Find f(g(x)) for the functions f(x)=5sqrt(x+1)-2 and g(x)=x^2-1

The circle equation in polar coordinates is:

   [tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]

Here we have the circle equation:

[tex](x - 2)^2 + (y + 2)^2 = 8[/tex]

First, we expand it to:

[tex]x^2 - 4x + 4 + y^2 + 4y + 4 = 8[/tex]

Now we can rewrite it as:

[tex]x^2 + y^2 -4x + 4y + 4 + 4 = 8\\\\x^2 + y^2 - 4x + 4y = 0[/tex]

Remember that:

[tex]x^2 + y^2 = r^2\\\\x = r*cos(\theta)\\y = r*sin(\theta)[/tex]

Replacing that, we get:

[tex]x^2 + y^2 - 4x + 4y = 0\\\\r^2 - 4r*cos(\theta) + 4r*sin(\theta) = 0[/tex]

That is the equation in polar form.

Now, because we can discard the solution r = 0, we can divide both sides by r to get:

[tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]

To simplify it.

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Step-by-step explanation:

[tex] = \tan(5\pi) [/tex]

[tex] = \tan(\pi + 4\pi) [/tex]

[tex] = \tan(\pi) [/tex]

[tex] = \tan(180 \degree) [/tex]

[tex] = 0[/tex]

The answer is A.

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:

96

Step-by-step explanation:

divide 42/7

=6

6x16=

96

Answer:

The answer is 96 pounds

Step-by-step explanation:

Multiply 16 with 42 and divide it by 7 and you get the answer 96 pounds

Answer:

3 months

Step-by-step explanation:

The first runner: $110 + $45 = $155 starting out, plus 25x for $25 each month.

The second runner: $50 starting out, plus 60x for $60 each month.

To find out when both runners have the same amount of money, we will set the expressions equal to each other and solve.

155 + 25x = 60x + 50

105 = 35x

x = 3

Brainliest, please :)

Answer:

C.  It is in Quadrant I

D.  It starts at the origin

Step-by-step explanation:

Parent function:  [tex]f(x)=\sqrt{x}[/tex]

Domain: set of all possible input values (x-values)

As the square root of a negative number does not exist in the set of Real Numbers, the domain for the parent function is:

Range: set of all possible output values (y-values)

As the domain of the parent function is x ≥ 0, the range will be:

As the range and domain both begin at zero, the graph of the parent function starts at the origin (0, 0).

Quadrant: a region of the Cartesian plane formed when the x-axis and y-axis intersect each other.

Quadrant I:  (x, y)

Quadrant II:  (-x, y)

Quadrant III: (-x, -y)

Quadrant IV:  (x, -y)

Therefore, as the range and domain of the parent function are positive, the graph is in Quadrant I.

Answer:

circumference: 5.65 m

area: 2.54 m

Step-by-step explanation:

here are some relationships between measurements of a circle:

C  = π d

(Circumference = pi · diameter)

A = π r²

(Area = pi · radius²)

[π / pi is the ratio of a circle's circumference to its diameter. this ratio is actually a constant across all circles, which is where we derive our circumference and area formula from. π ≈ 3.14159]

so, let's work on finding the circumference first.

C  = π d

we know the diameter = 1.8,    and we know that π ≈ 3.14159

so, if we multiply these two numbers together, we will get the circumference

[this equation makes sense if you read my explanation of pi]

1.8 × 3.14159 = 5.654862

We can round this number to 5.65

So, the circumference of our circle = 5.65 m

now, let's find the area

A = π r²

we know that π ≈ 3.14159, but we still haven't found "r"

r, or radius, is the measurement from the center of a circle to any point of the circle. Because the diameter is the measurement from one side of a circle to the opposite side, diameter = twice the radius

this means we can take our diameter, 1.8, and divide it by 2 to find our radius.

1.8 / 2 = 0.9

now, we can solve for area.

π ≈ 3.14159 , r = 0.9

A = π r²

A = π (0.9)²

A = (3.14159) (0.81)

A = 2.5446879

we can round this area to 2.54

so, the area of our circle = 2.54 m

Answer:

83.74

Step-by-step explanation:

First find the amount of the tax

79 * .06

4.74

Add this to the original price

79+4.74

83.74

Answer:

Last choice, [tex]\sqrt{15}[/tex] is irrational and [tex]\sqrt{0.001}[/tex] is rational

Step-by-step explanation:

Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers, ex. 0.4

Irrational Numbers: A type of real number which cannot be represented as a simple fraction (non ending decimal), ex. 0.4161446

[tex]\sqrt{15} = 3.8729[/tex] making it irrational

[tex]\sqrt{0.001} = 1/1000[/tex] making it rational

Hence, the last choice is correct

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Answer:

it is 2 spaces away. a positive number from zero would be +2 and a negative number would be -2

Step-by-step explanation:

Answer:

825

Step-by-step explanation:

hope it helps.good day

Domain: (-∞,∞)

Range: (-∞,-3]

Step-by-step explanation:

A quadratic equation graphs a parabola. Therefore there will be arrows on the bottom of the graph as it will go down forever. The domain (min x-values to max x-values) is

(-∞,∞) because the graph keeps on going down and to the right and left. The range (min y-values to max y-values) is (-∞,-3] because the lowest y-value the graph goes to is -∞ nd the highest y-value is -3.

Answer:

hope it helps.good day

in case you don't understand anywhere feel free to ask

Answer:

Step-by-step explanation:

[tex] \bf {x}^{2} + 5x + 6 = 0[/tex]

Write the equation in factored form.

[tex]\bf (x + 2)(x + 3) = 0[/tex]

Separate equations, and set each factor to zero.

[tex]\bf x + 2 = 0[/tex]

[tex]\bf x + 3 = 0[/tex]

Rearrange and isolate the variable to find the solutions

[tex]\bf x = - 2[/tex]

[tex]\bf x = - 3[/tex]

------------------------------------

Answer:

x=-3           x=-2

Step-by-step explanation:

x^2 +5x+6 =0

We need to factor the equation

What two numbers multiply to 6 and add to 5

3*2 = 6

3+2 =5

(x+3)(x+2)

Using the zero product property

x+3 =0  x+2 =0

x=-3           x=-2

Total area = 104+24 = 128 sq.in ,  Option C is the right answer.

The missing figure is attached with the answer.

The space occupied by a two dimensional figure is called Area.

The figure given in the question can be divided into two figure

A rectangle of 8 * 13 inch

and a triangle of 8 * 6 inch

The area of a rectangle is given by

Length * Breadth

8 * 13

= 104 sq.inch

The area of the triangle is given by

(1/2) * base * height

= (1/2) * 8 * 6

= 24 sq.inch

Total area = 104+24 = 128 sq.in

Therefore Option C is the right answer.

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Answer:

the answer is D)

a multiple of thirty

Data set two has the greater variability option (2) Data set two has the greater variability is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Two sets of scores have the same mean, but different standard deviations.

σ₁ and σ₂   (σ₂ > σ₁)

Coefficient of variation  = [SD/(mean)]×100

[tex]\rm CV = \dfrac{\sigma }{|x|}\times100[/tex]

σ₂ > σ₁

Divide by |x| on both sides

σ₂/|x| > σ₁/|x|

[tex]\rm \dfrac{\sigma }{|x_1|}\times100 > \dfrac{\sigma }{|x_2|}\times100[/tex]

(CV)₂ > (CV)₁

Thus, data set two has the greater variability option (2) Data set two has the greater variability is correct.

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Step-by-step explanation:

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Answer:

C

Step-by-step explanation:

C is the correct answer as both triangles have a similar angle of 105⁰ and both side lengths of triangle ABC are being divided by 4 to have the same two side lengths as triangle DEF

The triangles ΔABC and ΔDEF are similar triangles by SAS theorem

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔABC

The measure of side AB = 16

The measure of side AC = 36

And , the measure of ∠ABC = 105°

Let the first triangle be ΔDEF

The measure of side DE = 16

The measure of side DF = 36

And , the measure of ∠DEF = 105°

Now , the ratio of sides of the triangles is given by

AB / DE = AC / DF

4/16 = 9/36

1/4 = 1/4

So , corresponding sides of similar triangles are in the same ratio

And , the measure of angles = 105°

Therefore , by SAS , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Hence , they are similar triangles

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The correct answer is option A which is the number of cars sold for the price range of $4000 to $4999 will be 15.

A histogram is a graph for the representation of the data on the plot of the rectangular boxes. It has the data sets on the horizontal and the vertical axes.

As we can see from the histogram data we will conclude that the price range of $4000 to $4999 is shown by the third block and this third block reaches the height of 15.

Therefore the correct answer is option A which is the number of cars sold in the price range of $4000 to $4999 will be 15.

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multiply the actual length by the scale:

9 x 1/12 = 9/12 = 3/4

Answer: 3/4

"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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We conclude that 515 student tickets were sold, and 58 adult tickets.

Let's define the variables:

We can write the system of equations:

x = 9*y - 7

x*5 + y*8 = 3039

Now we can replace the first equation into the second one:

(9*y - 7)*5 + y*8 = 3039

45y + 8y  - 35 = 3039

53y = 3074

y = 3074/53 = 58

Now we can use:

x = 9y - 7 = 9*58 - 7 = 515

We conclude that 515 student tickets were sold, and 58 adult tickets.

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Answer:

X = 11

Step-by-step explanation:

Simplifying

X + 24 = 35

Reorder the terms:

24 + X = 35

Solving

24 + X = 35

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-24' to each side of the equation.

24 + -24 + X = 35 + -24

Combine like terms: 24 + -24 = 0

0 + X = 35 + -24

X = 35 + -24

Combine like terms: 35 + -24 = 11

X = 11

Simplifying

X = 11

Answer:

x+24=35

then collect like terms together, which means "x" terms in one side and numbers in one side:

x=35-(+24)

we need to change the signs when ever we change its place, like changing from one side to another

x=35-24

x=11. ✓

7 = Tenth

7 is the first decimal of the number making it a tenth.