Marieme wants to build a rectangular garden whose area is
24
2424 square meters.
1. Write an equation that represents the garden's length in meters (
l
ll) based on its width in meters (
w
ww).

The equation of the ellipse is equal to (x - 6)² / 49 + (y + 6)² / 36 = 1.

In this problem we must derive the equation of an ellipse based on information about the center, a vertex and a co-vertex thereof. The vertex represents the end of the major semiaxis that lies on the curve and co-vertex is the end of the minor semiaxis that lies on the curve. The major semiaxis is parallel with x-axis and the minor semiaxis is parallel with y-axis.

The standard form of the ellipse is shown below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

Now we proceed to derive the equation of the ellipse:

Major semiaxis:

A = (13, - 6) - (6, - 6)

A = (7, 0)

a = 7

Minor semiaxis:

B = (6, 0) - (6, - 6)

B = (0, 6)

b = 6

Equation of the elipse:

(x - 6)² / 49 + (y + 6)² / 36 = 1

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Each phrase can be epressed as an algebraic expression as:

n/8

4p,

b+14

90x

-16

24-k

3(w)

1+q

13/z

45+c

w-8

An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). A good example of an algebraic expression is 3x2 2xy + c.

A variable expression can be described using its terms and operations on the terms as an algebraic expression. For instance, "3 more than x" can be used to describe x + 3.

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a. Line A represents Duncan's wages. b. We can determine this by equation of the line. Luke's equation of line has an additional constant and thus it starts from the point 30 above from the origin.

In mathematics, a variable is a symbol that designates a mathematical object (from the Latin variabilis, "changeable"). Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable.

A variety of issues are resolved by algebraic calculations that treat variables like explicit integers in a single computation. The quadratic formula, for instance, can be used to solve any quadratic equation by exchanging the variables in the quadratic formula for the numerical values of the coefficients in the equation.

Let us suppose number of hours worked = x.

Given that,

Duncan gets paid R8,50 per hour. His equation of line is:

D = 850x

Luke gets R30 and R450 per hour. His equation of line is:

L = 450x + 30

a. From the graph we see that line A represents Duncan's wages.

b. We can determine this by looking at the equation of the line. Luke's equation of line has an additional constant and thus it starts from the point 30 above from the origin.

c. For x = 2 hours.

L = 450(2) + 30

L = 900 + 30 = R930

d. For D = 1000:

1000 = 850x

x = 1.17 hours.

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The inequalities represented on the graph is x ≥ -2.

In mathematics, an inequality is a mathematical expression where neither side is equal. Inequality in mathematics is defined as a comparison between two expressions or two numbers that is not equal. In mathematics, there are several varieties of inequality, including polynomial inequality, rational inequality, and absolute value inequality.

Given that,

Number line showing range from negative five to five. The left end point is a closed dot at negative two, with a ray pointing right past five.

From the above we observe that point on negative 2 is a closed dot hence the inequality would be ≥ or ≤.

Now, the ray point past five, that is it moves in positive direction.

Hence, the inequalities represented on the graph is x ≥ -2.

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The rule for the graph of g is g(x) = -4(x^2-3). This graph is a vertical stretch by a factor of 4 and a reflection in the x-axis of the graph of f(x) = x^2-3.

Answer:

$4

Step-by-step explanation:

The outcome of removing (2x-3)2 from 5x2 is therefore x2 + 12x - 9.

Therefore, it can be expressed as Minuend Subtrahend = Differential. As a result, the number being removed is known as Barely heard, and the number being deducted is known as Minuend. As a result, the amount that is being removed from is known as the minuend, and the number being deducted from is known as the subtrahend.

To answer this question, we need to expand (2x-3)² and then subtract it from 5x².

(2x-3)² means (2x-3) multiplied by itself:

(2x-3)² = (2x-3) × (2x-3)

The first term in the first parentheses can be multiplied by both terms in the second parentheses using the distributive property, and the second term in the first parentheses can be multiplied by both terms in the second parentheses using the distributive property:

(2x-3) × (2x-3) = 2x × (2x-3) - 3 × (2x-3)

Simplifying each of the two terms:

= 4x² - 6x - 6x + 9

= 4x² - 12x + 9

Now we can subtract this expression from 5x²:

5x² - (4x² - 12x + 9)

Distributing the negative sign:

5x² - 4x² + 12x - 9

Combining like terms:

x² + 12x - 9

Therefore, the result of subtracting (2x-3)² from 5x² is x² + 12x - 9.

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Ms. Howard's salary would be $360. Below, you will learn how to solve the problem.

Ms. Howard's salary can be found by first calculating the amount of money spent on groceries, entertainment, and transportation. 1/3 of her monthly salary was spent on groceries, so that would be $(1/3)x where x is her salary, 1/4 of her monthly salary was spent on entertainment, so that would be $(1/4)x. 2/5 of the remaining amount was spent on transportation, which is $(2/5)(x-(1/3)x-(1/4)x).

Ms. Howard then had $270 left, so we can set up the equation:

$(1/3)x + $(1/4)x + $(2/5)(x-(1/3)x-(1/4)x) = 270

Solving for x, Ms. Howard's salary would be $360.

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The total number of water tankers that were supplied to the project on the construction site by the water tanker in march 2022 is, 96.

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

The company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day.

Hence, We get;

Total number of water tanks loads are = 12 × 5 = 80

Here, On Saturdays, the company supplied a minimum of 4 water tankers, for a total of 16 water loads.

Thus, the total number of water loads supplied to the project on the construction site by the water tanker in March 2022 is,

⇒ 80 + 16

⇒ 96

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Complete question is this,

the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022​

Answer:

371.5 square units.

Step-by-step explanation:

the shaded region is a ring-shaped region between the two concentric circles, we can find the area of the shaded region as follows:

The area of the large circle is given by:

Area of large circle = π × r^2

where r is the radius of the large circle, which is 13.5.

Area of large circle = 22/7× (13.5)^2

Area of large circle ≈ 572.78

The area of the small circle is given by:

Area of small circle = π × r^2

where r is the radius of the small circle, which is 8.

Area of small circle = 22/7× (8)^2

Area of small circle ≈ 201.14

The area of the shaded region is the difference between the area of the large circle and the area of the small circle:

Area of shaded region = Area of large circle - Area of small circle

Area of shaded region ≈ 572.78 - 201.14

Area of shaded region ≈ 371.5

Therefore, the approximate area of the shaded region is 371.5square units.

Answer:

The area of the shaded region is 371.5 square units to the nearest tenth.

Step-by-step explanation:

To find the area of the shaded region of two concentric circles with a common center, subtract the area of the smaller circle from the area of the larger circle.

The formula for the area of a circle is A = πr², where r is the radius of the circle.

From inspection of the given diagram:

Therefore, the area of the shaded region is:

[tex]\begin{aligned}\textsf{Area of shaded region}&=\textsf{Area of larger circle}-\textsf{Area of smaller circle}\\&=\pi (13.5)^2-\pi (8)^2\\&=182.25 \pi - 64 \pi\\&=118.25 \pi\\&=371.493331...\\&=371.5\; \sf unit^2\;\;(nearest\;tenth)\end{aligned}[/tex]

The area of the shaded region is 371.5 square units to the nearest tenth.

In existence, there is the 1 dollar, 5, 10, 20, 50, and 100. The only way he could take out two different dollar bills and it be worth less than 10 bucks is if he pulls out a 1 and a 5. In these odds, it would be 2 / 12 chance of pulling out two dollar bills and it being worth less than 10 bucks.

Answer:

i have no clue whats going on sorry i cant help

Step-by-step explanation:

The set of equation that models the point of intersection of the arrow

and the target is the option; y = -0.004·x² + 0.25·x + 8 and y = 0.22·x

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix. Parabola is an integral part of conic section topic and all its concepts parabola are covered here.

here, we have,

The given parameters are;

Point of intersection of the line and the parabola is the point (48.63, 10.7)

Therefore, the point (48.63, 10.7) satisfies both the equation of the

parabola and the equation of the line, which by plugging in the value x =

48.67 in the different parabolas, we have;

The first set;

y = -0.004 × 48.67² + 0.25 × 48.67 + 8 ≈ 10.7, which corresponds with the ordered pair.

The linear function in the first set should be excluded, given y ≠ x in the

ordered pair.

In third set,

y = -0.004 × 48.67² + 0.25 × 48.67 + 8 ≈ 10.7,

while, from the ordered pair, we have;

y = C·x

10.7 = 48.63·x

Therefore;

y ≈ 0.22·x

The set of equations that best models the point of intersection of the arrow and target are therefore;

y = -0.004·x² + 0.25·x + 8 and y = 0.22·x

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These roots are also complex conjugates, so the step response will be oscillatory with a decay factor. The response will look like a damped sinusoid. the value of s1 and s2 is 25i and -25j.

Here are the solutions for the given transfer functions and the corresponding step response plots:

G(s) =[tex]400 / (s^2 + 12s + 400)[/tex]

First, let's find the roots of the denominator:

[tex]s^2 + 12s + 400 = 0[/tex]

Using the quadratic formula, we get:

s1 = -6 + 14.96j

s2 = -6 - 14.96j

These roots are complex conjugates, so the step response will be oscillatory with a decay factor. The response will look like a damped sinusoid.

G(s) =[tex]900 / (s^2 + 90s + 900)[/tex]

The denominator can be factored as [tex](s + 45)^2[/tex]. Therefore, the roots are:

s1 = s2 = -45

Since both roots are negative and equal, the response will be critically damped.

G(s) = [tex]225 / (s^2 + 30s + 225)[/tex]

The denominator can be factored as[tex](s + 15)^2[/tex]. Therefore, the roots are:

s1 = s2 = -15

Again, since both roots are negative and equal, the response will be critically damped.

G(s) = [tex]625 / (s^2 + 625)[/tex]

The denominator can be factored as (s + 25j)(s - 25j). Therefore, the roots are:

s1 = 25j

s2 = -25j

Note: The step response plots can be sketched by considering the damping ratio and natural frequency of each transfer function. For critically damped systems, the response reaches steady-state the fastest, but it also overshoots the most.

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0.02 Bitcoin is in dollar is 497.928000 US Dollar (USD)

1 Bitcoin = 24872.70 US Dollar (USD)

so 0.02 bitcoin in dollar is

0.02 * 42872.70 =  497.928000 US Dollar (USD)

Bitcoin has a high inverse correlation with the US Dollar Index (DXY). This makes conceptual sense as it has a fixed supply and is most commonly traded against the US dollar more than any other currency. Now, looking at the weekly data from early 2018, the correlation is around -70% (R2 is 0.5877).

Volker successfully curbed the extreme inflation of the late 1970s and early 1980s with aggressive monetary policy, pushing the dollar to a very high level. Like today, the U.S. hasn't experienced similarly high levels of inflation and may have already peaked. As a result, the US dollar is unlikely to hit her early 1980s highs.

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The two longest ribbons that were cut from the spool measure a combined 132 inches in length.

A combination of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division make up an algebraic expression in mathematics. Mathematical, scientific, engineering, and engineering problems are represented and solved using algebraic expressions.

One or more variables, which represent unknowable or varying quantities, and one or more constants, which represent fixed values, can both be present in an algebraic expression. Typically, the variables are represented by letters like x, y, or z. The symbols +, -, x, and y, respectively, stand in for addition, subtraction, multiplication, and division. Additionally, terms are grouped and the order of operations are indicated by using parentheses.

For instance, the mathematical formula 3x + 2y - 5 combines the two variables x and y with the three constants 3, 2, and 5. While -5 is a constant term, the terms 3x and 2y are the variables multiplied by their coefficients.

By combining like terms, or terms with the same variable raised to the same power, algebraic expressions can be made simpler. For instance, the terms 3x and 4x, as well as 2y and -3y, are like terms in the expression 3x + 2y - 5 + 4x - 3y. These terms combined result in the abbreviated expression 7x - y - 5.

Mathematical operations like solving equations, graphing functions, and evaluating formulas all use algebraic expressions. Additionally, they are used in practical applications like figuring out interest rates, resolving optimization issues, and simulating natural phenomena.

The two longest ribbons cut from the spool are those with lengths of 63 and 69, according to the provided stem-and-leaf plot. Their total is therefore:

63 + 69 = 132

So, the total length of the 2 longest ribbons cut from the spool is 132 inches.

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The correct option is A.

A right triangle is a type of triangle in which one of its angles measures exactly 90 degrees (π/2 radians). This angle is called the right angle, and it is located opposite to the longest side of the triangle, which is called the hypotenuse. The other two sides are called the legs of the triangle.

The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, is one of the most important properties of right triangles. This theorem can be written algebraically as:

a^2 + b^2 = c^2

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Right triangles also have several other important properties, including:

The acute angles (those that are not the right angle) are complementary, which means that their sum is equal to 90 degrees.

The side opposite the right angle is always the longest side (the hypotenuse).

The legs are always perpendicular to each other.

The altitude (height) from the right angle to the hypotenuse divides the triangle into two smaller triangles that are similar to the original triangle and to each other.

Right triangles are used in many areas of mathematics and science, including trigonometry, calculus, geometry, physics, and engineering. They are also used in practical applications, such as in construction, surveying, and navigation.

In a right triangle EFG, where angle EFG = θ, the sine of θ is defined as the ratio of the length of the side opposite θ (EF) to the length of the hypotenuse (EG). Therefore, the answer is:

A. sin(θ) = EF/EG

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For the given graph we have:

Domain [-4, 7]

Range [-5, 7]

For a function y = f(x) we define the domain as the set of the inputs and the range as the set of the outputs.

To identify the domain on a graph we need to see the horizontal axis, here we can see that the graph starts at x = -4 and ends at x = 7, then the domain is [-4, 7]

For the rangewe need to look at the vertical axis, here we can see that it starts at y = -5 and ends at y = 7

Then the range is [-5, 7]

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The equations that are parallel to the given line are C. 6x + 2y = -4 and D. 6x - 2y = -4.

What is the slope-intercept form?

The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.

Two lines are parallel if they have the same slope. The given line y = 3x - 5 is in slope-intercept form, which means its slope is 3.

A line in slope-intercept form has the equation y = mx + b, where m is the slope and b is the y-intercept. Therefore, any line of the form y = 3x + c, where c is a constant, will have a slope of 3 and be parallel to the given line.

Let's check each of the given equations to see which ones are of this form:

A. y = 3x - 7: This equation has the same slope as the given line, but it is not in the form y = 3x + c. Therefore, it is not parallel to the given line.

B. y = -3x - 5: This equation has a slope of -3, which is not the same as the slope of the given line. Therefore, it is not parallel to the given line.

C. 6x + 2y = -4: We can rearrange this equation to slope-intercept form by solving for y:

2y = -6x - 4

y = -3x - 2

This equation has the same slope as the given line, so it is parallel to the given line.

D. 6x - 2y = -4: We can rearrange this equation to slope-intercept form by solving for y:

-2y = -6x - 4

y = 3x + 2

This equation has the same slope as the given line, so it is also parallel to the given line.

Therefore, the equations that are parallel to the given line are C. 6x + 2y = -4 and D. 6x - 2y = -4.

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Answer:

Step-by-step explanation:

With this the probabiitiy is high. In saying that look at 3 that is your answer. So that answer would be mostly 0.100. Hope this helps

The rate of $18 an hour will be approximately  $157248  for a year .

In order to find how much $18 an hour is in a year,

We need to know how many hours are present in a year.

The number of weeks in 1 year is = 52 weeks ;

and 1 week consists of 168 hours , as 1 week has 7 days and 1 day has 24 hours .

So , 1 year (52 weeks) is = 52 × 168 = 8736 hours .

We get that 1 year consists of 8736 hours ,

Now , multiplying the number of hours by $18 ,

We get ,

⇒ 8736 × 18 = $157248 .

Therefore , $18 an hour will be $157248 for a year .

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The probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

The tree diagram makes it easier to arrange and see all of the potential possibilities. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end. To determine when to multiply and when to add, use tree diagrams.

Let A be an event: the first ticket extracted was the 5.

Let B be an event: the second ticket is 2.

The probability for the following is given as:

P (B/ A) = 2/7

Hence. the probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

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Answer:

26 Students

Step-by-step explanation:

4% is also 0.04 multiplied by the number of students. 650 * 0.04 = 26

The value of the angle ∠EDC is 25 degrees for the triangle ABC.

According to the exterior angle theorem, an external angle's measure is equal to the sum of its remote interior angles' two opposite measures. Let's review a few fundamental facts concerning triangle angles: Three of a triangle's interior angles always add up to 180 degrees. This theorem is applied to all six of the exterior angles of the object. In order to make a linear pair of angles, an outer angle must be complementary to the neighbouring interior angle.

Given that, ∠B = ∠C and ∠BAD = 50 degrees.

Now, AE = AD hence, ∠ADE = ∠AED

Let ∠ADE = ∠AED = y.

From triangle ADC we have:

∠ADC = y + z

y + z = 50 + ∠B (exterior angles)

∠B = y + z - 50

Now, ∠B = ∠C thus,

∠C = y + z - 50

In triangle EDC we have:

∠E = x + y (exterior angles)

Also,

∠E + ∠D + ∠C = 180 (sum of interior angles of a triangle)

(x + y) + z + (y + z - 50) = 180

x + 2y + 2z = 230.........(1)

In triangle ADE,

x + 2y = 180

Substituting the values in 1 we have:

180 + 2z = 230

z = 25

Hence, the value of the angle ∠EDC is 25 degrees for the triangle ABC.

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The complete question is:

Refer to the figure below. In triangle ABC, Angle B = Angle C. Given that point D is on BC,angle BAD = 50 degrees , AE = AE. Then what is angle EDC.

Never. Correlation coefficients are used to measure the strength of a linear relationship between two variables, not to prove cause and effect. To determine causation, it is necessary to conduct an experiment or study in which the independent variable is manipulated and the dependent variable is measured.

Correlation coefficients are used to measure the strength of a linear relationship between two variables. They can measure the degree to which variables move together, but they cannot be used to prove cause and effect. To determine causation, it is necessary to perform an experiment or study in which one variable is manipulated and the other is measured. This allows researchers to control for confounding variables and to determine if the manipulation of the independent variable had a direct effect on the dependent variable. Therefore, correlation coefficients cannot be used to support a claim of cause and effect.

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The most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8) is a kite.

Option C is the correct answer.

A kite is a quadrilateral where the adjacent sides are equal which means there are two pairs of equal sides.

We have,

Quadrilateral ABCD:

A = (4, 4)

B = (5, 8)

C = (8, 8)

D = (8, 5)

Now,

A__________B

|                      |

|                      |
|                      |

D_________ C

We see the distance between the two points.

AB = √(8 - 4)² + (5 - 4)² = √(4² + 1) = √17

AD = √(5 - 4)² + (8 - 4)² = √(1² + 4²) = √17

AB = AD

BC = √(8 - 8)² + (8 - 5)² = √9 = 3

CD = √(5 - 8)² + (8 - 8)² = √9 = 3

BC = CD

AB and AC are adjacent sides.

CD and DB are adjacent sides.

So,

The quadrilateral ABCD is a kite.

Thus,

The quadrilateral ABCD is a kite.

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answer:

answer:1/8

answer:1/8explanation :

answer:1/8explanation :0.125 as a fraction in simplest form is 1/8

answer:1/8explanation :0.125 as a fraction in simplest form is 1/8Step 2: Find the HCF or the highest common factor of 125 and 1000.

answer:1/8explanation :0.125 as a fraction in simplest form is 1/8Step 2: Find the HCF or the highest common factor of 125 and 1000.hope this helped.

20h⁵ - 35h⁴ is the simplified and dispersed expression.

What does math's distribution mean?

Something is divided, shared, or given away when it is "distributed." What does this mean for the distributive property of mathematics? Basic arithmetic operations like addition and subtraction are used to divide the results of multiplication according to the distributive property of the law of multiplication.

We may utilize the distributive property of multiplication, which asserts that a(b + c) = ab + ac, to distribute and simplify 5h³(4h² - 7h).

The 5h³ is first distributed to both words inside of the parenthesis as follows:

5h³(4h² - 7h) is equal to 5h³ * 4h² - 5h³ * 7h.

Secondly, by multiplying the coefficients and adding the exponents, we simplify each term:

20:5 + 5:3 + 4:2 + 5:3 + 7:4 = 35:4

When we add everything together, we get the following: 5h³(4h² - 7h) = 20h⁵- 35h⁴.

Hence, 20h⁵ - 35h⁴ is the simplified and dispersed expression.

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Answer:

The slope of the dotted line is -1. The slope of the solid line is 4.