Solve for x:

5(1 – x) = 20

x = __

Step-by-step explanation:

[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } [/tex]

[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } [/tex]

[tex] = \frac{ 2( \sqrt{2} - \sqrt{3} )( \sqrt{2} - \sqrt{3} )}{ { \sqrt{2} }^{2} - { \sqrt{3} }^{2} }[/tex]

[tex] = \frac{2(2 - \sqrt{6} - \sqrt{6} - 3) }{2 - 3} [/tex]

[tex] = \frac{2( - 1 - 2 \sqrt{6} )}{ - 1} [/tex]

[tex] = \frac{ - 2(1 + 2 \sqrt{6} )}{ - 1} [/tex]

[tex] = 2(1 + 2 \sqrt{6} )[/tex]

[tex] = 2 + 4 \sqrt{6} [/tex]

We conclude that after 50 days, there will be 67 lily pads.

We know that the number increases by 25% every 10 days.

In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.

We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:

N = 22*(1 + 25%/100)*...*(1 + 25%/100%)

( the factor (1 + 25%/100%) appears five times)

So we can rewrite:

N = 22*(1 + 25%/100%)⁵

N = 22*(1 + 0.25)⁵ = 67.1

Which can be rounded to the nearest whole number, which is 67.

So we conclude that after 50 days, there will be 67 lily pads.

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Using the normal distribution, we have that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the parameters are given as follows:

[tex]\mu = 57, \sigma = 22, n = 17, s = \frac{22}{\sqrt{17}} = 5.3358[/tex]

Hence:

The probabilities are the p-value of Z when X = 58 subtracted by the p-value of Z when X = 55, hence, for a single movie:

X = 58:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{58 - 57}{22}[/tex]

Z = 0.05.

Z = 0.05 has a p-value of 0.5199.

X = 55:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 57}{22}[/tex]

Z = -0.1.

Z = -0.1 has a p-value of 0.4602.

0.5199 - 0.4602 = 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.

For the sample of 17 movies, we have that:

X = 58:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{58 - 57}{5.3358}[/tex]

Z = 0.19.

Z = 0.19 has a p-value of 0.5753.

X = 55:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{55 - 57}{5.3358}[/tex]

Z = -0.38.

Z = -0.38 has a p-value of 0.3520.

0.5753 - 0.3520 = 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.

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Answer:

  m∠K = 37° and n = 31

Step-by-step explanation:

A lot of math is about matching patterns. Here, the two patterns we want to match are different versions of the same Law of Cosines relation:

Comparing the two equations, we note these correspondences:

Comparing these values to the given information, we see that ...

Abby apparently knew that ∠K = 37° and n = 31.

__

Additional comment

Side and angle naming for the Law of Sines and the Law of Cosines are as follows. The vertices of the triangle are labeled with single upper-case letters. The side opposite is labeled with the same lower-case letter, or with the two vertices at either end.

Vertex and angle K are opposite side k, also called side NM in this triangle.

"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is

D= 510 km. Option B. This is further explained below.

Generally, In the study of astrodynamics, an ellipse of the satellite is often referred to as a Kepler Orbit

The function of the elliptical orbit is

[tex]\frac{(x-h)^2}{a^2}+\frac{(x-k)^2}{b^2}=1[/tex]

compared to

[tex]\frac{(x^2)^2}{47334400}+\frac{(y^2)^2}{43956900}=1[/tex]

Hence

a = √(47,334,400 km²)

a= 6,880 km.

In conclusion, The distance of the satellite above the Earth's surface.

D = a - r

D= 6,880 km - 6,370 km

D= 510 km

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"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is D= 510 km. Option B.

An elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0.

The function of the elliptical orbit is

[tex]\frac{{(x-h)}^2}{a^2}+ \frac{{(y-k)}^2}{b^2} = 1[/tex]

compared to

  √([tex]\frac{({x^2)}^2}{47,334,400} + \frac{({y^2)}^2}{43956900} = 1[/tex]

a = √(47,334,400 km²)

a= 6,880 km.

