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Choose the similar triangles that have a hypotenuse defined by the equation

Logarithms are used for a variety of purposes in mathematics, science, engineering, and other fields. Some common uses of logarithms are mentioned below:

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

They are used for:

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Answer:

Step-by-step explanation:

1). By applying cosine rule in the given triangle,

   cos(x°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

   cos(x°) = [tex]\frac{6}{8}[/tex]

   x = [tex]\text{cos}^{-1}(\frac{3}{4} )[/tex]

   x = 41.41°

2). By applying cosine rule in the given triangle,

   cos(x°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

   cos(x°) = [tex]\frac{4}{5}[/tex]

   x = [tex]\text{cos}^{-1}(0.8)[/tex]

   x = 36.87°

3). By applying cosine rule in the given triangle,

   cos(x°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

   cos(x°) = [tex]\frac{51}{85}[/tex]

   x = [tex]\text{cos}^{-1}(0.6)[/tex]

   x = 53.13°

Answer:

20

Step-by-step explanation:

c² = a² + b²

25² = 15² + b²

625 = 225 + b²

b² = 625 - 225

= √400

= 20

Answer:

Area:80mi^2

Perimeter:40mi

Step-by-step explanation:

You roll a 100 sided die with sides 1-100. The optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.

The 100-sided die Lou Zocchi created is known by the trademark "Zocchihedron," and it made its debut in 1985. It assumes the appearance of a ball with 100 flattened planes, unlike other polyhedran dice. It is also known as "Zocchi's Golfball."

optimal strategy is to stop and take dollar if roll > x, and to pay $1 and continue when roll <= x (as applicable to all/any turn/roll). We need to find x in order to maximize E.

Assuming optimal expected value to be E, once you cast the first roll, there are two possible scenario:

1) we get roll value > x with probability (100-x)/100, and decide to take that amount, expected winning = (x+1+100)/2 (that amount varies uniformly from x+1 to 100 in this case, take the average)

2) we get roll value <= x with probability x/100 and decide to continue, with future expected winning again = E and 1$ loss in fee. Total expected winning in this scenario = E-1

[math]E=\frac{(100-x)}{100}\times\frac{ (x+1+100)}{2}[/math][math] + \frac{x}{100}\times(E-1)[/math]

[math]E = \frac{(100-x)(101+x) - 2x}{200 - 2x}[/math]

maximizing E w.r.t. x,

dE/dx = 0

2x^2 - 400x + 19600 = 0

x = ( 400+/- sqrt(160000-4*2*19600) ) / 4

Since, 1<= x <= 100, therefore x = ( 400+ sqrt(160000-4*2*19600) ) / 4

x = 85.85786

We just have to calculate E(x=85) and E(x=86) and compare.

E((x=86) = 87.35 and E(x=85) = 87.33

so optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.

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Step-by-step explanation:

x² - 32 = 4x

x² - 4x - 32 = 0

with a little bit experience we see immediately that this is

(x - 8)(x + 4) = 0

the positive x for this to be true is x = 8.

formally, the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (4 ± sqrt((-4)² - 4×1×-32))/(2×1) =

= (4 ± sqrt(16 + 128))/2 = (4 ± sqrt(144))/2 =

= (4 ± 12)/2 = 2 ± 6

x1 = 2 + 6 = 8

x2 = 2 - 6 = -4

we were right at the beginning.

the positive solution is x = 8.

Answer:

yesssssss!!!!!!!!!!!

Answer:

4+

5+4+2

+2+4+9+3

+3.5+3.5

=99cm

Answer:

x = 46, y = 67

Step-by-step explanation:

x = ∠ AEC = 46 ( alternate angles )

Since Δ ACE is isosceles then the base angles are congruent, then

y = [tex]\frac{180-46}{2}[/tex] = [tex]\frac{134}{2}[/tex] = 67

Answer:

x=46° and y=67°

Step-by-step explanation:

triangle ACE is isosceles, meaning <A=<B=y

any triangle is add up to 180. <A+<B+<C=180

y+y+46=180

2y=180-46

2y=134

divide both sides by 2

y=134/2

y=67°

for angle x°

since AB is parallel to CD,hence

<AEC=<ECD

x=46°

Answer:

y=1.5x+2

Step-by-step explanation:

Mark me brainliest pls

2 is the y intercept so a+ 2 is already part of the equation

slope = y2-y1/x2-x1

6-4.5/2-1 = 1.5

y=1.5x + 2

Answer:

in step 2, 60 should be multiplied by the quantity 8-15, not by 8

Step-by-step explanation:

i looked at the image they provided and figured this out, and solved it on my own account but the image wont load

The triangles can be proved congruent by SAS theorem.

Two or more triangles are said to be congruent if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.

To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.

Therefore in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;

Opposite sides of a parallelogram are equal in length. Thus, it can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.

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Answer: Is the question to find unit price, if it is, the answer is $16.77. Divide 200/12 to get the unit price. Hope this helps and good luck to having a bright future ☀️

Step-by-step explanation:

Answer:

[tex]1\ c = 8\ fl\ oz[/tex]

[tex]\frac{1}{8}\ c = 1\ fl\ oz[/tex]

[tex]\frac{1}{4}\ c = 2\ fl\ oz[/tex]

Step-by-step explanation:

The options are not properly formatted;

So, I will solve the question using general notations

Required

Conversion factors of cups and fluid ounces

Let

[tex]c = cup[/tex]

[tex]fl\ oz = fluid\ ounces[/tex]

In standard conversion

[tex]1\ c = 8\ fl\ oz[/tex]

Divide both sides by 8

[tex]\frac{1\ c}{8} = \frac{8\ fl\ oz}{8}[/tex]

[tex]\frac{1}{8}\ c = 1\ fl\ oz[/tex]

Multiply both sides by 2

[tex]2 * \frac{1}{8}\ c = 1\ fl\ oz * 2[/tex]

[tex]\frac{1}{4}\ c = 2\ fl\ oz[/tex]

Answer:

the answer would be C

Step-by-step explanation:

Answer:

15degrees

Step-by-step explanation:

From the given diagram

<1+<2 + <DCB = 180

<1+<2+120 = 180

<1+<2 = 180 - 120

<1+<2 = 60

<2 = 60 - <1

<2 = 60 - 45

<2 = 15degrees

Hence the measure <2 is 15degree

Answer:

The total profit made when a person buys an item for $2.25 and then sells the item for $2.25.

Step-by-step explanation:

The item is bought for $2.25 and sold for the same rate. There is no profit.

        Final value is 0.

Answer:

[tex]y-intercept=(0,26)[/tex]

[tex]x-intercept=(-13/2,0)[/tex]

Step-by-step explanation:

Given

[tex]y-6=4(x+5)[/tex]

→ [tex]y=4(x+5)+6[/tex]

→ [tex]y=4x+20+6[/tex]

→ [tex]y=4x+26[/tex]

To find the y-intercept we will plug in x=0

Now to find the x-intercept we will plug in y=0

[tex]0=4x+26\\[/tex]

→ [tex]4x=-26[/tex]   → [tex]x=\frac{-26}{4}[/tex]

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

hope it helps...

have a great day!!!

Answer:

https://dlsfile.com/dd/MTQ1ODE5dnJpZ3doanhobV8zNDEzMjU

Step-by-step explanation:

I would help you.. but after what u did I'd rather do my work instead then helping you.. and see how it feels

GGFCTVBHBGVGBHTVfhjdcnjddjhfbvncdfbvf

DFGTBHGVFGHNHYJ  dhnchvfdhngvjgf

Answer: It is a straight line

Step-by-step explanation:

Answer:

（1）：

angle1/2/3/4=90

angle6=51

angle7=40

angle8=89

angle9=51

angle10=40

angle12=50

angle13=130

angle14=50

Step-by-step explanation:

Q1：

angle1 2 3 4 divided 360 into four equal parts

so 360/4=90

angle11=110degree

so angle12 is 180-130=50 degree

because angle 12 3 10 are in triangle

their sum is 180

so angle 10=180-90（angle3）-50（angle12）=40

because angle 10 5 6 sum is 180

so angle 6 is=180-89（angle5）-40（angle10）=51

because angle 5 6 7 sum is 180

angle7=180-51（angle6）-89（angle5）=40

angle8=angle5=89

angle9=angle6=51

angle12 &13sum is 180

so angle13=180-50=130

angle14=angle12=50

According to the solving the team average is g/17 and Chris sold (g/8) - 17  games.

The term "Average" refers to a value that should be used to describe the sample as a whole. The average is determined by dividing the total number of values in a set by the total number of values. also known as the arithmetic mean.

Average A collection of integers are added, their count is divided, and the sum is used to determine the arithmetic mean.

average game sold = g/8

since Chris sold 17 games less than average

hence, Chris sold   games

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Answer:

Step-by-step explanation: a=4, b=2.

Answer:

b = 39

Step-by-step explanation:

[tex]a-6=b[/tex]

if a = 45:

[tex]45-6=b\\39=b[/tex]

Hope this helps

In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.

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Answer:

54 apples

Step-by-step explanation:

i know that he most likely didnt eat the same amount of apples per year but, if you divide the number of apples he ate overall by his age you get 54 apples.

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]

By considering the reflection, the coordinates of the reflected square D'E'F'G' are:

D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)

A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle, but with all sides equal. The opposite sides of a square are parallel and of equal length. A square can be defined by its side length or by the coordinates of its vertices.

Reflection is a type of transformation in geometry in which a shape is flipped over a given line, called the line of reflection. The image that is created is a mirror image of the original shape. The line of reflection can be a horizontal line, a vertical line, or any line that is not parallel to the axes. Reflecting a shape over a line involves taking the coordinates of each point of the shape and applying a specific rule (such as multiplying or adding a constant) to the x or y coordinate, depending on the line of reflection. This rule is often simple and easy to apply, such as reflecting over x = 1. The reflected shape will be in the same plane as the original shape but with a different orientation or position.

When a square is reflected in the line x=1, each of the points on the square will have their x-coordinate replaced by 1 subtracted from their original x-coordinate.

The coordinates of the reflected square D'E'F'G' can be found by applying this rule to the original coordinates of square DEFG:

D(1,1) => D'(1-1,1) => D'(0,1)

E(1,6) => E'(1-1,6) => E'(0,6)

F(6,6) => F'(6-1,6) => F'(5,6)

G(6,1) => G'(6-1,1) => G'(5,1)

So the coordinates of the reflected square D'E'F'G' are:

D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)

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