Graph the function.
f(x)=3z-5
Use the Line tool and select two points to graph

Considering the circle described, the height of the roller coaster is modeled by the following equation:

[tex]y = \sqrt{900 - x^2}[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In this problem, the roller coaster is represented by a circle centered at the origin, with radius 30, hence:

[tex]x^2 + y^2 = 30^2[/tex]

[tex]x^2 + y^2 = 900[/tex]

The height is the value of y, hence, considering it is a positive value:

[tex]y^2 = 900 - x^2[/tex]

[tex]y = \sqrt{900 - x^2}[/tex]

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Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Step-by-step explanation:

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

First, let's edit the given equations.

[tex]2(32-x^2)=4x4-2\\\\64-2x^2=14[/tex]

Then, to check if [tex]x=5[/tex] is a solution to this equation, let's put the [tex]5[/tex].

[tex]64-2(5)^2=14\\\\64-50=14[/tex]

That's correct!

[tex]4^2-x\leq x(6-5)\\\\16-x\leq 6x-5x\\\\16-x\leq x\\\\16\leq 2x\\\\x\geq 8[/tex]

Then, we must put [tex]15[/tex].

[tex]15\geq 8[/tex]

That's correct!

Good luck! If you have any question(s), then feel free to ask in comments!

Hi Student!

Let us first look at what the first question is asking for us to do and what is provided to do that.  Looking at the first question we see that they are asking if x = 5 is a solution to the expression that they provided.  This type of problem is fairly simple and what we basically do is just plug in the value 5 for the variable x in the expression and the simplify both sides to see if they are the same.

Plug in the values

Simplify the square and subtract inside of the parenthesis

Simplify both sides

Looking at the final expression that we have, we can see that we have 14 is equal to 14 which is true and therefore x = 5 is a solution of the expression provided.

Moving onto the next question, we can see that it asks for us to do something really similar to the previous question but this time to check if x = 15 is a solution of a different expression.  Let's follow the same steps that we did last time.

Plug in the values

Distribute the x

Simplify both sides

Looking at the final expression that we have, we can see that it states that 1 is less than or equal to 15 and that is true.  Therefore, x = 15 is a solution of the expression that was provided.

Answer:

here's the answer

Step-by-step explanation:

19/100*x=6.46

x=$34

Answer:

hmmm I get 216

Step-by-step explanation:

(10×7)+(6×8) the front n back triangle +(6×7)+(8×7)

Answer:

the point through which it passes i.e (1,5)

Answer:

(1,5)

Step-by-step explanation:

All points on the line is solution of the equation.

(1 ,5) is on the line and so it is the solution

The amount of Rita deposit is $2556.

The interest calculated on the principal amount or the initial investment.

It is given in the question

If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days.

P = ?

S.I. =  $63.90

Interest = 6%

T = 150days

S.I. = (P *R*T)/100

63.90 = P * 6 * 150*100 /360

63.90 * 360*100 /( 150 *6) = P

P = $2556

Therefore the amount of Rita deposit is $2556.

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Answer:

f(4) = 1612

Step-by-step explanation:

using the recursive formula and f(1) = 3 , then

f(2) = f(1)² + 3 = 3² + 3 = 9 + 3 = 12

f(3) = f(2)² + 3 = 144 + 3 = 147

f(4) = f(3)² + 3 = 147² + 3 = 1609 + 3 = 1612

Answer:

The Median Best Describes The Monthly Rents

the mean is add up all the numbers and then divide by the amount of numbers so it is 4820 then divide by 5 = 964 so the mean of all of then is 964

the median you have to put it in slamets to biggest so 650 650 800 820 1900 and then you have to put the one(s) in the middle witch is 800 so the median is 800

the mode is the most common numbers that show up and there is 2 650 and one of everything else so the mode is 650

Hope This Helped

A function assigns the value of each element of one set to the other specific element of another set. The inverse of the function g(x)=-2x -3.

A function assigns the value of each element of one set to the other specific element of another set.

Two function are inverse of each other if,

f(g(x))=x

g(f(x)) = x

Since the function is inverse, therefore, we can write,

g(f(x)) = a(-1x/2 - 3/2) + b

x = -ax/2 - 3x/2 + b

-a/2 = 1

a = -2

-3a/2 + b = 0

b= -3

Thus, the inverse of the function g(x)=-2x -3.

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Answer:

the inverse of the function g(x)=-2x +3 .

Step-by-step explanation:

5y³(y-2)-15y(y-2)

= (y-2)×(5y³-15y)

Answer:   E) None of these

As you can see in the picture below, the line falls at around 66 degrees, so it can't be any of the given choices. If this answer turns out to be wrong, then it is probably B.

Hope this helps!

Answer:

B.) f(x) = |x|  ,  g(x) = 9x + 2

Step-by-step explanation:

The expression f о g = H is identical to f(g(x)) = H. In other words, when you put the function g(x) in the "x" position of the f(x) function, it should look like the H(x) function.

If g(x) = 9x + 2, put the entire function in for "x" in f(x) = |x|. Once you do this, you get the function f(g(x)) = |9x + 2|.

Answer:B.) f(x) = |x|  ,  g(x) = 9x + 2

Step-by-step explanation:

The expression f о g = H is identical to f(g(x)) = H. In other words, when you put the function g(x) in the "x" position of the f(x) function, it should look like the H(x) function.

If g(x) = 9x + 2, put the entire function in for "x" in f(x) = |x|. Once you do this, you get the function f(g(x)) = |9x + 2|.

Try this suggested option:

Step-by-step explanation:

f(x)=2(2x²+4x)+3; ⇔

f(x)=4(x²+2x)+3; ⇔

f(x)=4(x²+2x+1)+3-4; ⇔

f(x)=4(x+1)²-1; ⇔

f(x)=(2x+1)(2x+3).

Then the roots are:

[tex]\left[\begin{array}{ccc}x=-1.5\\x=-0.5\end{array}.[/tex]

The shape of the resulting cross-section will be equal to the trapezoid.

A trapezoid is a quadrilateral having four sides whose two sides are parallel to each other and the other two sides are nonparallel to each other.

As it is given in the question the figure is sliced through points J. K. and When the shape is sliced from the given points it will create the trapezoidal shape that will have two parallel sides and the other two sides are Non-parallel

Therefore the shape of the resulting cross-section will be equal to the trapezoid.

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Answer:

Trapezoid

Step-by-step explanation:

I got it right on Edmentum

Hook me up with a 5 star and a thanks :)

Answer:

see the attachment photo!

Find when f(x) = 0. By factorizing, we have

-x² + 8x - 7 = - (x - 7) (x - 1) = 0

so either x - 7 = 0 or x - 1 = 0, or simply x = 1 or x = 7.

Split the domain into three intervals, and check the sign of f(x) over each interval at some test point in the interval. The sign will tell you when the icicle is dripping (positive) or not (negative).

• [0, 1) : at x = 0, we have f(0) = -7 < 0

• (1, 7) : at x = 2, we have f(2) = 5 > 0

• (7, 10] : at x = 8, we have f(8) = -7 < 0

This tells us that the icicle is not dripping when 0 ≤ x < 1, begins to drip when x = 1, drips for the duration of 1 < x < 7, stops dripping when x = 7, and keeps on not dripping when 7 < x ≤ 10.

Answer:

6,010 mg

Step-by-step explanation:

1 gram = 1,000 milligrams that means

(6+.01)*1000=6,010mg

The amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.

A cuboid is a three dimensional shape , with 6 faces , each face is a rectangle.

The concrete can be considered as in the shape of a cuboid.

Length = 18

Breadth = 24'

Height = 4"

Volume of Cuboid = Length * Breadth * Height

Volume of the cuboid = 18 * 24 * 4 *12*12 *(0.0278)³

=5.34 cu.yard.

Therefore the amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.

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If any constant is added in the variable of the function. Then the function will shift towards left. Then the correct option is C.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The functions are given below.

y = ∛(0.5 + x)

y = ∛x

If any constant is added in the variable of the function. Then the function will shift towards left.

Then the correct option is C.

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Answer:

Step-by-step explanation:

The statement describe g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function is option C; Translate the parent function 5 units down and 7 units to the right.

How does transformation of a function happens?

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

The transformed function can be written as

y = ∛(x - 5) + 7

Where f(x) = ∛x, this is of the form

y = ∛(x - 5) + 7

These numbers in these places correspond to ...

The statement describe g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function is option C; Translate the parent function 5 units down and 7 units to the right.

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The functions in order from least to greatest according to their average rates of change are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]

The rate of change is calculated using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

For function g at the interval [2,3], we have:

[tex]m = \frac{g(3) - g(2)}{3- 2}[/tex]

This gives

[tex]m = \frac{20 - 4}{3- 2}[/tex]

[tex]m =16[/tex]

For function h at the interval [0,2], we have:

[tex]m = \frac{h(2) - h(0)}{2- 0}[/tex]

Where:

h(2) = 3(3)^2 - 9 = 18

h(0) = 3(3)^0 - 9 = -6

This gives

[tex]m = \frac{18 + 6}{2 - 0}[/tex]

[tex]m = 12[/tex]

For function f at the interval [1,2], we have:

[tex]m = \frac{f(2) - f(1)}{2- 1}[/tex]

This gives

[tex]m = \frac{12 - 6}{2 - 1}[/tex]

[tex]m = 6[/tex]

Hence, the functions are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]

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Answer:

Step-by-step explanation:

Your exponential formula is in the form y = ab^x. In this form, the coefficient 'a' is the initial value, the y-intercept, the value when x=0. The value 'b' is the growth factor, which is 1 more than the growth rate per increment of x. This problem is asking for the growth rate to be expressed as a percentage.

__

Given p(x) = 78500(1.02^x), we can compare to the exponential function form to see that ...

The value of x is zero in the year 2000, so the population that year is ...

  p(0) = a = 78,500

The increase per year is the value of 'b' with 1 subtracted:

  growth rate = 2% per year

Answer:

68 degrees Fahrenheit

Step-by-step explanation:

to find the average also known as mean, just add the numbers and divide by how many numbers there are.

66+71+68+70+65=340

Now, divide by how many numbers there are. There are 5.

So,

340÷5 = 68

the average is 68.

Answer:

E

Step-by-step explanation:

The diagram below shows the correct use of diverging lens for correction of myopia.

Inequalities help us to compare two unequal expressions. The correct option is D.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The sentence that correctly compares the two numbers 5.395 and 5.385 is 5.385<5.395. Hence, the correct option is D.

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Answer:

a. volume= 784 is the answer