g(x) = 3x²
Step 1: Make a table of values for g(x) = 3x²

The derivative of F(x) with respect to x is  [tex]8x^7 + 60x^4 + (1-3x^(-3/2))*\sqrt(3)*x^(-5/2) - 2x/(x^2+\sqrt(x))^2 + e^x + 2e^(2x).[/tex]

The sum rule is a rule of differentiation in calculus that states that the derivative of the sum of two functions is equal to the sum of their derivatives.

To differentiate the function F(x), we need to use the appropriate differentiation rules to each term of the function. Using the sum rule and chain rule of differentiation, we obtain:

F(x) = [tex]x^8 + 12x^5 + x^(2-3/2)*\sqrt(3) + 1/(x^2+\sqrt(x)) + e^x + e^(2x)[/tex]

F'(x) = [tex]8x^7 + 60x^4 + (2-3/2)x^(2-5/2)\sqrt(3) - 2x(x^2+√(x))^(-2) + e + 2e^(2x)[/tex]

We can simplify the expression further by combining like terms and simplifying the power of x in the third term using the power rule. The final answer is:

F'(x) = [tex]8x^7 + 60x^4 + (1-3x^(-3/2))*\sqrt(3)*x^(-5/2) - 2x/(x^2+\sqrt(x))^2 + e^x + 2e^(2x)[/tex]

Therefore, the derivative of F(x) with respect to x is [tex]8x^7 + 60x^4 + (1-3x^(-3/2))*\sqrt(3)*x^(-5/2) - 2x/(x^2+\sqrt(x))^2 + e^x + 2e^(2x).[/tex]

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Differentiate F(x) such that F(x)=x8+12x5+x2−−√3+1x2+xx−−√+ex+e2x.

Answer:

4 centimeters.

Step-by-step explanation:

The Answer is four centimeters. Since 1 centimeter is equal to 2 kilometers we must find the multiple that will get us to 8 milometers which is 4, 2 x 4 =8 so the answer is 4 centimeters

Answer:

4 centimeters.

Step-by-step explanation:

The Answer is four centimeters. Since 1 centimeter is equal to 2 kilometers we must find the multiple that will get us to 8 milometers which is 4, 2 x 4 =8 so the answer is 4 centimeters

Answer: D

Step-by-step explanation:

The given expression is 2w3 + 7w2 - 4w.

The power of the expression is the highest exponent of the variable w, which is 3. However, this is not one of the options given.

A factor of the expression is a term or expression that divides the given expression completely. -4w is not a factor of the given expression.

The coefficient of a term is the numerical factor that is multiplied by the variable. The coefficient of the first term 2w3 is 2, and the coefficient of the second term 7w2 is 7. The coefficient of the last term -4w is -4. Therefore, the statement "The coefficient of the expression is w" is false.

The given expression has three terms: 2w3, 7w2, and -4w. Therefore, the statement "The expression has 3 terms" is true.

The equations that are true for x = -2 and x = 2 are:

x² – 4 = 0

4x² = 16

A quadratic equation is a type of polynomial equation of degree 2, which means that the highest exponent of the variable is 2. It can be written in the standard form:

ax² + bx + c = 0

where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus," meaning "square."

Quadratic equations can have one or two real solutions, depending on the values of a, b, and c. The solutions can be found using various methods, such as factoring, completing the square, or using the quadratic formula:

x = (-b ± √(b²-4ac)) / 2a

The equations that are true for x = -2 and x = 2 are:

x² – 4 = 0

4x² = 16

The other three equations are not true for x = -2 and x = 2:

a) x² = -4 has no real solutions because the square of any real number is always non-negative, so x² can never be equal to a negative number.

b) 3x² + 12 = 0 simplifies to x² + 4 = 0, which has no real solutions because x² is always non-negative and can never be equal to -4.

2(x – 2)² = 0 simplifies to (x - 2)² = 0, which has only one solution at x = 2.

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In the given parallelogram WXYZ,

Q9)measure of angle WZX is 41°  

Q10)measure of XR=6x - 23

What is parallelogram?

A parallelogram is a four-sided polygon or quadrilateral with two pairs of parallel sides. Both sides of an argument must be fair and consistent. A parallelogram has four corners and four edges. A parallelogram is a two-dimensional form with two matching pairs of its opposite sides having parallel, equal-length sides. The angles inside the two sides of the shape must add up to 180 degrees, or 360 degrees in total. On either side, it has parallel and equal sides. Equally opposing angles are present. Its diagonal lines split in two.

Q9)Given that ∠XYZ=68° and ∠WXZ=71° ,then ∠WZX=?

We know that in a parallelogram, angles on opposite are equal and angles in adjacent are supplementary

∴∠XYZ = XWZ (opposite)

∠XYZ = ∠XWZ = 68°

To find  ∠WZX , consider ΔWXZ

In ΔWXZ, ∠XWZ=68° , ∠WXZ=71°  and ∠WZX=?

By angle sum property,

∠XWZ + ∠WXZ=71° + ∠WZX=180

68° + 71°  + ∠WZX=180

∠WZX=180-139

∠WZX=41°  

Q10)Given that XZ=8x-18 and RZ=2x+5, then XR=?

We know that in a parallelogram, diagonal bisect each other

consider diagonal XZ,

XZ= XR + RZ

8x-18=XR+2x+5

XR=8x - 18 - 2x - 5

    = 8x - 2x -18 - 5

    =6x - 23

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The given expression rs+10s−5r−50 can be factorized by grouping as (r+10)(s-5)

Factorization is the process of breaking down an expression into simpler factors. In mathematics, factorization is often used to simplify expressions, solve equations, and find common factors.Factorization is an important tool in algebra and is used in many areas of mathematics, including number theory, geometry, and calculus.

The given terms can be reqrouped into two proportional parts as ; (rs+10s) +(-5r - 50), the we can Factor the expression as ;

s(r+10) +(-5r - 50)

s(r+10) -5(r + 10)

(r+10)(s-5)

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Answer:

n > -5

Step-by-step explanation:

2(6n-6)>-72

Solve the inequality.

Divide each side by 2.

2(6n-6)/2>-72/2

(6n-6)>-36

Add 6 to each side.

6n-6+6>-36+6

6d> -30

Divide by 6.

6n/6 > -30/6

n > -5

Answer:

n > -5

Step-by-step explanation:

2 ( 6n - 6 ) > - 72

Solve the brackets.

12n - 12 > - 72

Add 12 to both sides.

12n > - 72 + 12

12n > -60

Divide both sides by 12.

n > -5

Answer:

------------------------------

We need to find the distance between line L and point A(6, -1).

To find the distance d between the point and the line, we'll use the point-to-line distance formula, which is given by:

      [tex]d = \dfrac{ |Ax + By + C| }{\sqrt{A^2 + B^2} }[/tex]

where, A, B, and C are the coefficients of the line Ax + By + C = 0.

For line L, we have the equation y = - x - 2, which can be rewritten as:

The coordinates of point A are x = 6, y = - 1.

Now we can plug these values into the formula:

   [tex]d = \dfrac{ |1*6 + 1*(-1) + 2| }{\sqrt{1^2 + 1^2} }=\dfrac{|7|}{\sqrt{2} } =\dfrac{7}{\sqrt{2} } =5.0[/tex]

So, the distance between line L and point A(6, -1) is approximately 5.0 units, rounded to the nearest tenth.

Answer:

[tex] \frac{3}{5} = 0.6[/tex]

Step-by-step explanation:

By dividing the denominator and numerator by 4 you get:

[tex] \frac{12}{20 } = \frac{3}{5} [/tex]

The given triangles △BAE ≅ △CAD by the HL Congruence Theorem.

Hypotenuse-Leg (HL) Congruence Theorem:

The Hypotenuse-Leg (HL) Congruence Theorem, also known as the RHS (Right-angle, Hypotenuse, Side) Congruence Theorem, is a theorem used to prove congruence between two right triangles.

The HL Congruence Theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.  

Here we have

Triangles BAE and CAD are connected at point A.

Angle BAE is a right angle, and the sides BA and AC are congruent.

Sides BE and CD are congruent.

From the figure,

Hypotenuses: BA is congruent to AC

Legs: BE is congruent to CD

Angle: Angle BAE is a right angle and angle CAD is also a right angle

Therefore,

The given triangles △BAE ≅ △CAD by the HL Congruence Theorem.

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hundreths

Because its talking about percentages, 1% = 1/100 = 0.01

Answer:

254.5 mm²

Step-by-step explanation:

Area of circle:

[tex]S_{circle}=\pi r^2[/tex]

          =9^2 * pi

          = 81 pi

          ≈254.5 mm^2

The statement "then x ∈ H implies x^n ∈ H for all n ≥ 0 and x^(-1) ∈ H" holds true in this case.

The term "abstract" refers to the fact that in abstract algebra, the focus is on studying algebraic structures in their own right, without necessarily referring to any specific set of numbers or operations. For example, instead of studying the arithmetic properties of the real numbers or the integers, abstract algebra studies the general properties of groups, which are sets equipped with a binary operation that satisfies certain axioms.

The statement "then x ∈ H implies[tex]x^n[/tex]∈ H for all n ≥ 0 and[tex]x^(-1)[/tex]∈ H" means that if x is an element of the set H, then x raised to any non-negative power (including 0) is also an element of H. Additionally, the inverse of x, denoted by [tex]x^(-1),[/tex] is also an element of H.

This statement is often used in the context of groups, where H is a subgroup of a larger group, and x is an element of that group. In this context, the statement means that if x is an element of H, then all powers of x (including the inverse) are also elements of H. This is because a subgroup is closed under the group operation, which in this case is multiplication (i.e., raising an element to a power).

For example, if H is the set of all positive integers, and x is the number 2, then[tex]x^2 = 4, x^3[/tex]= 8, and so on, are all elements of H. Additionally, the inverse of x, which is 1/x = 1/2, is also an element of H. Therefore, the statement "then x ∈ H implies[tex]x^n[/tex] ∈ H for all n ≥ 0 and[tex]x^(-1)[/tex]∈ H" holds true in this case.

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12 + 6 - 4 × 16

12 + 6- 64

18 - 64

-46

Hope it helps.

Answer:

Step-by-step explanation:

using BODMAS

bracket digits will be solved first.  12+6-4*8(3)

12+6-4*24

12+6-96

18-96

-78

ans -78

Answer:

D) y= + 0.8x + 46

Step-by-step explanation:

Hope it helps

Answer:

x>7/3 and x≤ -7/3

Step-by-step explanation:

Solve for x in the inequality

−3x+8<15 is x>7/3 the to find a second solution set, flip the inequality and the switch the sign x≤ -7/3

Answer:

Step-by-step explanation:

−3x+8<15

2x> -7

divide both side by 3

x→ [tex]-\frac{7}{3}[/tex]

Answer: a) The probability of matching the first five selected numbers to the later five numbers drawn is given by the formula:

P = (C(69,5) / C(69,5)) * (C(5,5) / C(26,1))

where C(n,r) is the number of combinations of n items taken r at a time. The first term in the product represents the number of ways to choose the first five numbers from the pool of 69, and the second term represents the probability of choosing the correct number from the second set of 26 numbers.

Simplifying the expression, we get:

P = (1) * (1/26) = 1/26

Therefore, the probability of matching the first five selected numbers to the later five numbers drawn is 1/26.

b) The probability of matching the sixth selected number to the later number drawn from the second set is given by:

P = C(1,1) / C(26,1) = 1/26

Therefore, the probability of matching the sixth selected number to the later number drawn is 1/26.

c) The probability of winning the jackpot is the product of the probabilities of matching the first five selected numbers to the later five numbers drawn and matching the sixth selected number to the later number drawn. Using the results from parts (a) and (b), we get:

P = (1/26) * (1/26) = 1/676

Therefore, the probability of winning the jackpot is 1 in 676.

Step-by-step explanation:

Answer: The area of Ryan's chessboard is given as 64x^6y^8 square units.

We know that the area of a square is given by A = s^2, where A is the area and s is the side length.

To find the side length of the square, we can use the formula for the side length of a square in terms of its area, which is s = √A.

Substituting A = 64x^6y^8, we get:

s = √(64x^6y^8)

Using the properties of square roots, we can simplify this expression as follows:

s = √(2^6 * (x^2)^3 * (y^2)^4)

s = √(2^6) * √((x^2)^3) * √((y^2)^4)

s = 2^3 * x^3 * y^4

Therefore, the expression for the side length of Ryan's chessboard is 2^3 * x^3 * y^4.

Step-by-step explanation:

Answer:

It is not possible to tell from the graph whether k is greater than or less than zero. The graph only shows the shape of the function and the location of its intercepts and does not provide any information about the values of its parameters.

Answer:

Based on the graphed values of f(x) and independent variable x, the graph shows that C. k is greater than zero.

What is the value of k?

We have a c value of -1 which is where the y axis is intercepted.

We know that k isn't zero because the x and y values are not the same. We can also tell that k is not less than 0 because if it was, the f(x) for the smaller x value would lead to a larger f(x) value.

The only logical conclusion therefore, is that k is greater than zero.

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the value of p is 3/2, the value of q is 3t, and the value of r is 2/9.with  the sum of the first n terms of the arithmetic series formula we are able to solve it

what is arithmetic series  ?

An arithmetic series is a series of numbers in which each term is obtained by adding a fixed number to the preceding term (known as the common difference). The sum of the terms in an arithmetic series can be found by multiplying the average of the first and last

In the given question,

We know that the first term of the arithmetic series is given by (2t+1) and the common difference is 3. Therefore, the nth term can be written as:

aₙ = a₁ + (n-1)d

(14r - 5) = (2t + 1) + (n-1)3

14r - 5 = 2t + 1 + 3n - 3

14r - 4 = 2t + 3n

7r - 2 = t + (3/2)n --------(1)

Now, we need to find the values of p, q, and r for the sum of the first n terms of the series, which is given by:

Sₙ = (n/2)[2a₁ + (n-1)d]

