A line has ____ rotational symmetry

A. Four-fold

B. Six-fold

C. Seven-fold

D. Two-fold

The value of \((313 mod 14)^2\) mod 21 is 4.

To calculate the given expression, let's break it down step by step:

Calculate (313 mod 14):

The modulus operator (%) returns the remainder when dividing the number 313 by 14.

So, 313 mod 14 = 5.

Calculate\((5^2 mod 21):\)

Here, "^" denotes exponentiation. We need to calculate 5 raised to the power of 2, and then find the remainder when dividing the result by 21.

5^2 = 25.

25 mod 21 = 4.

Therefore, the value of\((313 mod 14)^2\)mod 21 is 4.

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The equations a line, obtained from the coordinate points on the straight line on the graph, are;

Slope-intercept form; y = (-3/4)·x + 6

Point-slope form; y - 6 = (-3/4)·x

Standard form; (-3/4)·x + y = 6

The slope-intercept form of the equation of a line is the form; y = m·x + c, where m is the slope, and c is the y-intercept.

Whereby each unit scale on the graph is one unit, we get;

The coordinate points on the graph are; (0, 6), and (8, 0)

The point (0, 6) is the y-intercept, therefore, the value of the variable c in the slope-intercept form of the equation of a line is; c = 6

The slope of the line is; m =(0 - 6)/(8 - 0) = -6/8 = -3/4

The equation of the line in slope-intercept form is; y = (-3/4)·x + 6

The point-slope form of the equation of a line is; y - y₁ = m·(x - x₁), where, (x₁, y₁) is a specified point and m is the slope f the graph

The point-slope form of the equation of the line with regards to the point (0, 6) is therefore; y - 6 = (-3/4)(x - 0) = (-3/4)·x

Point slope form; y - 6 = (-3/4)·x

The standard form of the equation of straight line is the form a·x + b·y = c

The standard form, obtained from the point-slope form is therefore;

Standard form; (-3/4)·x + y = 6

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An inequality that expresses the interval of values that n may have is (B) \((5 < n < 17)\)

The sides of a triangle are 5, 12, and n.

To write an inequality that expresses the interval of values that n may have, we use the Triangle Inequality Theorem.

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So for this question, the inequality that expresses the interval of values that n may have is given as:\(5 + 12 > n12 + n > 5n + 5 > 12\)

Simplifying the above inequality: \(n > -7n > 7\)

The interval for n will be \([7,∞)\), where n has to be greater than 7.

Option D \((7 < n < 12\)) is not the correct answer.

Hence, the correct answer is option B\((5 < n < 17).\)

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The geometric series that has been provided is of divergence, since r>5.

The series is given as /10 + 3/2 + 15/2 + 75/2 + 325/2 +.....

The common ratio is

3/2 ÷ 3/10

= 3/2 ×10/3

= 5

Then,

15/2 ÷ 3/2

= 15/2 × 2/3

= 5

Thus, the common ratio is greater than 5. Therefore, the series is divergence.

Hence, the given geometric series is divergence, since r>5.

A series is considered to be convergent if the partial sums tend to a particular value, also known as a limit. In contrast, a divergent series is one whose partial sums do not approach a limit. Typically, the Divergent series either reach, reach, or don't reach a particular number.

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A) Some of the requirements for opening a bank account are:

A bank account is simply a formal arrangement whereby an individual or an organization enters into an agreement with a bank to allow the bank to keep its money and give it back when required.

B) The fees differ from bank to bank. Some banks charge zero fees, others charge a little sum for carrying out automated backgrounds checks and address verification.

C) the options about which type of account to open is totally dependent on the purpose for which the account opener needs the accounts. For example, if the account is for regular expenses, then a checking account is the best option.

D) Minimum deposits differ from bank to bank. Some banks will accept a zero deposit, others may stipulate about $50. It all depends on the nature of the account to be opened.

E) Hidden items may come in the form of transactional fees that are fully explained at the onset.

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Answer:

between B and D.

probably D because is periodic and the line is not continuous.

Then, between the units 4 (max) and 6 (min) is decreasing

In question 1a, we need to evaluate an expression containing variables and trigonometric functions. In question 1b, we are asked to simplify a rational expression.

1a) To evaluate the expression [{e^r + (2t - 1)^2 + sin(-3t) + cos(5t)}], we substitute the given value of 't' into the expression and simplify. Let's assume the given value for 't' is 't_0'. First, we replace 't' with 't_0' in each term:

e^r + (2t_0 - 1)^2 + sin(-3t_0) + cos(5t_0)

Now, we can calculate each term separately using the given value of 't_0'. Compute the values of e^r, (2t_0 - 1)^2, sin(-3t_0), and cos(5t_0) to obtain a numerical result.

1b) For the expression L = [16 + 16 / (-12) - 1] / [s^2 + 8 - (s)], we need to simplify the rational expression. Begin by simplifying the numerator. In the numerator, the expression [16 + 16 / (-12) - 1] can be simplified step by step. First, divide 16 by -12, which equals -4/3. Then, combine this result with 16 and subtract 1 to get -4/3 + 16 - 1. Next, simplify this expression further to obtain a single value for the numerator.

After simplifying the numerator, focus on the denominator. Combine the terms s^2 and -s in the expression [s^2 + 8 - (s)]. Rearrange the terms to obtain a simplified form for the denominator. Now, divide the simplified numerator by the simplified denominator to evaluate the rational expression L.

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Answer:

f(x) = x × 0.12 if  15,000 ≤ x ≤ 30,000

        x × 0.18 if  x ≥ 30,000

Step-by-step explanation:

I. When 12% is 12/100 = 0.12

 and 18% is 18/100 = 0.18

Answer:

$400

Step-by-step explanation:

150 + 300 = 450

450 - 50 = 400

Answer:

150+300=450 then 450-50=400

Step-by-step explanation:

I hope this is the right answer  ^-^

Answer:

0.8 or 8/10

Step-by-step explanation:

1/10 can be converted to decimal form as 0.1.

70/100 can be converted to decimal form as 0.7

0.1 + 0.7 = 0.8

Another way is making use of a common denominator:

Common denominator --> 100

1/10 --> mutiply numerator and denominator by 10 --> 10/100

10/100 +70/100 = 80/100 = 8/10 = 0.8

Answer:

6o×40=2400

area 1/4=2400÷4=600

area 1/6=600÷6=100

(d)=100 ft2

Answer: r+7 is irrational

Step-by-step explanation:

1) If r is irrational, that means that it goes on and on forever.

2) 7 is a rational number because it can be expressed as a quotient of 2        integers (7÷1=7)

3) If you add a rational number to an irrational number it is still irrational. The numbers after the decimal point keep going and going. You are just changing the whole number, which if to the left of the decimal point.

Answer:

The new coordinates of the triangle J'K'L' are J'(0, -3), K'(3, -4), and J'(6, 0)

Step-by-step explanation:

The given coordinates of the triangle JKL are;

J(3, 0), K(4, 3), L(6, 0)

The rotation of the point of a preimage (x, y) by 90° clockwise gives the point of the image after rotation as (y, -x)

Therefore;

The rotation of point J(3, 0) by 90° clockwise gives J'(0, -3)

The rotation of point K(4, 3) by 90° clockwise gives K'(3, -4)

The rotation of point L(6, 0) by 90° clockwise gives J'(6, 0)

The new coordinates of the triangle J'K'L' are J'(0, -3), K'(3, -4), and J'(6, 0)

Answer:

answers below

Step-by-step explanation:

a) As the number of days,d, Kenton has been training increases, the total number of miles he ran, t, increases.

Alternative: As the day number increases, the total number of miles Kenton ran also increases.

b) t = 2.5*d

Step-by-step explanation:

8.75×10^8 this is the standard form

Answer:

48^2 =2304 < 2345 < 2401 = 49^2

=> Smallest number should be: 2401 - 2345 = 56

Hope this helps!

:)

Answer:

56

Step-by-step explanation:

sqrt(2345) = 48.425...

Nearest integer is 49

So, the nearest perfect is 49²

49² = 2401

To be added:

2401 - 2345

56

A correlation coefficient is a statistic that tells us the strength and direction of the linear relationship between two variables.

The correlation coefficient is a measure of the degree of association between two variables. It quantifies how closely the data points align along a straight line. The coefficient can range from -1 to +1, where -1 represents a perfect negative linear relationship, +1 represents a perfect positive linear relationship, and 0 indicates no linear relationship.

The sign of the coefficient indicates the direction of the relationship, while the magnitude indicates the strength. A correlation coefficient of 0 does not necessarily imply the absence of any relationship; it only means that there is no linear association between the variables. It is important to note that correlation does not imply causation, as other factors may be influencing the relationship.

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Answer:

Step-by-step explanation:

The solution of this systems of equations is the intersection of both graphs

Let's kick start with a:

a)

\(y+12 = x^2+x \\ \\ x+3 = y\)

From the first attached diagram by using graph:

the solution is the set {(-5, 8), (3, 0)}

b)

\(y-15=x^3+4x \\ \\ x-y =1\)

Using the graph tool from the last diagram below;

the solution is the set⇒( there is no solution)

c)

\(y+5 =x^2-3x \\ \\ 2x+y =1\)

From the second attached diagram by using graph:

the solution is the set {(-2, 5), (3, -5)}

d)

\(y-6=x^2-3x \\ \\ x+2y =2\)

the solution is the set ⇒ there is no solution (shown in the last diagram  below)

e)

\(y-17=x^2-9x \\ \\ -x+y =1\)

the solution is the set {(2, 3), (8, 9)} as shown in the third diagram

f) Lastly:

\(y-15=-x^2+4x \\ \\ x+y =1\)

Using the graph tool from the fourth diagram below;

the solution is the set  {(-2, 3), (7, -6)}

The solution to the system of equations are the truth values of the system of equations

\(\mathbf{(a)\ y + 12 = x^2 + x,\ x + 3 = y}\)

The graphs of the equations intersect at (-5,8) and (3,0).

So, the solution set is {(-5,8), (3,0)}

\(\mathbf{(b)\ y - 15 = x^3 + 4x,\ x - y = 1}\)

The graphs of the equations do not intersect

So, the system has no solution

\(\mathbf{(c)\ y + 5 = x^2 - 3x,\ 2x + y = 1}\)

The graphs of the equations intersect at (-2,5) and (3, -5).

So, the solution set is {(-2, 5), (3, -5)}

\(\mathbf{(d)\ y - 6 = x^2 - 3x,\ x + 2y = 2}\)

The graphs of the equations do not intersect

So, the system has no solution

\(\mathbf{(e)\ y - 17 = x^2 - 9x,\ -x + y = 1}\)

The graphs of the equations intersect at (2,3) and (8,9).

So, the solution set is {(2, 3), (8, 9)}

\(\mathbf{(f)\ y - 15 = -x^2 + 4x,\ x + y = 1}\)

The graphs of the equations intersect at (-2,3) and (7,-6).

So, the solution set is {(-2, 3), (7, -6)}

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Answer:

Step-by-step explanation:

Slope intercept form

y + 7 = 3(x  + 4)                 Change all the double minuses to pluses.

y + 7 =  3x + 12                  Remove the brackets.

y + 7 - 7 = 3x + 12-7           Subtract 7 from both sides

y = 3x + 5

Slope

Whatever number is in front of the x is the slope Answer: 3

y intercept

Whatever comes after the plus sign (or minus sign) is the y intercept. It is a single number.  Answer: 5

x intercept.

This occurs when y = 0

0 = 3x + 5                      Subtract 5 from both sides

-5 = 3x + 5 -5

-5 = 3x                            Divide by 3

-5/3 = 3x / 3

-5/3 = x                          

Answer: x_intercept = -5/3

I am sorry but I cannot see the picture properly, can you add another photo? Sorry for the inconvenience.

Answer:

102594

Step-by-step explanation:

2.34 + 45.6 + 978 = ___

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Answer:

A. 18.2

Step-by-step explanation:

b^2 + 14^2 = 23^2

b = sqrt(333) = 18.248

Answer:

..............................

