The polygons are similar. find the missing length. i will give brainliest to first correct answer! HELP

The height of the right triangle is 24 centimeters. This is determined by solving the equation for the area of the triangle, which is given as 96 cm², and considering that the height is 3 times the length of the base. By substituting the values and solving the equation, we find that the height is indeed 24 centimeters.

To determine the height of the right triangle, we can use the formula for the area of a triangle, which is given by the formula A = (1/2) * base * height. In this case, the area is known to be \(96 cm^2\).

Let's denote the length of the base as x. According to the problem statement, the height is 3 times the length of the base, so the height can be expressed as 3x.

Substituting these values into the area formula, we get:

\(96 = (1/2) * x * 3x\)

Simplifying the equation:

\(96 = (3/2) * x^2\)

To solve for x, we can divide both sides of the equation by (3/2):

\(64 = x^2\)

Taking the square root of both sides, we find:

x = 8

Since the height is 3 times the length of the base, the height is:

3 * 8 = 24 centimeters.

Therefore, the height of the right triangle is 24 centimeters.

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The limit does not exist.

In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).

Try approaching \((0,0)\) along the x-axis.

This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).

We obtain:

\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)

Now evaluate approaching \((0,0)\) along the y-axis.

This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).

\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)

Approaching the origin via these two methods results in distinct limits.

\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)

Answer:

Step-by-step explanation:

Therefore, the average height of the particle on the interval [-1, 5] is approximately 33.67 feet.

To find the average height of the particle on the interval [-1, 5], we need to evaluate the definite integral of the position function f(x) = 3x^2 + 6x over that interval and divide it by the length of the interval.

The average height (H_avg) is calculated as follows:

H_avg = (1 / (b - a)) * ∫[a to b] f(x) dx

In this case, a = -1 and b = 5, so the average height is:

H_avg = (1 / (5 - (-1))) * ∫[-1 to 5] (3x^2 + 6x) dx

To evaluate the integral, we can use the power rule of integration:

∫ x^n dx = (1 / (n + 1)) * x^(n+1) + C

Applying this rule to each term in the integrand, we get:

H_avg = (1 / 6) * [x^3 + 3x^2] evaluated from -1 to 5

Now, we can substitute the limits of integration into the expression:

H_avg = (1 / 6) * [(5^3 + 3(5^2)) - ((-1)^3 + 3((-1)^2))]

H_avg = (1 / 6) * [(125 + 75) - (-1 + 3)]

H_avg = (1 / 6) * [200 - (-2)]

H_avg = (1 / 6) * 202

H_avg = 33.67 feet

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The volume of the solid obtained by rotating the region enclosed by y=x^2 and y=3x about the line y=9 using the method of washers is (27/2)π cubic units, obtained by integrating π(-x^4 + 15x^2 - 54x) over [0,3].

To find the volume of the solid obtained by rotating the region enclosed by y=x^2 and y=3x about the line y=9, we can use the method of washers.

Consider a vertical slice of the solid at an arbitrary value of x

The slice has width dx and thickness dy. The distance between the line y=9 and the curve y=x^2 is 9-x^2, and the distance between the line y=9 and the line y=3x is 9-3x. Therefore, the area of the washer at x with inner radius 9-3x and outer radius 9-x^2 is:

dA = π[(9-x^2)^2 - (9-3x)^2]dy

  = π[(x^4 - 6x^2 + 81) - (9x^2 - 54x + 81)]dy

  = π(-x^4 + 15x^2 - 54x)dy

Integrating this expression over the region of interest [0,3], we get:

V = ∫[0,3] π(-x^4 + 15x^2 - 54x)dy

 = π[-(1/5)x^5 + 5x^3 - (27/2)x^2]_[0,3]

 = π[(243/10) - (135/2) - (27/2)]

 = (27/2)π

Therefore, the volume of the solid is (27/2)π cubic units.

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The approximate standard deviation of the returns on an average stock is typically around 15 to 25 percent. This indicates the volatility or risk associated with the stock's returns.

However, it's important to note that the actual standard deviation can vary depending on various factors, such as market conditions, industry trends, and company-specific factors.

Therefore, it is recommended to consider historical data, market analysis, and professional guidance when evaluating the standard deviation of a specific stock.

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Answer:

you worked 14 hours

Step-by-step explanation:

W = 52 + 8h

164 = 52 + 8h

112 = 8h

14 = h

Answer:

The answer is 14 hours

Step-by-step explanation:

The question states that h means hours and w is the total amount of money received.

164 = 52 + 8h

-52   -52

112 = 8h

112/8 = 8h/8

14 = h

The answer is 14 hours (but you don't need to include the label when you submit your form). Plus we can see your email address which i suggest you shouldn't show next time :)

Hope this helps!

The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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the capacity of the largest container that can measure the contents of each drum an exact number of times is 36 liters.

To find the capacity of the largest container that can measure the contents of each drum an exact number of times, we need to determine the greatest common divisor (GCD) of the volumes of the drums.

The GCD is the largest positive integer that divides each of the given numbers without leaving a remainder. In this case, we want to find the GCD of 36, 45, and 72.

First, let's find the prime factorizations of these numbers:

36 = 2^2 * 3^2,

45 = 3^2 * 5,

72 = 2^3 * 3^2.

To find the GCD, we take the product of the common prime factors raised to the lowest powers they appear in the factorizations:

GCD(36, 45, 72) = 2^2 * 3^2 = 4 * 9 = 36.

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Answer:

\(3(2+7a)=6+\)

\(6 + 21a = 6\)

\(21a + 6 = 6 + 21a\)

answer is 21a

For the given figure, we will prove the triangles BGH and BDH are congruent.

So, the proof will be as follows:

Statement Reason

1) m∠F = m∠FEG = m∠FGE Given

2) ΔFGE is an equilateral triangle from (1), the definition of an equilateral Δ

3) FG = GE from (2), the definition of equilateral Δ

4) FG = ED Given

5) m∠ GEH = m∠DEH Given

6) EH = EH Reflexive property

7) ΔGEH ≅ Δ DEH SAS postulate

8) GH = DH from (7) CPCTC

9) m∠GHE = m∠DHE from (7) CPCTC

10) m∠GHB = m∠DHB Definition of supplementary angles

11) HB = HB Reflexive property

12) ΔBGH ≅ ΔBDH SAS postualte

13) ΔAGB is an isosceles Δ Given

14)AG = AB Definition of isosceles Δ

15) ΔBCD is an isosceles Δ Given

16) CB = CD Definition of isosceles Δ

17) CB = AG Given

18) m∠CDB = m∠CBD Definition of isosceles Δ

19) m∠ABG = m∠AGB Definition of isosceles Δ

20) m∠CDB = m∠AGB Given

21) m∠ABG = m∠CBD Transitive property

22) Δ AGB ≅ ΔCBD AAS postualte

Answer:

m∠1 = 25° (opposite angles are congruent)

m∠2 = 87° ⇒ 180 - (25 + 68)

m∠3 = 68° ⇒ 180 - (87 + 25)

Hope this helps!

Answer:

  x = 12

Step-by-step explanation:

Given congruent triangles ABD and CBD, and expressions for corresponding angles ABD and CBD, you want the value of x in the expression for angle CBD.

Corresponding parts of congruent triangles are congruent, so we know ...

  ∠ABD ≅ ∠CBD

  99° = (9x -9)° . . . . use the given expressions

  11 = x -1 . . . . . . . . divide by 9°

  12 = x . . . . . . . . add 1

The value of x is 12.

Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

The distance between point P and line l is

1. Distance = 2√2

2. Distance =0

3. Distance =6

4. Distance =1

5. Distance =√10

To find the distance between a point and a line, we can use the formula for the distance between a point and a line in the coordinate plane. The formula is:

Distance = |Ax + By + C| / √(A² + B²)

1. Line & contains points (0, -3) and (7, 4). Point P has coordinates (4,3).

The equation of the line is y = x - 3. We can rewrite it as x - y + 3 = 0.

So, Distance = |4 - 3 + 3| / √(1² + (-1)²)

= |4| / √2

= 4 / √2

= 2√2

2. Line & contains points (11, -1) and (-3, -11). Point P has coordinates (-1, 1).

The equation of the line is y = -2x - 1. We can rewrite it as 2x + y + 1 = 0.

So, Distance = |2(-1) + 1 + 1| / √(2² + 1²)

= |-2 + 2| / √5

= 0 / √5

= 0

3. Line & contains points (-2, 1) and (4, 1). Point P has coordinates (5, 7).

The equation of the line is y = 1.

So, Distance = |0(5) + 7 - 1| / √(0² + 1²)

= |6| / √1

= 6

4. Line & contains points (4, -1) and (4, 9). Point P has coordinates (1, 6).

The line is vertical, and its equation is x = 4.

so, Distance = |1 - 4 + 4| / √(1² + 0²)

= |-1| / √1

= 1

5. Line & contains points (1, 5) and (4, -4). Point P has coordinates (-1, 1).

The equation of the line is y = -3x + 8.

So, Distance = |3(-1) + 1 - 8| / √(3² + 1²)

= |-3 - 7| / √10

= |-10| / √10

= 10 / √10

= 10√10 / 10

= √10

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The given problem is about finding the linear speed of a vehicle when each of its tire has a diameter of 32 inches and is moving at 800 revolutions per minute. In order to solve this problem, we will use the formula `linear speed = (pi) (diameter) (revolutions per minute) / (1 mile per minute)`.

Since the diameter of each tire is 32 inches, the radius of each tire can be calculated by dividing 32 by 2 which is equal to 16 inches. To convert the units of revolutions per minute and inches to miles and hours, we will use the following conversion factors: 1 mile = 63,360 inches and 1 hour = 60 minutes.

Now we can substitute the given values in the formula, which gives us:

linear speed = (pi) (32 inches) (800 revolutions per minute) / (1 mile per 63360 inches) x (60 minutes per hour)

Simplifying the above expression, we get:

linear speed = 107200 pi / 63360

After evaluating this expression, we get the linear speed of the vehicle as 5.36 miles per hour. Rounding this answer to the nearest tenth gives us the required linear speed of the vehicle which is 5.4 miles per hour.

Therefore, the linear speed of the vehicle is 5.4 miles per hour.

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The image after a dilation by a scale factor of 4 centered at the origin is (-132,-352).

Scale factor is a mathematical term that refers to the ratio of two corresponding sides of similar shapes. It is used to compare the size of objects or figures by determining the size of a model in relation to its actual size. For example, if two shapes are similar, then their scale factor will be the same. This is useful in engineering and architecture when building scaled models of structures and machines. Scale factors can also be used to determine the proportions and measurements of an object in relation to similar objects.

This is because a dilation by a scale factor of 4 is the same as multiplying the original coordinates by 4. So, if the original coordinates were (-3,-8), then the new coordinates would be (-12,-32). Then, the coordinates are shifted by the center (the origin), so the new coordinates are (-132,-352).

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Answer:

23

Step-by-step explanation:

The opposite of a number is the opposite sign of it. So, the opposite of a negative number is a positive number:

Opposite of -23 is 23

Answer:

x= 5/3

Step-by-step explanation:

Answer:

9 plus 11 plus 12 =

Step-by-step explanation:

x is 22

Answer:

384 cm^3

Step-by-step explanation:

the volume formula:

     V = a*b*c,

where a - length, b - width, c - height

so, the volume of the solid is V = 4*8*12 = 384 cm^3

The volume of the solid, if the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters is 384 cm³.

To find the volume of the solid, we need to multiply the length, width, and height together. So, the volume of the solid is:

V = l x w x h
V = 4 cm x 8 cm x 12 cm
V = 384 cm³

Therefore, the volume of the solid is 384 cubic centimeters (cm³).

To find the volume of a solid with given dimensions, you can use the formula for the volume of a rectangular prism, which is Volume = Length × Width × Height. In this case, the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters.

Now, let's plug these values into the formula:

Volume = (4 cm) × (8 cm) × (12 cm)

By multiplying these numbers together, you'll get the volume of the solid:

Volume = 384 cubic centimeters (cm³)

So, the volume of the solid with the given dimensions is 384 cm³.

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Answer:

20

Step-by-step explanation:

1 hour is 60 minutes 1/3x60=20

Answer:

1200 seconds

Step-by-step explanation:

1/3 of an hour is 20 minutes. There are 60 seconds in a minute. 60 times 20 = 1200.

Answer:

The numerical length of RS is 22 units

Step-by-step explanation:

∵ Point S is on the line segment RT

→ That means S divide RT into two parts RS and ST

∴ RS + ST = RT

∵ RS = 4x - 10

∵ ST = 2x - 10

∵ RT = 4x - 4

→ Substitute them in the statement above

∴ 4x - 10 + 2x - 10 = 4x - 4

→ Add the like terms in the left side

∴ (4x + 2x) + (-10 + -10) = 4x - 4

∴ 6x + (-20) = 4x - 4

∴ 6x - 20 = 4x - 4

→ Add 20 to both sides

∴ 6x -20 + 20 = 4x - 4 + 20

∴ 6x = 4x + 16

→ Subtract 4x from both sides

∴ 6x - 4x = 4x - 4x + 16

∴ 2x = 16

→ Divide both sides by 2 to find x

∴ \(\frac{2x}{2}=\frac{16}{2}\)

∴ x = 8

→ Substitute the value of x in Rs to find its length

∵ RS = 4(8) - 10

∴ RS = 32 - 10

∴ RS = 22 units

The numerical length of RS is 22 units

Answer:

RS=4

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

\({:}\longrightarrow\)\(\sf BD={\dfrac {1}{2}}AE \)

\({:}\longrightarrow\)\(\sf BD={\dfrac {1}{2}}21\)

\({:}\longrightarrow\)\(\sf BD={\dfrac {21}{2}}\)

\({:}\longrightarrow\)\(\sf BD=10.5cm \)

The line BD will be 10.5cm in the triangle ABC. Thus option D is correct.

A closed shape with both inner and exterior angles, a triangular is created by three lines.  the fundamental geometric shapes. a vertex-filled triangle. There is only one distinct triangle if the product of two fades on the sides is bigger than the longest side. 

The value of AE is given as 21.

From the diagram that is given, it is indicated that according to the midpoint theorem

BD║AE

Also, BD= 1/2 ×AE

BD = 21/2

BD = 10.5 cm.

Therefore, option D is the correct option.

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The question is incomplete, the complete question will be :

A. 42

B. 21

C. 11.5

D. 10.5​

Answer:4p-7=13

Step-by-step explanation:combine like terms