Sₙ = (n/2)[2(2t+1) + (n-1)3]

Sₙ = n(3n+4t+2)/2

We can simplify this expression by factoring out a 2 from the numerator:

Sₙ = n(3n+4t+2)/2 = (2n/2)(3n+4t+2)/2

Sₙ = (n/2)(3n+4t+2) = (3/2)n² + 2tn + n

Now, we need to write this expression in the form p(qt-1). To do this, we need to factor out (3/2):

Sₙ = (3/2)(n² + 4/3 tₙ + 2/3 n)

Sₙ = (3/2)[n² + 4/3 tₙ + (2/9)(3n)]

Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n]

Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n + (4/9)t² - (4/3)tₙ + (4/3)tₙ]

Sₙ= (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n + (4/3)tₙ]

Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)(3t*n)]

Now we can see that p=3/2, q=3t, and r=2/9. Therefore, the value of p is 3/2, the value of q is 3t, and the value of r is 2/9.

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Answer: 2/3q + 7/12

Step-by-step explanation: on khan academy

Answer:Height

Height is up and down, so up or above ground is height.

The statements provided about fractions and percentage of yogurt cups and the strawberry flavor are, respectively, true, false, true, false.

In a case of 30 yogurt cups, 6 out of every 10 are strawberry. Therefore, there are a total of 18 strawberry yogurt cups in the case.

To find the fraction of yogurt cups that are strawberry, you divide the total number of strawberries (18) by the total number of cups (30), which gives 18/30.

The total number of strawberry yogurt cups is 18, based on the fact that there are 30 yogurt cups in the case.

60% of the yogurt cups are strawberry, which is the result of multiplying the fraction of strawberry yogurt cups (18/30) by 100%.

To find the percentage of yogurt cups that are not strawberry, you subtract the percentage of strawberry yogurt cups (60%) from 100%, which gives 40%.

Therefore, we can conclude we have correctly answered this question.

The complete question is the following:

Mrs. Dimitri purchased a case of yogurt cups. Out of every 10 yogurt cups, 6 are strawberry. There are 30 yogurt cups in the case. Choose True or False for each statement.

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The scale factor in the example given, which employs 10 blocks, is 62.5.

We must first make an educated guess as to how many blocks make up your model.

Suppose you utilized 10 blocks.

Since we know that each block is 2 feet tall, the model's height is:

10*2ft = 20ft

Given that the Empire State Building is 1,250 feet tall, we would like to adjust the scale from 20 feet to 1250 feet.

We divide the larger value by the smaller value to obtain that:

k = 1250ft/20ft = 62.5

This indicates that each foot on the model corresponds to 62.5 feet on the actual structure.

Therefore, the scale factor in the example given, which employs 10 blocks, is 62.5.

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Answer:

[tex] {25}^{ \frac{1}{2} } = \sqrt{25} = 5[/tex]

The statement D. (x, y) ⇒ (x + 4, y – 2) shows the rule for the translation. Thus, option D is correct.

In geometry, a transformation is an operation that shifts, flips, or alters a shape to create a different one. A translation, which consistently and uniformly moves each point in a figure in one direction, is an example of a transformation. Translations are frequently referred to as slides.

For (x, y) => (x – 4, y – 2)  

x decreases by 4 and y decreases by 2 in other words, we may say that the graph shifts to the left by 4 units and downward by 2 units.

For (x, y) => (x – 4, y + 2)

x decreases by 4 and y increases by 2 in other words, we may say that the graph shifts to the left by 4 units and upward by 2 units.

For (x, y) => (x + 4, y + 2)

x increases by 4 and y increases by 2 in other words, we may say that the graph shifts to the right by 4 units and upward by 2 units.

For (x, y) => (x + 4, y – 2)

x increases by 4 and y decreases by 2 in other words, we may say that the graph shifts to the right by 4 units and downward by 2 units.

Thus, the correct option is option D.

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Answer:

the answer is D on edge

Step-by-step explanation:

picture below

Answer:

No, (-2, 3) is not a solution

Step-by-step explanation:

Substitute x with -2 and y with -3.

x = -2

-2 = -2   true

2x + 3y = 6

2(-2) + 3(3) = 6

-4 + 9 = 6

5 = 6    false

Answer: a) Line segment OA is a radius of the circle, and any other radius will have the same length as OA. So, line segments OB, OE, OF are also definitely equal in length to OA.

b) Triangle OAB is definitely isosceles because it has two equal sides, OA and OB, which are radii of the circle.

An equation of a line parallel to that passes y = 3x + 1 through the point (-4, 1) is y = 3x + 13.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is parallel to y = 3x + 1, the slope is equal to 3.

At data point (-4, 1) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 3(x - (-4))  

y - 1 = 3(x + 4)

y = 3x + 12 + 1

y = 3x + 13

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