A linear function and an exponential function are shown below


Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?

Answer:

B.) 20

Step-by-step explanation:

We know the midpoint of half of the segment, which is 5. You can use this to find the length of half, after which you can find the entire length by multiplying by 2:

\(RN+NS=RS\\5+5=10\\HR+RS=HS\\10+10=20\)

The length of HS is 20.

The transformations that are applied to pentagon ABCDE to create A"B"C"D"E" are:

1) Translation (x, y) → (x + 8, y + 2)

2) Reflection across the x-axis (x, y) → (x, -y)

So, the overall transformation given in the graph is (x, y) → {(x + 8), -(y + 2)}.

The transformation rules are:

The pentagons in the graph have vertices as

For the pentagon ABCDE: A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), and (-2, 4)

For the pentagon A"B"C"D"E": A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), and E"(6, -6)

Consider the vertices A(-4, 5) from the pentagon ABCDE and A"(4, -7) from the pentagon A"B"C"D"E".

Applying the Translation rule for the pentagon ABCDE:

The rule is (x, y) → (x + a, y + b)

So, the variation is

-4 + a = 4

⇒ a = 4 + 4 = 8

5 + b = 7

⇒ b = 7 - 5 = 2

So, the pentagon ABCDE is translated by (x + 8, y + 2).

Applying the Reflection rule for the translated pentagon:

The translated pentagon has vertices (x + 8, y + 2).

When applying the reflection across the x-axis,

(x + 8, y + 2) → {(x + 8), -(y + 2)}

Therefore, the complete transformation of the pentagon ABCDE to the pentagon A"B"C"D"E" is (x, y) → {(x + 8), -(y + 2)}

Verification:

A(-4, 5) → ((-4 + 8), -(5 + 2)) = (4, -7)A"

B(-6, 4) → ((-6 + 8), -(4 + 2)) = (2, -6)B"

C(-5, 1) → ((-5 + 8), -(1 + 2)) = (3, -3)C"

D(-2, 2) → ((-2 + 8), -(2 + 2)) = (6, -4)D"

E(-2, 4) → ((-2 + 8), -(4 + 2)) = (6, -6)E"

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Answer:

6, 10, 8 is the correct answer.

Step-by-step explanation:

Given that, the recursive function:

\(a_n=a_{n-1}-(a_{n-2}-4)\)

6th term, \(a_{6} =0\)

5th term, \(a_{5} =-2\)

To find:

First three terms of the sequence = ?

Solution:

Putting n = 6 in the recursive function:

\(a_6=a_{5}-(a_{4}-4)\\\Rightarrow 0=-2-(a_{4}-4)\\\Rightarrow 2=-(a_{4}-4)\\\Rightarrow -2=(a_{4}-4)\\\Rightarrow -2+4=a_{4}\\\Rightarrow a_{4}=2\)

Putting n = 5 in the recursive function:

\(a_5=a_{4}-(a_{3}-4)\\\Rightarrow -2=2-(a_{3}-4)\\\Rightarrow -2-2=-(a_{3}-4)\\\Rightarrow 4=(a_{3}-4)\\\Rightarrow a_{3}=8\)

Putting n = 4 in the recursive function:

\(a_4=a_{3}-(a_{2}-4)\\\Rightarrow 2=8-(a_{2}-4)\\\Rightarrow 2-8=-(a_{2}-4)\\\Rightarrow 6=(a_{2}-4)\\\Rightarrow a_{2}=10\)

Putting n = 3 in the recursive function:

\(a_3=a_{2}-(a_{1}-4)\\\Rightarrow 8=10-(a_{1}-4)\\\Rightarrow 8-10=-(a_{1}-4)\\\Rightarrow -2=-(a_{1}-4)\\\Rightarrow 2=a_{1}-4\\\Rightarrow a_{1}=4+2\\\Rightarrow a_{1}=6\)

So, first, second and third terms are 6, 10, 8.

Answer:

b = 11\(\frac{1}{4}\) (or 11.25)

Step-by-step explanation:

From the diagram,

b = 15 - a

Since the triangles in the figure are all right angled, apply the appropriate trigonometric function to first determine x. We have;

Sin θ = \(\frac{opposite}{hypotenuse}\)

Sin 30 = \(\frac{x}{15}\)

x = Sin 30 x 15

  = 7.5

x = 7.5

To determine a,

Cos θ = \(\frac{adjacent}{hypotenuse}\)

Cos 60 = \(\frac{a}{7.5}\)

a = cos 60 x 7.5

  = 3.75

a = 3.8

b = 15 - 3.75

  = 11.25

b = 11\(\frac{1}{4}\)

Answer:  B 9:21

Step-by-step explanation:

9 reduces to three and 21 reduced to 7

x^2 = the first integer

(x - 1)^2 = the second integer.

x^2 - (x - 1)^2 = ?

First, let's plug a number into our equation for x.

(2)^2 - (2 - 1)^2 = ?

4 - (1)^2 = ?

4 - 1 = 3

As we can see the difference is odd but it's also the sum of the two consecutive integers.

2 + 1 = 3.

This works for all numbers. Let's plug another number into our equation for x.

(4)^2 - (4 - 1)^2 = ?

16 - (3)^2 = ?

16 - 9 = 7

4 + 3 = 7

Try any number and it will always be odd.

Answer: D.

Step-by-step explanation:

For an absolute value function, the vertex of \(f(x) = |x+h| + k\) is defined as the point (-h, k) for the coordinate (x, y).

When x is equal to negative h, the value for x and value for h effectively cancel out, and only the positive k remains, hence the vertex being (-h, k).

The function given has a vertex at (2, 3). We know that the vertex of an absolute function is (-h, k), so h must equal -2 and k must equal 3.

The equation:

\(f(x) = |x-2| + 3\)

B. sigma^infinity_k = 0 x^k + 3, and the interval of convergence is (-1, 1).

To find the power series representation for g(x), we need to rewrite g(x) in terms of the given geometric series.

Notice that g(x) can be written as:
g(x) = x^3/1 - x = x^3 * (1/1-x)

We can now substitute the formula for the geometric series to get:

g(x) = x^3 * sigma^infinity_k = 0 x^k
= sigma^infinity_k = 0 (x^3 * x^k)
= sigma^infinity_k = 0 x^(k+3)

Therefore, the power series representation for g(x) is:
sigma^infinity_k = 0 x^(k+3)

The interval of convergence of this series is the same as that of the geometric series, which is |x| < 1.

In interval notation, this can be written as (-1, 1).

Therefore, the correct answer is B. sigma^infinity_k = 0 x^k + 3, and the interval of convergence is (-1, 1).

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The slope of the line is 3

The difference between the consecutive term of the sequence is (1, 3)

To get the slope of the graph, we will use the coordinate points (2, 10) and  (3, 13)

Slope = 13-10/3-2

Slope = 3/1

Slope = 3

Hence the slope of the line is 3

The difference in the term for the x-coordinate is given as:

The difference in the term for the y-coordinate is given as:

Hence the difference between the consecutive term of the sequence is (1, 3)

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As per the given Ratio difference between the amount of money spent and the amount of money saved in a week is $2.

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.

The ratio formula can be used to represent a ratio as a fraction. For any two quantities, say a and b, the ratio formula is a:b = a/b. Because a and b are separate amounts for two portions, the total quantity is given as (a + b).

et 5x be the money he spends and 4x be the amount he saves

therefore, 5x+4x= 18

9x= 18

x= 18/9= 2

Tom spends, 5×2 = $10

and he saves, 4×2= $8

Difference, = $10-$8= $2

Therefore, as per the given ratio in the question difference between the amount of money spent and the amount of money saved in a week is $2.

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Tom receives $18 from his father in a week. The ratio of the amount of

the money he spends to the amount of money he saves in a week is 5:4

What is the difference between the amount of money spent and

amount of money saved in a week?

Answer:112

Step-by-step explanation: 1/4 divided by 28/1 = 1/112

Answer:

112 and very light

Step-by-step explanation:

Answer:if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function.

Step-by-step explanation:So it is a no ok.

After 3 years, Joe will have $579.14 in their savings account if they do not withdraw any money.

To solve the given problem, we need to use the formula for the amount of money in a savings account with compounded interest, which is given by:

A = P(1 + r/n)^(nt), where A is the final amount of money,P is the principal (the initial amount of money deposited),r is the annual interest rate,n is the number of times the interest is compounded per year, and t is the time in years.

Using the given values, we can substitute them into the formula and solve for the final amount of money that Joe will have after 3 years:A = $\(500(1 + 0.045/1)^(^1 ^× 3)A = $500(1.045)^3A\)= $579.14.

Therefore, after 3 years, Joe will have $579.14 in their savings account if they do not withdraw any money.

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Answer:

I think it's 4/9 the first one

the measure of the largest angle of the triangle is Largest angle = 4x + 10 = 4(25) + 10 = 110 So, the largest angle of the triangle has a measure of 110 degrees.

tLet x be the measure of the smallest angle of the triangle.

According to the problem statement, the measure of the largest angle of the triangle is 10 more than 4 times the measure of the smallest angle. Therefore, we can write:

Largest angle = 4x + 10

The measure of another angle is 20° more than the smallest angle. Therefore, we can write:

Other angle = x + 20

Since the sum of the measures of the angles in a triangle is always 180 degrees, we can write an equation based on this fact:

Smallest angle + Largest angle + Other angle = 180

Substituting the expressions we have for the largest angle and the other angle, we get:

x + (4x + 10) + (x + 20) = 180

Simplifying the expression, we get:

6x + 30 = 180

Subtracting 30 from both sides, we get:

6x = 150

Dividing both sides by 6, we get:

x = 25

Therefore, the measure of the largest angle of the triangle is:

Largest angle = 4x + 10 = 4(25) + 10 = 110

So, the largest angle of the triangle has a measure of 110 degrees.

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The velocity to be 40π rad/s. Therefore, the correct option is (E) 40π.

Given that the wheel makes 20 revolutions in one second.

To find the approximate velocity in radians per second we need to use the formula given below.

The formula for velocity is given as:

v = ω * r,

where ω = Angular velocity

r is Radius

The formula for angular velocity is given as:

ω = θ / t

where

θ = Angular displacement

t = Time

Thus the formula for velocity can be written as:

v = (θ / t) * r

On substituting the values, we get:

v = (20 * 2π) / 1

= 40π rad/s

Thus the wheel's approximate velocity in radians per second is 40π rad/s. Hence, the correct answer is 40π .

Conclusion: Wheel makes 20 revolutions in one second. We need to find its approximate velocity in radians per second using the formula

v = ω * r.

On substituting the values, we get the velocity to be 40π rad/s. Therefore, the correct option is (E) 40π.

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S is a chi-squared random variable with n₁ + n₂ + ... + nk degrees of freedom.

Let Y = X₁² + X₁² + ... + Xn², where the X;'s are independent Gaussian (0, 1) random variables with PDF fx(x) = (1 / sqrt(2phi)) e^-x²/2.

Then Y is known to be a = 2πT chi-squared random variable with n degrees of freedom.

To find the MGF of Y, øy (s), we need to follow the given below steps:øy (s) = E [e^sY]øy (s) = E [exp (s (X1² + X2² + ... + Xn²))]øy (s) = E [exp (sX1²) * exp (sX2²) * ... * exp (sXn²)]

Here, the Xs are independent Gaussian variables, so they have characteristic functionsøy (s) = [øx (s)]nøy (s) = [(1 - 2is)⁻¹/2]nøy (s) = [1 - 2is]⁻n/2

The MGF of Y is øy (s) = [1 - 2is]⁻n/2.(b)

Let S = Y₁ + Y₂ + ··· + Yk, where the Y's are independent random variables, with Y; be a chi-squared random variable with n; degrees of freedom.

To show that S is a chi-squared random variable with n₁ + n₂ + ... + nk degrees of freedom, we need to follow the given below steps

We know that MGF of chi-squared random variable with n degrees of freedom is [1 / (1 - 2t)]n.So, for each Yi, the MGF is [1 / (1 - 2t)]n.

When S = Y1 + Y2 + ... + Yk, the MGF of S isøs (t) = øy1 (t) øy2 (t) ··· øyk (t)Putting the MGF of each Yi, we haveøs (t) = [1 / (1 - 2t)]n1 [1 / (1 - 2t)]n2 ··· [1 / (1 - 2t)]nkøs (t) = [1 / (1 - 2t)]n1 + n2 + ... + nk∴ S is a chi-squared random variable with n₁ + n₂ + ... + nk degrees of freedom.(b)

Summary: S is a chi-squared random variable with n₁ + n₂ + ... + nk degrees of freedom.

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Answer: the perimeter of the rectangle is 30

Step-by-step explanation: so we know that the width of the rectangle is 5. Then it says that the length is two times more than the width....

5 times 2

Which is 10

Now all is left, you find the perimeter (all sides)

5+5+10+10

10+20

30

Therefore,

The perimeter of the rectangle is 30

Answer: 30

Step-by-step explanation: If the width is 5 and the length is twice the width then the length is going to be 10.

p=2(L+W)= 2(10+5)

                  2 x 15= 30

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Determine the corresponding sides by the same opposite angles.

Opposite sides to 24° angle are FG and KL.

Correct expression is A:

Answer:

three (3).

Step-by-step explanation:

H=O+A

c^2=5^2+12^2

c^2=25+144

c^2=169

c=√169

c=13

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's calculate the value of c using Pythagoras theorem ~

\(\qquad \sf  \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} \)

\(\qquad \sf  \dashrightarrow \: c {}^{2} = {5}^{2} + {12}^{2} \)

\(\qquad \sf  \dashrightarrow \: c = \sqrt{25 + 144} \)

\(\qquad \sf  \dashrightarrow \: c = \sqrt{169} \)

\(\qquad \sf  \dashrightarrow \: c = 13 \: units\)

The compound interest rate charged is given as follows:

13% per year.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for this problem are given as follows:

P = 12000, A(t) = 22109.22, n = 1, t = 5.

Hence the interest rate is obtained as follows:

22109.22 = 12000(1 + r)^5

(1 + r)^5 = 22109.22/12000

1 + r = (22109.22/12000)^(1/5)

1 + r = 1.13

r = 1.13 - 1

r = 0.13.

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The rational roots of the given equation x(3x − 4) (x − 5) = 0 are x = 0, 4/3 and 5

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have common divisible.

x(3x − 4) (x − 5) = 0

So we can put every term equal to zero to find it's root.

1st case, x = 0

2nd, 3x-4 = 0

        3x = 4

         x= 4/3

3rd, x-5 = 0

        x = 5

Hence, the rational roots of the given equation are x = 0, 4/3 and 5

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Answer:

4 1/2 m

Step-by-step explanation:

Area of the patio = 14 5/8 m²

Width = 3 1/4m

Length = ?

Area of the patio = length ×width

Substitute

14 5/8 = 3 1/4 × L

Convert to improper fractions

117/8 = 13/4 L

Cross multiply

8 ×13L = 117×4

2 ×13L= 117

2×L = 9

2L = 9

L = 9/2

L. = 4 1/2 m (in mixed fraction)

Answer:

Depends on the x value

Step-by-step explanation:

f(x) can only be a function if the x values are not repeating.

Answer:

5 HOURS

Step-by-step explanation:

Answer:

5 hours

Step-by-step explanation:

Answer:

1,056 gifts

Step-by-step explanation:

If twelve relatives give gifts to one another

This means each of the twelve relatives gets gifts from the other 11 relatives

=12 relatives * 11 gifts

= 132 gifts per year

They have been doing it for 8 years

Total gifts exchanged for 8 years= 132 gifts × 8 years

=1,056 gifts

Therefore, number of gifts exchanged for 8 years among 12 relatives is 1,056 gifts

Answer: 3.11*10^7/7.69*10^6

3110/769

4.04

Step-by-step explanation: