What is the value of tan(60°)?
A
12
30°
B
60°
14

To show that set D of all differentiable functions on an interval I is a vector space, we need to demonstrate that it satisfies the properties of a vector space under ordinary addition of functions and multiplication of a function by a real number.

Closure under addition: For any two functions f(x) and g(x) in D, their sum f(x) + g(x) is also a differentiable function on I. The sum of differentiable functions is differentiable, so closure under addition is satisfied.

Associativity of addition: For any three functions f(x), g(x), and h(x) in D, the associativity property holds: (f(x) + g(x)) + h(x) = f(x) + (g(x) + h(x)).

Commutativity of addition: For any two functions f(x) and g(x) in D, the commutativity property holds: f(x) + g(x) = g(x) + f(x).

Identity element: The zero function, denoted as 0(x), where 0(x) = 0 for all x in I, serves as the identity element for addition. For any function f(x) in D, f(x) + 0(x) = f(x).

Inverse element: For any function f(x) in D, there exists a function -f(x) such that f(x) + (-f(x)) = 0(x).

Closure under scalar multiplication: For any function f(x) in D and any real number c, the product cf(x) is also a differentiable function on I.

Distributive properties: For any functions f(x) and g(x) in D and any real numbers c and d, the distributive properties hold: (c + d)f(x) = cf(x) + df(x) and c(f(x) + g(x)) = cf(x) + cg(x).

Scalar multiplication associativity: For any function f(x) in D and any real numbers c and d, the associativity property holds: (cd)f(x) = c(df(x)).

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Answer:

$5.6

Step-by-step explanation:

Answer:

8*30/100= 2.4

so present cost = 8.0 - 2.4 = $ 5.6

Step-by-step explanation:

The cardiac output can be calculated using the formula CO = HR x SV, where HR is the heart rate and SV is the stroke volume.

Cardiac output refers to the amount of blood pumped by the heart in one minute and is calculated by multiplying the heart rate (HR) by the stroke volume (SV). The heart rate is the number of times the heart beats per minute, and the stroke volume is the amount of blood pumped by the heart with each beat.

Using the given values of HR = 144 BPM and SV = 70 ml, we can calculate the cardiac output as follows:

CO = HR x SV = (144 BPM) x (70 ml) / (1000 ml/L) / (60 s/min) = 1.68 L/min

Therefore, the cardiac output is approximately 1.68 L/min.

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Answer:

Thats hard

Step-by-step explanation:

Answer:

ya that's so hard but I think the slopes of the two function is the same

Answer:

diagramming, knowing your properties well, understand and know the angles, and have a good math understanding

Step-by-step explanation:

hope this helps

Answer:

y=17x-55

Step-by-step explanation:

y-(-4)=17(x-3)

y+4=17x-51

y=17x-55

Answer:

3971.570

Step-by-step explanation:

The times colin and dan take as a ratio is 1 : 3

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

Dan = 1 hour

Collin = 20 minutes

Convert hour to minutes

So, we have

Dan = 60 minutes

Collin = 20 minutes

When expressed as ratio, we have

Collin : Dan = 20 minutes : 60 minutes

Simplify

Collin : Dan = 1 : 3

Hence, teh ratio is 1 : 3

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Answer:

-3

Step-by-step explanation:

GCF = greatest common factor

What is in common with 3x and 18? They are both multiples of 3.

3 times x = 3x

3 times 6 = 18

However, it is -3x and -18

So we can add a negative sign in front of the 3

Therefore, the GCF is -3.

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Answer:

the answers would be: A, C, and E

Step-by-step explanation:

Answer:

A,C,E Are the answers

Step-by-step explanation:

Its a,c,e because 5.40 divided by 2 gallons is 2.70. Its C because 3.38 divided by 1.25 gallons is 2.70. Its E because 2.03 divided by 0.75 is 2.70.

Answer:

Jeff is moving faster.

Step-by-step explanation:

To compare two speeds, first we make them in one unit.

We know that,

1 km/h = 0.2777 m/s

7 km/h = 1.94 m/s

Jeff can run at a speed of 7 km/h i.e. 1.94 m/s while Cameron can run with a speed of 10 m/min or 0.167 m/s.

On comparing 1.94 m/s and 0.167 m/s, we found that Jeff is moving with more speed.

So, Jeff is faster.

Answer:

See below

Step-by-step explanation:

At 160 miles, Maya will have less gas by what looks like a gallon (hard to tell becuase the picture is blurry)

At 200 miles they have the same amount of gas, Maya still has less gas remaining

Answer:

  P'(3, -12)

Step-by-step explanation:

Assuming we're dilating the figure by a factor of 3 using the origin as the center of dilation, the coordinates of P' will be 3 times those of P:

  P' = 3P

  P' = 3(1, -4)

  P' = (3, -12)

if the function is divided and we get the remainder of  zero then  it is said to be a factor of a function

According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.

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Answer:  see proof below

Step-by-step explanation:

Use the following Double Angle Identities: cos 2A = 1 - 2sin²A

                                                                        sin 2A = 2sinA · cosA

\(\text{Given:}\quad \tan A = \dfrac{x}{y}\)

Proof LHS = RHS

y cos 2A + x sin 2A = y

                  x sin 2A = y - y cos 2A

                  x sin 2A = y(1 - cos 2A)

                  \(\dfrac{x}{y}=\dfrac{1-\cos2A}{sin\ 2A}\)

                  \(\dfrac{x}{y}=\dfrac{1-(1-2sin^2A)}{2\sin A\cdot \cos A}\)

                  \(\dfrac{x}{y}=\dfrac{2sin^2A}{2\sin A\cdot \cos A}\)

                  \(\dfrac{x}{y}=\dfrac{\sin A}{\cos A}\)

                  \(\dfrac{x}{y}=\tan A}\)

This is a TRUE statement since it was given that  \(\tan A = \dfrac{x}{y}\)  

30% of students mean 30 students wear contact lenses from a random selection of 100 students studying in a university.

Percentage is a fraction or a ratio of a random sample in which the value of whole is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.

Percentage is defined as a certain fraction or number out of a hundred. It is a fraction with the denominator 100, and the sign for it is "%."

Finding the proportion of a whole in terms of 100 is the goal of percentage calculations. There are two methods to calculate a percentage:

Use the unitary approach or try adjusting the fraction's denominator to 100.

How to solve?

30 % = 30/100 of a sample = 0.3 of a sample

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The correct answer is: No, neither method shows that factors are necessary or sufficient.

The methods of agreement and difference are both used in causal inference to analyze the relationship between factors and outcomes. However, neither method alone can determine whether factors are necessary or sufficient conditions.

The method of agreement examines cases where the outcome occurs and compares the presence or absence of different factors. If a factor is consistently present in all cases where the outcome occurs, it suggests that the factor may be related to the outcome. However, this method does not provide information about whether the factor is necessary or sufficient.

On the other hand, the method of difference compares cases where the outcome occurs and cases where it does not, identifying factors that are present in the former but absent in the latter. This method helps identify factors that are associated with the outcome, but it also does not establish whether the factors are necessary or sufficient conditions.

To determine whether a factor is necessary or sufficient, additional evidence and reasoning are required. Additional experiments, data analysis, or theoretical considerations are needed to establish the causal relationship and determine the nature of the factor's influence on the outcome. Hence, "No, neither method shows that factors are necessary or sufficient" is the correct option.

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Answer:

Step-by-step explanation:

Because of the Isosceles Triangle Theorem, both the base angles of that triangle measure a. We also know that a + b = 180 because of the definition of supplementary angles. So we have 2 equations from that info. First is the fact that

a + 7x = 180 and the second is

2x + a + a = 180 because of the Triangle Angle-Sum Theorem. If the left side of the first equation = 180 and the left side of the second equation also = 180, then by the transitive property of equality,

a + 7x = 2x + a + a and

a + 7x = 2x + 2a and

5x = a. Now that we know that a = 5x, we go back to our triangle and fill in 5x as a:

5x + 5x + 2x = 180 (the Triangle Angle-sum Theorem again) and

12x = 180 so

x = 15. If x = 15, then

a = 5(15) = 75,

b = 7(15) = 105, and

c = 2(15) = 30

If 4 - 5i is a zero of a quadratic function with real coefficients, then 4 + 5i is also a zero. The zeros of a quadratic function with real coefficients always occur in conjugate pairs.

In a quadratic function with real coefficients, the complex zeros occur in conjugate pairs due to the nature of the quadratic equation. The quadratic equation can be factored as (x - a)(x - b), where "a" and "b" represent the zeros of the function. If 4 - 5i is one of the zeros, it means that (x - (4 - 5i)) is a factor of the quadratic equation.

By expanding this factor, we get x - 4 + 5i. To ensure the coefficients remain real, the conjugate of 4 - 5i must also be a zero. Therefore, the other zero will be 4 + 5i. This property of complex zeros occurring in conjugate pairs is essential when dealing with quadratic functions with real coefficients.

When a quadratic function with real coefficients has a complex zero of 4 - 5i, it will also have a complex zero of 4 + 5i. This is due to the conjugate pair property, where complex zeros occur in pairs that differ only in the sign of the imaginary part.

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Answer: 2=x

Step-by-step explanation: -x+3 = 2x + 1 , 2 = x

Answer:

definitely  b.

Step-by-step explanation:

Answer:

I'm just going with the person above me that the answer is B. Yes, he used systematic random sampling.

Step-by-step explanation:

Tell me if I'm wrong.

Answer:

Option 1 (4, -5)

Step-by-step explanation:

In order to solve the system of equations, we can substitution.

Since we have y = 1/4x -6, we can substitute this for y in the equation 3x + y=7:

\(y=1/4x-6\\3x+y=7\\\\3x+(1/4x-6)=7\\13/4x-6=7\\13/4x=13\\x=4\)

Now we can either simply notice that there is no other option with a positive 4 or be super comprehensive and plug this 4 into any of the two equations to find y:

\(y=1/4(4)-6\\y=1-6\\y=-5\)

Answer:

a) \(a_n=3n-1\)

b) \(a_n=2n+7\)

Step-by-step explanation:

a)  From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:

14 - 11 = 3

11 - 8 = 3

8 - 5 = 3

5 - 2 = 3

(so the common difference = 3)

General equation of arithmetic sequence:  \(a_n=a+(n-1)d\)

(where \(a\) is the first term and \(d\) is the common difference between terms)

Given:

\(\implies a_n=2+(n-1)3\)

\(\implies a_n=2+3n-3\)

\(\implies a_n=3n-1\)

b)  From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:

17 - 15 = 2

15 - 13 = 2

13 - 11 = 2

11 - 9 = 2

(so the common difference = 2)

General equation of arithmetic sequence:  \(a_n=a+(n-1)d\)

(where \(a\) is the first term and \(d\) is the common difference between terms)

Given:

\(\implies a_n=9+(n-1)2\)

\(\implies a_n=9+2n-2\)

\(\implies a_n=2n+7\)

So nearest hundred of calories of pizza is 3384.

As it is given that its an pizza of 16 inches .

A Calorie is unit of heat used to indicate the amount of energy foods produce in the human body that is equal to 1000 calories.

Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.

So as we all know pizza of 16 inches contains 3384.00 calories

And its been asked to the nearest hundred so divide it by 100And we get 3384 calorie. So a 16 inch pizza contains 3384 calories.

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Answer:

4*(-5) = -20

Step-by-step explanation:

Triangles are singular because you can only ever draw one. A triangle can be created using two side lengths and the angle's measurement.

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Answer:

x = √149

Step-by-step explanation:

Compartmentalize the odd figure into a rectangle (with sides 3 and 7) and a triangle (with sides 10 and x). Now, that you have a triangle, you can use the rectangle underneath to find the bottom side of the triangle--it is 7. The triangle that has been formed is a right triangle, so we can use the Pythagorean Theorem to find x, which is the hypotenuse.

10² + 7² = x²

100 + 49 = x²

149 = x²

√149 = x

Answer:

7√2

Step-by-step explanation:

Remark

Draw another line parallel to 7.

Move to the other end of 3

that makes the vertical leg on the left 10 - 3 = 7

You now have a smaller right triangle.

Equation

a = 7

b = 7

c = x

Solution

x^2 = 7^2 + 7^2

x^2 = 49 + 49

x^2 = 98

x^2 = 7 * 7 *2

sqrt(x^2) = sqrt(7 * 7 * 2)

The rule about square roots is for every pair of factors you can take one out of the square root sign and throw the other one away.

x = 7 sqrt(2)

a. The number of student surveyed is = 12 + 7 - 4 + 47 = 62

b. The number of student that are math major but not biology major = 7

c. The number of student that are neither math major nor biology major = 47

d. The number of student that are both math and biology major = 4

Answer:

(2,0)

Step-by-step explanation:

   2 (x + 2y) = (2)

      2x + 4y = 4

-    2x + 5y = 4

-1y = 0

y = 0

2x + 5(0) = 4

2x = 4

x = 2

Answer:

x=2 y=0

Step-by-step explanation:

solve for y

x+2y=2

x=2-2y

2(2-2y)+5y

4-4y+5y=4

4+y=4

y=0

plug into equation

2x+5(0)=4

x=2

and

x+2(0)=2

x=2