Describe the difference between direct variation and inverse variation.

The  swimmer will swim 15.23 cm.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, the Pythagoras equation can be used to any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.

Given:

Perpendicular = 14 m

Base = 6 m

Using Pythagoras theorem

H²= P² + B²

H² = 14² + 6²

H² = 196 +36

H² = 232

H= 15.23 cm

Hence, the swimmer will swim 15.23 cm.

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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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Two angles have sum as 180° called supplementary angle so the measure of angle C m∠C will be 68.68°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

Given that,

Angle A and angle B are supplementary

Since the supplementary angle has a sum of 180 degrees.

So,

m∠A + m∠B = 180°

16x - 7 + 21x + 2 = 180

16x + 21x + 7 - 2 = 180

37x + 5 = 180

37x = 175

x = 4.78

So,

m∠A = 16(4.78) - 7 = 68.68°

Since m∠C = m∠A

So,

m∠C = 68.68°

Hence"The measure of angle C m∠C will be 68.68° ".

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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.

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 function definition is an arithmetic sequence and the value of the function f(6) is -12

The function definition is given as

f(1) = 8

f(n) = f(n + 1) + 4

Rewrite the above function as

f(n + 1) = f(n) - 4

Set n = 1

So, we have

f(1 + 1) = f(1) - 4

This gives

f(2) = f(1) - 4

So, we have

f(2) = 8 - 4

Evaluate

f(2) = 4

Set n = 2

So, we have

f(2 + 1) = f(2) - 4

This gives

f(3) = f(2) - 4

So, we have

f(3) = 4 - 4

Evaluate

f(3) = 0

Set n = 3

So, we have

f(3 + 1) = f(3) - 4

This gives

f(4) = f(3) - 4

So, we have

f(4) = 0 - 4

Evaluate

f(4) = -4

Set n = 4

So, we have

f(4 + 1) = f(4) - 4

This gives

f(5) = f(4) - 4

So, we have

f(5) = -4 - 4

Evaluate

f(5) = -8

Set n = 5

So, we have

f(5 + 1) = f(5) - 4

This gives

f(6) = f(5) - 4

So, we have

f(6) = -8 - 4

Evaluate

f(6) = -12

Hence, the value of the function f(6) is -12

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Answer:

Step-by-step explanation:

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

Answer:

This is the graph on a number line.

Hope it helps.

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:

12.5

Step-by-step explanation:

To round to one decimal place you have to round the number to its "tenths". When you are rounding, any number which is 5 or above is rounded to the tenth above or in this situation 6 making it 12.5. But any number below 5 is going to be rounded to the tenth below so if the number was 12.44172 then the answer would 12.4. GL and mb if i messed up.

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:

y = 60x

slope: 6 0 probably

Step-by-step explanation:

Dunnno

Answer:

y = 60x

slope: 6 0

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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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]

Answer:

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

Step-by-step explanation:

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: mean: 32.375 median: 30 mode: 30 range: 39

Step-by-step explanation:

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

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: 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]

Answer:

19=

2:3=

Step-by-step explanation:

Im not good at explaining things

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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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.

[Mathematical Problem]

[tex]9.14[/tex] ÷ [tex]0.04[/tex]

Solution:

[tex]228.5[/tex]

Hope this helps! Thanks and good luck!

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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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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 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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