Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the axis of symmetry and the vertex for this function:

\(h(x) = (x-5)^{2} - 7\)

please answer this with a picture or screenshot of a graph with the correct graph

The maximum value of 5x₁ + 5x₂ + 7x₃ + x₄ subject to the condition x₁² + x₂² + x₃² + x₄² = 100 occurs when x₁ = -5, x₂ = -5, x₃ = -7, and x₄ = -1.

To find the point on the surface 4x + y - 6 = 0 closest to the point (-7, -3, -6), we can use Lagrange multipliers. Let's denote the coordinates of the closest point as (x, y, z).

We need to minimize the distance between the point (-7, -3, -6) and the point (x, y, z), which can be expressed as the square of the distance to avoid square roots:

Distance^2 = (x + 7)^2 + (y + 3)^2 + (z + 6)^2

Now, we need to set up the Lagrangian function, combining the distance function and the constraint equation of the surface:

L(x, y, z, λ) = (x + 7)^2 + (y + 3)^2 + (z + 6)^2 + λ(4x + y - 6)

To find the minimum, we differentiate L with respect to x, y, z, and λ, and set the derivatives equal to zero:

∂L/∂x = 2(x + 7) + 4λ = 0

∂L/∂y = 2(y + 3) + λ = 0

∂L/∂z = 2(z + 6) = 0

∂L/∂λ = 4x + y - 6 = 0

Solving these equations simultaneously will give us the coordinates of the closest point on the surface.

From the equation ∂L/∂z = 2(z + 6) = 0, we find z = -6.

Substituting z = -6 into the other equations, we have:

2(x + 7) + 4λ = 0

2(y + 3) + λ = 0

4x + y - 6 = 0

Solving these equations simultaneously will give us the values of x, y, and λ.

From the equation 2(x + 7) + 4λ = 0, we find x = -λ - 7.

From the equation 2(y + 3) + λ = 0, we find y = -λ - 3.

Substituting x = -λ - 7 and y = -λ - 3 into the equation 4x + y - 6 = 0, we can solve for λ:

4(-λ - 7) + (-λ - 3) - 6 = 0

-5λ - 34 = 0

λ = -34/5

Substituting λ = -34/5 back into x = -λ - 7 and y = -λ - 3, we can find the values of x and y:

x = -(-34/5) - 7 = 34/5 - 7 = -1/5

y = -(-34/5) - 3 = 34/5 - 3 = -1/5

Therefore, the point on the surface 4x + y - 6 = 0 closest to the point (-7, -3, -6) is (-1/5, -1/5, -6).

Now, let's move on to the second part of your question.

To find the maximum value of 5x₁ + 5x₂ + 7x₃ + x₄ subject to the condition x₁² + x₂² + x₃² + x₄² = 100, we can again use Lagrange multipliers.

We need to maximize the objective function 5x₁ + 5x₂ + 7x₃ + x₄ while satisfying the constraint x₁² + x₂² + x₃² + x₄² = 100. Let's denote the Lagrangian function as L(x₁, x₂, x₃, x₄, λ).

L(x₁, x₂, x₃, x₄, λ) = 5x₁ + 5x₂ + 7x₃ + x₄ + λ(x₁² + x₂² + x₃² + x₄² - 100)

We differentiate L with respect to x₁, x₂, x₃, x₄, and λ, and set the derivatives equal to zero:

∂L/∂x₁ = 5 + 2λx₁ = 0

∂L/∂x₂ = 5 + 2λx₂ = 0

∂L/∂x₃ = 7 + 2λx₃ = 0

∂L/∂x₄ = 1 + 2λx₄ = 0

∂L/∂λ = x₁² + x₂² + x₃² + x₄² - 100 = 0

Solving these equations simultaneously will give us the values of x₁, x₂, x₃, x₄, and λ.

From the equations ∂L/∂x₁ = 5 + 2λx₁ = 0 and ∂L/∂x₂ = 5 + 2λx₂ = 0, we find x₁ = -5/(2λ) and x₂ = -5/(2λ).

Substituting these values into the equation ∂L/∂x₃ = 7 + 2λx₃ = 0, we can solve for x₃:

7 + 2λx₃ = 0

x₃ = -7/(2λ)

Similarly, from the equation ∂L/∂x₄ = 1 + 2λx₄ = 0, we find x₄ = -1/(2λ).

Substituting x₁ = -5/(2λ), x₂ = -5/(2λ), x₃ = -7/(2λ), and x₄ = -1/(2λ) into the equation ∂L/∂λ = x₁² + x₂² + x₃² + x₄² - 100 = 0, we can solve for λ:

(-5/(2λ))² + (-5/(2λ))² + (-7/(2λ))² + (-1/(2λ))² - 100 = 0

25/(4λ²) + 25/(4λ²) + 49/(4λ²) + 1/(4λ²) - 100 = 0

100/(4λ²) - 100 = 0

100 - 400λ² = 0

400λ² = 100

λ² = 1/4

λ = ±1/2

Substituting λ = 1/2 and λ = -1/2 back into x₁ = -5/(2λ), x₂ = -5/(2λ), x₃ = -7/(2λ), and x₄ = -1/(2λ), we can find the values of x₁, x₂, x₃, and x₄.

For λ = 1/2:

x₁ = -5/2(1/2) = -5

x₂ = -5/2(1/2) = -5

x₃ = -7/2(1/2) = -7

x₄ = -1/2(1/2) = -1

For λ = -1/2:

x₁ = -5/2(-1/2) = 5

x₂ = -5/2(-1/2) = 5

x₃ = -7/2(-1/2) = 7

x₄ = -1/2(-1/2) = 1

Therefore, the maximum value of 5x₁ + 5x₂ + 7x₃ + x₄ subject to the condition x₁² + x₂² + x₃² + x₄² = 100 occurs when x₁ = -5, x₂ = -5, x₃ = -7, and x₄ = -1.

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24 centimeters. Hope this helped!

Probability of stores not violating the standard = 1 - (X / N)

To find the probability that a randomly selected store does not violate the institute's scanner accuracy standard, we need to determine the probability of stores that do not violate the standard out of all the investigated company stores.

Let's assume that the total number of company stores investigated is N, and the number of stores that violated the institute's scanner accuracy standard is X.

First, we need to calculate the probability of stores that violated the standard:

Probability of stores violating the standard = X / N

To find the probability of stores that do not violate the standard, we can subtract the probability of stores violating the standard from 1 (since the sum of the probabilities of both categories should be equal to 1):

Probability of stores not violating the standard = 1 - (X / N)


Therefore, the probability that a randomly selected store does not violate the institute's scanner accuracy standard can be calculated using the given information about the number of stores that violated the standard and the total number of investigated company stores.

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Answer:

-2x-2

Step-by-step explanation:

(−4x+3)−(−2x+5)

To find the opposite of −2x+5, find the opposite of each term.

−4x+3−(−2x)−5

The opposite of −2x is 2x.

−4x+3+2x−5

Combine −4x and 2x to get −2x.

−2x+3−5

Subtract 5 from 3 to get −2.

−2x−2

out of a group of 12, the possible arrangements are possible are 495.

What do you mean by arrangements in permutation and combinations?

Finding the total number of different configurations for a collection of elements is a straightforward definition of the term permutation. According to permutation, the arrangement is classified as a non-distinct item, which essentially classifies things that are impossible to identify from one another.

according to the question, out of 12 people, 4 are to be chosen

so the possible arrangements are 12C4 =495

Hence, the possible arrangements are 495.

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Answer:

Sin A = 4/5

Step-by-step explanation:

sin theta = opposite / hypotenuse

sin A = 40/50

Sin A = 4/5

Answer:

0.8

Step-by-step explanation:

SinA = opposite/hypotenuse

= CB/CA

= 40/50

= 4/5

= 0.8

Answer:

A'(3, 2 ), B'(6, 6 ),C'(6, - 3 )

A translation of 2 units right is equivalent to adding 2 to the x- coordinate with no change to the y- coordinate.

A(1, 2 ) → A'(1 + 2, 2 ) → A'(3, 2 )

B(4, 6 ) → B'( 4 + 2, 6 ) → B'(6, 6 )

C(4, - 3 ) → B'(4 + 2, - 3 ) → B'(6, - 3 )

Step-by-step explanation:

Hope this helps:)

The slope of the estimated regression equation is significantly different from zero. The interpretation of 70 is that for every one-unit increase in X, there will be an average increase of 70 units in Y.

a. Interpretation of 70 In the given estimated simple linear regression equation of X and Y:

\(Y = 8 + 70X70\)  is the slope of the line,

which represents the change in Y that occurs with a one-unit increase in X.

Therefore, the interpretation of 70 is that for every one-unit increase in X, there will be an average increase of 70 units in Y.

b. The t-test is used to test the null hypothesis that there is no significant relationship between the independent variable (X) and the dependent variable (Y).

The null hypothesis is rejected if the absolute value of the t-statistic is greater than the critical value at the appropriate significance level.

In this case, the t-test statistic is 3.3, which is greater than the critical value at a 5% significance level.

As a result, we reject the null hypothesis and conclude that the slope of the estimated regression equation is significantly different from zero.

c. The p-value (sig) is the probability of obtaining a t-statistic as extreme or more extreme than the observed value under the null hypothesis.

In this case, the p-value is 0.008, which is less than the 0.05 level of significance.

Because the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a statistically significant relationship between X and Y.

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Answer:

we know

perimeter of triangle = sum of all sides

here lengths of sides are consecutive integers so

length  of three sides = x, (x+1) and (x+2)

now

Perimeter = 111

or,  x + (x+1) + (x+2) = 111

or 3x + 3 = 111

or 3x = 108

x = 36

x = 36

(x+1) = 36 + 1 = 37

(x+2)= 36 + 2 = 38

Answer:

x = - 11

Step-by-step explanation:

3(x + 5) = x - 7

3x + 15 = x - 7

2x  = -7 - 15

2x = - 22

x = - 11

Hope this helps!

Answer:

2.25 feet

Step-by-step explanation:

Alright so the scale is 1:3

(1 represents the diagram and 3 represents the actual doghouse)

In the diagram the length is 0.75ft

We can use this Information to set up this equation:

\(\frac{1}{3}=\frac{0.75}{x}\)

Simplify: (cross multiply, if confused scroll down, I explained)

x=3(0.75)

x=2.25

Hope this helps

*************************

Cross multiplying:

It's simply this:

If   \(\frac{a}{b}=\frac{x}{y}\\\)

Then we can say

a(y)=b(x)

*************************

Answer:

3

Step-by-step explanation:

length

width

height

Answer:

x=25

Step-by-step explanation:

(2x-10)=(65-x)

2x +x= 65+10

3x = 75

x=75/3

x =25

I hope I helped you^_^

The measure of angle C is -

∠C = 302° - 6x.

The relation between the angles of a quadrilateral is as follows -

∠A + ∠B + ∠C + ∠D = 360°

Given is a Quadrilateral ABCD is inscribed in this circle.

We know that the relation between the angles of a quadrilateral is as follows -

∠A + ∠B + ∠C + ∠D = 360°

(x + 20) + 3x + (2x + 38) + ∠C = 360°

6x + 58 + ∠C = 360°

6x + ∠C = 302°

∠C = 302° - 6x

Therefore, the measure of angle C is -

∠C = 302° - 6x.

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Answer:

a) 4x+4

b) 7x-14

c) 12x +18

d) 10x-10y

Answer:

4x+4

7x-14

12x+18

10x-10y

Step-by-step explanation:

Answer:

january = 10/20 = 1/2

februry = 7/14 = 1/2

so, we conclude that the auto dealership didn't have a lower ratio, since the ratio is equal in both months.

hope it helps :)

Answer:

The base and height of three parallelograms with the same area as the 12 square inches rectangle are

1) First parallelogram;

Base length of parallelogram = 4 units

Height of parallelogram, = 3 units

2) Second parallelogram

Base length of parallelogram = 6 units

Height of parallelogram, = 2 units

3) Third parallelogram

Base length of parallelogram = 5 units

Height of parallelogram, = 2.4 units

Step-by-step explanation:

The vertices of the rectangle are; (0, 0), (4, 0), (4, 3), and (0, 3)

Let ABCD represent the vertices of the rectangle such that we have;

A(0, 0), B(4, 0), C(4, 3), and D(0, 3)

The area of the rectangle, A = The length of AB × The length of CB

The length of AB = √((4 - 0)² + (0 - 0)²) = 4

The length of CB = √((4 - 4)² + (3 - 0)²) = 3

∴ The area of the rectangle, A = 4 × 3 = 12 square units

The area of a parallelogram = Base length × Height

The base and height of three parallelograms with the same area as the 12 square inches rectangle are;

1) Base length of parallelogram = 4 units

Height of parallelogram, = 3 units

The area of the parallelogram, A = Base × Height;

∴ A = 4 units × 3 units = 12 units²

2) Base length of parallelogram = 6 units

Height of parallelogram, = 2 units

The area of the parallelogram, A = Base × Height;

∴ A = 6 units × 2 units = 12 units²

3) Base length of parallelogram = 5 units

Height of parallelogram, = 2.4 units

The area of the parallelogram, A = Base × Height;

∴ A = 5 units × 2.5 units = 12 units².

Answer:

Step-by-step explanation:

Construction: To copy angle CAB.

i. On angle CAB, with center A and any radius; draw an arc to intersect CA at E and AB at F.

ii. Place a divider at EF to copy the angle.

iii. Draw a separate straight line MN of approximate length to AB.

iv. Mark point P on MN. Place the divider with radius EF at P to mark Q.

v. Draw a line LM from M through Q.

vi. Therefore, angle CAB would be equal to angle LMN.

The proposed solution y = xr leads to r = -2 for the given differential equation.

By substituting the proposed solution y = xr into the differential equation \(x^2y'' + 5xy' + 4y = 0\), we can find the value of r that satisfies the equation.

First, we differentiate y = xr twice to find the first and second derivatives.

\(y' = rx^(r-1)\)and \(y'' = r(r-1)x^(^r^-^2^).\)

Substituting these derivatives into the differential equation, we have:

\(x^2(r(r-1)x^(^r^-^2^)) + 5x(rx^(^r^-^1^)) + 4xr = 0\).

Simplifying the equation, we get:

\(r(r-1)x^r + 5rx^r + 4xr = 0\).

Factoring out the common term \(x^r\), we have:

\(x^r(r(r-1) + 5r + 4) = 0\).

For this equation to hold true for all x, the coefficient in front of \(x^r\) must be zero. Thus, we have:

r(r-1) + 5r + 4 = 0.

Simplifying the equation further, we get:

\(r^2 - r + 5r + 4 = 0,r^2 + 4r + 4 = 0,(r + 2)^2 = 0\).

From this equation, we find that r = -2. Therefore, the proposed solution y = xr leads to r = -2 as the solution for the given differential equation.

The proposed solution method for solving differential equations is based on the assumption that the solution can be expressed in a specific form. In this case, the proposed solution y = xr assumes that the solution is a power function of x. By substituting this solution and its derivatives into the differential equation, we can determine the value of r that satisfies the equation.

The process involves substituting the proposed solution and its derivatives into the differential equation, simplifying the equation, and identifying the condition under which the equation holds true. In this case, after simplifying the equation, we obtain a quadratic equation in terms of r. Solving this quadratic equation leads to the value r = -2, which satisfies the original differential equation.

The proposed solution method is a powerful technique used in solving linear homogeneous differential equations, where the equation can be expressed as a linear combination of the derivatives of the dependent variable with respect to the independent variable. By substituting the proposed solution, we can determine the values of the constants or exponents that satisfy the equation and find the general solution.

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The diagrams showing pairs of adjacent angles and the given description is shown in the attachments below.

Adjacent angles are angle that share the same vertex and also has a side in common.

a. An obtuse angle is greater than 90°.

Figure 1 shows a pair of adjacent angles that are obtuse which are ∠ABD and ∠CBD

b. Figure 2 shows two adjacent angles, ∠ABD and ∠CBD whose sum equals 180 degrees.

c. Figure 3 shows two adjacent angles, ∠ABD and ∠CBD whose sum equals 60 degrees.

