Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

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:

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

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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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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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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

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:

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

The area of Maria’s circle is 18π square units option fourth is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The figure is missing.

Please refer to the attached picture for the figure.

We have given the radius of the circle as 3 units

r = 3 units

Area of circle = πr² = π(3)² = 9π square units

The area of Maria’s circle = 2(9π) = 18π square units

Thus, the area of Maria’s circle is 18π square units option fourth is correct.

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The polynomial function with the given properties is; y = 2(x - 3)³(x + 4)²

Polynomials are defined as algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.

We need to form a polynomial expression with the following properties;

fifth-degree, 3 is a zero of multiplicity 3, −4 is the only other zero and ,the leading coefficient is 3. Thus, the polynomial will be;

y = 2(x - 3)³(x + 4)²

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Answer:

x = 3

Step-by-step explanation:

8/2 = 4

6/2 = 3

x = 3

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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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?

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]

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: -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]

"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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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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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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Answer:

7.07106781187

Answer:

20-2h

Step-by-step explanation:

20 is the original amount. The variable stands for the number of hours. You are TAKING AWAY 2 degrees every hour so you would subtract.

Answer:

No

Step-by-step explanation:

There are multiple coordinates with the same x coordinate

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:

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.

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.

Answer:

B

Step-by-step explanation:

A hexagon has 6 sides. If you divide the perimeter(12) by the number of sides(6), you get the length of one side(2).