The second statement is the
of the first.
Foundations of Geometry

Answer: the answer will be negative.

Step-by-step explanation: Once you have the numerical answer, then you can apply a very simple rule to determine the sign of the answer: When the signs of the two numbers are the same, the answer will be positive. When the signs of the two numbers are different, the answer will be negative.

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Considering the closure under property the polynomials f(x) = a 0 + a 1 x + a 2 x^ 2 ... + a n x^ n; and g(x) = b 0 + b 1 x + b 2 x^ 2 ... + b m x^ m

In mathematics, a set is considered closed if we are able to apply and complete an operation on its components while consistently receiving a component from the same set.

A set therefore either possesses closure for a given mathematical operation or it does not.

Use of real numbers is the closure property of addition. Addition of two real numbers results in areal number

In the given problem, the set considered is polynomial addition and the addition of the two polynomial will give a sum which is a polynomial hence we say it is closed under addition.

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Answer:

1.21

Step-by-step explanation:

2 liter = 0.0706

3.5 seconds = 0.0583 minutes

0.0706/0.0583 = 1.21 cubic feet/minute

The rate of flow in cubic feet per minute is 1.21 cubic feet/minute if the water flows through a pipe at a rate of 2 liters every 3.5 seconds.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Water flows through a pipe at a rate of 2 liters every 3.5 seconds.

As we know:

2 liter = 0.0706

3.5 seconds = 0.0583 minutes

= 0.0706/0.0583

= 1.21 cubic feet/minute

Thus, the rate of flow in cubic feet per minute is 1.21 cubic feet/minute if the water flows through a pipe at a rate of 2 liters every 3.5 seconds.

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The answer is (C) 104. If f(x) = 3x + 12, g(x) = x + 6, h(x) = x + 1,

What is the function?

A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, a function is a rule or procedure that takes one or more inputs and produces a corresponding output.

We need to start by evaluating the innermost function first, so:

fog(x) = f(g(x)) = f(x + 6) = 3(x + 6) + 12 = 3x + 30

Next, we evaluate the composition of f and g again, using the result from above:

f×f×g(x) = f(f×g(x)) = f(3x + 30) = 3(3x + 30) + 12 = 9x + 102

Now, we evaluate the composition of h and the result from above:

hohofofog(x) = h(h×f×f×g(x)) = h(h(9x + 102)) = h(9x + 103) = 9x + 104

Finally, we evaluate the entire composition at x = 0:

h×h×f×f×g(0) = 9(0) + 104 = 104

Therefore, the answer is (C) 104. If f(x) = 3x + 12, g(x) = x + 6, h(x) = x + 1,

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Answer: The area is 45 square feet

Step-by-step explanation: Use the formula (base*height)/2. Base in this case is 15, while height is 6. (15*6)/(2) It should equal 45 square feet.

Answer:

45^ft

Step-by-step explanation:

1/2 B ×H

1/2(6)×15=45^ft

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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9514 1404 393

Answer:

  7 2/3

Step-by-step explanation:

The even number of minus signs cancel, so the problem is an addition problem.

  5 2/5 +2 4/15

The fractions can be added only when they have a common denominator. 15 works for that purpose.

  5 6/15 +2 4/15 = (5 +2) +(6/15 +4/15) = 7 10/15

The fraction 10/15 can be reduced by removing a common factor of 5 from numerator and denominator.

 = 7 2/3

Answer:

The answer is A.

Step-by-step explanation:

1 plus 2x (276-5y) + 69= A.

Answer:

For this case we must explain how to simplify the following expression:

( -9)(-6)(15)(-7+7)

According to the PEMDAS algebraic resolution order method, operations within parentheses must be performed first.

So, we have:

-7+7

Different signs are subtracted and the major sign is placed.

-7+7=0

Rewriting the original expression we have:

(-9)(-6)(15)(0)=

Every number multiplied by "0" results in "0".

Then, the expression is zero.

(-9)(-6)(15)=0

Answer:

(-9)(-6)(15)(-7+7)=0

Answer:

The area is 60

Step-by-step explanation:

You had to multiply 5×4×3

Answer:

my math teacher said that to find the area multiple all the numbers together so I got 47

Answer:

Step-by-step explanation:

I and II

Pages in a book and leaves on a tree can be counted precisely. They are discrete.

The height of a person cannot be measured exactly. We can get very good

approximations (to a lot of decimal places) but never exact. This is continuous.

Answer:

1, 3, 9, and 27

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

The implications of Constructivist approach in teaching mathematics is that it helps the students to develop a better way to comprehend the content of what they are being taught.

A constructive approach of teaching mathematics believes that students construct knowledge rather than just passively take in information.

A constructive approach of teaching also believes that students integrate new knowledge with existing knowledge to create a deeper understanding of the mathematics being taught to them.

Therefore, constructive approach of teaching can help the students to comprehend the content of what they are being taught.

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Answer:

9.100

9.10,00

1. 1,098,000

1.109,800,000

The divisibility rule for 3 on any integer number  is proven in the detailed explanation of the solution.

Given a non-decimal number, n.