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Hello! (:

3x+4=y

We want to convert it into slope-intercept form:

y=mx+b

Our equation looks like this:

y=3x+4

Now, parallel lines have the same slope. So if one line has a slope of 3, the line parallel to it has a slope of 3 as well.

Now, we have the slope and a point, so we write the equation in point-slope form:

y-y1=m(x-x1)

y-(-2)=3(x-4)

y+2=3x-12

y=3x-12-2

y=3x-14

Hence, that is the required equation, Hope it helps you!

If you have any question or query, feel free to ask! (:

~An excited gal

\(SparklingFlower (:\)

Answer:

(3,4)

Step-by-step explanation:

Step-by-step explanation:

f''(x) = 12x² + 6x - 4

f'(x) = 4x³ + 3x² - 4x + c

f(x) = x⁴ + x³ - 2x² + cx + d

f(0) = 5 = 0⁴ + 0³ - 2×0² + c×0 + d

d = 5

f(1) = 4 = 1⁴ + 1³ - 2×1² + c×1 + 5

4 = 1 + 1 - 2 + c + 5

4 = c + 5

c = -1

f(x) = x⁴ + x³ - 2x² - x + 5

Answer:

  yes

Step-by-step explanation:

You want a graph of P = 125 +50W.

The given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.

Usually, the independent variable is graphed on the horizontal axis, which you have done.

The dependent variable is graphed on the vertical axis, which you have done.

The axes are correctly labeled and graduated.

The "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.

The slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.

Yes, you properly graphed the equation.

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Answer:

Given distance=360 km.

Let the speed of the train be x km/hr.

Speed when increased by 5 km/hr =(x+5) km/hr

x

360

−

(x+5)

360

=1

x(x+5)

[360x+1800−360x]

=1

x

2

+5x−1800=0

x

2

+45x−40x−1800=0

x(x+45)−40(x+45)=0

(x−40)(x+45)=0

x=40,−45

The speed of the train is 40 km/hr.

Step-by-step explanation:

thanks... ☺️

Answer:

2 ez cuh the answer is

20 x

Step-by-step explanation:

please give me brainlist I just need 3 more

Answer:

20

Step-by-step explanation:

Ok so,

2^2 = 4

*i'm just rewriting the expression*

so now it would be 5x4 which would be 20.

hope this helps! have a good day! pls mark brainliest!!!

\(\\ \rm\rightarrowtail {\displaystyle{\int}}(5\sqrt{9x+2})DX\)

\(\\ \rm\rightarrowtail {\displaystyle{\int}}5 dx\times {\displaystyle{\int}}(9x+2)^{\dfrac{1}{2}}dx\)

\(\boxed{\sf {\displaystyle{\int}}x^n=\dfrac{x^{n+1}}{n+1}}\)

\(\\ \rm\rightarrowtail 5x\left(\dfrac{(9x+2)^{\dfrac{1}{2}+1}}{\dfrac{1}{2}+1}\right)\)

\(\\ \rm\rightarrowtail 5x\left(\dfrac{(9x+2)^{\dfrac{3}{2}}}{3/2}\right)\)

\(\\ \rm\rightarrowtail \dfrac{10x(9x+2)^{\dfrac{3}{2}}}{3}\)

the value of the side a will be 20feet.

What is Pythagoras theorem?

The Pythagoras theorem says that if a triangle has a straight angle (90 degrees), the square of the hypotenuse is equal to the sum of the squares of the other two sides. To illustrate this, the triangle ABC has the formula BC2 = AB2 + AC2. This equation includes the bases AB, height AC, and hypotenuse BC. It is important to note that the hypotenuse is the right-angled triangle's longest side.

h²=b²p²

b²=25²-15²

b²=675-215

b=√400

b=20 feet

Hence, the value of the side a will be 20feet.

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Answer:

the scale factor is times 0.5

Explanation:

20 plus 10 is 30. Half of 20 is 10 so that is 0.5

It is also like that for the others

Answer: 3/4

Step-by-step explanation:

Answer: 5.

Step-by-step explanation:

the distance from zero in either the positive or negative direction. 3/4 and -3/4 is written as |3/4| in absolute terms and is true for any value |5|.