Find the value of x.

Answer:

m=10

n=12

Step-by-step explanation:

[tex]\frac{1}{5} m-\frac{1}{6} n=0\\m=\frac{5}{6} n\\5 \times \frac{5}{6} n-4n=2\\25n-24n=12\\n=12\\m=\frac{5}{6} \times 12=10[/tex]

Answer:

(x, y) = ( 5, 6)

(x, y) = ( - 1, 0)

Step-by-step explanation:

[tex] \begin{cases} y + x^2 - 5x = 6\\\\ y - x = 1\implies y = x + 1\end{cases} [/tex]

Plug [tex] y = x +1 [/tex] in the equation [tex] y + x^2 - 5x = 6[/tex] we find:

[tex] x + 1 + x^2 - 5x = 6[/tex]

[tex] x^2 - 4x - 5=0[/tex]

[tex] x^2 - 5x +x- 5=0[/tex]

[tex] x(x - 5) +1(x- 5)=0[/tex]

[tex] (x - 5) (x+1)=0[/tex]

[tex] (x - 5) =0, \: (x+1)=0[/tex]

[tex] x =5, \: x=-1[/tex]

[tex] When \:x =5 \implies y =5+1=6 [/tex]

(x, y) = ( 5, 6)

[tex] When \:x =-1 \implies y =-1+1=0 [/tex]

(x, y) = ( - 1, 0)

Options:

A. [1,10]        B. [10,20]      C. [15,25]     D. [1,30]

Answer:

A. [1,10]

Step-by-step explanation:

Given

[tex]N(t) = 100e^{-0.023t}[/tex]

Required

Interval with the fastest rate of decay

The rate of change over [a,b] is calculated as:

[tex]Rate = \frac{N(b) - N(a)}{b - a}[/tex]

So, we have:

A. [1,10]        

[tex]Rate = \frac{N(10)-N(1)}{10 - 1}[/tex]

[tex]Rate = \frac{N(10)-N(1)}{9}[/tex]

Calculate N(10) and N(1)

[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]

[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]

So:

[tex]Rate = \frac{79.45-97.73}{9} = \frac{-18.28}{9} = -2.03[/tex]

B. [10,20]      

[tex]Rate = \frac{N(20)-N(10)}{20 - 10}[/tex]

[tex]Rate = \frac{N(20)-N(10)}{10}[/tex]

Calculate N(20) and N(10)

[tex]N(20) = 100e^{-0.023*20} = 100e^{-0.46} = 63.13[/tex]

[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]

So:

[tex]Rate = \frac{63.13 - 79.45}{10} = \frac{-16.32}{10} = -1.632[/tex]

C. [15,25]    

[tex]Rate = \frac{N(25)-N(15)}{25 - 15}[/tex]

[tex]Rate = \frac{N(25)-N(15)}{20}[/tex]

Calculate N(25) and N(15)

[tex]N(25) = 100e^{-0.023*25} = 100e^{-0.575} = 56.27[/tex]

[tex]N(15) = 100e^{-0.023*15} = 100e^{-0.345} = 70.82[/tex]

So:

[tex]Rate = \frac{56.27 - 70.82}{10} = \frac{-14.55}{10} = -1.455[/tex]

D. [1,30]

[tex]Rate = \frac{N(30)-N(1)}{30 - 1}[/tex]

[tex]Rate = \frac{N(30)-N(1)}{29}[/tex]

Calculate N(30) and N(1)

[tex]N(30) = 100e^{-0.023*30} = 100e^{-0.69} = 50.16[/tex]

[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]

So:

[tex]Rate = \frac{50.16 - 97.73}{29} = \frac{-47.57}{29} = -1.64[/tex]

By comparing the values of the calculated rates,

-2.03 is the smallest, in other words; the fastest rate

Hence, the interval [1,10] has the fastest rate of decay

The required average rate of change is the fastest on [tex][1,10][/tex].

The formula for the average rate of change on the interval [tex][a,b][/tex]  is,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{b-a}[/tex]

Now, applying the given function into the above function is,

Now, [tex]a=1,b=10[/tex] then,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{10-1} =-2.03[/tex]

Now, [tex]a=10,b=20[/tex] then,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{20-10} =-1.6325[/tex]

Now, [tex]a=15,b=25[/tex] then,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{25-15} =-1.455[/tex]

Now, [tex]a=1,b=30[/tex] then,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{30-1} =-1.64[/tex]

So the average rate of change is fastest on [tex][1,10][/tex]

Learn more about the topic of the average rate of change:

https://brainly.com/question/20884505

Answer:

146°.................plz mark me brainliest

Answer:

24 x 25/100 = 6

of means multiplication so you are multiplying the percent to the regular price. Always consider cent as a hundred and a percent out of 100 in fractions.

Answer:

18 dollars

Step-by-step explanation:

half of 24 is 12 and half of that is 6 so 24-6=18 :)

Answer:

[tex]y \: intercept : when \: x = 0 \\ y = (3 \times 0) - 1 = - 1 \\ = > (0, - 1) \\ x \: intercept : when \: y = 0 \\ 0 = 3x - 1 \\ x = \frac{1}{3} \\ = > ( \frac{1}{3} ,0) \\ intercepts : (0, - 1) \: and \: ( \frac{1}{3} ,0)[/tex]

Answer:

400 grams

Step-by-step explanation:

If the equation is density = mass / volume, fill it out to find mass

10 = x / 40

400 = x

x = 400 g

Answer:

D)2^3 x 3^2

Step-by-step explanation:

2 x 2 x 2 = 8

3 x 3 = 9

8 x 9 = 72

Given:

The graph of a function and a blue line.

To find:

The correct name for the blue line.

Solution:

Domain: It is the set of inputs. These are the x-values for which the function is defined.

Range: It is the set of outputs. These are the y-values for the function.

Asymptote: The function approaches to a line as x approaches to -∞ or ∞ but not intersect the line, then the line is known as asymptote.

y-intercept: It is the intersection point of the function and the y-axis.

From the given graph it is clear that the function approaches to the blue line as x approaches to -∞ but not intersect the blue line.

So, the blue line is an asymptote of the function.

Look at the graph shown below the blue line represents an asymptote of the graph.

Answer:

110 minutes or 1 hour 50 minutes

Step-by-step explanation:

44 divided into 4 since we want to find out how much time it takes to run 1 mile, so 44 divided into 4 is 11

then simply multiply 11 with 10 and the answer is 110

: )

Answer:

direct answer 20

Step-by-step explanation:

Answer:

I believe it's the first option.

9514 1404 393

Answer:

  x = 20

Step-by-step explanation:

The external angle at V is half the difference of the subtended arcs:

  (65° -25°)/2 = x° = 40°/2

  x = 20

Answer:

The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

i also provided with a chart i dont know if it will help

Answer:

5.9

Step-by-step explanation:

Answer:

y=5/3x-8

Slope = 5/3

Y int = (0,-8) or y=-8

Step-by-step explanation:

Answer: 5/3x - 8

Step-by-step explanation:

-3y=24-5x

/3

5x/3 -8

5/3x - 8

Answer:

La segunda montaña más alta del mundo tiene 8611 metros.

Step-by-step explanation:

La montaña más alta del mundo es Everest cuya altura es de 8.848m.

La altura de la segunda montaña más alta es de 2hm 3dam y 7m menos. Para calcular la altura que tiene la segunda montaña más alta del mundo, debes realizar primero un cambio de unidades sabiendo que

Entonces podes aplicar las siguientes reglas de tres simple:

Si 1 hm equivale a 100 m, 2 hm equivale a ¿Cuántos metros?

[tex]metros=\frac{2 hm*100 m}{1 hm}[/tex]

metros= 200

Si 1 dam equivale a 10 m, 3 dam equivale a ¿Cuántos metros?

[tex]metros=\frac{3 dam*10 m}{1 dam}[/tex]

metros=  30

Entonces, la altura de la segunda montaña más alta es de 200 m+30 m+ 7 m menos que el Everest. Esto es, 237 metros menos que la montaña más alta del mundo. Entonces:

8848 metros - 237 metros= 8611 metros

La segunda montaña más alta del mundo tiene 8611 metros.

Answer:

73 feet

Step-by-step explanation:

50 + 23 = 73 feet

Answer:

Step-by-step explanation:

Answer:

y=5 x=-2

Step-by-step explanation:

Answer: [tex]33,007.9\ ft[/tex]

Step-by-step explanation:

Given

The plane is cruising at an altitude of [tex]h=10,200\ ft[/tex]

The angle of depression is [tex]\theta=18^{\circ}[/tex]

Suppose the distance of the plane to the runway is x

from figure

[tex]\Rightarrow \sin 18^{\circ}=\dfrac{h}{x}\\\\\Rightarrow \sin 18^{\circ}=\dfrac{10,200}{x}\\\\\Rightarrow x=33,007.9\ ft[/tex]

Answer:

17.5  

Step-by-step explanation:

180 = 40+ 8x

140 = 8x

17.5  = x

Answer:

17.5 is the correct answer to the question

Step-by-step explanation:

8x+40=180

8x=180-40

8x=140

X=140/8

X=17.5

Answer:

5/8 - 2/4 = 1/8

(Hope this helps! Btw, I answered first. Brainliest please! :D)

Answer:

127x10^-3

Step-by-step explanation:

0.127=

[tex]127 \times {10}^{ - 3} [/tex]

we know that

when you want to figure out a tip, you take your total bill and multiply it by the percentage you would like to tip them

so

15%=15/100------> 0.15

$63*0.15=$9.45

the answer is

$9.45

Answer:

wrong

Step-by-step explanation:

Answer:

(y-3) = 2(x-1)

Step-by-step explanation:

Point slope form is

(y-y1) = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

(y-3) = 2(x-1)

Answer:

(x−5)^2+(y+6)^2=9

Step-by-step explanation: