Proving the Congruent Supplements Theorem

Given <1 and <2 are suplements

Given

One US dollar was worth 0.69 euro.

To find:

a) How many dollars was 71.33 euro worth?

b) How many euro was 117.99 dollars worth?

Explanation:

It is given that,

One US dollar was worth 0.69 euro.

Then,

a) Let x be the number of dollars.

That implies,

Since 1 dollar=0.69euro.

Then,

Answer: 9/16 or 0.5625 or (3/4)^2 inches per month

Step-by-step explanation:

divide by two

(1 1/8) / 2

9/16 or 0.5625 or (3/4)^2

Answer:

To find the perimeter of the regular pentagon.

O is the center of the regular pentagon from the figure.

we know that, There are 360 degrees around a point, the angle formed over each side are equal that is eual to 360/5 =72

In the triangle made by the side and line joinging center, we get

whereb x is the angle made by the line joining to the center and one of the side.we get,

Consider the right angled triangle,

we know that,

we get,

Side of a pentagon (s)= 2x7.26=14.52

Perimeter of a pentagon is,

Perimeter of a pentagon is 72.6 units.

Answer:   The correct answer is c=4/x^2

Step-by-step explanation:

Solve for c:

5x^2c+50/5=30

Add -10 to each side:

5cx^2+10+(−10)=30+(−10)

5cx^2=20

Divide both sides by 5x^2:

(5cx^2)/(5x^2)=20/(5x^2)

c=4/x^2

The linear equation that passes through the point (4, -6) that is perpendicular to the line y = -3 is:

x = 4.

Im only answering the first question, like the guidelines say.

We want to find a line that passes through the point (4, -6) that is perpendicular to the line y = -3.

Now, line y = -3 is an horizontal line, so a line perpendicular to this one will be a vertical line of the form:

x = a.

Where a is a real number.

this line x = a must pass through (4, -6) where the x-value is 4, then the equation for the line will be:

x = 4.

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Since the exponential and natural logarithm are inverses each other, we can apply natural logarithm to both sides and get

or equivalently,

Threfore, the answer is the last option

{-3,0,3} is closed under multiplication.

Curly brackets are often used to denote sets in writing. For instance, a set of the integers 3, 4, 5, and 6 is denoted by "3, 4, 5, 6." In a calculus or physics lecture, angular brackets like 1,3> may denote an inner product, and square brackets may denote a matrix. Mathematicians often use brackets to group similar phrases or numbers together, which is a very important use of these symbols. An expression or thing encompassed by brackets is implied to be given precedence over other things by the presence of brackets. The most popular method for enclosing extra information from a third party is to use square brackets (someone other than the original author). In writing, a list of equal options is frequently denoted by curly brackets.

The set consist of numbers -3, 0 and 3 so if we use any combination of those 3 numbers under some operation and get as result one of those 3 numbers that means set is closed under that operation.

for multiplication you get:

0 × 3 = 0

0 × -3 = 0

-3 × 3 = -9

So all combinations used and answers are 0 and -9 which means set is closed under multiplication.

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We know that the hypotenuse is 6.5 units long, and x is the opposite leg to angle 50.

To find the value of x, use the sine trigonometric reason.

aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾ is the explicit formula for the geometric sequence: 4, 20, 100, 500.

A geometric progression is simply a sequence of non-zero numbers, every term after the first can be determine by multiplying the previous number by a common ratio.

The nth term of a geometric sequence is expressed as;

aₙ = a₁ × r⁽ⁿ ⁻ ¹⁾

Where a₁ is the first term, r is the common ratio and n is the number of terms.

Given the sequence in the question;

4, 20, 100, 500, ...

First determine the common ratio.

r = any term / previous term

r = 20/4

r = 5

Th first term in the sequence is 4.

Plug these into the geometric sequence formula and simply.

aₙ = a₁ × r⁽ⁿ ⁻ ¹⁾

aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾

Therefore, the explicit formula for the sequence is aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾

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Starting with the equation:

Multiply both sides by 4.6:

Simplify the left hand side:

Simplify the right hand side:

The answer is: 16.1.

To check your answer, substitute x=16.1 into the first equaton to see if you obtain the same number in both sides:

Simplify the left hand side:

Ok, so

Remember that the surface area of a rectangular prism can be found using:

If we replace our values:

l = 2.4

h = 3.6

w = 4.2

We got that:

Then, the surface area of this rectangular prism is 67.68 yd2.

7x-(x-3)=4x-2​

We need to solve first the brackets

7x-x+3=4x-2

Next, we need to put all the terms with x on one side and all the terms without x on the other side, remember is you change the side of a term the sign will be the opposite that's why 4x change to -4x on the other side

7x-x-4x=-2-5

then we sum of the term

2x=-7

the term with x the 2 is multiplying x so on the other side change to divide the seven

x=-7/2

In order to perform the given transformation, we just have to replace the x and y-coordinates into the transformation rule, like this:

A(5, 7), by replacing 5 for x and 7 for y into (x - 5, -y + 2), we get:

(5 - 5, -7 + 2) = (0, -5)

A(5, 7) -> A'(0, -5)

Then, the coordinates of the new point A' are (0, -5)

question 1 =60

2=54

3=-56

4=-88

5=-48

The points on the curve for the tangent is horizontal will be;

⇒ (1, -6) and (-2, 21)

What is mean by Tangent?

The tangent is defined by the line touching the ellipse and the circle at the only one point.

Given that;

The function is;

⇒ y = 2x³ + 3x² - 12x + 1

Now, Find the point on which the tangent is horizontal is find as;

The function is;

⇒ y = 2x³ + 3x² - 12x + 1

Differentiate it with respect to x as;

⇒ dy/dx = d/dx (2x³ + 3x² - 12x + 1)

⇒ dy/dx = 2 × 3x² + 3 × 2x - 12 × 1 + 0

⇒ dy/dx = 6x² + 6x - 12

Equate it to zero;

⇒ dy/dx = 0

⇒ 6x² + 6x - 12 = 0

Take common 6;

⇒ 6 (x² + x - 2) = 0

⇒ x² + x - 2 = 0

Solve for x, by the factorization as;

⇒ x² + 2x - x - 2 = 0

⇒ x (x + 2) - 1 (x + 2) = 0

⇒ (x - 1) (x + 2) = 0

We get two condition;

⇒ (x - 1) = 0 or (x + 2) = 0

⇒ x = 1 or x = -2

Substitute x = 1 in equation , we get;

y = 2x³ + 3x² - 12x + 1

y = 2 × 1 + 3 × 1 - 12 × 1 + 1

y = 2 + 3 - 12 + 1

y = - 6

Hence, The point = (1, -6)

Substitute x = -2 in equation , we get;

y = 2x³ + 3x² - 12x + 1

y = 2 × (-2)³ + 3 × (-2)² - 12 × -2 + 1

y = - 16 + 12 + 24 + 1

y = 21

Hence, The point = (-2, 21)

Therefore, The points on the curve for the tangent is horizontal will be;

⇒ (1, -6) and (-2, 21)

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Answer:

[tex]y=\frac{2}{3}x+4[/tex]

Step-by-step explanation:

The given function is

The domain of the function would be all real numbers.

But the range would be all real numbers greater than zero because the function approximates to y = 0 but it doesn't go through.

The MAD tells you that most of the data values are greater than the mean.

MAD is an abbreviation for mean absolute deviation. Mean absolute deviation measures the variation of a data set. It measures the spread of the dataset from the mean. The higher the value of the mean absolute deviation compared to the mean, the greater the spread or variation of the dataset.

MAD =  (1 / n) ∑ l x - m(x) l

Mean is a measure of the center of a data set. It is the sum of the dataset divided by the total number in the dataset. Mean is also known as average.

Mean = sum of the data / total number in the dataset

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Based on the circle graph and portions that are represented by rent and savings, the fractional portion of the graph that is not represented by rent and savings is 84.2%

First, find the degrees in the circle graph that is not represented by rent and savings. This is:

= Total number of degrees in circle graph - degrees represented by rent and savings

= 360 - 50 - 7

= 303 °

The fractional portion which isn't represented by either rent or savings is:

= Degrees not represented by rent or savings / Total number of degrees  x 100%

= 303 / 360 x 100%

= 84.2%

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The rule of reflection over the x-axis is:

as shown in the figure:

The coordinates of point A = ( 2, 5 )

the coordinates of point B = (6, 3)

Apply the rule to the given points:

So,

A' = ( 2, -5)

B' = ( 6, -3)

So, the answer is option B

Answer: The answer is either $83 or $70

The volume of the cylinder is 3418.1 cubic feet

The volume of a cylinder is given by the formula:

Where r is the radius and h is the height.

The radius of the given cylinder is is 8 ft, the height is 17 ft

Volume is:

The rate of change of elevation is 0.18

Given the function:

To find the rate of change, we take the derivative of f(x)

At the point x = 1, we have:

The rate of change of elevation is 0.18

Answer:

1.8%

Explanation:

Given the original price as $2.84 and the new price as $2.89, let's go ahead and determine the increase in price as seen below;

We'll use the below formula to determine the percentage increase;

Answer: (6, -19)

Step-by-step explanation:

y = 4x + b

substitute ( 10, -3) to find b

b = -43

equation of line is:

y = 4x -43

substitute (6, r)

y = 4(6) - 43

solve for y to find r

y = -19

this means that the missing coordinate r is -19

the full coordinate is (6, -19)

Answer:

Domain: [tex](-\infty, \infty)[/tex]

Range: [tex][0, \infty)[/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.