(b) Let M be the function defined by M (x) = f(x) + h (x). Find M' (3).

Area of the sheep pen = 1600feet square

The amount of space occupied by a flat (2-D) surface or form of an object is known as its area.

180 feet of fence were purchased.

The perimeter of a rectangular sheep pen is equal to two times the length plus the width, or two times the length plus 180. One side of the rectangular sheep pen is covered with a barn, which equals the width.

The rectangular sheep pen's covered side:

180 =2 length + width

180 = 2 x80 +width

180 - 160 = width

20= width

Area = l*b = 80*20

Area of sheep pen = 1600 feet square

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Given polynomial equation x3 - 8 = 0

x3-8 is a cubic polynomial is in the form a3 - b3 = (a - b)(a2 + ab + b2)

x3 - 23 = (x - 2)(x2 + 2x + 4)

One root is 2

x2 + 2x + 4 = 0

x = -b ± √(b2 - 4ac) / 2a

x = -2 ± √22 - 4(4) /2

x = -2 ± √4 - 16 /2

x = -2 ± √-12 /2

x = -1 ± √3i

Therefore, x = 2, -1 ±√3i

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Given,

polynomial equation x3 - 8 = 0

x3-8 is a cubic polynomial is in the form a3 - b3 = (a - b)(a2 + ab + b2)

x3 - 23 = (x - 2)(x2 + 2x + 4)

One root is 2

x2 + 2x + 4 = 0

x = -b ± √(b2 - 4ac) / 2

x = -2 ± √22 - 4(4) /2

x = -2 ± √4 - 16 /2

x = -2 ± √-12 /2

x = -1 ± √3i

Therefore, x = 2, -1 ±√3i

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Answer:

x = 2.5y - 1

Step-by-step explanation:

Subtract 2 from both sides

then you get 2x = 5y - 2

then divide everything by 2 for the answer

x = 2.5y -1

Answer:32

Step-by-step explanation:

Answer:  the solution to the system of equations is x = 12 and y = 16.

Step-by-step explanation: To solve this system of equations, you can use the method of substitution.

First, solve one of the equations for one of the variables. For example, you can solve the first equation for x:

2x + y = 40

2x = 40 - y

x = (40 - y)/2

Then, substitute this expression for x in the second equation:

x - 2y = -20

(40 - y)/2 - 2y = -20

Multiplying both sides by 2, we get:

40 - y - 4y = -40

-5y = -80

y = 16

Substituting this value for y in the first equation, we can solve for x:

2x + 16 = 40

2x = 24

x = 12

Therefore, the solution to the system of equations is x = 12 and y = 16.

Answer:

Addition, Distributive, Addition, Multiplication, Division

Step-by-step explanation:

Answer:

(- 4, 2 )

Step-by-step explanation:

x + 5y = 6 → (1)

x + 3y = 2 → (2)

subtract (2) from (1) term by term to eliminate x

(x - x) + (5y - 3y) = 6 - 2

0 + 2y = 4

2y = 4 ( divide both sides by 2 )

y = 2

substitute y = 2 into either of the 2 equations and solve for x

substituting into (1)

x + 5(2) = 6

x + 10 = 6 ( subtract 10 from both sides )

x = - 4

solution is (- 4, 2 )

Answer:

5/8

Step-by-step explanation:

We can solve this by turning 2 1/2 into a decimal.

2 1/2 = 2.5

2.5 ÷ 4 = 0.625

0.625 = 5/8

2 1/2 divided by 4 is 5/8

The required function f(x) is represented by -1 + F(x + sin(x)).

To find the function f(x), you can use the formula for integration by substitution:

f(x) = F(g(x)) + C

where F is an antiderivative of f, g is a function such that g'(x) = f(x), and C is a constant.

In this case, we can take g(x) = x + sin(x). Then g'(x) = cos(x), so f(x) = F(g(x)) + C = F(x + sin(x)) + C.

We are given that f'(π) = 2 and f(π) = -1, so we can use these values to find the constants C and F.

First, we can find F by taking the derivative of F(x + sin(x)). This gives us:

F'(x + sin(x)) = f(x) = cos(x)

Substituting x = π and using the fact that F'(x + sin(x)) = f'(π) = 2, we get:

F'(π + sin(π)) = 2

Since sin(π) = 0, this simplifies to:

F'(π) = 2

Then, using the fact that F(x + sin(x)) = f(π) = -1 when x = π, we can find the value of F(π):

F(π) = -1

Now that we have found the values of F and F', we can use these to find the value of C.

Since F(x + sin(x)) = F(x) + F'(x) sin(x), we can substitute x = π to get:

F(π + sin(π)) = F(π) + F'(π) * sin(π)

Substituting the values we found above, this becomes:

F(π + 0) = -1 + 2 x 0

Which simplifies to:

F(π) = -1

Since F(π) = -1, we can conclude that C = -1.

