find the missing side of the triangle

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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Using inequality, the daughter's age to her mother's is 12x < 40.

Inequality is a mathematical statement that two algebraic expressions are unequal.

Inequalities are depicted as:

The age of the mother = 40

The age of the daughter = 12

The number of times the mother's age is to her daughters = 3.33 times (40/12).

Let the number of times the mother's age is more than her daughter's age = x

40 > 12x

or 12x < 40

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Answer: We will use long division to find the quotient of (x³ - 3x² + 5x + 3) ÷ (x + 1).

    x² - 4x + 9  

___________________

x + 1 | x³ - 3x² + 5x + 3

- (x³ + x²)

--------------

-4x² + 5x

-(-4x² - 4x)

------------

9x + 3

-(9x + 9)

-------

6

Therefore, the quotient of (x³ - 3x² + 5x + 3) ÷ (x + 1) is x² - 4x + 9 with a remainder of 6.

Step-by-step explanation:

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 :))

The smallest possible area of a square which can be made from the three pieces is 11833.203125 cm².

To find the smallest possible area of a square, we need to make sure that we use the longest pieces to form the sides of the square. Therefore, we need to divide the 360 cm steel bar into equal parts first, then use the remaining parts to divide the other two steel bars.

Let's call the length of each part x.

The 360 cm steel bar can be divided into n parts of length x, where:

n = 360/x

Similarly, the 300 cm steel bar can be divided into m parts of length x, where:

m = 300/x

And the 210 cm steel bar can be divided into k parts of length x, where:

k = 210/x

To form a square, we need to use all the parts we cut from the steel bars. Therefore, the length of the sides of the square will be nx + mx + kx, which is equal to (n + m + k)x.

The area of the square will be (n + m + k)x²

To find the smallest possible area, we need to minimize (n + m + k)x². Since x can be any positive number, we can focus on minimizing n + m + k.

n + m + k = (360/x) + (300/x) + (210/x)

n + m + k = (870/x)

To minimize (n + m + k), we need to maximize x. However, x cannot be greater than the smallest steel bar, which is 210 cm long.

Therefore, x must be a factor of 210.

Let's try x = 1 cm. In this case, n + m + k = 870 cm, which means we can form a square with sides of length 870 cm/4 = 217.5 cm.

The area of this square is 217.5^2 = 47250.625 cm².

Let's try x = 2 cm. In this case, n + m + k = 435 cm, which means we can form a square with sides of length 435 cm/4 = 108.75 cm.

The area of this square is 108.75² = 11833.203125 cm².

Let's try x = 3 cm. In this case, n + m + k = 290 cm, which means we cannot form a square using all the parts we cut from the steel bars.

Therefore, the smallest possible area of a square which can be made from the three pieces is 11833.203125 cm², and this can be achieved by cutting the steel bars into parts of length 2 cm.

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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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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 solutions to the quadratic equation x^(2)=2x+8 are x=4 and x=-2.

To solve the quadratic equation x^(2)=2x+8 by factoring, we need to rearrange the equation to make it equal to zero and then factor the trinomial.

Step 1: Rearrange the equation to make it equal to zero.
x^(2)-2x-8=0

Step 2: Factor the trinomial using the "AC Method."

The "AC Method" involves finding two numbers that multiply to the product of the coefficient of the x^(2) term (a) and the constant term (c), and add to the coefficient of the x term (b).

In this case, a=1, b=-2, and c=-8.
The product of a and c is (1)(-8)=-8.
The two numbers that multiply to -8 and add to -2 are -4 and 2.

Step 3: Rewrite the equation using the two numbers found in Step 2.
x^(2)-4x+2x-8=0

Step 4: Factor by grouping.
(x^(2)-4x)+(2x-8)=0
x(x-4)+2(x-4)=0

Step 5: Factor out the common factor (x-4).
(x-4)(x+2)=0

Step 6: Set each factor equal to zero and solve for x.
x-4=0  or  x+2=0
x=4  or  x=-2

Therefore, the solutions to the quadratic equation x^(2)=2x+8 are x=4 and x=-2.

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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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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.

Since 100% of the children are served both meals, this means that all 25 children are served both meals. Therefore, the answer is 25 children.

To find the number of children who are served both meals, we can use the following formula:

Number of children served both meals = (percentage of children served both meals / 100) x total number of children

Plugging in the given values, we get:

Number of children served both meals = (100 / 100) x 25

Number of children served both meals = 1 x 25

Number of children served both meals = 25

Therefore, the number of children who are served both meals is 25. .

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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:

A researcher will use a regression equation to predict the relationship between the GPAS (y variable) and Hours of Studying per week (x-variable) for 100 students. The regression equation will try to predict the GPA for students who study 10 hours per week by estimating the relationship between the two variables. The regression equation is a mathematical model that is used to predict the value of one variable based on the value of another variable.

In this case, the regression equation will try to predict the GPA for students who study 10 hours per week based on the relationship between GPAS and Hours of Studying per week.

The goal of the regression equation is to provide an accurate prediction of the GPA for students who study 10 hours per week, based on the data collected by the researcher.

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The statement that √s^2 is equals to the value of s is false, as s² is an even function, hence √s^2 can be equal either to the value of s or to -s.

The s² function is even, hence, for example:

sqrt[(-3)²] = sqrt(9) = 3.

Which proves by contradiction that the statement is false.

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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 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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These are the x-coordinates of the points where the graph intersects the x-axis. We can use these points to sketch the curve of the function.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

The function ƒ(x) = −x³ + 4x² − 2 is a cubic function, which means that it is a polynomial of degree 3. The general form of a cubic function is:

ƒ(x) = ax³ + bx² + cx + d

where a, b, c, and d are constants. In the given function, we have:

a = -1

b = 4

c = 0

d = -2

Therefore, we can rewrite the function as:

ƒ(x) = -x³ + 4x² - 2

This function can be graphed to show the shape of the curve it creates. The graph of a cubic function is a curve that can either be concave up or concave down, depending on the sign of the leading coefficient. In this case, the leading coefficient is negative, so the graph will be concave down. The function has a y-intercept of -2, which means that it intersects the y-axis at the point (0, -2). To find the x-intercepts, we can set ƒ(x) equal to zero and solve for x:

ƒ(x) = -x³ + 4x² - 2 = 0

We can use factoring or the quadratic formula to solve for x, but in this case, the equation can be simplified by factoring out a common factor of x²:

-x²(x - 4) + 2 = 0

Now we can solve for x:

x² = 2/(4 - x)

x = ±√(2/(4 - x))

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Complete question:

Solve for x when  ƒ(x) = −x³ + 4x² − 2.

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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The equilibrium quantity of items is 25.

The question is asking for the equilibrium quantity of items when the demand and supply functions given are graphed together. The equilibrium quantity can be found by solving for q when the demand and supply functions are equal.

Demand: d(q) = 562.5 - 0.4q2

Supply: s(q) = 0.5q2

Set the demand and supply functions equal to each other and solve for q:

562.5 - 0.4q2 = 0.5q2

0.9q2 = 562.5

q2 = 625

q = 25

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Answer:

56.14

Step-by-step explanation:

673.36/12

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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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

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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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.

Answer: 59.26°

Step-by-step explanation:

Use the equation 174(0.95)^21

The 174 represents the temperature difference

The 21 represents the amount of time (in minutes) that has passed

To get 0.95, because the temperature is decreasing, you subtract

1-0.05=0.95 (0.05 and not 5 because you move the decimal over two places when working with percents)

That's the standard equation that you use when solving questions like these, and when you solve this equation you should get 59.26° (you need a calculator to solve it all at once)

The price of the item 10 years from today will be approximately $37,607.56

Algebraic expression can be defined as combination of variables and constants.

To find the current price of the item, we need to substitute t = 0 in the given equation.

So we get:

[tex]p(0) = 25000(1.034)^0 = 25000(1) = 25000[/tex]

Therefore, the current price of the item is $25,000.

To find the price 10 years from today, we need to substitute t = 10 in the given equation. So we get:

[tex]p(10) = 25000(1.034)^{10} = 37607.56[/tex]

Therefore, the price of the item 10 years from today will be approximately $37,607.56.

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The streetlight is approximately 16.41 feet tall, and the length of its shadow is approximately 27.35 feet.

What is the proportion?

A proportion is a statement that two ratios are equal. In other words, a proportion is an equation that shows that two fractions or two ratios are equivalent. A proportion can be written in the form of:

a/b = c/d

We can use the properties of similar triangles to solve this problem. Let's call the height of the streetlight h, and the length of the shadow cast by the streetlight x. We can set up the following proportion:

(height of person) / (length of person's shadow) = (height of streetlight) / (length of streetlight's shadow)

or

6 / 10 = h / x

Simplifying this proportion, we get:

x = (10h) / 6

We also know that the person is standing 18 feet from the streetlight, and that the length of the person's shadow is 10 feet. Using the Pythagorean theorem, we can set up the following equation:

6^2 + 10^2 = (18 + x)^2

Simplifying and substituting x, we get:

36 + 100 = (18 + (10h/6))^2

136 = (18 + (10h/6))^2

Taking the square root of both sides, we get:

√136 = 18 + (10h/6)

Simplifying, we get:

√136 - 18 = (10h/6)

Multiplying both sides by 6, we get:

6(√136 - 18) = 10h

Simplifying, we get:

h ≈ 16.41 feet

Now, we can substitute this value of h into the expression for x that we derived earlier:

x = (10h) / 6 ≈ 27.35 feet

Therefore, the streetlight is approximately 16.41 feet tall, and the length of its shadow is approximately 27.35 feet.

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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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