a coral reef is 5 miles due north of its closest point along a straight shoreline. a visitor is staying in a cottage that is 6 miles east of that point. the visitor is planning to go from the cottage to the coral reef. suppose the visitor runs at a rate of 8 mph and swims at a rate of 1 mph. how far should the visitor run to minimize the time it takes to reach the coral reef? round to two decimal places.

If the diameter of the pool is 24ft, the area is 452.16 ft²

Here we have a circular pool and we want to find its area.

Remember that the area of a circle of radius R is given by:

A = pi*R²

Where pi = 3.14

Here we want to define the diameter as a value between 12 and 24 ft, so I will use 24 ft.

The radius is half of that, then we have:

R = 24ft/2 = 12ft

Then the area of the pool is:

A = 3.14*(12 ft)² = 452.16 ft²

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The equation of the tangent line to the graph of the function f(x)=x 1x−4 at the point (0,−14) is 4x + y +14 = 0.

To find the tangent equation we need slope and intercept for the equation.

To find slope we need to differentiate the given function as the differentiation at a given point gives us the slope :

firstly differentiate the given function :

    f(x)=x(x−4)

         = x^2 - 4x

f'(x) = 2x - 4

f'(x) at (0,-14) = 2(0) - 4  

                     = -4

Hence , the slope is -4

Use the formula to find the equation of the tangent line that passes through a point (x1, y1) with the slope m, that is, y-y1=m(x-x1).

y-y1=m(x-x1) at a point (0,−14)

y - (-14) = -4 (x-0)

y+14 = -4x

therefore, 4x + y +14 = 0 is the required equation of the tangent.

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Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.

When use the formula to solve a problem, the "discriminant" is the value that helps in recognizing the various sorts of solutions. In a mathematical formula (a quadratic equation), it is a special function of a cross that reveals information out about bases of the equation. The "b" term must be square-rooted before the "a" term and "c" term may be isolated by four times to calculate the discriminant. It has a (delta) next to the letter "D" that stands for discrimination. Positive discriminant describes a quadratic equation with two unique real number solutions. Repeated positive integer solutions exist for a quadratic equation with a characteristic of zero. A negative discriminant reveals that none of the solutions is a real number.

given

x2 - 5x + 2 = 0

the roots of the equation

x = -b ±[tex]\frac{\sqrt{b^{2} - 4ac} }{2a}[/tex]

x = 5 ± [tex]\sqrt{17} / 2[/tex]

Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.

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If a = [tex]\left[\begin{array}{ccc}1&0&-4\\0&3&-2\\-2&6&3\end{array}\right][/tex] , b = [tex]\left[\begin{array}{ccc}4\\1\\-4\end{array}\right][/tex] and we denote the columns of A by a₁, a₂, a₃, and let W = Span {a₁, a₂, a₃,} , then b is not in {a₁, a₂, a₃} .

The Span of set of vectors is set of all linear combinations of those vectors. In other words, it's the set of all possible vectors that can be created by taking a weighted sum of the original vectors.

The span of a set of vectors is a subspace of the vector space in which the vectors lie, and it's the smallest subspace that contains all of the original vectors.

The vector b is not in {a₁,a₂,a₃} because "b" is not equal to any of the column vectors of A. Clearly, there are only 3 vectors in {a₁,a₂,a₃}.

The given question is incomplete , the complete question is

a = [tex]\left[\begin{array}{ccc}1&0&-4\\0&3&-2\\-2&6&3\end{array}\right][/tex] , b = [tex]\left[\begin{array}{ccc}4\\1\\-4\end{array}\right][/tex] . Denote the columns of A by a₁, a₂, a₃, and let W = Span {a₁, a₂, a₃,}.  Is b in {a₁, a₂, a₃} ?

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The value of the variable x in the given right angle expression is; x = 11

We know that a right angle simply means an angle that is equal to 90 degrees.

Now, we see that the sum total of the angle in the diagram is 90 degrees and as such the sum of the two internal angles will be 90 degrees.

Thus;

5x + 35 = 90

Subtract 35 from both sides to get;

5x = 55

x = 55/5

x = 11

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Answer:

Step-by-step explanation:

x=8

Discrete mathematics is focused on discrete objects and the relationships between them, while calculus is focused on continuous change and motion.

Discrete mathematics and calculus are two branches of mathematics that deal with different types of mathematical objects and concepts. Discrete mathematics studies discrete objects, such as integers, graphs, and algorithms, while calculus deals with continuous and smooth objects and their derivatives and integrals.

Discrete mathematics provides the mathematical foundations for computer science, especially in areas such as algorithm design, data structures, and complexity theory.

In contrast, calculus is a branch of mathematics that focuses on continuous change, and provides a foundation for many other branches of mathematics and science, including physics, engineering, and economics.

In discrete mathematics, concepts are studied in a finite and countable manner, meaning that the objects and structures being studied can be counted and identified.

For example, in graph theory, discrete mathematical structures like vertices and edges are studied and their properties are analyzed. In discrete mathematics, the focus is on finding relationships between discrete objects and how they can be manipulated, such as in combinatorics and number theory.

On the other hand, calculus deals with the study of change and motion, specifically the rate at which objects change and the accumulation of these changes over time.

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Answer:56

Step-by-step explanation:

You divide 14kg by 2kg and get 7kg. So then you times 7kg by 8 seeds.

Hope this helps :)

For, -3 |2x + 6| = -12 the value of x = -1 and - 5

Correct option is: x = -1 and x = -5. This can be solved using the concept of equation.

Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

-3 |2x + 6| = -12

or, 2x + 6 = 4

or, 2x + 6 = ± 4

or, 2x + 6 = 4

or, 2x = -2

or, x = -1

on the other hand,

2x + 6 = -4

or, 2x = - 10

or, x = -5

So, the value of x = -1, and -5

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The height of the water tank given the volume, length and width is 40 cm

Volume of the water tank= 40 liters

Length of the water tank= 50 cm

Width of the water tank= 20 cm

Height of the water tank= x

convert liters to centimeters

1 liter= 1000 cm

40 liters= 40,000 cm

Volume of the water tank= length × width × height

40,000 = 50 × 20 × x

40,000 = 1000x

divide both sides by 1000

x = 40,000 / 1000

x = 40 cm

Therefore, the height of the water tank is 40 cm

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Answer:

Infinitely many solutions

Explanation:

1) subtract “1” from both sides to get y by itself

Y=-2x-1

2) 4y+8x=-4 share a gcf of “4” so you can divide the whole equation by 4

y+2y=-1

Now substitute “-2x-1” as y

(-2x-1)+2x=-1

-2x and 2x cancel each other and so does -1 and -1

Hence, this system has infinitely many solutions

Answer:

x = 0, y = 1.

Step-by-step explanation:

We can solve for the variables x and y by using substitution. Let's start by solving the first equation for one of the variables:

-1 = 2x - y

y = 2x + 1

Next, we'll substitute y = 2x + 1 into the second equation:

8x - 4y = -4

8x - 4(2x + 1) = -4

Expanding the second equation:

8x - 8x - 4 = -4

-8x - 4 = -4

-8x = 0

x = 0

Finally, we can use one of the equations to find y:

y = 2x + 1

y = 2(0) + 1

y = 1

So, the solution is x = 0, y = 1.

Caroline should cut the fabric into 63 inches wide each

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

For example if a number is added to 20 and gives 50. what is the numbers

x+20 = 50

x = 50-20

x = 30

The total width of the pieces of fabrics = 90 + 36 = 126 inches

To cut the pieces into two equal part with maximum width, we divide the total width by 2

= 126/2

= 63 inches

therefore the fabric should be cut into 63 inches wide each

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The best approximation to a solution of the system of equations is x = -11 and y = 22.

A system of equations is a collection of two or more equations with the same variables. Solving a system of equations means finding the values of the variables that satisfy all the equations in the system.

In this case, you have a system of two equations:

4x + 2y = 0 and x + y = 11.

To find the best approximation to a solution of the system, we can use substitution or elimination methods.

First, we can isolate one of the variables in one of the equations.

=> 4x + 2y = 0.

Dividing both sides by 2, we get:

=> 2x + y = 0.

Now we have one equation in terms of one variable, which is y.

Next, we can substitute the expression for y from this equation into the second equation:

=> x + y = 11.

Replace y with -2x

=> x + (-2x) = 11.

=> -x = 11.

=> x = -11.

Finally, we can substitute the value for x back into one of the original equations to find the value of y.

Let's substitute x = -11 into the first equation:

=>  4(-11) + 2y = 0.

=> -44 + 2y = 0.

=> 2y = 44.

=> y = 22.

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Answer:

Step-by-step explanation:

Equivalent rates can be used to compare different sets of quantities that have the same value. A rate that compares a quantity to one is called a unit rate. The unit rate has a denominator equal to one when written as a fraction. Unit rates can be used to find larger equivalent rates.In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour

The length of the side AD that needed to be replaced is D. 5.1

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, tan = opposite/adjacent.

tan30° = DB/12.

DB = 12×tan30°.

DB = 6.93.

Now, m∠BCA = 30° + 15° = 45°.

Therefore,

tan45° = (AD + DB)/12.

AD + DB = 12.

AD = 12 - 6.93.

AD = 5.1.

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Answer:

5.1

Step-by-step explanation: got right on test

Answer:

11 + C

Step-by-step explanation:

Sum= +

You add 11 and C

One pound of nitrogen or mixed fertilizer is recommended per 1,000 square feet of lawn and your particular fertilizer contains 20% nitrogen.

How many pounds would be needed to cover 1088 square feet?

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Answer:4

Step-by-step explanation:

3

The probability of failure after 1 year of use will be approximately 109/1,000,000 = 0.000109 or 0.0109%.

The failure rate (fpmh) is the number of failures per million hours. If a device is used for 5 hours per day, every day, it will be used for 365 days * 5 hours/day = 1,825 hours in a year.

The probability of failure after 1 year of use can be calculated as:

Failure rate * total hours used = 0.06 fpmh * 1,825 hours = 0.06 * 1,825 failures = 109.35 failures

So, there will be approximately 109 failures after 1 year of use. Since the failure rate is per million hours, and there were 1,825 hours of use, the probability of failure after 1 year of use will be approximately 109/1,000,000 = 0.000109 or 0.0109%.

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6 cm, 8 cm, 10 cm meaurement repreent the ide length of a right triangle.

A right triangle, like the triangle below, is one in which one of the angles measures 90 degrees (a right angle). In most cases, right angles are shown by drawing a square at the angle's vertex.

For a right triangle, where c is the hypotenuse and a and b are the smaller sides, the Pythagorean Theorem gives us a2 + b2 = c2.

The hypotenuse is usually the longest. Any triple would still represent the sides of a right triangle if we multiplied it by a constant. Therefore, the sides of a right triangle would be 6, 8, and 10.

a2 + b2 = c2.

= 6^2 + 8^2  =  10^2

36 + 64 = 100.

so,

6 cm, 8 cm, 10 cm meaurement repreent the ide length of a right triangle.

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Answer:

ladder has to be at least 13 ft long

Step-by-step explanation:

l = length of the ladder

12.6² + 3.2² = l²

l² = 158.76 + 10.24 = 169

√l² = l = √169 = 13

The ladder is the hypotenuse of a right triangle with sides 12.6 and 3.2

The solution is , The equation of g(x) is g(x) = 2*x^(1/2).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

The original function f(x) is defined

as f(x) = x^(1/2)

which is the square root of x.

When the function is stretched horizontally by a factor of 2,

the x term becomes 2x.

So the new function g(x) is defined

as g(x) = 2*x^(1/2)

Hence, The solution is , The equation of g(x) is g(x) = 2*x^(1/2).

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Answer is 2 5/8 tuna filling at first.

At first, he made 2 5/8 kg of tuna filling.

M r Abdul made tuna and curry potato filling for some puffs.

3/5 of the filling he made was tuna and the rest was curry potato.

So, amount of curry potato = 1- 3/5 = 2/5

Ratio of tuna & curry potato = tuna : curry potato

                                              = 3/5 : 2/5  = 3 : 2

Let amount of tuna = 3x & amount of curry potato = 2x

After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.

According to the question, he then had equal amounts of tuna filling and curry potato filling left.

So, 3x - 1/8 = 2x + 3/4

Multiplying 8 in both sides we get,

⇒ 24x - 1 = 16x +6

⇒ 24x - 16x = 7

⇒ 8x = 7

⇒ x = 7/8

So, 3x = (3×7/8) = 21/8 kg = 2 5/8 tuna filling at first.

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The average rate of change for a city population of the city was growing steadily and can be used to predict future population growth.

The average rate of change for a city can be calculated by subtracting the initial population (23,000 in 2010) from the final population (25,000 in 2015) and then dividing that number by the total number of years (five). The equation for this calculation is:

(Final Population - Initial Population) / (Number of Years)

Using this equation, the average rate of change for the city is calculated as follows:

(25,000 - 23,000) / 5 = 2,000 / 5 = 400

Therefore, the average rate of change for the city between 2010 and 2015 was 400 people per year. This means that on average, the population of the city increased by 400 people each year during this time interval. This calculation shows that the population of the city was growing steadily and can be used to predict future population growth.

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Simplifying the given expression can be rewritten as:  [tex](512m^9n^3)[/tex].

The main power rules are presented below.

For simplifying the given expression, it is necessary to apply the presented power rules previously.

The given expression is (-4mn)³*(-2m²)³. Thus,

       (-64m³n³) * [tex](-8m^6)[/tex]

        Note that the rule should be apply in numbers and letters.

      [tex](512m^9n^3)[/tex]

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Answer:

C

Step-by-step explanation:

the circumference of a circle is

2×pi×r

r being the radius, which is half of the diameter.

in our case

r = 18/2 = 9 mm

so, the circumference is

2×3.14×9 = 18×3.14 = 56.52 mm

ochala bought a music system on hire purchase. He paid a total of sh 5,200 .if he started by paying a deposit of sh 2,300 for how many months did he pay the remaining money if each monthly installment was sh 2,900

The equation which would help determine the cost of 21 glue sticks is 5 / 9.65 = 21 / x, where x is the cost of 21 glue sticks.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Given that,

Cost of 5 glue sticks = $9.65

Let x be the cost of 21 glue sticks.

Using proportional concept,

5 / 9.65 = 21 / x

Hence the equation is 5 / 9.65 = 21 / x

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Note that the hint to demonstrating the above proof (that ΔABC ≅ ΔADE) is to compare the slopes of DE and BC. See the computation below.

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

Comparing both slopes, we have:

Slope of DE = 2-1/4-5 = 1/-1 = -1

Slope of BC = 3-1/6-8 = 2/-2 = -1

Since the slope of DE and BC are the same an they are not intersection, it means they are parrallel lines.

Since DE || BC

In ΔABC and ΔADE

∠DAE = ∠BAC

∠ADE ≈ ∠ABC (Correspoinding Angle)

∠AED = ∠ACB (Corresponding Angles)

Thus,  ΔABC ≅ ΔADE.

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Full Question:

Given A(2,1), B(6,3), C(8,1), D(4,2) and E(5,1), shown below, prove that ΔABC ≅ ΔADE

The actual distance in miles between the campsite and the trail is 9 miles.

Map can be defined as  a symbolic depiction emphasizing relationships between elements of some space such as objects and regions.

To convert from centimeters on the map to miles, we use the scale of 1 centimeter represents 5 miles.

So, 1.8 centimeters on the map represents 1.8 * 5 = 9 miles in real life.

Therefore, The actual distance in miles between the campsite and the trail is 9 miles.

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The measure of the acute base angle is 69°

The measure of the obtuse base angle is 111°

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Isosceles triangles mean two sides are equal and the angles opposite to the equal sides are also equal.

Now,

Isosceles trapezoid

Vertex angle = 42

This means,

The other two angles will be the same.

x + x + 42 = 180

2x = 180 - 42

2x = 138

x = 69

Now,

The opposite angles of an isosceles trapezoid are supplementary.

So,

Obtuse base angle + Acute base angle = 180

Obtuse base angle + 69 = 180

Obtuse base angle = 180 - 69 = 111

Thus,

Acute base angle = 69°

Obtuse base angle = 111°

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