What is the constant of proportionality representing on this graph

The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K

Step 1: As we know that Unit Rate

Step 2: Notice that the in graph K line passes through the point (1,3)

Step 3: (1,3)

It means the value of function is 3 when x= 1

Step 4: So the unit rate of graph K is, 3/1

Step 5: Simplify the expression.

3/1 = 3

Step 6: Similarly we can see that the graph P have the point (2, 1)

Step 7: So the unit rate of graph P will be 1/2

Step 8: Simplify the expression.

1/2 = 0.5

Step 9: The graph F have point (1, 1) so it have unit rate of 1/1

Step 10: Simplify the expression.

1/1 = 1

Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5

Step 12: Putting them in least to greater order as,

0.5, 1, 3

It follows that;

graph P, graph F, graph K

Therefore, the required answer is,

Unit rate of graph K = 3

Unit rate of graph P = 0.5

Unit rate of graph F = 1

And the order from lower to greater is, Graph P, graph F, graph K

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Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5

The given lines L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t and L2 ⇒ x = 3+8s, y = -6s, z = 7+2s  are parallel lines .

In the question ,

it is given that ,

the two lines are :

L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t

L2 ⇒ x = 3+8s, y = -6s, z = 7+2s

If the lines are intersecting then :

5 - 12t = 3 + 8s

8s + 12t = 2

4s + 6t = 1 ;   .....equation(1)

and 3 + 9t = -6s

3t + 2s + 1 = 0

multiplying both sides by 2 ,

we get ,

6t + 4s + 2 = 0  ....equation(2)

Solving equation(1) and equation(2) , we get

3 ≠ 0 .

So , the lines are not intersecting .

For lines to be parallel , the cross product of their directions must be 0 .

So , \(\left|\begin{array}{ccc}i&j&k\\-12&9&-3\\8&-6&2\end{array}\right|\)

On simplifying further ,

we get ,

⇒ 0i - 0j + 0k

= 0

So , the cross product is 0 ,  lines will be parallel .

Therefore , the lines L1 and L2 are parallel .

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Jenny's Average swimming speed is 1.5 km/h.

Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.

We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.

Thus, the distance she swam is S * 1 = S km.

Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.

Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.

Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.

She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.

The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.

Therefore, we can write the equation:

S + 8S + 28S = 55.5.

Simplifying the equation, we get:

37S = 55.5.

To solve for S, we divide both sides of the equation by 37:

S = 55.5 / 37 = 1.5.

Thus, Jenny's average swimming speed is 1.5 km/h.

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Answer:

The answer is 7400000000!

Step-by-step explanation:

The set containing all the colors of the marbles is given as follows:

{blue, yellow, purple, green, pink}.

A set of elements is composed by elements that respect a given characteristic, or are present in an experiment.

In this problem, we need to find the colors present in each marble, which are given as follows:

Then we have to list all these colors in a set, which are opened and closed by the brackets {}.

The color blue appears in both sets, however, it will appear only once in the set of the colors, as the elements are not repeated.

Thus, the set containing all the colors of the marbles is given by the set presented as follows:

{blue, yellow, purple, green, pink}.

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Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Answer:

An answer is a thing said, written, or done to deal with or as a reaction to a question, statement, or situation.

Answer:

f(-1)=6×(-1)^-4=6/(-1)^4=6/1=6

Answer:

C. Yes, no two ordered pairs in this list has a repeat of the domain element.

Step-by-step explanation:

An equation that produces a set of ordered pairs defines a function, but it needs to be a proper function!

A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate. Which means that answer C is correct.

Answer:

C. Yes, no two ordered pairs in this list has a repeat of the domain element.

Step-by-step explanation:

ODY 2022

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Answer:

Hope you can understand my handwriting though

The set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

The side length of the triangle is shown in the option:

As we know,

Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

Using Pythagoras' theorem:

From option(D):

3, 4 and 5

(3)² + (4)² = 5²

9 + 16 = 25 (True)

Thus, the set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.

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Answer:

The margin of error is  \(E = 6.9 \)

The 95% confidence interval is  \( 26.5  <  \mu < 40.3 \)  

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  31

     The mean is  \(\mu = 33.4 \ ng/ml\)

      The standard deviation is  \(\sigma = 19.6 \ ng/ml\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>  \(E = 1.96  *  \frac{19.6  }{\sqrt{31 } }\)

=>  \(E = 6.9 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=> \( 33.4  - 6.9 <  \mu < 33.4  +  6.9 \)

=> \( 26.5  <  \mu < 40.3 \)  

Cesar initially had $2,500 in savings.

Let's solve the problem step by step.

Let's assume that the initial amount of money Cesar had is represented by "x" dollars.

According to the problem, Cesar spent 15% of his savings on a cellphone, which means he has 85% of his initial savings left. We can represent this mathematically as:

0.85x = 2,125

To find the initial amount of money Cesar had, we need to solve for x. We can do this by dividing both sides of the equation by 0.85:

x = 2,125 / 0.85

Calculating this value:

x = 2,500

Cesar initially had $2,500 in savings.

Please note that the calculations are done assuming a straightforward interpretation of the problem. If there are additional factors or context that could affect the interpretation, it's important to consider them in order to arrive at an accurate answer.

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Answer:

Step-by-step explanation:

B; So this is a transformation problem from the parent function of f(x)=|x| so the function is is moved 3 units down giving it the -3 at the end and is moved to the right 7 units so it would be x-7

Answer:

the (x, y) pair solution to the system is: (-2, -4)

That is x = -2 and y = -4

Step-by-step explanation:

I presume there is a variable y missing in the first equation, and in fact the system looks like:

(1/2) x + (3/2) y = - 7

- 3 x + 2 y = -2

In such case, we proceed to multiply both sides of tye first equation by 6

6 (1/2) x + 6 (3/2) y = - 42

3 x + 9 y = - 42  and we add term by term this equation to the second one, so as to cancel out the term in x:

3 x + 9 y = - 42

- 3 x + 2 y = -2

_____________

11 y = - 44

divide both sides by 11 to isolate y

y = -44 / 11 = -4

Then with the value y = -4, now we replace it in the second equation to solve for x:

- 3 x + 2 y = - 2

- 3 x + 2 (- 4) = -2

- 3 x - 8 = - 2

add 8 to both sides

- 3 x = 6

divide both sides by (-3) to isolate x

x = 6 / (-3) = - 2

Therefore the (x, y) pair solution to the system is: (-2, -4)

That is x = -2 and y = -4

Answer:

The equation is  

✔ d = 5l

.

As the number of  

✔ laps

increases, the number of  

✔ dollars

also increases.

Step-by-step explanation:

Using the concept of expressing an equation , the required expression is n + 13 = 43

Let the number be : n

The number increased by 13 can be expressed thus :

Equating the expression to the result, we'll have :

Therefore, the required expression, is n + 13 = 43

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The distance from G to the nearest point on the circle is going to be 5.61 cm.

The given figure (image attached below) has the segments GA and GB tangent to a circle at A and B, and AGB is at a 48-degree angle. We have been told that GA = 12 cm. We have to find the distance from G to the nearest point on the circle.

For this, first what we need to do is draw radii to A and B. Next draw OG which bisects the 48-angle G into two 24-angles. Let P be the point where OG intersects the circle. This becomes the distance from G to the nearest point on the circle which we need to find (image attached below).

In the right triangle AOG, radius AO is the side opposite angle AGO-

= Tangent = Perpendicular / Base

= tan(24) = r / 12

= r = 12tan(24)            (i)

For OG -

= cos(24) = Base / Hypotenuse = 12 / OG

= OG = 12cos(24)        (ii)

Now, we subtract (i) and (ii) -

= 12tan(24) - 12cos(24)    

= 5.61 cm

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Answer

sixty nine

Step-by-step explanation:

four twenty

Answer:

Step-by-step explanation:

3x - 2 = 2x + 8

x - 2 = 8

x = 10

Answer:

12

Step-by-step explanation:

Arranging in ascending order -> 9, 10, 12, 12, 13, 15, 16

n = 7

Median = value of ((n + 1) / 2) th term

             = value of (7+1) / 2 th term

             = value of 4 th term

             = 12

Hope it helps :)

The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

Step-by-step explanation:

x=11

Answer:

11

Step-by-step explanation:

Move 14 to the right side

7x = 4x + 33

Move 4x to the left side

3x = 33

Divide both sides by 3

\(\frac{3x}{3} =\frac{33}{3}\)

so your answer would be  11

Answer: 5(1-x) over x

Step-by-step explanation: Combine the rational expressions using the least common denominator (LCD).

Finn would run 18 miles after 6 track practices.

We have,

Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.

Unit rate: 6 miles / 2 practices = 3 miles per practice

To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.

Total miles: 3 miles/practice * 6 practices = 18 miles

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Answer:

c.p<-1

Step-by-step explanation:

im good at math