A fruit shop bought 500 kg of apples for R900 and sold them for R2,80 per kg. a) What is the profit per kilogram?
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The basis for the principle of substitution is the fact that algebraic equations and expressions remain unchanged when the same quantity is substituted into them. This principle allows us to solve equations and simplify expressions by substituting one expression for another.

The principle of substitution is a powerful tool used in algebra and calculus to solve equations and simplify expressions. This principle works by allowing us to substitute one expression for another, and the resulting equation or expression remains unchanged.

For example, when solving equations, we can substitute one value for the unknown variable to obtain a simpler equation which can then be solved. Similarly, when simplifying an expression, we can substitute one expression for another to reduce the complexity of the expression.

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The angle measure BAC is the sum of angles BAD and CAD.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Given a triangle ABC.

A line is drawn inside the triangle from vertex A to the opposite side BC.

Given that AD = BD = CD.

That is the line AD bisects the line BC.

So here we have two smaller triangles ABD and ACD.

Two corresponding sides of both the triangles are equal.

Then the third side is also equal.

AB = AC

And we get angle A is bisected.

By the angle bisector theorem,

Measure of angle BAC = Measure of angle BAD + Measure of angle CAD

Hence, Measure of angle BAC = Measure of angle BAD + Measure of angle CAD

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The value of x is x = 5, and the value of y is y = 6.

What is Pythagorean theorem?

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

We have to find the values of x and y.

First to find the value of x.

Since, by Pythagorean theorem,

3^2 + 4^2 = x^2

     9 + 16 = x^2

          25 = x^2

            5 = x

            x = 5

Now to find the value of y.

Again by using the Pythagorean theorem,

[tex](3 + 5)^2 + 6^2 = (y+4)^2\\64 + 36 = y^2 + 8y + 16\\100 = y^2 + 8y + 16\\y^2 + 8y - 84 = 0\\y^2 + 14y - 6y - 84 = 0\\y(y+14) - 6(y + 14) = 0\\(y -6)(y+14)=0[/tex]

(y - 6) = 0,   (y + 14) = 0

y = 6,  y = -14

Length is not negative.

⇒ y = 6

Hence, the value of x is x = 5, and the value of y is y = 6.

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The length of BD is approximately 22.67cm.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental result in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). It is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that it is knowledge that was already known to the ancient Babylonians and Indians.

The theorem can be written mathematically as:

c^2 = a^2 + b^2

This is a classic problem in trigonometry known as the Pythagorean theorem in a right triangle. Since BD is perpendicular to AC, we can use the Pythagorean theorem to find the length of BD, which states that in a right triangle, the square of the length of the hypotenuse (BD in this case) is equal to the sum of the squares of the other two sides (AB and AD).

So, BD^2 = AB^2 + AD^2

We are given that AB = 17cm and AD = 15cm, so we can substitute those values into the equation and solve for BD:

BD^2 = (17cm)^2 + (15cm)^2 = 289 + 225 = 514

To find the length of BD, we take the square root of both sides:

BD = √514cm

BD ≈ 22.67cm

Hence, the length of BD is approximately 22.67cm.

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Answer:

1,230 square miles

Step-by-step explanation:

100 times bigger than 12.3 square miles is

100 × 12.3 square miles

= 1,230 square miles

The best estimate for the perimeter of the triangle will be 23.7 inches.

In Δ ABC ∠B =90° , ∠C = 30° , ∠A = 60° and hypotenuse AC = 10 inches

It has been described in the attachment.

Now, we shall calculate side AB and BC by using Trigonometric Ratios.

Sin 30° = AB / AC

or,  AB = 10 × Sin 30° = 10 × 0.5 = 5 inches

And, Cos 30° = CB / AC

or,CB =  10 × Cos 30° = 10 × 0.866 = 8.66 inches

Now, we calculate the perimeter of the given triangle

The perimeter of the triangle is = AB + BC + CA

                                                     = (5.0 + 8.66 + 10.0 ) inches

                                                     = 23.66 inches ≈ 23.7 inches

Hence, the best estimate for the perimeter of the triangle will be 23.7 inches.

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The complete question is:

A triangle has angles that measure 30°, 60°, and 90°. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle? Round to the nearest tenth.

Answer:

[tex]x=35^o\\y=85^o[/tex]

Step-by-step explanation:

[tex](2x + 25)^o = (3x - 10)^o\\2x + 25 = 3x - 10 \\2x - 3x = -10 - 25\\-x = -35\\x = 35[/tex]

[tex](2x+25)^o+y^o=180^o\\ 2(35) + 25 + y = 180\\70 + 25 + y = 180\\95 + y = 180\\y = 180 - 95\\y = 85[/tex]

Two centimeters of dilation is considered early labor. At this stage, the cervix is considered "soft" or "favorable" for labor to begin. The cervix has become thinner and softer, allowing the baby to move into the birth canal.

However, the cervix is still long and closed, and the baby is not yet ready to come out.  During this stage, contractions may become more frequent and intense, but they are usually not regular and will often stop and start. Women in early labor may feel cramping, backache, and increased pressure in the pelvis and vagina as the cervix begins to open. If a woman is not having regular contractions, she may be instructed to rest until labor progresses to the active phase.  

Women in early labor may also begin to experience increased vaginal discharge, the "bloody show," as the cervix further softens and thins. At this stage, it is common for the amniotic sac to begin to bulge out of the cervix. This is a sign that the cervix is continuing to dilate, and it may rupture when contractions become more powerful.

At two centimeters of dilation, labor is just beginning, but the cervix is showing signs that it is opening and preparing for delivery. Women should be aware of the signs of early labor and discuss any changes they experience with their healthcare provider.

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The fundamental color-programming unit on a computer screen or in a digital image is the pixel, a word that was created from the phrase "picture element." Consider it more as a conceptual than a physical unit. In a digital display, pixels are the smallest unit.

The smallest component of a visual display or digital image is a pixel, also known as a picture element. A grid of pixels is used to create computer screens. Red, blue, and green illumination components make up each pixel, which may produce millions of distinct colors by combining them in various ways and at various intensities.

For instance, a computer with a display resolution of 1280 x 768 will create up to 98,3040 pixels on a display screen. The number of pixels per inch of the monitor screen affects image quality; more pixels per inch produce better images.

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Applying the equation of free fall the time it will take for the ball dropped from a TV tower 2120 feet high to reach the ground is 11.51 seconds

The equation relating time and distance travelled which is  s = -16t² + 2120, as used in the problem is a quadratic equation

The equation is already modelled for the height of the tower which is 2120 feet high. because of this calculating the time the ball will reach the ground is done when the s = 0

Time when the ball will reach the ground

s = -16t²  + 2120

0 = -16t²  + 2120

16t² = 2120

divide both sides by 16

t² = 132.5

t = √132.5

t = 11.51 seconds

The time is 11.51 seconds

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The graph of the equations are added as attachment

Choose two linear equations

In this case, we make use of the following linear equations

y = 2x + 4 and y = -3x + 5

The slope and y-intercept of each equation

A linear equation is represented as

y = mx + c

Where

Slope = m and y-intercept = c

This means that the slope and y-intercept of each equation are

y = 2x + 4

Slope = 2

y-intercept = 4

y = -3x + 5

Slope = -3

y-intercept = 5

See attachment for the graph of the functions

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After solving, the slope when y = -10 is 0.

In the given question, we have to find the slope when y = -10.

The formula known as the slope relates to the method for calculating a line's steepness and inclination. The x and y coordinates of the locations along the line can be used to determine the slope of the lines. It is the ratio of the change in the y-axis to the change in the x-axis, to put it another way.

By utilizing the line equation, the slope of any line may be expressed as

y = mx + b, where m = slope.

When we compare the given equation y = -10 by the standard equation, we get m = 0.

So the slope when y = -10 is 0.

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The simplification of y=85,821.84 x (x-2) is y = 85,821.84x^2 - 171,643.68x

Mathematical simplification is the process of using basic mathematical operations (such as addition, subtraction, multiplication, and division) to reduce a complex equation or expression to its simplest form.

Also, a mathematical simplification is the process of making an expression or equation simpler and easier to understand or work with, without changing its value or meaning. This can involve combining like terms, factoring, canceling out common factors, and other techniques. For example, the expression 2(x+3) + 4(x+3) can be simplified to 6x + 18.

Therefore, the simplified expression is 85,821.84x^2 - 171,643.68x

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Aiden run and walk in 60 ​minute, then the distance = 9180 meters

Given that,

Aiden run at a constant peed of 3. 5 meter per second for 1/2 hour.

Then, he walk at a rate of 1. 6 meter per second for 1/2 hour.

(1) 3. 5 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

[tex]\frac{1}{2}[/tex] hour = 1800 seconds

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

So,

We can write,

Distance = speed * time

3.5 * 1800 = 6300 meters    (Equation-1)

(2) 1. 6 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

[tex]\frac{1}{2}[/tex] hour = 1800 seconds

So,

We can write,

Distance = speed * time

1.6 * 1800 = 2880 meters       (Equation-2)

Then,

We can add the equation - 1 and 2,

= 6300 meters + 2880 meters  

= 9180 meters

Therefore,

Aiden run and walk in 60 ​minute, then the distance = 9180 meters

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The probability that [tex]\hat{p}_D-\hat{p}_E[/tex] is greater than 0.1917 is 0.4681.

Simply put, probability measures how likely something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is mainly the study of events subject to probability.

In Population D:

Population Proportion :Turtles have shell length greater than 2 feet = 0.3

Random Sample = 40

Turtles have shell length greater than 2 feet in random sample = 15

In Population E:

Population Proportion :Turtles have shell length greater than 2 feet = 0.2

Random Sample = 60

Turtles have shell length greater than 2 feet in random sample = 11

Let  [tex]\hat{p}_D[/tex] represents sample proportion for D

Let  [tex]\hat{p}_E[/tex] represents sample proportion for E

[tex]$ \text{SampleProportion} =\frac{\text { Count of Success }}{\text { Size of the population }}$[/tex]

[tex]$$\begin{aligned}\hat{p}_D & =\frac{\text { Turtles have a shell length greater than } 2 \text { feet in random sample }}{\text { Random Sample }} \\& =\frac{15}{40} \\& =0.375\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\hat{p}_E & =\frac{\text { Turtles have a shell length greater than 2 feet in random sample }}{\text { Random Sample }} \\& =\frac{11}{60} \\& =0.183\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\text { Difference in sample proportion } & =\hat{p}_D-\hat{p}_E \\& =0.375-0.183 \\& =0.1917\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\hat{\boldsymbol{p}} & =\frac{X_1+X_2}{N_1+N_2} \\& =\frac{15+11}{40+60} \\& =0.26\end{aligned}$$[/tex]

[tex]$$\begin{aligned}Z & =\frac{\left(\hat{p}_D-\hat{p}_E\right)-\left(p_D-p_E\right)}{\sqrt{\hat{p}(1-\hat{p}) \times\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}} \\& =\frac{(0.375-0.183)-(0.3-0.2)}{\sqrt{0.26 \times 0.74 \times\left(\frac{1}{40}+\frac{1}{40}\right)}} \\& =\frac{0.0917}{\sqrt{0.1924 \times 0.04166}} \\& =0.0087\end{aligned}$$$$[/tex]

[tex]\begin{aligned}P\left(\hat{p}_D-\hat{p}_E\right. & > 0.1917) \\& =P(Z > 0.0087) \\& =1-P(Z \leq 0.0087) \\& =0.4681\end{aligned}$$[/tex]

Therefore, The probability that [tex]\hat{p}_D-\hat{p}_E[/tex] is greater than 0.1917 is 0.4681.

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Answer:

The answer is 0

Step-by-step explanation:

The rules of signs:

+ * - = -

- * - = +

- * + = -

+ * + = +

So, using the rules of signs, your question is basically asking, what is 5-5, for which the answer is 0.

Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.

Given its three sides and three vertices, a triangles is a polygon. A fundamental geometric shape, it. Triangle ABC refers to a triangle that has the points A, B, and C as its corners. When four parts are not collinear, a solitary plane and triangle are discovered in geometric shapes. Triangles are known as polygons because of their upper right and three corners. A triangle's three points of intersection are referred to as its corners. By multiplying triple triangle angles, 180 degrees can be obtained.

Here,

The given number indicates that FG is 8 & GH is 14.

FG + GH = FH thanks to the segment addition postulate.

In the equation FG Plus GH = FH, 8 should be used in place of FG and 14 should be used in place of GH.

This results in FH = 8 + 14 => FH = 22.

Therefore, is 22 miles away.

Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.

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The complete question is " Find FH in the given triangle FGH where FG=8,GH=14 and the FH is the equal to sum of FG and GH"

In this case, the highest power on any variable is 23. As a result, the degree of polynomial is 23.

The degree of a polynomial in mathematics is the highest of the degrees of the polynomial's monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer. The degree of a polynomial is the greatest or maximum power of a variable in a polynomial equation. A degree represents the polynomial with the greatest exponential power. Finding the degree of a polynomial. 2 x 2 + 2 x - 364 = 0. The maximum degree of the polynomial in the preceding equation.

Here,

Given : 2x^2 + 5x^23 + 7

Degree of polynomial = Highest power of a variable.

Here, 23 is the highest power on any variable. So, degree of polynomial is 23.

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Answer:

$7.09

Step-by-step explanation:

5% times 6.75 and add that is 7.09 dollars including tax

Answer:

He makes $123.48 a week

The number of y-intercepts for g(x) is larger than that for f. (x). The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).

When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.

given

The graph of f(x) is moved two units to the right and three units downward to get the graph of g. (x).

The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).

Given that a>0, f(x) and g(x) are ascending parabola.

Since the origin is f(x vertex, )'s f(x) has just one y-intercept, or (0,0).

Given that g(x) is an upward parabola with a vertex at (2,-3), g(x) has two y-intercepts.

Because of this, the number of y-intercepts for g(x) is larger than that for f. (x).

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Answer:

u ≤ 15

Step-by-step explanation:

=> u/3 ≤ 5

Multiplying both sides by 3

=> 3×u/3 ≤ 5 ×3

=> u ≤ 15

Answer:

1. yes

2. no

3. no

4. yes

Step-by-step explanation:

The third angle measure is 112°, and the triangle is an obtuse triangle.

A triangle has 3 angles, and the sum of all angles inside a triangle is 180°.

So, 22 + 46 + x = 180

x = 112°

Since the triangle contains an angle measure greater than 90° (the 46° angle), it is an obtuse triangle.

An obtuse triangle is a triangle with one angle measure greater than 90°. In this triangle, the angle measure of 46° is the obtuse angle, and the other two (22° and 112°) are acute angles. Obtuse triangles are often used in construction and engineering applications because of their stability. The third angle measure is 112°, and the triangle is an obtuse triangle.

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So, on solving the question we can say  all sum of angles of a pentagon are 540 ; x = 340

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

coordinates (a,b)

all sum of angles of a pentagon are 540

90 + 30 + 120 +x = 540

x = 340

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Answer:

x=15

Step-by-step explanation:

[tex]\angle A+\angle B+\angle C=180^\circ\\(5x-27)^\circ+(7x-26)^\circ+[180^\circ-(10x-23)^\circ]=180^\circ\\12x-53+180-10x+23=180\\2x-30+180=180\\2x-30=0\\2x=30\\x=15[/tex]

Answer:

x = 15.

Step-by-step explanation:

By the External angle of a triangle theorem:-

The external angle = the sum of the 2 opposite internal angles.

So:

10x - 23 = 7x - 26 + 5x - 27

10x - 7x - 5x = -27 - 26 + 23

-2x = -30

x = 15.

The graph of the linear relationship is represented by the equation y = 3x - 5

An equation is an expression relating two or more numbers and variables.

The standard form of a linear equation is:

Ax + By = C

where A, B and C are constants

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The graph of the linear relationship was plotted using the points from the table. The graph is attached

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The factorization of the given expression is 16x² + 8x + 1- 9y² = (4x +3y +1)(4x -3y +1).

What is the meaning of  Factorize?

Factorization or factoring is defined in mathematics as the breaking or breakdown of one entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together provide the original number or matrix, etc.

Given expression is 16x² + 8x + 1- 9y²

Now make two groups of the expression:

(16x² + 8x + 1)- (9y²)

= (16x² + 8x + 1)- (3y)²

Now applying Algerical identity (a + b)² = a² + 2ab + b².

= ((4x)² + 2×4x×1 + 1²)- (3y)²

= (4x + 1)² - (3y)²

Now applying Algerical identity (a² - b²) = (a+ b)(a - b)

= (4x + 1 + 3y)(4x + 1 - 3y)

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The set of ordered pairs (x, y) that could represent a linear function include the following:

A. A = {(0, 3), (3, 0), (6, -3), (9, -6)}

C. C = {(−6,4),(−3,3),(1,2),(7,0)}.

In order to determine the ordered pairs that could represent a linear function, we would have to determine the slope of each ordered pair. In Mathematics, the slope of a linear function can be calculated by using this this mathematical expression;

Slope = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (0 - 3)/(3 - 0) = (-6 + 3)/(9 - 6)

Slope = -1 = -1 (it represents a linear function).

For ordered pair B, we have:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (7 - 9)/(2 + 1) = (3 - 5)/(7 - 4)

Slope = -2 ≠ -1 (it does not represents a linear function).

For ordered pair C, we have:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (3 - 4)/(-3 + 6) = (0 - 2)/(7 - 1)

Slope = -1/3 = -1/6 (it represents a linear function).

For ordered pair C, we have:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (-1 + 2)/(0 + 3) = (3 - 0)/(8 - 2)

Slope = 1/3 ≠ 1/2 (it does not represents a linear function).

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Answer:

4:8=1:2

3:9=1:3

10:2=5

3:18 is the same thing as 3:18