Which expression would be easier to simplify if you used the associative property to change the grouping?

The greatest possible area of the triangle be

Area = 1/2 sq. units.

Given, a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle.

we have to find the greatest possible area of the given triangular region.

Let the height of the triangle be, h and the base of the triangle be b.

using Pythagoras theorem, we get

1² = h² + (b/2)²

1 = h² + b²/4

h² = 1 - b²/4

Now, the area of the triangle be,

A = 1/2×b×h

squaring both the sides,

A² = 1/4×b²×h²

A² = 1/4×b²×(1 - b²/4)

A² = 1/4×b²×(4 - b²)/4

A² = 1/16×b²(4 - b²)

On differentiating, we get

2AA' = 1/16×[2b(4 - b²) -2b³]

2AA' = 1/8×[b(4 - b²) -b³]

2AA' = 1/8×(4b - 2b³)

2AA' = 1/4×(2b - b³)

On equating with zero, we get

b(2 - b²) = 0

b = √2

so, h = 1/√2

Therefore, the greatest possible area of the triangle be

A = 1/2 sq. units.

Hence, the greatest possible area of the triangle be

A = 1/2 sq. units.

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The expression 7x−3(x−1) written as another expression is 4x + 3

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

7x−3(x−1)

There are brackets in the above expression

So, the first step is that we remove the bracket

So, we have the following representation

7x−3(x−1) = 7x − 3x + 3

Looking at the equation closely, we have like terms

So, the next step is to evaluate the like terms

Solving further, we evaluate the like terms

7x−3(x−1) = 4x + 3

The above equation cannot be further simplified

Hence, the solution or equivalent of the expression is 4x + 3

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Answer: 2(x-3)2+13

To find the equivalent expression, we can use the property of square roots that says that the square of the difference of two numbers is the difference of the squares of the numbers. This property is given by the following equation:

(a-b)2 = a2-2ab+b2

In this case, the expression we are trying to simplify is 2x2-12x+23, which we can rewrite using the property of square roots as follows:

2x2-12x+23 = 2(x2-6x+11)

Then, we can use the property of square roots that says that the square of the difference of two numbers is the difference of the squares of the numbers to simplify the expression as follows:

2x2-12x+23 = 2(x2-6x+11) = 2(x2-6x+36-25)

Finally, we can use the commutative property of addition and the associative property of addition to simplify the expression even further:

2x2-12x+23 = 2(x2-6x+36-25) = 2((x-3)2+11) = 2(x-3)2+22

Therefore, the equivalent expression to 2x2-12x+23 is 2(x-3)2+13. This means that the correct answer is 2(x-3)2+13.

A) Both the graphs A and B are functions, here the vertical lines can intersect the curve A and B more than once. So, A and B graphs are functions.

B) The incorrect graph is A

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

A) Examine the graph to determine whether any vertical lines generated meet the curve more than once. If such a line exists, the graph does not reflect a function. The graph represents a function if no vertical line intersects the curve more than once.

A and B are functions, according to this.

B) A is the incorrect graph.

Because Robert's acceleration will change

Curved lines have varying slopes; they can begin with a very modest slope and then curve quickly (either upwards or downwards) towards a huge slope. In either case, the curving line with a changing slope indicates fast motion (i.e., changing velocity).

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Answer:

4680

Step-by-step explanation:

The area to the left of 25 is 0.6664, the area to the left of 17 is 0.2389, the area to the right of 22 is 0.5000, the area to the right of 27 is 0.2389, and the area between 17 and 30 is 0.6340.

