If the length of the hypotenuse of the right triangle is 5 units, and the area of p is 9 square units, then what is the area of R?

The pair of triangles shown can be seen to be similar by SAS.

When comparing two triangles, one way to tell if they are similar is to apply the SAS (Side-Angle-Side) similarity criterion. This criterion states that two triangles are comparable if they have two pairs of corresponding sides in proportion and congruent included angles between those sides.

Triangles must have an equal ratio of their matching sides' lengths. The respective sides' included angles must be equivalent.

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Answer:

  (3) 60°

Step-by-step explanation:

You want the measure of the third angle (E) in triangle EFG, given that two of the angles have measures 75° (angle F) and 45° (angle G).

The angle sum theorem tells you the sum of angles in any triangle is 180°. This means ...

  E + F + G = 180

  E + 75 + 45 = 180

  E = 60 . . . . . . . . . . . . . subtract 120 from both sides and simplify

The measure of angle E is 60°.

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Answer:

6 in³

Step-by-step explanation:

volume = width X length X height

= 3 X 1 X 2

= 6 in³

The approximate height difference between the birdhouse and the tree house is 3 ft.

It is less than the approximate difference in height between the swing set and the tree house.

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

We have:

height of birdhouse = 14[tex]\frac{9}{16}[/tex] ft

height of tree house = 11[tex]\frac{13}{16}[/tex] ft

Thus, the approximate height difference between the birdhouse and the tree house will be:

14[tex]\frac{9}{16}[/tex] ft - 11[tex]\frac{13}{16}[/tex]  = 2[tex]\frac{3}{4}[/tex] ft

                   = 2.75 ft

                  = 3 ft

To determine if it is greater than or less than the approximate difference in height between the swing set and the tree house, we have to find the approximate difference in height between the swing set and the tree house. That is:

height of swing set = 8[tex]\frac{1}{4}[/tex] ft

height of tree house = 11[tex]\frac{13}{16}[/tex] ft

difference = 11[tex]\frac{13}{16}[/tex] - 8[tex]\frac{1}{4}[/tex]

                    = 3[tex]\frac{1}{2}[/tex]

                    = 3.5

                    = 4 ft

Therefore, it is less than the approximate difference in height between the swing set and the tree house

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Descartes must be thinking of the number 0.

Now, Let's call the number Descartes is thinking of "x".

Hence, According to the problem, if Descartes multiplies "x" by 9, he gets "x" back. In other words, 9 times "x" is equal to "x".

So we can write this as an equation:

⇒ 9x = x

Now we need to solve for "x". We can start by subtracting "x" from both sides of the equation:

⇒ 9x - x = 0

⇒ 8x = 0

divide both sides by 8 to get:

⇒ x = 0

Thus,  Descartes must be thinking of the number 0.

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Answer: 10:22

Step-by-step explanation:

9:55 + :05 = 10:00

10:00+ :22 = 10:22

An equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4,-3) is: C. y + 3 = 1/4(x + 4) .

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-3 - 1)/(0 + 1)

Slope (m) = -4

m₁ × m₂ = -1

-4 × m₂ = -1

m₂ = -1/-4

Slope, m₂ = 1/4

At data point (-4, -3) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 3 = 1/4(x + 4)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

To prove that (secx+tanx)² = (cscx+1)/(cscx-1), we will start with the left-hand side (LHS) of the equation and simplify it step by step until it matches the right-hand side (RHS) of the equation.

LHS: (secx+tanx)²

Using the trigonometric identities secx = 1/cosx and tanx = sinx/cosx, we can rewrite the LHS as:

LHS: (1/cosx + sinx/cosx)²

Now, let's find a common denominator and simplify:

LHS: [(1+sinx)/cosx]²

Expanding the squared term, we get:

LHS: (1+sinx)² / cos²x

Next, we will simplify the denominator:

LHS: (1+sinx)² / (1 - sin²x)

Using the Pythagorean identity sin²x + cos²x = 1, we can replace 1 - sin²x with cos²x:

LHS: (1+sinx)² / cos²x

Now, let's simplify the numerator by expanding it:

LHS: (1+2sinx+sin²x) / cos²x

Next, we will simplify the denominator by using the reciprocal identity cos²x = 1/sin²x:

LHS: (1+2sinx+sin²x) / (1/sin²x)

Now, let's simplify further by multiplying the numerator and denominator by sin²x:

LHS: sin²x(1+2sinx+sin²x) / 1

Expanding the numerator, we get:

LHS: (sin²x + 2sin³x + sin⁴x) / 1

Now, let's simplify the numerator by factoring out sin²x:

LHS: sin²x(1 + 2sinx + sin²x) / 1

Using the fact that sin²x = 1 - cos²x, we can rewrite the numerator:

LHS: sin²x(1 + 2sinx + (1-cos²x)) / 1

Simplifying further, we get:

LHS: sin²x(2sinx + 2 - cos²x) / 1

Using the fact that cos²x = 1 - sin²x, we can rewrite the numerator again:

LHS: sin²x(2sinx + 2 - (1-sin²x)) / 1

Simplifying the numerator, we have:

LHS: sin²x(2sinx + 1 + sin²x) / 1

Now, let's simplify the numerator by expanding it:

LHS: (2sin³x + sin²x + sin²x) / 1

LHS: 2sin³x + 2sin²x / 1

Finally, combining like terms, we get:

LHS: 2sin²x(sin x + 1) / 1

Now, let's simplify the RHS of the equation and see if it matches the LHS:

RHS: (cscx+1) / (cscx-1)

Using the reciprocal identity cscx = 1/sinx, we can rewrite the RHS:

RHS: (1/sinx + 1) / (1/sinx - 1)

Multiplying the numerator and denominator by sinx to simplify, we get:

RHS: (1 + sinx) / (1 - sinx)

Now, we can see that the LHS and RHS are equal:

LHS: 2sin²x(sin x + 1) / 1

RHS: (1 + sinx) / (1 - sinx)

Therefore, we have proven that (secx+tanx)² = (cscx+1)/(cscx-1).

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Step-by-step explanation:

For some side x, we are given two angles so let use law of sines

We don't know the angle opposite of the x side so we using the triangle interior property

[tex]120 + 51 + x = 180[/tex]

[tex]x = 9[/tex]

So the missing angle is 9.

The law of sines formula is that

[tex] \frac{a}{ \sin( \alpha ) } = \frac{b}{ \sin( \beta ) } [/tex]

where a and b are side lengths.

And alpha, and Beta are angles that are OPPOSITE of the side lengths, a and b, respectively

Let a be 25,

therefore alpha is 120

Let b be x,

therefore beta is 9.

[tex] \frac{25}{ \sin(120) } = \frac{x}{ \sin(9) } [/tex]

Solving for x.

[tex]25 \times \frac{ \sin(9) }{ \sin(120) } = x[/tex]

[tex]x = 4.51587[/tex]

Round if needed so our answer is

[tex]x = 4.5[/tex]

The area of the triangle in the shaded region is derived to be 29.75 square inches.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

For the triangle in the shaded region;

base = 8.5 inches

height = 7 inches

area of the triangle = 1/2 × 8.5 in × 8.5 in

area of the triangle = (59.5/2) in²

area of the triangle = 29.75 in²

Therefore, the area of the triangle in the shaded region is derived to be 29.75 square inches.

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Answer:

Step-by-step explanation:

Answer:  2

Step-by-step explanation:

List the factors(numbers that multiply to make that number for each number

6: 1, 2, 3, 6

34: 1, 2, 16, 34

2: 1, 2

Whichever is the factor that is the greatest that they all have in common is your greatest common factor.

2

Answer:

21

Source:

trust me bro

Answer:

1.3136363636363637

Step-by-step explanation:

Bc u times 17 times 17 devide by 220

Answer:

1836.50 square inches of the bulletin board is NOT covered with art work.

Step-by-step explanation:

The question focuses on the area covered by the paintings and the board, since area is defined as:  the amount of space enclosed within the boundaries of a flat, two-dimensional shape, such as a square, circle, or rectangle.

Step 1:  First, we need to know the total area of the five paintings.  

A = lw, where

We can allow 8.5 to be the length and 11 to be the width:

A = 8.5 * 11

A = 93.5 square inches

Multiplying 93.5 by 5 shows us the the total area covered by the five pieces of artwork is 467.50 square inches as 93.5 * 5 = 467.50

Step 2:  Now we need to find the area of the bulletin board.

A = s^2, where

48 is s in the area formula:

A = 48^2

A = 2304 square inches

Thus, the area of the bulletin board is 2304 square inches.

Step 3:  Finally, subtracting the total area of the five pieces of artwork from the area of the bulletin board will tell us how much of the bulletin board is NOT covered with art work:

2304 - 467.50 = 1836.50 square inches

Thus, 1836.50 square inches of the bulletin board is not covered with art work.

Answer:

[1;1;1]

Step-by-step explanation:

try this option; all the details are in the attachment.

Step-by-step explanation:

remember, when we multiply the same base, we add the exponents, when we divide the same base we subtract the exponents.

when we have exponent of exponent, we multiply the exponents.

so,

the expression is

(z^ac / z^bc) × (z^ab / z^ac) × (z^bc / z^ab) = 1

we have in there the commutative and associative properties of multiplication : the sequence of operands do not matter at all.

and therefore we have in there the terms :

z^ac / z^ac

z^bc / z^bc

z^ab / z^ab

all three are 1

and so the main expression is

1 × 1 × 1 = 1

which is true, of course, and therefore the original equation is true.

we know that,

★ The sum of the angles in a triangle is always 180° ...

__________________________________

Thus, the Value of x is 34°.

Answer:

Step-by-step explanation:

We know that,

Sum of three side of triangle is 180°

so,

100° + 46° + x = 180°

146° + x = 180°

x = 180° - 146°

x = 34°

[tex]\underline{\rule{190pt}{4pt}}[/tex]

Answer:

the answer is C

Step-by-step explanation:

any negative power is the reciprocal

so m^(-2) = 1/m^2

and so on

1/n^(-3) = n^(3)

The expression that is equivalent to the trigonometry ratio (sin²θ + cos²θ)/tan²θ is (a) cot²θ

From the question, we have the following parameters that can be used in our computation:

The trigonometry ratio given as

(sin²θ + cos²θ)/tan²θ

In trigonometry,

sin²θ + cos²θ = 1

So, we have the following representation

(sin²θ + cos²θ)/tan²θ = 1/tan²θ

Evaluate the quotient

(sin²θ + cos²θ)/tan²θ = cot²θ

Hence, the expression that is equivalent to the trigonometry ratio is (a) cot²θ

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Every day, the number of people who receive the email grows by a factor of 3.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided above, an exponential function for the total number of people who received the email is given by;

[tex]P(t) = 4(3)^t[/tex]

By comparison, we have the following parameters;

Initial value, a = 4.

Growth rate, b = 3.

In conclusion, the number of people who receive the email from Elon every day grow by a factor of 3.

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Answer:

(x - 3)² + (y + 4)² = 29

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

we have the coordinates of the centre but require to find the radius r

the radius is the distance from the centre to a point on the circle.

using the distance formula to find r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (3, - 4 ) centre and (x₂, y₂ ) = (8, - 2) point on circle

r = [tex]\sqrt{(8-3)^2+(-2-(-4))^2}[/tex]

  = [tex]\sqrt{5^2+(-2+4)^2}[/tex]

  = [tex]\sqrt{25+2^2}[/tex]

  = [tex]\sqrt{25+4}[/tex]

  = [tex]\sqrt{29}[/tex]

then equation with centre (3, - 4 ) and r = [tex]\sqrt{29}[/tex] , is

(x - 3)² + (y - (- 4) )² = ([tex]\sqrt{29}[/tex] )² , that is

(x - 3)² + (y + 4)² = 29

When a dilation is performed on a triangle, the angles and side lengths of the preimage and image are related in a specific way. The correct answer is B. The angles are congruent, and the side lengths are proportional.

In a dilation, each corresponding angle of the preimage and image triangles is congruent. This means that if an angle in the preimage triangle measures 60 degrees, the corresponding angle in the image triangle will also measure 60 degrees.

However, the side lengths of the preimage and image triangles are not necessarily congruent. Instead, they are proportional. This means that the ratio of corresponding side lengths remains constant throughout the dilation. For example, if one side of the preimage triangle is twice as long as another side, the corresponding side in the image triangle will also be twice as long as its corresponding side.

It's important to note that the center of dilation and the scale factor determine the specific proportions between the side lengths. The scale factor represents the ratio of corresponding side lengths in the preimage and image triangles.

Therefore, in a dilation, the angles are congruent, and the side lengths are proportional.

The right answer is B. The angles are congruent and the side lengths are proportional.

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Answer:

Să rezolvăm această problemă pas cu pas. Să denotăm vârsta Denisei ca D, vârsta mamei sale ca M și vârsta tatălui ei ca F. Din informațiile date, putem scrie următoarele ecuații:

M = D + 27 (Denisa are cu 27 de ani mai puțin decât mama ei) F = M + 1 (mama Denisei are cu un an mai puțin decât tatăl ei) F = 5D (Denisa este de cinci ori mai tânără decât tatăl ei)

a) Din ultima ecuație, putem vedea că Denisa este F - D cu ani mai tânără decât tatăl ei. Înlocuind F cu 5D, înțelegem că Denisa este 5D - D = 4D cu ani mai tânără decât tatăl ei.

b) Pentru a determina vârsta Denisei, putem rezolva sistemul de ecuații. Din prima ecuație, obținem acel M = D + 27. Înlocuind acest lucru în a doua ecuație, obținem acel F = D + 27 + 1 = D + 28. Înlocuind acest lucru în a treia ecuație, obținem acel D + 28 = 5D. Rezolvând pentru D, obținem acel D = 7.

Deci Denisa are 7 ani.

Answer:

Denisa are 7 ani

Step-by-step explanation:

Based on the given values, the value of A is given as 5

To find the value of A, we need to solve the equation for the expected value, E(X) = 5.75, using the provided probabilities and x values.

The expected value formula is:

E(X) = Σ[x * P(x)]

Plugging in the given values:

5.75 = (4 * 0.15) + (A * 0.55) + (8 * 0.3)

To solve for A, we can first simplify the equation:

5.75 = 0.6 + 0.55A + 2.4

Now, combine constants and subtract from the left side:

2.75 = 0.55A

Finally, divide by 0.55 to find the value of A:

A = 2.75 / 0.55 ≈ 5

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Movie B has approximately 25% more frames than Movie A.

For Movie A the duration is 100 minutes

Frame rate: 24 frames per second

Total frames in Movie A:

Total frames in Movie A = 100×60×24

Movie B:

Duration: 100 minutes

Frame rate: 30 frames per second

Total frames in Movie B:

Total frames in Movie B = 100 × 60 × 30

To find the percent more frames in Movie B compared to Movie A, we can use the following formula:

Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100

Total frames in Movie A = 100 × 60× 24

Total frames in Movie B = 100 ×60 × 30

Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100

Percent more frames = ((100 × 60× 30) - (100 × 60×24)) / (100 × 60× 24)×100

Percent more frames = (180,000 - 144,000) / 144,000 * 100

Percent more frames = 36,000 / 144,000 * 100

Percent more frames = 25%

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The best representation of the mean number of sports played by middle school students is 2.75 sports and the MAD is about 0.84 sports.

To find the best representation of the mean number of sports played by middle school students, we need to calculate the median of the given data.

The median represents the central tendency of the data and is less affected by extreme values.

Arranging the means of the samples in ascending order, we have:

1, 1, 2, 2.5, 3, 3, 3.5, 4

Since there are eight values, the median will be the average of the fourth and fifth values:

(2.5 + 3) / 2 = 2.75

Variability in the Distribution

Summing up the absolute deviations:

1.75 + 1.75 + 0.75 + 0.25 + 0.25 + 0.25 + 0.75 + 1.25 = 6.75

To find the MAD, we divide the sum of the absolute deviations by the total number of data points:

MAD = 6.75 / 8 = 0.84

Therefore, the MAD is about 0.84 sports.

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The basic ratio of minutes of painting to minutes of instruction is 7 : 6

From the question, we have the following parameters that can be used in our computation:

Painting = 63 minutes

Instruction = 54 minutes

The ratio can be represented as

Ratio = Painting : Instruction

When the given values are substituted in the above equation, we have the following equation

Painting : Instruction = 63 : 54

Simplify

Painting : Instruction = 21 : 18

Simplify

Painting : Instruction = 7 : 6

This  ratio cannot be simplified

Hence, the solution is 7 : 6

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In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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