A motor boat took 5 h to travel a distance of
60 km up a river, against the current. The return trip took 3 h. Find the average speed of the boat in still water and the speed of the current.

If the VAT in South Africa is 15%, then selling price of the laptop after the VAT is R4830 .

The cost price of the laptop before the VAT is R4200,

The VAT percent on goods and services is = 15%,

In order to calculate the selling price of the laptop that costs R4200 before VAT is added at 15% in South Africa, we can use the following formula:

⇒ Selling Price = Cost Price + (Cost Price × VAT )

Substituting the values,

We get,

⇒ Selling Price = R4200 + (R4200 × 0.15)

⇒ Selling Price = R4200 + R630

⇒ Selling Price = R4830

Therefore, the selling price of the laptop, including 15% VAT, will be R4830.

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The region that contains the solution to the system is region B

Given the following system of inequalities

y ≤ x - 2

y ≥ 1/4x - 4

Next, we analyze each of the inequalities expressions

Inequality 1: y ≤ x - 2

Inequality 2: y ≥ 1/4x - 4

Using the above as a guide, we have the following:

This means that the intersection regionn contains the solution

This is represented by the region (b)

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Answer: 41 hours and 15 minutes

Step-by-step explanation:

First, we count the time duration from 7:30am to 4:30pm, which is 9 hours.

Next, we subtract 45 minutes from 9 hours, which equals 8 hours and 15 minutes.

Last, we multiply that by 5 which equals 41 hours and 15 minutes.

Answer:

the answer is 4.

Step-by-step explanation:

-3 squared will give you 9. 73- 9 is 64 and cube root of 64 is 4

Answer:

56.14

Step-by-step explanation:

673.36/12

In its simplest radical form, the area of the right triangle is 8sqrt(3) square feet.

How is area determined?

The length of the other leg of the right triangle can be determined using the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

where the hypotenuse is c and the triangle's legs are a and b.

We are aware that the hypotenuse c is 8 feet long and that leg an is 4 feet long. Let's work out the answer for the opposite leg's length, b:

[tex]b^2 = c^2 - a^2\sb^2 = 8^2 - 4^2\sb^2 = 64 - 16\sb[/tex]

[tex]sqrt(48) = 4sqrt(3) foot where 2 = 48 b[/tex]

Given that we know the lengths of both legs, we can use the following formula to get the triangle's area:

[tex](1/2) * Base * Height = Area[/tex]

We may use the 4 ft leg as the base and the 4sqrt(3) ft leg as the height since one leg is 4 ft and the other is 4sqrt(3) ft:

Area: (1/2) * 4 feet * 4 square feet (3)

= 8sqrt(3) square feet

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The function f(x) in completely factored form is (4x+1)(5x-1)(x+5).

To write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, we can use synthetic division with the given zero of (-(5)/(2)).

Step 1: Set up the synthetic division with the given zero and the coefficients of the polynomial.

(-(5)/(2)) | 20  44  -17  -5
         |______________

Step 2: Bring down the first coefficient, 20, and multiply it by the given zero.

(-(5)/(2)) | 20  44  -17  -5
         |     -50
         |______________
         | 20

Step 3: Add the result of the multiplication to the next coefficient and repeat the process until all coefficients have been used.

(-(5)/(2)) | 20  44  -17  -5
         |     -50   3   10
         |______________
         | 20  -6  -14   5

Step 4: The last number in the bottom row is the remainder. If it is zero, then the given zero is a factor of the polynomial. In this case, the remainder is 5, so (-(5)/(2)) is not a factor of f(x).

Since (-(5)/(2)) is not a factor of f(x), we cannot use synthetic division to write f(x) in completely factored form. Instead, we can use factoring to find the factors of f(x).

f(x) = 20x^(3)+44x^(2)-17x-5

= (4x+1)(5x-1)(x+5)

Therefore, f(x) in completely factored form is (4x+1)(5x-1)(x+5).

