step-by-step explanation:

Answer:

Give the guy above me Brainlyist

Step-by-step explanation:

Answer:

Option A is correct.

Step-by-step explanation:

Given:

Coordinates of the figure are ( 3 , -5 ) , ( 5 , -2 ) , ( 10 , 4 ) and ( 8 , -7 )

To find: Shape of the figure.

First we plot the given coordinates of the point on the graph then see which shape we obtained.

Graphing these points we get attached graph.

Clearly from graph it is a parallelogram because opposite sides are equal and parallel.

It is not a rectangle as clearly from graph angles at vertex are not right angle.

Therefore, Option A is correct.

To identify the geometric figure that the coordinates represent, plot the points, determine the slopes and lengths of the sides, and verify the properties of the geometric figures such as parallel sides and right angles.

The student has provided the coordinates of a figure and asks which geometric figure they represent. To determine the figure, we need to consider the characteristics of the points given.

The coordinates provided are (3, -5), (5, -2), (10, -4), and (8, -7). By plotting these points on a Cartesian plane and connecting them in order, we could identify the figure based on the slopes of the sides and the lengths of the segments, which indicate parallel and perpendicular lines.

We need to calculate the distances between consecutive points and the slopes of the lines to confirm whether opposite sides are equal and parallel (a characteristic of a parallelogram) and whether all angles are right angles (a characteristic of a rectangle). These calculations can confirm the identity of the figure.

Answer:

The answer is the option A

[tex]\frac{1}{2}(\sqrt{[(y2)^{2}+(x2)^{2}]*[(y1)^{2}+(x1)^{2}]})[/tex]

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

The area of the triangle is equal to

[tex]A=\frac{1}{2}bh[/tex]

where

b is the base

h is the height

In this problem

[tex]b=AB, h=AC[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

[tex]A(0,0), B(x2,y2)[/tex]

substitute

[tex]dAB=\sqrt{(y2-0)^{2}+(x2-0)^{2}}[/tex]

[tex]dAB=\sqrt{(y2)^{2}+(x2)^{2}}[/tex]

Find the distance AC

[tex]A(0,0), C(x1,y1)[/tex]

substitute

[tex]dAC=\sqrt{(y1-0)^{2}+(x1-0)^{2}}[/tex]

[tex]dAC=\sqrt{(y1)^{2}+(x1)^{2}}[/tex]

Find the area of the triangle

we have

[tex]b=\sqrt{(y2)^{2}+(x2)^{2}}, h=\sqrt{(y1)^{2}+(x1)^{2}}[/tex]

substitute  

[tex]A=\frac{1}{2}(\sqrt{(y2)^{2}+(x2)^{2}})(\sqrt{(y1)^{2}+(x1)^{2}})[/tex]

[tex]A=\frac{1}{2}(\sqrt{[(y2)^{2}+(x2)^{2}]*[(y1)^{2}+(x1)^{2}]})[/tex]

Answer:

A for plato users

Step-by-step explanation:

The shortest possible time for the woman to reach the point diametrically opposite on the other side of the lake is 0.8 hours, regardless if she chooses to walk around the lake or row across it.

The subject of this problem is about distance and speed, and involves optimizing the total travel time. The woman has two main options: to walk around the lake or to row across it. The diameter of the lake is 2r=8, if she walked, it would take her 8/10=0.8 hours to reach point C.

However, if she rows straight across the lake, the distance is the radius of the lake, which is 4 miles. The time taken to row across the lake is therefore 4/5=0.8 hours.

So, both options take the exact same time of 0.8 hours. Therefore, the shortest amount of time it would take for her to reach point C is 0.8 hours whether she chooses to walk around the lake or row across it.

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The shortest amount of time it would take for the woman to reach point C is [tex]2[/tex] hours.

1. Walking from A to B:

  - Distance [tex]\( AB = 4 \)[/tex] miles

  - Walking speed = 10 mph

  - Time [tex]\( \text{Time}_{\text{walk}} = \frac{4}{10} = 0.4 \) hours[/tex]

2. Rowing from B to C:

  - Distance [tex]\( BC = 8 \)[/tex] miles (since [tex]\( AC = 8 \)[/tex] miles and [tex]\( AC = 8 \)[/tex] miles)

  - Rowing speed = 5 mph

  - Time [tex]\( \text{Time}_{\text{row}} = \frac{8}{5} = 1.6 \) hours[/tex]

3. Total time:

 [tex]\( \text{Total time} = \text{Time}_{\text{walk}} + \text{Time}_{\text{row}} = 0.4 + 1.6 = 2 hours[/tex]

Therefore, the shortest amount of time it would take for the woman to reach point C is [tex]2[/tex] hours.

Answer:

[tex]u=-x^4-2x^2y+y-y^2[/tex]

Step-by-step explanation:

We are given that

[tex](1-2x^2-2y)\frac{dy}{dx}=4x^3+4xy[/tex]

We have to solve the given differential equation

[tex](1-2x^2-2y)dy=(4x^3+4xy)dx[/tex]

[tex](1-2x^2-2y)dy-(4x^3+4xy)dx=0[/tex]

Compare with [tex]Mdx+ndy=0[/tex]

Then, we get [tex]M=-(4x^3+4xy),N=(1-2x^2-2y)[/tex]

Exact differential equation

[tex]M_y=N_x[/tex]

[tex]M_y=-4x[/tex]

[tex]N_x=-4x[/tex]

[tex]M_y=N_x[/tex]

Hence, the differential equation is an exact differential equation.

Solution of exact differential is given by

[tex]u=\int M(x,y)dx+K(y)[/tex] where K(y) is a function of y.

[tex]u=\int -(4x^3+4xy) dx+k(y)[/tex] y treated as constant

[tex]u=-x^4-2x^2y+k(y)[/tex]

[tex]u_y=N[/tex]

[tex]-2x^2+k'(y)=1-2x^2-2y[/tex]

[tex]K'(y)=1-2y[/tex]

[tex]k(y)=y-y^2[/tex]

Substitute the value then we get

Then, [tex]u=-x^4-2x^2y+y-y^2[/tex]

Final answer:

The given differential equation is exact, and by integrating the respective terms and finding the function H(y), the solution for z(x, y) for the differential equation is determined to be
     -x⁴ + y - y² + C, where C is a constant.

Explanation:

To solve the differential equation (1-2x² - 2y)dy/dx = 4x³ + 4xy, let's rearrange the equation in the form M(x, y)dy + N(x, y)dx = 0, which is the standard form for a first-order differential equation. We can rewrite our equation as (-4x³ - 4xy)dx + (1-2x² - 2y)dy = 0.

Now, we check if the equation is exact, that is, if ∂M/∂y = ∂N/∂x. If it is exact, there exists a function z(x, y) such that dz = M dy + N dx.

In this case, ∂M/∂y = -4x, and ∂N/∂x = -4x. Since the partial derivatives are equal, the differential is exact, meaning there exists some function z(x, y) such that dz = Ndx + Mdy. To find z(x, y), we integrate N with respect to x and M with respect to y and combine the resulting functions, making sure to include the functions of the other variable that may arise from the partial integration.

For N(x, y), we integrate -4x³dx to get -x⁴. For M(y), we integrate (1-2y)dy to get y - y². Thus z(x, y) = -x⁴ + y - y² + H(y), where H(y) is a function of y.

To find H(y), differentiate z with respect to y and equate it to M: dz/dy = 1 - 2y + H'(y) = 1 - 2y, which implies that H'(y) = 0, hence H(y) is a constant. Therefore, the function that satisfies the differential equation is z(x, y) = -x⁴ + y - y² + C, where C is a constant.

Answer:

[tex]f(n)=2240+(\frac{170}{Week}).n[/tex]

Step-by-step explanation:

In order to make an expression that represents the situation we need to make a function that represents Henry's savings.

This will be a function ''f(n)'' because it will depend of the variable ''n'' which is the number of weeks.

Let's start making the function by reading the problem.

''He earns $210 each week working part time after school and the weekends''

We can write :

[tex]f(n)=(\frac{210}{Week}).n[/tex]

Where ''210'' is actually $210

''Henry currently has $2240 in savings'' ⇒ We need to add this amount of money to the function.

[tex]f(n)=(\frac{210}{Week}).n+2240[/tex]

''His parents put $100 in his savings account each week and he saves one-third of his paycheck each week'' ⇒ We need to add ($100).n to the expression due to his parents and multiply by [tex]\frac{1}{3}[/tex] the expression that represents its paycheck ⇒

[tex]f(n)=(\frac{1}{3}.\frac{210}{Week}).n+2240+(\frac{100}{Week}).n[/tex]

Now, if we work with the expression :

[tex]f(n)=(\frac{70}{Week}).n+2240+(\frac{100}{Week}).n[/tex]

[tex]f(n)=2240+(\frac{170}{Week}).n[/tex]

Where the units of ''2240'' and ''170'' are $.

That is the final expression which represents the situation.

Answer:

y=3x+2 is in slope intercept form. If you have a graph to go with this problem, if this equation is correct there should be points on (0,2) and (1,3)

Step-by-step explanation:

Answer:

x=4+-isqrt(5/7

Step-by-step explanation:

$2,026.15 is the payment for  every two weeks

Two or more expressions with an Equal sign is called as Equation.

Given that annual salary is $52,680 and you are paid biweekly.

In a year we have 52 weeks

If you are planning your monthly budget based on a two week pay period

So there are 52/2 = 26 periods where you get paid

For every two weeks we get paid of 52680/26 = 2,026.153846

Hence, $2,026.15 is the payment for  every two weeks

To learn more on Equation:

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Answer:

D

Step-by-step explanation:

i just did the quiz

Answer:

0.00000146

Step-by-step explanation:

Your welcome, and you better call saul

The standard form of 1.46e - 6 is 0.00000146.

To convert the number 1.46e-6 to standard form, we need to move the decimal point to the left as many times as indicated by the exponent of the scientific notation, which is -6 in this case.

This means moving the decimal point six places to the left.

Start with the number in scientific notation:

1.46e - 6.

Move the decimal point six places to the left (because of the negative exponent):

0.00000146.

Answer:

Cost of each student ticket is, $4.35

Step-by-step explanation:

Given the statement: Elise pays $21.75 for 5 student tickets to the fair.

Unit rate defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.

[tex]unit rate = \frac{Total ticket Cost}{No of students}[/tex]

Given total cost paid by Elise = $21.75

Number of students = 5

then;

Unite rate per student = [tex]\frac{21.75}{5} = \$4.35[/tex]

Therefore, the cost of each student ticket is, $4.35