Therefore, the function f(x) is given by:

f(x) = F(x + sin(x)) + C = F(x + sin(x)) - 1

= -1 + F(x + sin(x))

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Answer: Table

Step-by-step explanation: Hope you find it helpful!

The solution of given equation by using the property of equality is x = 2.

An equation has been presented to us.

3(2x + 6) -4x = 2(5x -2) + 6

Our given equation has to be solved step-by-step.

Step 1: Utilize the distributive property;

3×2x + 3×6 - 4x = 2×5x -2×2 + 6

6x + 18 -4x = 10x - 4 + 6

Step 2: combine similar phrases.

6x + 18 -4x = 10x - 4 + 6

2x + 18  = 10x + 2

Step 3: Apply the equality's subtraction property

2x - 2x + 18  - 2 = 10x + 2 - 2x - 2

16 = 8x

Step 4: Apply the equality's divisional property:

16/8 = 8x/8

x = 2

As a result, is our given equation's answer is x = 2.

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The correct question is-

Follow the steps to solve this equation. 3(2x + 6) – 4x = 2(5x – 2) + 6 1. Use the distributive property: 6x + 18 – 4x = 10x – 4 + 6 2. Combine like terms: 2x + 18 = 10x + 2 3. Use the subtraction property of equality: 18 = 8x + 2 4. Use the subtraction property of equality: 16 = 8x 5. Use the division property of equality:

Answer:

g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x)

Step-by-step explanation:

Answer:

uh  nose

Step-by-step explanation:

Answer:

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. If the coordinates of one endpoint are (x1, y1) and the coordinates of the other endpoint are (x2, y2), then the coordinates of the midpoint are given by:

M = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the coordinates of the midpoint are (4, 0), and the coordinates of AA are (3, -1). Therefore, the coordinates of BB must be (5, 1).

You can confirm this by calculating the midpoint using the coordinates of AA and BB:

M = ((3 + 5)/2, (-1 + 1)/2)

= (4, 0)

This shows that the point (5, 1) is indeed the other endpoint of the line segment, and the coordinates of BB are (5, 1).

Step-by-step explanation:

Answer:

Assuming angle 1 is 75º.

1 -> 75

2 -> 105

3 -> 75

4 -> 105

5 -> 75

6 -> 105

7 -> 75

8 -> 105

Answer:

C

Step-by-step explanation:

The measure of each angle in an equilateral triangle is [tex]60^{\circ}[/tex], not [tex]120^{\circ}[/tex].

The value of y is -30.

Direct variation is y = kx

15 = k(-3)

Divide by -3 on both sides

-15/3 = k

-5 = k -------> 1

Substituting 1 and x = 6, in Direct Variation

y = -5*6

y = -30

Therefore, the value of y is -30.

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Answer: 12

Step-by-step explanation:

[tex]f(9)=3+9=12[/tex]

After evaluation of the given expression, the value obtained in mixed fraction form is equal to -4 3/10.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given expression in the question,

(-5 - (-4 1/2)) × 3 + (-2 4/5)

The expression in simplified form will be,

(-5 + 9/2) × 3 - 14/5

(-10 + 9) × 3 -14/5

-3/2 - 14/5

= (-15 - 28)/10

= -43/10

It can also be written in mixed fraction form,

= -4 3/10

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From the given triangle diagram figure, angles are -

m∠1 = 72°

m∠2 = 114°

m∠3 = 66°

m∠4 = 66°

m∠5 = 56°

m∠6 = 32°

Depending on how many sides a polygon has, it is given a unique name. Because "tri" is a word that indicates "three," the polygon with three sides is known as a triangle. This polygon has three angles, as indicated by its name. Poly means numerous in the prefix.

Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed at a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

In the given problem,

m∠6 = 180° - (90° + 58°)

so, m∠6 = 32°

Next, m∠1 +m∠6  = 180° - (42° +34°)

                             = 104°

so, m∠1 = 104° - 32°

             = 72°

Next, m∠5 = 90° - 34°

m∠5 = 56°

Again, m∠4 = 180° - (56° + 58°)

m∠4 = 66°

Now from the figure, m∠3 and m∠4 are vertically opposite angle.

So, m∠3 = 66°

Again, m∠2 = 180° - 66° = 114°

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The image after the transformations of rotation, translation or reflection can be found by certain operation or rotation.

We can find how to know the image of certain figures after the given transformations are done.

91) Here it is translation.

x coordinates are shifted to right by 3 units and y coordinates are shifted to  down by 5 units.

So the entire graph will be shifted to right by 3 units and down by 5 units.

92) Here, the translation is by not shifting the x coordinates and shifting the y coordinates 2 units to the down.

So the entire graph will be shifted to down by 2 units.

93) When a graph is reflected across x = -2, then the graph is moved horizontally such that the original figure and the image will be at the same distance from x = -2.

94) When a graph is reflected across y = 1, then the graph is moved vertically such that the original figure and the image will be at the same distance from y = 1.

95) When a graph is rotated about the origin 180°, if it is clockwise or anticlockwise, each of the coordinates (x, y) in the graph will become (-x, -y).

96) If the rotation is 90° counterclockwise about the origin, the coordinates (x, y) in the original graph becomes (-y, x).

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Answer:

x = 21

Step-by-step explanation:

[tex]\frac{x}{9}[/tex] = [tex]\frac{35}{15}[/tex]

[tex]\frac{35}{15}[/tex] can be simplified to [tex]\frac{7}{3}[/tex] if we divide the numerator and denominator by 5

[tex]\frac{x}{9}[/tex] = [tex]\frac{7}{3}[/tex]  cross multiply and solve for x

3x = 63  Divide both sides by 3

x = 21

Answer: t = 37.8 degree

Step-by-step explanation:

We know that a circle has 360 degrees, this is half a circle, so it total is 180 degrees.

We add 63.7 with 78.7 = 142.4 degree

Take 180 - 142.2 = 37.8 degree

Answer:

multiplying factor = 1.15

Step-by-step explanation:

the original amount is 100%

the increase is 15%

then increasing the original amount by 15% is

100% + 15% = 115% = [tex]\frac{115}{100}[/tex] = 1.15

multiplying factor is 1.15

In linear equation, plant b height will exceed the height of plant a after 16 days.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.        

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Plant a: 5 cm tall and rate of change = 2.5 cm per month

Plant b: 4  cm tall and rate of change = 4.5 cm per month.

Now we have to form the linear equations.

Plant a:

y = 2.5x + 5, where y is the total height and "x" be the number of months.

Plant b:

y = 4.5x + 4 , where y is the total height and "x" be the number of months.

Now we have to when the height of the plant a and plant b are the same.

To do that, we have to equivate both the equations and find x.

2.5x + 5 =4. 5x + 4

Isolate the variables terms and constants.

4.5x - 2.5x = 5 - 4

2x = 1

Dividing both sides by 2, we get

x = 1 ÷ 2

x = 0.5 months.

So after 15 days, the height of the plant a and plant b are the same.

Therefore, plant b height will exceed the height of plant a after 16 days.

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Answer:

0.009754

Step-by-step explanation:

(.65)^4 x (0.35)

By saying that he makes a free throw on the fifth show, he did not make the first four, therefore 4 of the times he shot, he did not get it in.

If he makes the shot 35% of the time, he doesn't make it 65% of the time: (1-0.35=.65)

On the last shot he made it, which he makes 35% of the time therefore:

You want to multiply : 0.35 (which is = 35%) by itself four times and then multiply that by 0.65 (since the last shot was made)

0.35 x 0.35 x 0.35 x 0.35 x 0.65 = 0.009754 or 0.9754%

There is a 0.9754% chance he makes it BUT a 0.009754 probability

The coordinates of P' after the transformation are (-1, 1)

From the question, we have the following parameters that can be used in our computation:

Point P' = (2, -4)

This point can be represented as

(x, y) =  (2, -4)

Also, from the question, we have the transformation to be:

(x-3, y-3) and reflection line y=x

Mathematically, this can be expressed as

(x, y) = (y - 3, x - 3)

So, we have

Point P' = (2, -4)

This means that

y -3 = 2

x - 3 = -4

Evaluate

y = 1

x = -1

Hence, the point P after transformation is (-1, 1)

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To obtain an amount of 3 / 2 cups of flour, then we need three halves of cup by means of a 1 / 2 cup measuring cup.

In this problem we have the case of recipe that requires 3 / 2 cups of flour in terms of certain number of measuring cups with an amount of 1 / 2 cups. The number of measuring cups (n) is equal to the total required by the recipe (M) divided by the amount of the measuring cup (m), both in cups. That is:

n = M / m

If we know that m = 1 / 2 cup and M = 3 / 2 cup, then the number of measuring cups is:

n = (3 / 2 cup) / (1 / 2 cup)

n = 3

In other words, we need 3 halves of a cup of flour to obtain the required amount of 3 / 2 cups.

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Answer:

25°

Step-by-step explanation:

We know the opposite angles must be equal when two lines intersect, so 67 = 42+t. Subtracting 42 from both sides gives t=25, which is our answer

answer:

25 degrees

step-by-step explanation:

67=42+t so using that equation the answer can be determined. hope that helps!

Part A

[tex](b/2)^2 =(-3/2)^2 =\boxed{9/4}[/tex]

Part B

[tex]-x^2 -3x+2\\\\=-(x^2 +3x)+2\\\\=-(x^2 +3x+2.25-2.25)+2\\ \\=-((x+1.5)^2 -2.25)+2\\\\=-(x+1.5)^2 +2.25+2\\\\\boxed{y=-(x+1.5)^2 +4.25}[/tex]