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The missing degrees in the circle are 260 degrees.

What is circle ?

A circle is a geometrical shape that represents a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the diameter of the circle is the distance across its widest point, passing through the center.

To find the missing degrees in the circle, we need to use the fact that the sum of the central angles in a circle is equal to 360 degrees.

In this circle, we have two central angles: one measuring 100 degrees and the other measuring x degrees. We also know that the sum of these two central angles is equal to 360 degrees.

Therefore, we can set up the following equation:

100 + x = 360

To solve for x, we can subtract 100 from both sides:

x = 260

Therefore, the missing degrees in the circle are 260 degrees.

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Area of the triangle ≈ 7.5 (to the nearest tenth).

To find the area of the triangle given its side lengths, we will use Heron's formula:

s =(a + b + c)/2

A = sqrt(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, and A is the area of the triangle.

For the given triangle, we have:

a = 3

b = 5

c = 6

The semiperimeter s can be calculated as:

s = (a + b + c) / 2 = (3 + 5 + 6) / 2 = 7

Using this value of s, we can apply Heron's formula to find the area A:

A = √(s(s-a)(s-b)(s-c))

= √(7(7-3)(7-5)(7-6))

≈ 7.48

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The possible rational roots of P(x).

According to the Rational Root Theorem, the possible rational roots of P(x) are the fractions ±p/q, where p is a factor of the constant term (-7) and q is a factor of the leading coefficient (3). The possible values for p are ±1 and ±7, and the possible values for q are ±1 and ±3. Therefore, the possible rational roots of P(x) are:

±1/1 = ±1
±7/1 = ±7
±1/3 = ±1/3
±7/3 = ±7/3

So, the possible rational roots of P(x) are ±1, ±7, ±1/3, and ±7/3.

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25-9x² can be expressed in factor form as (5+3x)(5-3x)

An expression is combination of variables, numbers and operators.

The given expression is 25-9x²

We have to factor it completely

We have an identity that a²-b²=(a+b)(a-b)

25-9x² can be written as 5²-(3x)²

Now apply the identity

(5+3x)(5-3x)

Hence, 25-9x² can be expressed in factor form as (5+3x)(5-3x)

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The ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).

A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

The given inequality is y > 3x + 4. To check which ordered pair is not a solution of this inequality, we need to substitute the values of x and y from each ordered pair into the inequality and check whether the inequality holds or not.

Checking the ordered pairs one by one, we have:

(2, 12): y = 12 and x = 2, so 12 > 3(2) + 4 is true. Therefore, (2, 12) is a solution of the inequality.

(0, 5): y = 5 and x = 0, so 5 > 3(0) + 4 is true. Therefore, (0, 5) is a solution of the inequality.

(-2, 1): y = 1 and x = -2, so 1 > 3(-2) + 4 is false. Therefore, (-2, 1) is not a solution of the inequality.

(1, 7): y = 7 and x = 1, so 7 > 3(1) + 4 is true. Therefore, (1, 7) is a solution of the inequality.

Therefore, the ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).

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The percent of error is 20.9302%. The solution has been obtained by using percent error.

What is percent error?

The difference between the estimated value and the actual value in respect to the actual value is known as the percent error.

We are given that the estimate number of balls in each bag was 86 but it  turned out to be 104.

So, the percent error is

⇒Percent error = [Estimated Value - Actual value] / Actual value

⇒Percent error = [104 - 86] / 86

⇒Percent error = 18 / 86

⇒Percent error = 20.9302%

Hence, the percent of error is 20.9302%.

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As a result, the length of the second rectangle is 22.5 inches.

Every square is also a rectangle because a square is a parallelogram with all particular corners at right angles. Yet not all rectangles are squares; for a rectangle to be a square, all of its sides must be the same length.

We can infer that the two rectangles may have a similar shape but differ in size because we can see how similar they are to one another.

By using the fact that the ratio of the adjacent angles of two comparable rectangles is the same, we can determine the length of the following rectangle.

Let x be the second rectangle's length. Then we can establish a ratio:

9/6 = x/15

We can cross-multiply to find x:

9 x 15 = 6 × x

135 = 6x

x = 22.5

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Answer:

Mei and Ming both improved their yards by planting rose bushes and ivy they bought from the same store. Mei spent $36 on 3 rose bushes and 1 pot of ivy, while Ming spent $168 on 9 rose bushes and 8 pots of ivy. The cost of one rose bush and one pot of ivy would be $21, since the cost of one rose bush is $7 and one pot of ivy is $14

Step-by-step explanation:

The line of fit's y-intercept is 80. This suggests that a student's anticipated test grade is 80% if they don't study at all.

A scatter plot is a type of graph that illustrates data and the connection between two variables. With one variable plotted on the x-axis and the other variable drawn on the y-axis, each data point is represented by a point on the plot. Data analysis use scatter plots to find patterns and connections between variables.

The line of fit's y-intercept is 80. This suggests that a student's anticipated test grade is 80% if they don't study at all.

This indicates that studying is positively connected with test performance in the context of the data. Higher exam scores are anticipated for students who study more. The amount of time spent studying alone may not account for other elements that may potentially affect exam performance, such as prior knowledge or test-taking techniques.

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Answer:

I CAN NOT SEE THAT OML

Step-by-step explanation:

They are relatively prime.

Proof: Let fn and fn-1 be any two consecutive terms in the Fibonacci sequence. By definition, fn = fn-2 + fn-1. Since both fn and fn-1 are integers,

they must have no common factors other than 1,

so they are relatively prime.

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For the arithmetic sequence:

f(n) = f(1) + (n - 1)*4

Where the first term of the sequence is f(1) = 2

are:

f(1) = 2

f(2) =  6

f(3) = 10

f(4) =  14

f(5) =  18

We want to write the first five terms of a sequence, so first let's define the sequence.

We can define an arithmetic sequence with the recursive formula:

f(n) = f(n) + 4

And the explicit formula.

f(n) = f(1) + (n - 1)*4

Where we can define the first term of the sequence as f(1) = 2

Then the first five terms are:

f(1) = 2

f(2) = 2 + 4 = 6

f(3) = 6 + 4 = 10

f(4) = 10 + 4 = 14

f(5) = 14 + 4 = 18

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For two vectors to be orthogonal, their dot product should be zero.

(a) The dot product of u and v is k+21k=22k. For u and v to be orthogonal, 22k=0, which means k=0.

(b) The dot product of u and v is -2k^2+5k^2+k^2=4k^2. For u and v to be orthogonal, 4k^2=0, which means k=0.

Therefore, in both cases, the vectors are orthogonal when k=0.

Let AB and AC be vectors joining the points A(0,-1), B(1,-2), and C(4,1), respectively. Then,

AB = (1-0, -2-(-1)) = (1,-1)

AC = (4-0, 1-(-1)) = (4,2)

The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).

(a) Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(4) + (-1)(2))/sqrt(2^2+1^2 * 4^2+2^2) = 2/3

Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (4(1) + 2(-1))/sqrt(4^2+2^2 * 2^2+1^2) = 1/3

Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(3) + (-1)(-1))/sqrt(2^2+1^2 * 2^2+1^2) = 5/9

(b) Let AB and BC be vectors joining the points A(3,0,2), B(4,3,0), and C(8,1,-1), respectively. Then,

AB = (4-3, 3-0, 0-2) = (1, 3, -2)

BC = (8-4, 1-3, -1-0) = (4, -2, -1)

AC = (8-3, 1-0, -1-2) = (5, 1, -3)

The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).

Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(5) + 3(1) + (-2)(-3))/sqrt(1^2+3^2+(-2)^2 * 5^2+1^2+(-3)^2) = 0

Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (5(1) + 1(3) + (-3)(-2))/sqrt(5^2+1^2+(-3)^2 * 1^2+3^2+(-2)^2) = -7/9

Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(4) + (

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Using the leg rule and the Pythagorean theorem, we have:

x = 4

y ≈ 4.5

The leg rule that can be use to solve the missing measures of the right triangle is given as:

hypotenuse/leg = leg/part

We have the following:

Hypotenuse = 9

Leg = 6

Part = x

Plug in the values:

9/6 = 6/x

9x = 36

x = 36/9

x = 4

Use the Pythagorean theorem to find y:

y = √(6² - 4²)

y ≈ 4.5

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The measure of center that would best summarize the plot is given as follows: Median of 11.

The measure of variability is given as follows: IQR of 1.5.

A box and whisker plots shows these five features from a data-set, listed as follows:

From the plot, these features are given as follows:

The median is the best measure of center of the data-set.

There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:

IQR = 11.5 - 10

IQR = 1.5.

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The coordinates of point L are (s/2, s√3/2). If we know the value of s, we can determine the specific coordinates of point L.

To determine the coordinates of point L in an equilateral triangle with vertices J and K, we first need to know the location of J and K.

Since the triangle is equilateral, the distance from J to K is the same as the distance from J to L or from K to L. Let's assume that the side length of the equilateral triangle is s. Then, the distance from J to K is also s. We can assume that J is located at the origin (0,0), and K is located at (s,0).

To find the coordinates of point L, we can use some trigonometry. Let's draw a line from point K to point L, and let the angle between this line and the x-axis be θ. Since the triangle is equilateral, this angle is 60 degrees.

The x-coordinate of point L is then given by s cos θ. Since cos 60 = 1/2, the x-coordinate of point L is s/2.

The y-coordinate of point L is given by s sin θ. Since sin 60 = √3/2, the y-coordinate of point L is s√3/2.

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Answer:

122

Step-by-step explanation:

add the 2 angles together and there's your answer.

if you want to check take your answer and subtract from 180.

Answer: 122

Step-by-step explanation:

all triangles add up to 180

54+68=122

180-122=58

58=inner corner

180 (this is the measure of the line) -58 =122

hopefully this helps :))

Answer: 1030.301 rounded is $1,030

Step-by-step explanation:

1000(1+.01)^3=1030.301

You multiply your initial amount by 1 and add your percent after you convert it to a decimal by moving your point two paces to the left. If you're withdrawing, you subtract your decimal. Everything is them raised to the power of 3. You then can multiply it on paper, my teacher lets us use calculators though to ensure we don't get an incorrect answer.

The value of v is 8.83.

A rational equation is an equation that includes one or more fractions with polynomials. It can be solved by cancelling common factors between the numerator and the denominator, and then solving the resulting equation. It is important to note that when cancelling common factors, one must always check that the original equation is still satisfied.

To solve this rational equation that simplifies to linear, you need to solve for v. To do this, first multiply both sides by the denominator:

6(v-8) = 5

Then add 8 to both sides to get rid of the variable in the denominator:

6v - 48 = 5

Finally, add 48 to both sides to isolate the variable v:

6v = 53

Finally, divide both sides by 6 to solve for v:

v = 53/6 = 8.83

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For the given equation of the height the appropriate domain for this situation is 0 ≤ t ≤ 6.

The collection of all feasible input values that are appropriate for the circumstance being represented is known as the domain. In this instance, the domain stands for the range of time values relevant to the height of the football following a kick. The domain helps to avoid absurd or impossible outcomes by ensuring that the function is only evaluated for legitimate inputs.

The ball with follow a parabolic path, thus the maximum height is attained at:

t = -b/2a

Substituting the values we have:

t = -96/(-32) = 3 seconds.

The ball will then follow the downward path and will take an additional 3 seconds to reach the ground.

Thus, the total time taken will be 3 + 3 = 6 seconds.

Also, the ball initially starts from rest at 0 seconds.

Hence, the domain of the situation will be represented as 0 ≤ t ≤ 6.

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