Answer:

3/5

Step-by-step explanation:

the chance of landing on an even number (2 or 4) is 2/5

the chance of landing on the unshaded section (3) is 1/5

add the 2 together since the problem said "or" to get 3/5

Answer:

0.06 cubic meters per year...

Step-by-step explanation:

The rate of water flows through a pipe is 0.06 cubic meters per year.

It is the volume of fluid flows out from the container per unit time.

Given that,

Water flows through a pipe at a rate of 6 fluid ounces per day. It can be written as:

Water flows per day ⇔ 6 fluid ounces

∴ Water flows per year ⇔  365 x (6 fluid ounces)

Volume of water in milliliter,

Water flows per year ⇔  365 x (6 x 29.574 ml )

Volume of water in cubic meter,

Water flows per year ⇔  365 x (\(\frac{6 x 29.574}{1000000}\) \(m^{3}\)) = 0.06477   \(m^{3}\)

Hence Water flows per year round value to the nearest hundredth is 0.06  \(m^{3}\).

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The circumference of a circle with a diameter of 21 centimeters can be calculated using the formula C = πd, where C represents the circumference and d represents the diameter. Using the value of π as 22/7, the correct answer is 66 centimeters.

The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. In this case, the diameter is given as 21 centimeters. To calculate the circumference, we can substitute the value of π as 22/7 and the diameter as 21 into the formula:
C = (22/7) * 21
C = 22 * 3
C = 66
Therefore, the circumference of the circle is 66 centimeters. Among the given options, the correct answer is 66 centimeters, which represents the distance around the circle.

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Answer:

3 ÷ 8, option D

Step-by-step explanation:

the fraction 3/8 is the same as 3÷ 8.

The indefinite integral of (3t^5 - 4 + k) dt is (1/2)t^6 - 4t + kt + C.

The indefinite integral of ∫[4e^(i) + 5e^(i)] + 3 In tk dt = In 5 is (4e^(i) + 5e^(i))t + 3t^k ln(t^k) - 3t^k + ln(5) + C.

1. To evaluate the given integrals, let's take them one by one:

∫(3t^5 - 4 + k) dt = ∫3t^5 dt - ∫4 dt + ∫k dt

The integral of t^n is given by (1/(n+1))t^(n+1). Applying this rule, we have:

= (3/(5+1))t^(5+1) - 4t + kt + C

= (3/6)t^6 - 4t + kt + C

= (1/2)t^6 - 4t + kt + C

Therefore, the indefinite integral of (3t^5 - 4 + k) dt is (1/2)t^6 - 4t + kt + C.

2. To evaluate the integral ∫[4e^(i) + 5e^(i)] + 3 ln(t^k) dt, we can break it down into separate integrals and apply the appropriate rules:

∫4e^(i) dt + ∫5e^(i) dt + 3 ∫ln(t^k) dt

The integral of a constant multiplied by e^(i) is simply the constant times the integral of e^(i), which evaluates to e^(i)t:

= 4 ∫e^(i) dt + 5 ∫e^(i) dt + 3 ∫ln(t^k) dt

= 4e^(i)t + 5e^(i)t + 3 ∫ln(t^k) dt

Now let's focus on the remaining integral ∫ln(t^k) dt. We can use the rule for integrating natural logarithms:

∫ln(u) du = u ln(u) - u + C

In this case, u = t^k, so the integral becomes:

= 4e^(i)t + 5e^(i)t + 3 [t^k ln(t^k) - t^k] + C

Simplifying the expression further, we have:

= (4e^(i) + 5e^(i))t + 3t^k ln(t^k) - 3t^k + C

Since the result of the integral is given as In 5, we can equate the expression to ln(5) and solve for the constant C:

(4e^(i) + 5e^(i))t + 3t^k ln(t^k) - 3t^k + C = ln(5)

Therefore, the value of the constant C would be ln(5) minus the expression (4e^(i) + 5e^(i))t + 3t^k ln(t^k) - 3t^k:

C = ln(5) - (4e^(i) + 5e^(i))t - 3t^k ln(t^k) + 3t^k

Hence, the evaluated integral is:

(4e^(i) + 5e^(i))t + 3t^k ln(t^k) - 3t^k + ln(5) + C

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