μ = population mean = 22

σ = standard deviation = 7

The area from normal distribution can be calculated using z test or normal distribution formula.

a) The area to the left of 25 is

P(x ≤ 25) = P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])

= P(z ≤ [tex]\frac{25-22}{7}[/tex])

= P(z ≤ 0.43)

using z table and we get,

= 0.6664

b) The area to the left of 17 is

P(x ≤ 17) = P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])

= P(z ≤ [tex]\frac{17-22}{7}[/tex])

= P(z ≤ -0.71)

using z table and we get,

= 0.2389

c) The area to the right of 22 is

P(x > 22) = 1 - P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])

= 1 - P(z ≤ [tex]\frac{22-22}{7}[/tex])

= 1 - P(z ≤ 0.00)

using z table and we get,

= 1 - 0.5

= 0.5000

d) The area to the right of 27 is

P(x > 22) = 1 - P(z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])

= 1 - P(z ≤ [tex]\frac{27-22}{7}[/tex])

= 1 - P(z ≤ 0.71)

using z table and we get,

= 1 - 0.7611

= 0.2389

e) The area between 17 and 30 is

P(17 ≤ x ≤ 22) = P([tex]\frac{x-\mu}{\sigma}[/tex] ≤ z ≤ [tex]\frac{x-\mu}{\sigma}[/tex])

= P([tex]\frac{17-22}{7}[/tex] ≤ z ≤ [tex]\frac{30-22}{7}[/tex])

= P(-0.71 ≤ z ≤ 1.14)

= P(z ≤ 1.14) - P(z ≤ -0.71)

using z table and we get,

= 0.8729 - 0.2389

= 0.6340

Thus, the area is 0.6664 for area in the left of 25, the area is 0.2389 for area in the left of 17, the area is 0.5 for area in the right of 22, the area is 0.2389 for area in the right of 27, and the area is 0.634 for area between 17 and 30.

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Answer: 90

Step-by-step explanation:

7 * 10 = 70

2 * 10 = 20

70 + 20 = 90

All of the claims about the multiple regression output are correct. The first independent variable (X1) was a continuous-scale quantitative variable, whereas the second variable (X2) was coded 0 if Yes and 1 if No.

Multiple regression is an effective statistical approach for analyzing the associations between multiple independent variables and a single dependent variable. Multiple regression has numerous uses in the social sciences, and recent research used it to analyze the connection between two independent factors and a single dependent variable.

Finally, the total model is statistically significant, the slope coefficient for variable X1 is considerably different from zero, and the model explains almost 63% of the variance in the dependent variable.

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The rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall is [tex]\frac{527}{24}ft^2/sec[/tex].

What is triangle?

Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.

Given:

dx / dt = 2 feet / sec

We have to find dA/dt when x = 7.

Since,

Area = 1/2 x (xy)

A = 1/2 x (xy)

Differentiating both sides with respect to t

[tex]\frac{dA}{dt} = \frac{1}{2}(\frac{dx}{dt}y+\frac{dy}{dt}x)\\[/tex]                 ..(1)

We have,

x^2 + y^2 = 25^2

plug x = 7

⇒ y = √(25^2 - 7^2)

y = √(625 - 49)

y = √576

y = 24

Now plug x = 7, y = 24, dx/dt = 2 and dy/dt = -7/12 in equation (1)

[tex]\frac{dA}{dt} = \frac{1}{2} (2(24) + (-\frac{7}{12})(7)) \\ \frac{dA}{dt} = \frac{527}{24} ft^2/sec[/tex]

Hence, the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall is [tex]\frac{527}{24}ft^2/sec[/tex].

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Answer:

x=20

Step-by-step explanation:

6x+10 and 130 are equal to each other so to solve for x we set them equal

6x+10=130

   -10.  -10

6x=120

x=20

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Synthetic division yields the result 3x^2 + 2x - 7 when the equation

3x^3 - x^2 - 9x + 7 is divided by x - 1.

What is synthetic division?

Synthetic division in algebra is a technique that requires less writing and calculation than long division to manually divide polynomials into their Euclidean parts. The method can be applied to division by any polynomial, although it is typically taught for division by linear monic polynomials.

Consider the given polynomial 3x^3 - x^2 - 9x + 7.

We have to divide this polynomial by x - 1 using synthetic division.

           3x^2 + 2x - 7

________________________

(x - 1)√(3x^3 - x^2 - 9x + 7)

           3x^3 - 3x^2

______________________

                     2x^2 - 9x + 7

               -     2x^2 - 2x

__________________________

                              -7x + 7

                         -    -7x + 7

   _________________________

                                 0 + 0

Hence, Synthetic division yields the result 3x^2 + 2x - 7 when the equation 3x^3 - x^2 - 9x + 7 is divided by x - 1.

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The pool's water is changing height at a pace of 0.283 feet per minute.

Given,

Right circular cylinder shaped pool.

The radius of the pool = 3 feet

The height of the pool = 8 feet

Imagine that 6 cubic feet of water per minute is continuously being poured into a swimming pool in the shape of a right circular cylinder.

We have to find the rate of change of the height of the water in the pool when the depth of the water in the pool is 6 feet;

Here,

Due to the swimming pool's right circular cylinder shape, its volume equals;

V(c) = π × r² ×h

Where r is the radius of the base and h the height

We take differentiation on both sides of the equation to get:

dV/dt  = π × r² × dh/dt

Since the pool is a right circular cylinder and dV/dt is constant at 6 ft3/min, the rate of change in water height in the pool is independent of water height.

Then:

6  = π × r² × dh/dt

dh/dt = 6 / π × 3²

dh/dt = 8/113,04

dh/dt = 0.283 ft/min

Therefore,

The rate of change of the height of the water in the pool is 0.283 feet/min

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The equation that can be used to find the sum of the three numbers in the given situation is (C) (x) + (x + 1) + (x + 2) = - 21.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

So, allow x to be the first number.

Number two: x + 1

Number three: x + 2

Three numbers are added together to provide the sum x + x + 1 + x + 2.

Given that the sum of three consecutive numbers is -21.

So, (x) + (x + 1) + (x + 2) = - 21.

Therefore, the equation that can be used to find the sum of the three numbers in the given situation is (C) (x) + (x + 1) + (x + 2) = - 21.

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Correct question:
Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers?

a. x + x + x = - 21

b.  x + 2 x + 3 x = - 21

c.  x + (x + 1) + (x + 2) = - 21

d.  x + (x + 2) + (x + 4) = - 21

Answer: he need 6 day to get the 32 show

Answer:

ur not showing the points u need to plot

Step-by-step explanation:

The probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.

What is the probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Two dice are rolled.

Then the sample space (n) = 36

Possible outcomes = {(6,1), (6, 2), (6, 3), (6, 4)}

Probability = 4/36

                 = 0.11

Hence, the probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.

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The correct statement about the pair of lines will be;

''The lines are perpendicular because they intersect at a right angle.''

Option 4 is true.

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The pair of lines are shown in figure.

Now,

By figure, we see that;

The lines are perpendicular because they intersect at a right angle.

Thus, The correct statement about the pair of lines will be;

''The lines are perpendicular because they intersect at a right angle.''

Option 4 is true.

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In order to complete the square for the given equation x^2+16x=18, the number added to both sides is 64.

Complete the square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial. To complete the square, add or subtract the same value to both sides. In this case, add the square of half the coefficient of the x -term, (b/2)^2 to both sides of the equation. Hence, the number to add would be (16/2)^2 = 64.

Thus,

x^2+16x + 64 =18 + 64

x^2+16x + 64 =82

x^2+ 2*8x + 64 =82

(x + 8)^2 = 82

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The latest sentence of proof by using the triangle congruence method we can conclude that f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex].

Given that ΔABC and ΔCBD are right triangles

Therefore, one angle of both triangle is of 90°

So, ∠B is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.

Consequently, ∠A is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.

Similarly, When two triangles are similar then their corresponding angles are equal and their corresponding sides are also equal.

Therefore , the two proportions can be rewritten as

a² = cf ( equation 1 )

b² = ce ( equation 2 )

By adding b² on both side of equation 1 then we can write equation 1 as

[tex]a^{2} + b^{2} = b^{2}+cf[/tex]

[tex]a^{2} + b^{2} = ce+cf[/tex]

Because b² and ce are equal and substitute on the right side of equation 1

Using the converse of distributive property  in above equation then we get a new equation. That is,

[tex]a^{2} +b^{2} = c(f+e)[/tex]

Because distributive property is a(b+c)=a(b+ac)

a² + b² = c²

Because e + f = c²

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The length of the whole field will be 400 while the width will be 200 meters.

Perimeter is the addition of an external measure of sides it will always positive.

Perimeter of square = side + side + side + side

The perimeter of the circle = πd where d is the dia of the circle.