Now,

D = a - r

D= 6,880 km - 6,370 km

D= 510 km

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Answer:

7,500

Step-by-step explanation:

When you round you automatically round up unless told otherwise
so find the hundredth, which is 485 and you round that to 500
then put the 7 back → 7,500

The range of the function on the graph is C. all the real numbers greater than or equal to –3 .

We can see by the graph maximum value of y of function is -3 and the graph continues to extend upward .

So, the range contain all the real numbers greater than or equal to –3 .

Therefore, the range contain all the real numbers greater than or equal to –3 .

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Answer:

No

Step-by-step explanation:

There are multiple coordinates with the same x coordinate

Step-by-step explanation:

hope you can understand

The height of the triangle will be;

⇒ 58.5 mm

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The base of the triangle = 4.7 mm

The area of triangle = 137.475 mm²

Now,

We know that;

⇒ The area of triangle = 1/2 × Base × Height

Substitute all the values, we get;

⇒ 137.475 = 1/2 × 4.7 × h

⇒ 137.475 = 2.35 × h

⇒ h = 137.475 / 2.35

⇒ h = 58.5 mm

Thus, The height of the triangle = 58.5 mm

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Answer:

542

Step-by-step explanation:

So X is the number of finals graded by teacher last year

she graded 83 more finals than the last year

and the total number of finals she graded this year is 625 so we have an equation

X + 83 = 625

and as you solve it for X

X = 625-83

x = 542

Answer:

542,

Step-by-step explanation:

You could solve these types of problems with inverse operations, so if you subtract 83 from 625, you'd get 542.

That's because there's this thing called polite people

Answer:

Because she is nice unlike me

Step-by-step explanation:

give me brainiest pls

see? I am not nice :) But seriously can I get brainliest?

The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value  x = 3 , y = 8 .

An Equation is a mathematical statement which relates two algebraic expression with an equal sign in between.

The equations given in the question is

y = 2ˣ

This is an exponential function

-7x +3y = 3

This is a linear function

The equations have been plotted and the solution to the non linear system of equation has been determined

The point at which the graphs intersect is the solution to the system of non -linear equations.

(0,1) and (3,8)

x = 0 , y = 1 ; x = 3 , y = 8

The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value  x = 3 , y = 8 .

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Answer:

6

Step-by-step explanation:

The requried number of passes to reach the maximum is given as 10 passes.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,

We have 5 coins in your purse,
We Gain 1.5x the number of coins in your purse every time you pass the start. The maximum number of coins is 300.

According to the quesiton,
5 . 1.5ˣ = 300

Where x is the number of passes,
1.5ˣ = 60
x ≈ 10

Thus, the requried number of passes to reach the maximum is given as 10 passes.

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Answer:

take 1/2 multiply by sin 91°×2×8

Answer:

3x^2 + 3xz

Step-by-step explanation:

Under the assumption that I need to distribute,

(x + z)(x + 2x)

(x + 2x) is (3x)

3x(x + z) becomes 3x*x and 3x*z

3x*x = 3x^2

3x*z = 3xz

combine, 3x^2 + 3xz

AND WELCOME TO BRAINLY!

LET ME KNOW IF YOU NEED ANY MORE HELP :)

Using translation concepts, the equation for the graph is given as follows:

b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have a cosine function(zero at pi/2, this is zero at the origin), shifted pi/2 units to the right and 1 unit up(as the standard amplitude is between -1 and 1, here is between 0 and 2).

Hence the rule is given by:

b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].

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Answer: -15625

Step-by-step explanation:

The explicit formula for the sequence is

[tex]a_{n}=-1(5)^{n-1}\\\\\implies a_{7}=-1(5)^{7-1}=\boxed{-15625}[/tex]

The initial value of the sequence is 1

From the graph, we have the following ordered pairs

(x, y) = (1, 1), (2, 4) and (3, 8)

Remove the x values

y = 1, 4, 8

The first value in the above sequence is 1

Hence, the initial value of the sequence is 1

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Answer:

y=3x+8

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

you find the slope by using this formula:

then we figure out it is 3

then graph to find the y-intercept which is 8

Answer:

y = 3x + 8

Step-by-step explanation:

Below is the image for the formula of the slope.

1. Subtract y values:
17 - 5 - 12
2. Subtract x values:
3 - (-1) = 4
3. Divide y/x
12 / 4 = 3
Therefore, the slope is 3.

Next, you need to find the y-intercept. This is our equation so far:
y = 3x + b
We can substitute any of the points given to us from the problem. I will use the first point: (-1, 5).

When substituting, you get:
5 = 3 ( -1 ) + b
5 = -3 + b
b = 8

Therefore, the equation is y = 3x + 8

Answer:

See below.

Step-by-step explanation:

Problem:

Solve y=2x;y=−x+2

Steps:

I will solve your system by substitution.

y=2x;y=−x+2

Step: Solve y=2 x for y:

Step: Substitute 2x for y in y=−x+2:

y=−x+2

2x=−x+2

2x+x=−x+2+x(Add x to both sides)

3x=2

3x/3 = 2/3 (Divide both sides by 3)

x=2/3

Step: Substitute 2/3 for x in y = 2x

y=2x

y = 2(2/3)

y = 4/3 (Simplify both sides of the equation)

Answer:

x = 2/3 and y = 4/3

Answer:

only one at x = 2/3 y = 1 1/3

Step-by-step explanation:

At the same solution point Y = Y so

2x = -x + 2

3x = 2

x = 2/3

y intercept is 2, which shows while changing the jobs employees bring two customers.

A linear equation is in the form, y = mx + b where m is the rate of change (slope) and b is the y intercept (initial value of y).

The complete question is:

The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.

Time Employed (Month)

If the equation for the line of best fit is y = 4.5x + 2, which of the following can be used to interpret the y-intercept in context?

Employee training takes 2 months.

Employee training takes 4.5 months.

Employees are likely to bring 2 customers with them when changing jobs.

Employees are likely to bring 4.5 customers with them when changing jobs.

As, linear equation is

y = mx + b

Let y be the number of customers and x be the length of time.

Then, y = 4.5x + 2

As, y intercept is 2, which shows while changing the jobs employees bring two customers.

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Answer:

7.07106781187

Using a linear function, we have that:

The percentage will be 47% during the year 2001.

The predicted percentage in 2005 is of 44.97%.

Given that, the percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995.

Linear functions are those whose graph is a straight line. The standard form of the linear function is f(x)=y= mx + b. A linear function has one independent variable and one dependent variable.

Where, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0 and can also be interpreted as the initial value of the function.

The percentage in 1980 is considered as the initial amount, so b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by: m = (50.5 - 58.8)/15 = 0.5533.

Thus, the percentage in t years after 1980 is P(t) = 58.8 - 0.5533t.

Now, t + 1980, for which P(t) = 47.

So, P(t) = 58.8 - 0.5533t

47 = 58.8 - 0.5533t.

0.5533t = 11.8.

t = 11.8/0.5533

t = 21.3.

1980 + 21 = 2001, so the percentage will be 47% during the year 2001.

Now, 2005 is 25 years after 1980, so the percentage is P(25), given as follows: P(25) = 58.8 - 0.5533x25 = 44.97%.

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The transformation that can be used to show that ABCDE and its image are congruent is a 90° counterclockwise.

It should be noted that when we rotate a point through 90° counterclockwise, the mapping will be: (x, y) to (-y, x).

In this situation, it van be deduced that the x and y coordinates swapped positions. This illustrates a 90° counterclockwise rotation about the origin..

In this situation, since the rotation is a rigid motion, the two shapes are congruent.

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Answer:

212

Step-by-step explanation:

Simple addition and subtraction is to be used here.

5, 3 = 28

5-3 = 2 , 5+3 = 8

9 , 1 = 810

9-1 = 8 , 9+1 = 10

8 , 7 = 115

8-7= 1 , 8+7 = 15

6 , 2 = 48

6-2 = 4 , 6+2 = 8

7 , 5 = 212

7-5 = 2 , 7+5 = 12

Answer:

212

Step-by-step explanation:

Rule

5 - 3 = 2

5 + 3 = 8

Therefore: 28

9 - 1 = 8

9 + 1 = 10

Therefore: 810

8 - 7 = 1

8 + 7 = 15

Therefore: 115

6 - 2 = 4

6 + 2 = 8

Therefore: 48

7 - 5 = 2

7 + 5 = 12

Therefore: 212