Solve the equation for y
6у - 1.5х = 8

The derivative of f(x) = (x + |x|)^2 + 1 evaluated at x = 0 is f'(0) = 2. f'(0) = 0, indicating that the derivative of f(x) at x = 0 is 0.

To find the derivative of f(x), we need to consider the different cases separately for x < 0 and x ≥ 0 since the absolute value function |x| is involved.

For x < 0, the function f(x) becomes f(x) = (x - x)^2 + 1 = 1.

For x ≥ 0, the function f(x) becomes f(x) = (x + x)^2 + 1 = 4x^2 + 1.

To find the derivative, we take the derivative of each case separately:

For x < 0: f'(x) = 0, since f(x) is a constant.

For x ≥ 0: f'(x) = d/dx (4x^2 + 1) = 8x.

Now, to find f'(0), we need to evaluate the derivative at x = 0:

f'(0) = 8(0) = 0.

Therefore, f'(0) = 0, indicating that the derivative of f(x) at x = 0 is 0.

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Answer:

A. 136 sq. cm.

Step-by-step explanation:

First find the area of the rectangle:

16 times 7 is 112

13-7 is 6

16-8 is 8

The formula for the area of a triangle is ab/2

thus:

6 times 8 is 48/2

Which is 24

Add 112 with 24

Which is 136

Thus the answer is A. 136 sq. cm.

Hope this helps!

Step-by-step explanation:

In a rectangle

Area (A) = 248 m²

length (L) = 4 m

breadth (b) = ?

We know

A = L * b

248 = 4 * b

b = 62 m

Now

Perimeter of the rectangle

= 2 ( L + b)

= 2 ( 4 + 62)

= 2 * 66

= 132 m

Hope it will help :)

Answer:

first we have to get the width.

A=L*w

so, A =L *W

L L

W=A

L

248m²=4m*W

248m²=4m*w

4m 4m

w=248m²

4m

w=32m

now we can find the perimeter.

p=2(L+w)

p=2(4m+32m)

p=2(36m)

p=72m

there for the answer is 72m

Answer:

1. 20 (tens)

2. 8 (ones)

3. 0.6 (tenths)

4. 0.005 (Hundredths)

5. 0.0009 (thousandths)

6. 0.00007 (ten thousandths)

i hoped this helped!

Step-by-step explanation:

The accepted method for representing both integer and non-integer numbers is the decimal numeral system.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

Given the decimal number is 28.6597. The value of each digit in the decimal number will be calculated as,

1. 20 (tens)

2. 8 (ones)

3. 0.6 (tenths)

4. 0.005 (Hundredths)

5. 0.0009 (thousandths)

6. 0.00007 (ten thousandths)

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The expected value of the game is $4.40. The expected value of a game or situation is the average outcome that a player can expect to receive per round or per unit of time.

The expected value of a game is the average amount of money a player can expect to win or lose per round. To determine the expected value of this dice game, we need to calculate the probability of rolling each winning combination (2, 3, or 12) and multiply it by the payout for each combination.

The probability of rolling a 2 is 1/36, since there is only one way to roll a 2 (1 and 1 on the two dice). The probability of rolling a 3 is 2/36, since there are two ways to roll a 3 (1 and 2 or 2 and 1). The probability of rolling a 12 is 1/36, since there is only one way to roll a 12 (6 and 6). Therefore, the probability of winning is 4/36, or 1/9.

For a $5 bet, a winning player receives $35 and gets their bet back, for a total payout of $35 + $5 = $40. The expected value of the game is therefore 1/9 x $40 = $4.44. To the nearest cent, the expected value of the game is $4.40.

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Answer:

orange: 0.2$, apple: 0.4$

Step-by-step explanation:

we mark the price of an orange x and the price of an apple y. then we write down Maggie's and Tanya's purchases as a set of equations:

10 oranges and 5 apples for 4$ means:

\(10x + 5y = 4\)

9 oranges and 3 apples for 3$ means:

\(9x + 3y = 3\)

we use the second equation to isolate y:

\(3y = 3 - 9x \\ y = 1 - 3x\)

and plug it in the first equation:

\(10x + 5(1 - 3x) = 4 \\ 10x + 5 - 15x = 4 \\ 1 = 5x \\ x = 0.2\)

and then we find y:

\(y = 1 - 3 \times 0.2 \\ y = 0.4\)

Melanie's account balance after t years is, A = 500 x \((1 + 0.00425)^{4t\).

Compound interest is when you receive interest on both your interest income and your savings.

Given:

Initial deposit = $ 500

Interest rate = 1.7 % = 0.017/4 = annual compounded quarterly

Now, Account balance = Initial deposit x \((1 + r)^{4t\)

                                   A = 500 x \((1 + 0.00425)^{4t\)

Where:

A = Account balance

4t = Number of quarters (4 x Number of t years)

Suppose we want to calculate the account balance after 4.5 years, then we substitute this way:

A = 500 x \((1 + 0.00425)^{4(4.5)\)

A = 500 x (1 + 0.00425)¹⁸

A = 539.66

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Answer:

QUESTION 1: x³ - 2 x² - 5 x - 18 remainder 48

The first three terms of x[n] using the power series expansion are x[0] = 73, x[1] = 2, and x[2] = 13.

We can select the first three terms of x[n] using the power series development by expressing the given articulation X(z) as a polynomial in z. We should modify the articulation as follows to obtain the power series development: By comparing the given expression to the power series form, the coefficients can be identified: X(z) equals 2z3, 13z2, 7z, 73, 722/z, 2/z, and 1: a0 rises to 73, a1 approaches 2, a2 approaches 13, and a3 approaches 7. X(z) = a0, a1z, a2z2, a3*z3, and... Consequently, the following are the first three terms of x[n]:

The initial three terms of x[n] are provided by the power series development: x[0] = a0; x[1] = a1; x[2] = a2; x[0] = a0; The values of x[0] and x[1] are 73, 2, and 13.

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Exact Form:

1/27

Decimal Form:

0.037 (with a line over 037)

Answer:

y- 7 x = 5 answer of this question

Answer:

-0.5

Step-by-step explanation:

Answer:

The value of t (the amount of time it would take) is 1.46 hours.

Step-by-step explanation:

To solve, all we do is plug in the values. We know that the distance he traveled is 26.2 miles and the average speed is 18 miles per hour. This means that d (distance) will be 26.2, and r (rate) will be 18. Now make an equation.

Equation: 26.2=18*t

Now, divide both sides by 18 to find your answer. The answer will be 1.45555...

Note that since this never ends, you would have to round the above number. We will round to the hundredths place. That gives you 1.46.

By using the concept of parallel lines, it is obtained

x = 7, y = 22

What is corrosponding angle?

At first we need to understood what is angle, parallel lines and transversal

Angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Parallel lines

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Transversal

Transversal is a line that intersects two or more parallel lines

Alternate exterior angle

The angle formed on the same side of transversal when the transversal intersects two parallel lines.

Here,

\(9x + 42 = 105\\\) [Vertically opposite angle]

\(9x = 105 - 42\\9x = 63\\x = \frac{63}{9}\\x = 7\)

Angle next to \(4y - 13\) is \(15x\) [Corrosponding angle]

\(4y - 13 +15x = 180\) [ Angle on a straight line]

\(4y - 13 +15\times 7 = 180\\4y -13 + 105 = 180\\4y + 92 = 180\\4y = 180=92\\4y = 88\\y = \frac{88}{4}\\y = 22\)

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Answer:

Step-by-step explanation:

1-1=0

Answer:You will have 0 moms.

Step-by-step explanation:

First you take 1 away from 1.

After that you get your answer of 0.

If we used a parenthesis instead of a bracket in the interval notation, the meaning would change in that the interval would include all values greater than or equal to -3, up to, but not including, 2

Interval notation is a way of representing a range of real numbers using brackets and parentheses

When a parenthesis is used instead of a bracket in the interval notation, the meaning would change in that the interval would include all values greater than or equal to -3, up to, but not including, 2.

In other words, the endpoint 2 would be excluded from the interval. So the interval notation [-3,2) would include all values between -3 and 2, but not 2 itself.

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Answer:

Yes this is a function.

Step-by-step explanation:

You can tell this because there isnt any repeating x values. If there was ever a vertical (straight up and down) line then it isn't a funciton.

Answer:(2, 3)

Step-by-step explanation:

Because we are reflecting the point across the y axis, we know that we are changing the X coordinate. Reflecting across in this case, since there is no other given rule means we are changing the current X coordinate to be the negative version of itself, since it is already negative, this makes the new point a positive one.

This can be explained as moving the point across the given axis at the same distance as the original point from the axis, but in the opposite direction. If it is on the left of the axis, we move it the same distance from the axis to the right, and vice-versa.

We do not change the y coordinate, because we are reflecting the point across the Y axis, which is the vertical line that has an x origin of 0.

All of this means that the new coordinate for our point will be (2, 3).

To write Acos(?0t) + Bsin(?0t) in the form r*sin(?0t - ?), we can use the identities. The relationship among R, r, ? and ? is:
R^2 = r^2 (1 + (A/B)^2), tan? = r/R = B/A

r = sqrt(A^2 + B^2)
tan? = B/A

Therefore, r = sqrt(A^2 + B^2) and tan? = B/A.

To determine the relationship among R, r, ? and ?, we can use the identity:

R^2 = r^2 + (tan?)^2

Therefore, R = sqrt(r^2 + (tan?)^2) and tan? = r/R. Substituting the expression for tan? from earlier, we get:

tan? = B/A = r/R

Solving for R, we get:

R = r/tan? = r/(B/A) = rA/B

And substituting the expression for R in terms of r and tan?, we get:

R = sqrt(r^2 + (r/R)^2) * A/B

Simplifying this expression, we get:

R^2 = r^2 + (A/B)^2 * r^2

R^2 = r^2 (1 + (A/B)^2)

Therefore, the relationship among R, r, ? and ? is:

R^2 = r^2 (1 + (A/B)^2)
tan? = r/R = B/A

To show that Acos(ω₀t) + Bsin(ω₀t) can be written in the form r*sin(ω₀t - θ), we can use trigonometric identities. We know that:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Comparing this to the given expression, we have:

Acos(ω₀t) + Bsin(ω₀t) = r*sin(ω₀t - θ) = r[sin(ω₀t)cos(θ) - cos(ω₀t)sin(θ)]

Now, let's equate the coefficients of sin(ω₀t) and cos(ω₀t):

A = -r*sin(θ)
B = r*cos(θ)

To find r and θ in terms of A and B, we can use the Pythagorean identity:

A² + B² = (-r*sin(θ))² + (r*cos(θ))² = r²(sin²(θ) + cos²(θ)) = r²

Therefore, r = √(A² + B²).

Now, to find θ, we can use the tangent function:

tan(θ) = -A/B

Now, for the second part, if Rcos(ω₀t - θ) = r*sin(ω₀t - θ), we can use the sine-to-cosine transformation:

Rcos(ω₀t - θ) = Rsin(ω₀t - θ + π/2)

This implies that:

R = r
θ + π/2 = θ'

So, the relationship among R, r, θ, and θ' is:

R = r
θ' = θ + π/2

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The decision variable in this scenario is the model to be produced, which can be represented by the variables A, B, and C. The output variable is the cost of production for the next month.

To determine the model that should be produced to eliminate the cost for the next month, we need to analyze the cost of production for each model. The decision variable represents the choices available, which are models A, B, and C. Let's denote the decision variable as X, where X can take the values A, B, or C.

The output variable in this case is the cost of production for the next month. It is important to consider the costs associated with the raw materials, as well as other factors like delivery time and availability. To make an informed decision, we need to compare the costs associated with each model.

The decision can be made by evaluating the cost of production for each model based on the data provided in the table. By analyzing the cost for each model and considering other relevant factors, such as delivery time and availability of raw materials from the respective suppliers, we can determine which model should be produced to minimize the cost for the next month.

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\(f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16\)

\(divide \: by \: x - 2\)

\(4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} \)

\(g(x) = 4x {}^{2} - 16x + 16\)

\(4x \: into \: (x - 2) = 4x {}^{2} - 8x\)

\(z(x) = - 8x + 16\)

\( - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder\)

\(f(x) = (x - 2)(4x {}^{2} + 4x - 8)\)

\(f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ \)

\(x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1\)

\(x = 2\)

\(x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2\)

Answer: B

Step-by-step explanation:

Edge 2023

Answer is in the image

Step-by-step explanation:

Sorry if wrong or blurry

1. axis of symmetry = -3

vertex = ( -3,-5)

2. axis of symmetry = -2

vertex = ( -2,-13)

3. axis of symmetry = 1

vertex = ( 1,-1)

4. axis of symmetry = 4

vertex = (4,-5)

The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward.

The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.

The vertex is calculated as -b/2a and we substitute the value in the equation to get the y axis. The equation must be in the form ax²+bx + c

The axis of symmetry is calculated as -b/2a

1. x²+6x+4

axis of symmetry = -6/2 = -3

the y cordinate vertex = -3)²+6(-3)+4 = 9-18+4 = -5

therefore the vertex = ( -3,-5)

2. 2x²+8x-5

axis of symmetry= -8/2(2) = -8/4 = -2

the y cordinate of vertex = 2(-2)² + 8(-2) -5

= 8-16-5 = -13

therefore the vertex = ( -2,-13)

3. x²-2x

axis of symmetry = -(-2)/2 = 2/2 = 1

the y cordinate of vertex = 1²-2(1) = 1-2 = -1

vertex = ( 1,-1)

4. x²-8x-9

axis of symmetry = -(-8)/2 = 8/2 = 4

the y cordinate of the vertex= 4²-8(4) -9 = 16-12-9 = -5

therefore the vertex = (4,-5)

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n = 66

Step-by-step explanation:

you can make a proportion 3/99 = 2/x

\( \frac{3}{99} = \frac{2}{x} \)

99 * 2= 198

3 * x = 3x

so the equation would be 198 = 3x

than do 198 ÷ 3 on ur calculator

so x (or n in this context) would equal 66

Answer:

m^2-4m=-29

m^2-4m+4=-29+4

(m-2)^2=-25

m=2+-5i

Answer:

524.30

Step-by-step explanation:

The domain for the given function is {-1, 2, 33, 32}.

A function's or relation's domain is the set of all possible independent values that the relation can take. It is the sum of all possible inputs.

A function's or relation's range is the set of all possible dependent values that the relation can produce from the domain values. It is the sum of all possible outputs.

When dealing with sets of ordered pairs, we simply divide the pairs into x- and y-coordinates. The domain is formed by the x-coordinates, which are independent values. The y-coordinates are the dependent values, i.e. they define the range.The domain in the set of ordered pairs {(a,b); (c,d); (e,f); (g,h)} is the set of the first number in each pair (those are the x-coordinates): {a,c,e,g}. The range is the set of all the pairs with the second number (the y-coordinates): {b,d,f,h}.

Given,

The set of ordered pair =   {(-1,5) , (2,3), (33,6), (32,7)}

then,

the Domain = {-1, 2, 33, 32}

Range = {5, 3, 6, 7}

Thus, the domain for the given function is {-1, 2, 33, 32}

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Answer:

D - 33

Step-by-step explanation:

From 5 to 6, the number is increasing by 1. Then from 6 to 8, it increases by 2. From 8 to 11 it increases by 3. This pattern continues throughout the entire sequence. Since between 20 and 26, it increases by 6, 26+7 should equal the number between 26 and 41. This number would be 33.