As per the given three equal areas have been drawn,

The perimeter of this area will be as,

2x + 4y = 1600

Area A = xy

A = x(1600 - 2x)/4

A = 400x - 1/2x²

To find the maximum area take the first derivative,

dA/dx = =0

400(1) - (1/2)2x = 0

400 - x = 0

x = 400 meter

And, 4y = 1600 - 2(400)

y = 800/4 = 200 meter

Hence " The length of the whole field will be 400 while the width will be 200 meters".

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The proportional equation for c in terms of j as per the question statement will be equal to c = 0.39(j).

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given information in the question,

Price of 13 bottles = $5.07

Then, the price of each bottle = 5.07/13 = $0.39

As per the statement in the question,

The total cost is represented by c and the number of bottles will be j.

Then, the proportional equation will be,

c = 0.39(j)

As the number of bottles will increase, the total price will also increase with it.

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The number k is equal to 60 when the top right angle at the intersection of the lines y and x is (2 k + 11) degrees and the bottom left angle is 131 degrees.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A mathematical expression is a sentence that includes numbers, variables, or both. The equal sign is never used in expressions. A mathematical statement stating the equality of two expressions is known as an equation.

Here,

Those two angles have the same measure. so you have,

2k+11=131

22k=120

k=60

The value of k where at the intersection of lines y and x, the top right angle is (2 k + 11) degrees and at the intersection of lines z and x, the bottom left angle is 131 degrees is 60.

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Answer:

1/8 pounds

because half of 1/2 is 1/4 and half of that is 1/8 so into 4 eqaula parts ots would be 1/8

The slope of the line is 0.4, Kyle runs (2/5)th of a lap in a minute, and In 30 minutes, she would run 12 laps.

As per the given graph, the slope of the line as:

m = (4.4 - 2.2)/(11 - 5.5)

m = 0.4

The equation of line as:

y = 0.4x + 0

y = (2/5)x

So, Kyle runs (2/5)th of a lap in a minute.

In 30 minutes, she would run:

y = (2/5) x 30

y = 12 laps

Therefore, the slope of the line is 0.4, Kyle runs (2/5)th of a lap in a minute, and In 30 minutes, she would run 12 laps.

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The question seems to be incomplete the correct question has been attached

(7 , -3) : Quadrant 4

(0 , 1) : y-axis

(-3 , -2) : Quadrant 3

(4 , 4) : Quadrant 1

If a set of scores does have a standard deviation of 4 and just a mean of 54, the score that is 1 standard deviation well below mean is 50.

For the given values-

Mean = 54

standard deviation = 4

1 value below the standard deviation is;

54 - 4 = 50

Thus, if a group of scores does have a standard deviation of 4 and just a mean of 54, the score that is 1 standard deviation well below mean is 50.

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There is enough evidence to suggest p>0.5

What is hypothesis in statistics?

A type of statistical analysis called hypothesis testing involves testing your presumptions regarding a population parameter. It is used to estimate the relationship between 2 statistical variables.

Thus, a hypothesis is a set of possible explanations or resolutions applicable to a situation. In other words, the hypotheses pose different scenarios in which the aim is to explain the origin and eventual resolution of the problem.

Let's discuss few examples of statistical hypothesis from real-life -

We are testing :

H0: p <= 0.5

H1: p > 0.5

Test statistic:

Z = [(364/562) - 0.5] / √[0.5(1-0.5)] / 562

= 7.00

P-value = P(Z>7.00) = 0.0000

Hence, there is enough evidence to suggest p>0.5.

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The area of the rectangular pasture is found to be 80,000 ft².

Given:

Let the pasture's rectangular length be l feet.

Given that the rectangular pasture's length being 200 feet longer than its breadth, its width must be w = l200 feet.

The pasture's boundary is;

2(l + w) = 1200

2(l + l - 200) = 1200

2l - 200 = 600

l = 400 feet

Width; w = l - 200

w = 400 - 200 = 200 feet

Rectangular area;

A = l x w

A = 400 x 200

A = 80,000 ft²

Thus, the area of the rectangular pasture is found to be 80,000 ft².

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