Find the area of the triangle.

The simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]

The complete question is added as an attachment

The equation is given as

[tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex]

Subtract (x - 10)^2 from both sides

[tex](y- 6)^2 = 4^2 - (x - 10)^2[/tex]

Evaluate 4^2

[tex](y- 6)^2 =16 - (x - 10)^2[/tex]

Take the square root of  both sides

[tex]y- 6= \sqrt{16 - (x - 10)^2}[/tex]

Add 6 to both sides

[tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]

Hence, the simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]

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The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm

An equation is an expression that shows the relationship between two or more variables and numbers.

Let us assume that the pyramid has a volume of 75 cm³ and square base area of 25 cm², hence:

Volume = (1/3) * area of base * height

75 = (1/3) * 25 * height

height = 9cm

The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm

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Answer:

D.) x = 2y²

Step-by-step explanation:

You can find the inverse of an equation by swapping the positions of the "x" and "y" variables. Then, you would need to rearrange the equation to re-isolate the "y" variable.

As such, D.) is the correct option because it is identical to the original equation except that the variables are swapped.

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]y = 2x^2\hspace{5em}\stackrel{\textit{quick switcheroo}}{\boxed{x = 2y^2}}\implies \cfrac{x}{2}=y^2\implies \sqrt{\cfrac{x}{2}}=\stackrel{f^{-1}(x)}{y}[/tex]

Considering the given linear function, the inequality graphed is:

B. [tex]y \geq 2x + 2[/tex].

A linear function is modeled by:

y = mx + b

In which:

The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:

m = (4 - 2)/(2 - 1) = 2.

Thus the equation of the line is:

y = 2x + 2.

The left-side of the line is the values above the line, hence the inequality is:

B. [tex]y \geq 2x + 2[/tex].

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On solving the provided question, we can say that the solution of the System of Equation  3000 + 500x = 1000*

A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

A system of equations consists of two or more equations and looks for common answers. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."

The point provides a singular solution to the system of equations if the two lines cross at the same location. There are an endless number of solutions in the situation when the two lines meet, and there is none in the case where the two lines are parallel.

The equation for Appleville is

3000 + 500x,       in x years after the year 2000

The equation for Bananaville is

1000*   , in x years after the year 2000

The solution of the equations

3000 + 500x = 1000*

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The given polynomial function has 1 relative minimum and 1 relative maximum.

The given function is

f(x) = 2x³ - 2x² + 1

derivating the above function,

f'(x) = 6x² - 4x

At slope = 0, f'(x) = 0 (for maximum and minimum values)

⇒ 6x² - 4x = 0

⇒ 2x(3x - 2) = 0

2x = 0 or 3x - 2 = 0

∴ x = 0 or x = 2/3

Then the y-coordinates are calculated by substituting these x values in the given function,

when x = 0;

f(0) = 2(0)³ - 2(0)² + 1 = 1

So, the point is (0, 1)

when x = 2/3;

f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27

So, the point is (2/3, 19/27)

Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.

So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.

Thus, option A is correct.

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The measure of angle A rounded to the nearest whole number is 25°.

Hence, option C is the correct answer.

Given that?

First, we determine the length of side c using the law of cosines.

c = √( a² + b² - 2ab( cosC ) )

We substitute in our values

c = √( 20² + 13² - 2×20×13( cos 139° ) )

c = √( 400 + 169 - 520( cos 139° ) )

c = √( 569 + 392.44898 )

c = √961.44898

c = 31 cm

Next, we find Angle A, using the law of cosines.

A = cos⁻¹[ ( b² + c² - a² ) / 2cb ]

We substitute in our values

A = cos⁻¹[ ( 13² + 31² - 20² ) / ( 2 × 31 × 13 )  ]

A = cos⁻¹[ ( 169 + 961 - 400) / 806]

A = cos⁻¹[ 730 / 806]

A = cos⁻¹[ 0.9057 ]

A = 25°

The measure of angle A rounded to the nearest whole number is 25°.

Hence, option C is the correct answer.

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The value of the 4th iterate of the given function f(x) is -2.096

2nd option is correct.

A function's iterate is a function that is expressed as repetition of another (already iterated) function; this latter function may be referred to as the iterand.

Any function taken on its own is regarded as the first iteration.

A function is said to have an identity function at iteration zero.

According to the question,

f(x) = (3x-1)/[tex]x^{2}[/tex]

[tex]x_{o}[/tex] = -2

The first iterate is calculated by finding f(-2).

f(-2) = (3(-2)-1)/4

f(-2) = -1.75

Similarly, the next iterates are calculated as follows:

f(-1.75) = -2.048

f(-2.048) = -1.71

f(-1.71) = -2.096

Thus, the fourth iterate for the given function is [tex]x_{4}[/tex]= -2.096

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Probability that a card selected at random is purple = 7/25

Number of red cards, N(red) = 12

Number of blue cards, N(blue) = 17

Number of purple cards, N(purple) = 14

Number of yellow cards, N(yellow) = 7

Total number of cards, N(total) = 12 + 17 + 14 + 7

N(total) = 50

Probability that a card selected at random will be purple

P(purple) = N(purple) / N(total)

P(purple) = 14/50

Reduce to the lowest fraction

P(purple) = 7/25

Therefore, probability that a card selected at random is purple = 7/25

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Complete Question

There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple

The surface area of the composite solid is 579.84 square feet

The composite solid that completes the question is added as an attachment

From the attached figure, we have the following figures:

The surface area of a rectangular prism is

A = 2(lw + lh + wh)

Using the dimensions of the prism, we have:

A = 2(6 * 11 + 6 * 8 + 8 * 11)

This gives

A = 404

The surface area of a cylinder is

A = 2πr^2 + 2πrh

Using the dimensions of the cylinder, we have:

A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5

Evaluate

A = 226.08

The area of the circle between both shapes is

A = πr^2

This gives

A = 3.14 * 4^2

A = 50.24

The surface area of the composite solid is then calculated as:

Surface area = Area of rectangular prism + Area of cylinder - Area of circle

This gives

Surface area = 404 + 226.08 - 50.24

Evaluate

Surface area = 579.84

Hence, the surface area of the composite solid is 579.84 square feet

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Answers:

=========================================================

Explanation:

Problems 1, 2, and 5 are exponential functions of the form [tex]y = a(b)^x[/tex] where b is the base of the exponent and 'a' is the starting term (when x=0).

If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.

If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.

In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.

Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.

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

Problems 3 and 4 are linear functions of the form y = mx+b

m = slope

b = y intercept

This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.

If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.

On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.

Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.

Answer:

see below

Step-by-step explanation:

90 degree clockwise will change x, y coordinates to  y, -x

point D  1,3    becomes   3,-1

point E   4, 4   becomes  4,-4

point F  4, -2  becomes   -2,-4

point G  1,-1    becomes    -1, -1

Answer: [tex]g(x)=5^x - 10[/tex]

Step-by-step explanation:

g(x) is the graph of f(x) translated 10 units down.

Taking 1 in the box it creates an expression equivalent to 2 - 5.

The expressions represent the distance between the two points on the

number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.

What is integers on number line?

Integers are represented using a number line. A straight line of numbers is shown visually as a number line. It is made up of positive integers like 1, 2, etc., negative integers like - 1, - 2, etc., and a zero that is neither positive nor negative.

Part A:

2 - 5 = -3

2 + 1 = 3

The distance on the number line between a number and 0 is its absolute value.

             a. That distance is never negative.

             b. The symbol for Absolute Value is “ | | ”.

Hence, by taking 1 in the box it creates an expression equivalent to 2 - 5.

Part B:

|-3 -2| = 1

This point represent distance from -3 to -2 on the number line is 1 unit.

|2-(-3)| = 5

This point represent distance from 2 to -3 on the number line is 5 units.

|-3 + (-2)| = 5

This point represent distance from -3 to -2 on the number line is 5 units.

|-3 - (-2)| = 1

This point represent distance from -3 to -2 on the number line is 1 units.

Therefore,

Taking 1 in the box it creates an expression equivalent to 2 - 5.

The expressions represent the distance between the two points on the

number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.

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Answer:

[tex] [/tex] [tex] [/tex] [tex] [/tex] [tex] [/tex]

Step-by-step explanation:

x, y = 2 numbers

x = 2y

y - x/2 = 20

this is impossible to solve. there is no solution.

because the first equation tells us

y = x/2

and so the second equation is

x/2 - x/2 = 20

0 = 20

so, again, no solution.

Answer:

x=1

Step-by-step explanation:

1 + 1/3 = 4/9

1/3 also equals 3/9

hope this helped :)

Answer :

Step-by-step explanation :

>> (3 × x + x / 3) = 4 / 9

>> (3x + x / 3) = 4 / 9

>> (4x / 3) = 4 / 9

>> 4x × 9 = 3 × 4

>> 36x = 12

>> x = 12 / 36

>> x = 6 / 18

>> x = 3 / 9

>> x = 1 / 3

The area and circumference of a circle are 12.56square feet and 12.56ft respectively

The formula for calculating the area and circumference of a circle is expressed as:

A = πr²

C = πd

where

r is the radius and d is the diameter

Area = 3.14 * (2)²

Area = 12.56ft²

For the circumference

C = 3.14(4)

C = 12.54ft

Hence the area and circumference of a circle are 12.56square feet and 12.56ft respectively

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Answer:

x = 3, x = 9/4

Step-by-step explanation:

8x = 24

x = 3 Divide both sides by 8.

4x = 9

x = 9/4 Divide both sides by 4.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation \#1.}[/tex]

[tex]\mathsf{8x = 24}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{8x = 24}[/tex]

[tex]\huge\textbf{Divide \boxed{8} to both sides:}[/tex]

[tex]\mathsf{\dfrac{8x}{8} = \dfrac{24}{8}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{24}{8}}[/tex]

[tex]\mathsf{x = 3}[/tex]

[tex]\huge\textbf{Therefore, the answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x =}\frak{\ 3}}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation \#2.}[/tex]

[tex]\mathsf{4x = 9}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{4x = 9}[/tex]

[tex]\huge\textbf{Divide \boxed{9} to both sides:}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{9}{4}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{9}{4}}[/tex]

[tex]\mathsf{x = 2 \dfrac{1}{4}}[/tex]

[tex]\huge\textbf{Therefore, the answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = }\frak{\ \dfrac{9}{4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The probability that a randomly selected muffin will be a banana nut muffin is; P(banana nut muffin) = 0.5

From the table in the question, we are given;

Number of blackberry muffins = 10

Number of banana nut muffins = 25

Number of Chocolate chip muffins = 1

Number of blueberry muffins = 11

Number of pumpkin spice muffins = 3

Total number of muffins = 10 + 25 + 1 + 11 + 3

= 50

Probability = number of successful outcomes/Total number of outcomes

Thus;

P(banana nut muffin) = 25/50

= 0.5

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The length of side OA in the given rhombus is: 5 units.

A rhombus is a quadrilateral that has four sides that are all of the same length. Therefore, in the image given, the length of AB equals the length of OA.

Given the following:

Length of AB = |8 - 3}

Length of AB = 5 units.

AB = OA = 5 units.

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Answer:

  -5/4

Step-by-step explanation:

To evaluate the function, put the value of the argument where the variable is and do the arithmetic.

  f(x) = -x -3x²

  f(1/2) = -(1/2) -3(1/2)² = -1/2 -3(1/4) . . . . . use 1/2 in place of x

  f(1/2) = -2/4 -3/4 = -5/4

The value in simplest form is ...

  f(1/2) = -5/4

Answer:

Maybe the answer must be 90°

Answer:

d. 64

Step-by-step explanation:

x^1/2 = 8

Square each side

(x^1/2 )^2=( 8)^2

x = 64

Answer:

1/9, 3, 27

(A / the first option listed)

Step-by-step explanation:

Here, we are given an expression with an "x" in it, and we are to evaluate possible x values, which means we plug them in as the x in the expression

first,

x = -2

3ˣ → 3⁻²

when we raise something to a negative power, we simply find the positive version of that power, and put a 1 over it:

3²  =  3 · 3 =  9

so, 3⁻² =  [tex]\frac{1}{9}[/tex]  (1/9)

next,

x = 1

3ˣ → 3¹

now, here we have something raised to the power of 1, which is always itself, so  3¹ = 3

   (think of ^to the power of  as how many times we multiply that number, so 3² = 3 · 3, 3¹ = 3)

and finally,

x = 3

3ˣ → 3³

here, we can multiply 3 by itself 3 times:

3 · 3 · 3 = 27

so, 3³ = 27

[important note: when we raise something to a power, we are not multiplying the base number by that number, but this is a common mistake. but the exponent is how many times we are multiplying that number, which is confusing at first}

So, our answers in order are:

1/9, 3, 27 (the first option listed)

hope this helps! let me know if I should clarify anything :)

The angle of elevation that the instruments have to record to be at the correct height is given as 79°

We have 2x + 70 = 180

We have to find the value of x

2x = 110

x = 55

y/sin x = 225/sin70

This is the use of sine rule

From here we would have

y = 225(sinx/sin70)

Remember x = 55

y =  225(sin55/sin70)

y = 196.1378

tanθ = 1000/y

tan θ = 1000/196.1378

tanθ = 5.098

θ = tan⁻¹5.098

= 78.90°

Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.

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