Suppose n may be divided by 3.

n should be thought of in terms of its digits as

n = d × 1 × 10⁽ⁿ⁻¹⁾⁽ⁿ⁻¹⁾ + d  × 2 × 10⁽ⁿ⁻²⁾ + ... + d × m × 10⁰

where d 1, d 2,..., d m are its digits and m is the number of digits in n.

The result of the preceding equation with n = 3k is

3k = d  × 1 × 10(m-1) + d × 2 × 10(m-2) +... + d × m × 10(m-0)

3000 is subtracted from both sides of the equation, giving us

0 = d × 1 × 10⁽ⁿ⁻¹⁾⁽ⁿ⁻¹⁾ + d  × 2 × 10⁽ⁿ⁻²⁾ + ... + d × m × 10⁰

We obtain by adding 3k to both sides of the equation.

3k = d × 1 × 10⁽ⁿ⁻¹⁾+ d

The divisibility rule is a heuristic for determining if two positive integers can be divided evenly (i.e. there is no remainder left over). For instance, determining if a number's last digit is 2, 4, 6, 8, or 0 makes it simple to determine whether it is even.

By examining the digits of the number, a divisibility rule provides a simple shorthand for determining if an integer is divisible by a particular set of factors without actually doing the division. This page only offers recommendations and examples for decimal, or base 10, numbers despite the fact that there are distinct divisibility tests for numbers in each radix or basis.

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Sample D, Sample C, Sample A, Sample B

There are two solutions for the equation |1/2x + 1| = 5: x = 8 and x = -12.

To determine the number of solutions for the equation |1/2x + 1| = 5, we need to consider the possible cases based on the absolute value expression.

Case 1: 1/2x + 1 = 5

In this case, we isolate the absolute value expression by subtracting 1 from both sides:

1/2x = 4

To solve for x, we multiply both sides by 2:

x = 8

This is one solution.

Case 2: 1/2x + 1 = -5

In this case, we isolate the absolute value expression by subtracting 1 from both sides:

1/2x = -6

To solve for x, we multiply both sides by 2:

x = -12

This is another solution.

Therefore, we have found two solutions for the equation |1/2x + 1| = 5: x = 8 and x = -12.

It's important to note that the absolute value function |1/2x + 1| can be equal to 5 for both positive and negative values of x, resulting in two solutions.

The absolute value function yields the positive magnitude of the expression inside the absolute value bars, so we consider both positive and negative solutions.  

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9514 1404 393

Answer:

  c = 150p + 1000

Step-by-step explanation:

We know the variable cost is 150 per phone, so the total cost will be ...

  c = 150p +b . . . . for some value b

We also know the value of c for 8 phones, so we can find b:

  2200 = 150(8) + b

  2200 -1200 = b = 1000

Then the desired equation is ...

  c = 150p + 1000

Solving a system of equations we can see that the washer costs $750, and the dryer costs $250.

Let's define the variables:

x = cost of the washer.

y = cost of the dryer.

We know that the cost combined is $1000, then:

x  + y = 1000

And the washer cost 3 times the cost of the dryer, then we will get:

x = 3y

So we have a system of equations, we can replace the second equation into the first one, so we will get:

3y + y = 1000

4y = 1000

y = 1000/4

y = 250

The cost of the washer is:

x = 3*250 = 750

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Answer:

The P-value is between 2.5% and 5% from the t-table.

Step-by-step explanation:

We are given that a random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years.

Let \(\mu\) = true average age of all the students at the university.

So, Null Hypothesis, \(H_0\) : \(\mu \leq\) 24 years     {means that the average age of all the students at the university is less than or equal to 24}

Alternate Hypothesis, \(H_A\) : \(\mu\) > 24 years     {means that the average age of all the students at the university is significantly more than 24}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                               T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~   \(t_n_-_1\)

where, \(\bar X\) = sample average age = 25 years

             s = sample standard deviation = 2 years

             n = sample of students = 16

So, the test statistics =  \(\frac{25-24}{\frac{2}{\sqrt{16} } }\)  ~  \(t_1_5\)  

                                     =  2  

The value of t-test statistics is 2.

Also, the P-value of test-statistics is given by;

            P-value = P( \(t_1_5\) > 2) = 0.034 {from the t-table}

The P-value is between 2.5% and 5% from the t-table.

You did not copy the image with the question. Sometimes you have to screenshot or use the Snip-it app to get the image.

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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The linear function that has the greatest initial value is Function C.

Function B has the greatest rate of change.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Function A:

The initial value is o.

f(0) = 0

The rate of change.

= (f(4) - f(2)) / 4 - 2

= (10 - 5) / 2

= 5/2

= 2.5

Function B:

The initial value is

y = 3x - 1

y = 3 x 0 - 1 = 0 - 1 = -1

Let y = f(x)

The rate of change.

= (f(2) - f(1)) / (2 - 1)

= (5 - 2) / 1

= 3

Function C:

The initial value is 2.

(0, 2) is considered as when x = 0, y = 2.

Take two coordinates from the graph.

(3, 3) and (6, 4)

The rate of change.

= (4 - 3) / (6 - 3)

= 1/3

= 0.33

Thus,

Function C has the greatest initial value.

Function B has the greatest rate of change.

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A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

The function f(x) = -|x| − 3 can be graphed by following these steps:

Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

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Answer: x<-1943

Step-by-step explanation:

Answer:

I got you.

Step-by-step explanation: