ABCD is a rectangle that represents a park
The lines show all the paths in the park
The circular path is in the center of the rectangle and has a diameter of 15m
calculate the shortest distance from A to C across the park using only the lines shown
image is attached below

Answer:

Hana is 16

Step-by-step explanation:

Total is 80. Ratio is 7:3:6:4. Ratio adds to 20. 80÷20=4. Hana is last in Ratio which is 4. 4×4= 16.

The function that models the change in the animal population is

                   [tex]F(x) = x ( 1+ r)^{t}[/tex]

According to the question we have been given that

        population decreases = 3.5% per year

         Number of animals counted = 80

The formula to be used is

       [tex]F(x) = x (1 + r)^{t}[/tex]           (1)

where,  F(x) = amount of animals counted after t years

              x = initial amount of animals

               r = decrease or increase rate of animal species.

               t = time

Now according to the question,

           r = -0.035

           x = 80

Putting the required values in equation (1) we get  

      [tex]F(x) = 80 (1 - 0.035)^{t}\\ F(x) = 80 (0.965)^{t}[/tex]

Thus above is the required function that models the change in the animal population.

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Let's call the entire angle between the 10 and 5 sides to be x

Applying to cosine rule:

[tex]9 {}^{2} = 10 {}^{2} + 5 {}^{2} - 2(10)(5)cos(x) \\ 81 = 100 + 25 - 100cos(x) \\ 100cos(x) = 125 - 81 \\ cos(x) = \frac{44}{100} = 0.44 \\ x = arccos(0.44)\approx63.9[/tex]

We can conclude that the angle inside the small triangle is half of x, which i will denote by y

[tex]y = \frac{x}{2} = \frac{63.9}{2} = 31.95[/tex]

Similarly to find the angle which i will denote by z at the right lower corner of the small or large triangle, apply the cosine law again:

[tex]10{}^{2} = 5 {}^{2} + 9 {}^{2} - 2(9)(5)cos(z) \\ 100 = 25 + 81 - 90cos(z) \\ 90cos(z) = 106 - 100\\ cos(z) = \frac{6}{90} = 0.06666 \\ z = arccos(0.06666)\approx86.2[/tex]

The last angle in our small triangle which i will denote by w, will be 180 minus z and y

[tex]w = 180 - (y + z) \\ w = 180 - (31.95 + 86.2) \\ w = 61.85[/tex]

Let t be our missing side,

applying the law of sines:

[tex] \frac{5}{sin(w)} = \frac{t}{sin(y)} \\ t = \frac{5sin(y)}{sin(w)} = \frac{5sin(31.95)}{sin(86.2)} [/tex]

[tex]t \approx2.652[/tex]

Answer:

[tex]\frac{1}{4}[/tex] (t + 9) ≤ 9

Step-by-step explanation:

One-fourth multiplied by sum of t and 9 is at most 9

One-fourth [tex]\frac{1}{4}[/tex]

sum of t and 9 = t + 9

at most 9 = ≤ 9

Value of x = 2/3.

✓(6 - 3x) - 2 = 0

Adding 2 to both sides of the equation

✓(6 - 3x) - 2 + 2 = 0 + 2

✓(6 - 3x) - 2 = 2

Now, tor remove the square root from the Left Hand Side of the equation, square both the sides of the equation.

(✓(6 - 3x))² = 2²

6 - 3x = 4

3x = 6 - 4

3x = 2

x = 2/3

Thus, the value of x is 2/3.

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The domain of the function [tex]g(x) - f(x)[/tex] for [tex]f(x)=2 x+5[/tex]and [tex]g(x)=x^2-3 x+2[/tex]  is [tex]g(x) - f(x)[/tex] = [tex]x^2-4x-2[/tex]. The domain will be all real numbers for x, ( ∞,-∞)

The domain will be all real numbers for x, ( ∞,-∞)

As there are no values that can be substituted for x that can possibly make the function undefined.

Therefore,

[tex]g(x)=x^2-3 x+2 .[/tex]

[tex]f(x)=2 x+5[/tex]



[tex]g(x) - f(x)[/tex] = ([tex]x^2-3 x+2[/tex]) - ([tex]2 x+5[/tex])

[tex]g(x) - f(x)[/tex] = [tex]x^2 - 4x-2[/tex]

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Using the vertical line test, we conclude that the relation that is a function is the bottom right one.

A relation is a function only if all the inputs are mapped into a single output.

If we have the graph of a relation, it only will be a function if it passes the vertical line test.

This means that if we draw any vertical line on the coordinate axis, and it intercepts the graph of the relation more than once, then it is not a function.

With that we can see that the first 3 options are not functions, and the last one (bottom right) it is a function.

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Answer:

wait first of all where did they put grandma?

The domain of the function is {2, 4, 11, -21} and the range is {-5, 31,-11,3}

The domain and the range of a function are the set of input values and output values of the graph

We have the following ordered pairs of the function

(x, y) = {(2,-5) , (4,31), (11,-11), (-21,3)}

Remove the y values to determine the domain

x = {2, 4, 11, -21}

Remove the x values to determine the range

y = {-5, 31,-11,3}

Hence, the domain of the function is {2, 4, 11, -21} and the range is {-5, 31,-11,3}

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This figure begins with the sentence, “We substitute x equals 3 and y equals 2 into both equations.” The first equation reads 3 times x minus 7equals 7. Then, 3 times 3 minus 2 equals 7. Then 7 = 7 is true. The second equation reads x minus 2y equals 4. The n times 2 minus 2 times 2 = 4. Then negative 2 = 4 is false.

The ordered pair (3, 2) made one equation true, but it made the other equation false. Since it is not a solution to both equations, it is not a solution to this system.

Exercise  5.1.1

Determine whether the ordered pair is a solution to the system:  {x−y=−12x−y=−5

(−2,−1)

(−4,−3)

Answer

Exercise  5.1.2

Determine whether the ordered pair is a solution to the system:  {3x+y=0x+2y=−5

(1,−3)

(0,0)

Answer

Exercise  5.1.3

Determine whether the ordered pair is a solution to the system:  {x−3y=−8−3x−y=4

(2,−2)

(−2,2)

Answer

Solve a System of Linear Equations by Graphing

In this chapter we will use three methods to solve a system of linear equations. The first method we’ll use is graphing. The graph of a linear equation is a line. Each point on the line is a solution to the equation. For a system of two equations, we will graph two lines. Then we can see all the points that are solutions to each equation. And, by finding what the lines have in common, we’ll find the solution to the system.

Most linear equations in one variable have one solution, but we saw that some equations, called contradictions, have no solutions and for other equations, called identities, all numbers are solutions. Similarly, when we solve a system of two linear equations represented by a graph of two lines in the same plane, there are three possible cases, as shown in Figure  5.1.1 :

This figure shows three x y-coordinate planes. The first plane shows two lines which intersect at one point. Under the graph it says, “The lines intersect. Intersecting lines have one point in common. There is one solution to this system.” The second x y-coordinate plane shows two parallel lines. Under the graph it says, “The lines are parallel. Parallel lines have no points in common. There is no solution to this system.” The third x y-coordinate plane shows one line. Under the graph it says, “Both equations give the same line. Because we have just one line, there are infinitely many solutions.”

Figure  5.1.1

For the first example of solving a system of linear equations in this section and in the next two sections, we will solve the same system of two linear equations. But we’ll use a different method in each section. After seeing the third method, you’ll decide which method was the most convenient way to solve this system.

Exercise  5.1.4 : How to Solve a System of Linear Equations by Graphing

Solve the system by graphing:  {2x+y=7x−2y=6

Answer

Exercise  5.1.5

Solve each system by graphing:  {x−3y=−3x+y=5

Answer

Exercise  5.1.6

Solve each system by graphing:  {−x+y=13x+2y=12

Answer

The steps to use to solve a system of linear equations by graphing are shown below.

TO SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system.

If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.

If the lines are parallel, the system has no solution.

If the lines are the same, the system has an infinite number of solutions.

Exercise  5.1.7

Solve the system by graphing:  {y=2x+1y=4x−1

Answer

Exercise  5.1.8

Solve the system by graphing:  {y=2x+2y=−x−4

Answer

Exercise  5.1.9

Solve the system by graphing:  {y=3x+3y=−x+7

Answer

Both equations in Exercise  5.1.7  were given in slope–intercept form. This made it easy for us to quickly graph the lines. In the next example, we’ll first re-write the equations into slope–intercept form.

Exercise  5.1.10

Solve the system by graphing:  {3x+y=−12x+y=0

Answer

Exercise  5.1.11

Solve each system by graphing:  {−x+y=12x+y=10

Answer

Exercise  5.1.12

Solve each system by graphing:  {2x+y=6x+y=1

Answer

Usually when equations are given in standard form, the most convenient way to graph them is by using the intercepts. We’ll do this in Exercise  5.1.13 .

Exercise  5.1.13

Sopt form.y=12x−3m=12,b=−3{y=12x−3x−2y=4 If we solve the second equation for y, we get x−2y=4x−2y=−x+4y=12x−2m=12,b=−2

The two lines have the same slope but different y-intercepts. They are parallel lines.

Figure  5.1.3  shows how to determine the number of solutions of a linear system by looking at the slopes and intercepts.

 The value of the simplified expression is 8√3

 Simplification is a process of reducing terms to expressions, which do not generate changes or values.

 Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.

 As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.

    Since there are no denominators, we will only decompose the square root into factors for simplicity

2(2√3) - 4(3√3)

4√3 - 12√3

8√3

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After simplifying 2√12 -4√27 the answer will be -8√3.

For simplicity, we should basically convert the square root into its factors.

Now we know that the prime factorization of 12 is, 12 =1×2×2×3.

and for 27 it is 27=3×3×3.

Now 2√12 =2[tex]\sqrt{2^2.3}[/tex]=4√3.

And, 4√27 = 4[tex]\sqrt{3^2.3}[/tex]=12√3.

∴2√12 - 4√27

=4√3 - 12√3

=-8√3 .

∴2√12 - 4√27 =-8√3 .

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Answer: 10^-5 = 1/10^5

Step-by-step explanation: Every time you see a negative exponent, it would be 1/10^ (exponent number)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{10^{-5}}\\\\\mathsf{= \dfrac{1}{10\times10\times10\times10\times10}}\\\\\mathsf{= \dfrac{1}{100\times100\times10}}\\\\\mathsf{= \dfrac{1}{10,000\times10}}\\\\\mathsf{= \dfrac{1}{100,000}}\\\\\mathsf{= \dfrac{1}{10^5}}[/tex]

[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{\dfrac{1}{10^5}}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The simplified form of the real root  4√810,000 is 3600.

To simplify simply means to make something easier. In mathematics, simplifying an expression, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

By considering the given root

4√810,000

=4x 900

=3600

Making something simpler means making it less complicated or cluttered. When you explain a complex mathematical concept to a child in terms they can easily understand, you are simplifying. When you eliminate many of the activities that were keeping you busy and stressed out, you have simplified.

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[Mathematical Problem]

[tex]9.14[/tex] ÷ [tex]0.04[/tex]

Solution:

[tex]228.5[/tex]

Hope this helps! Thanks and good luck!

Answer:

y = 60x

slope: 6 0 probably

Step-by-step explanation:

Dunnno

Answer:

y = 60x

slope: 6 0

The correlation coefficient (r) is 0.9168.

The correlation coefficient can be improved by ignoring the bill for the month of July.

The 4th data point on the graph which indicates the month of July is the farthest away from the regression line in comparison to other points, and should not be included in the correlation coefficient improvement calculations for the electricity bill.

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Answer:

M=0.00671

Step-by-step explanation:

[tex] \sqrt{m} = 0.04[/tex]

[tex] \sqrt{m {}^{2} } = \sqrt{0.04} [/tex]

[tex]m = 0.0067082039[/tex]

would suggest rounding off

The temperature that water is increasing per minute is 2 degrees.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the digit above the line and the denominator is the number below the line. An example of a fraction is 3/7.

The first step is to determine what 2/5 of a minute is equivalent to in seconds.

1 minute = 60 seconds

2/5 x 60 = 24 seconds

The formula that can be used to determine the temperature that water is increasing per minute is :

Temperature increase per minute = (degree it rises to 2/5 of a minute x seconds in a minute) / seconds in 2/4 of a minute

(4/5 x 60) / 24 = 2 degrees

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The exponential form of the function 5 = log₂ₓ₊₁(a₊b) is (2x ₊ 1)⁵ = (a₊b).

Given the function is:5 =  log₂ₓ₊₁ (a₊b)

we are asked to determine the exponential form of the above function.

The exponential form is an easier way to represent repeated multiplication involving exponents and bases.

It is easy to quickly convert an exponentially written expression into a logarithm using the following formula.

here we have the form loge b  =a5 =  log₂ₓ₊₁(a₊b)

then, e = 2 , a = 5 and

b = (a₊b)5 =  log₂ₓ₊₁(a₊b)

therefore, exponential form is:

(2x ₊ 1)⁵ = (a₊b).

hence we get the required exponential form as (2x ₊ 1)⁵ = (a₊b).

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Answer:

Step-by-step explanation:

8 more= +8

twice a number = 2x
difference between the number and 5=

2x+8=4x(5-x)
2x+8=9x-x
2x+8=8x
8=8x-2x
8=6x
x=6/8
x=3/4

Answer:

19=

2:3=

Step-by-step explanation:

Im not good at explaining things

Answer:

2/3

Step-by-step explanation:

Let's simplify the value,

→ 14/21

→ (14 ÷ 7)/(21 ÷ 7)

→ 2/3

Thus, the value is 2/3.

Answer:

The elevator is two floors below the ground level. The integer to represent this is -2.

Step-by-step explanation:

Based on these values, the interval  that likely to contains the true mean number of pizzas eaten in the previous year by the population is :5.1-7.7

What does a margin of error mean?

The margin of error of 1.3 means that the interval that contains the true mean of the people sampled is the mean plus or minus the margin of error, in other words, the mean of 6.4 could either be greater by 1.3 or less by 1.3

interval containing the true mean number=mean± marginal of error

upper limit of the mean interval=6.4+1.3

upper limit of the mean interval=7.7

lower limit of the mean interval=6.4-1.3

lower limit of the mean interval=5.1

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Answer:

Step-by-step explanation:

Its not that hard.. just use your brain or wait for someone else.

keeping in mind that a line with an undefined slope is always a vertical line, check the picture below.

now, we could use those two points from that line and check its slope

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{6}}} \implies \cfrac{4 +2}{0}\implies \cfrac{6}{0}\implies und efined[/tex]