Find the coordinates of the centroid of the triangle with the given vertices. (Lesson 5-2)
X(-11,0), Y(-11,-8), Z(-1,-4)

We are given the following equation:

First we will solve the square:

Now we will solve the product:

Now we will add the numbers:

Now we will multiply both sides by 2:

Now we add the terms on the right side:

Now we will divide both sides by 9:

To solve the exponential equation 8eˣ - 18 = 15, we can use logarithms to isolate the variable x. By taking the natural logarithm of both sides, we can find the value of x either in terms of logarithms or correct to four decimal places.

Additionally, to find a formula for the exponential function passing through the points (-1,3/5) and (2,75), we can use the two-point form of an exponential function to determine the specific equation. For the equation 8eˣ - 18 = 15, we can solve for x using logarithms. Taking the natural logarithm (ln) of both sides, we have: ln(8eˣ - 18) = ln(15). Simplifying further: ln(8eˣ) = ln(33). Applying logarithmic properties, we get: ln(8) + ln(eˣ) = ln(33). Using the fact that ln(eˣ) = x, we have: ln(8) + x = ln(33). Finally, solving for x: x = ln(33) - ln(8). To find the exponential function passing through the points (-1,3/5) and (2,75), we can use the two-point form of an exponential function, which is given by: f(x) = a * bˣ. Substituting the coordinates of the points into the equation, we get two equations: 3/5 = a * b^(-1), 75 = a * b². Solving these equations simultaneously, we can find the values of a and b. Once we have the values of a and b, we can write the specific equation for the exponential function.

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Answer:

let f(m) = u

multipling both sides by 2

We have 2f(m)=m

therefore m=2

The expected value of the sum of the numbers that come up is 10.5 and the variance of the sum of the numbers that come up is 8.75.

Let the three dice be A, B, and C. The expected value of a single die is 3.5, and the variance is 35/12. Using these two pieces of information, we can compute the expected value and variance of the sum of the three dice.

a) The expected value of the sum of the numbers that come up is:

E(A+B+C) = E(A) + E(B) + E(C) = 3(3.5) = 10.5. b)

The variance of the sum of the numbers that come up is:

Var(A+B+C)

= Var(A) + Var(B) + Var(C)

= 3(35/12)

= 35/4

= 8.75.

Therefore, the expected value of the sum of the numbers that come up is 10.5 and the variance of the sum of the numbers that come up is 8.75.

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Answer:

The correct answer is -$1,209.85-verified by Edg. Thank you.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

400 grams

Step-by-step explanation:

If the equation is density = mass / volume, fill it out to find mass

10 = x / 40

400 = x

x = 400 g

Answer:

12 upon 30 is the write answers I think and it would help you

Answer:

Ivan had 288 sweet while Ken had 672 sweets

Step-by-step explanation:

Let the number of sweets owned by Ken and Ivan be k and v respectively.

After Ken gave away 5/7 of his sweet, what he had left

= k - 5k/7

= 2k/7

he had 2/3 as many sweets as Ivan then

2k/7 = 2v/3

Divide both sides by 2 and cross multiply

7v = 3k

Ivan then gave away 120 sweets, Ivan would have

v - 120 = k/4

multiply both sides by 4

4v - 480 = k

7v = 3(4v - 480)

7v = 12v - 1440

12v - 7v = 1440

5v = 1440

v = 1440/5

= 288

7v = 3k

7 * 288 = 3k

k = 7 * 288/3

= 672

Answer:

None of the following

Step-by-step explanation:

Answer:

Radius duh

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

The volume of the cube container is the amount of space in it, and the maximum measurement of the edge of the larger cube is 5.5 inches

The volume of the container is given as:

V = 64 cubic inches

When it increases by a maximum of 100 cubic inches, the new volume becomes

V = 164 cubic inches

The volume of a cube container is calculated using:

V = l³

Where l represents the edge length of the cube

Substitute 164 for V

l³ = 164

Take the cube root of both sides

l = 5.5

Hence, the maximum measurement of the edge of the larger cube is 5.5 inches

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The stem-and-leaf display of the data is

Stem | Leaves

1 | 2

2 | 2

3 | 3

4 | 5, 8

To start, let's assume we have a set of data values, such as 12, 22, 33, 45, 48, 53, 61, 62, 72, 83, 91, 96, 99.

The stem-and-leaf display consists of two parts: the "stem" and the "leaf." The stem represents the leading digit(s) of the data values, and the leaf represents the trailing digit(s). For example, the number 12 has a stem of 1 and a leaf of 2.

Now, let's organize the data values into their corresponding stems:

Stem 1: 12

Stem 2: 22

Stem 3: 33

Stem 4: 45, 48

Next, we list the leaves corresponding to each stem. The leaves are listed in ascending order next to their respective stems:

Stem 1: 2

Stem 2: 2

Stem 3: 3

Stem 4: 5, 8

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Answer:

77.42

Step-by-step explanation:

48/62=77.42

Answer:

132min (mark brainliest?)

Step-by-step explanation:

noon = 12pm

2:12pm - 12pm = 2 hours and 12 min

2 hours *( 60 min) = 120 min

120 min + 12 min = 132 min

Answer:

-72

Workout:
= -3(5)^2-(-3)

= -3(25)+3

= -75+3

= -72 (answer)

Answer:

The difference in elevation between these two points is 30,384 feet.

Step-by-step explanation:

First, I decided to let the 1,349 below sea level represent a negative number, since, in this context, it's below 0, or sea level.

This gives us the equation 29,035 - (-1,349) = ?

Since we need to find the difference in elevation, we will need to subtract the two values.

29,035 - (1,349) = 30,384

Hope this helps.

The final image of the given points after the given translation and dilation of D4,  T3,5 is  (27, -23).

For the given image point of (6, -7) .

First there is a dilation of 4.

Thus,

Image = (6×4 , -7×4)

Image = (24, -28)

Now, there is translation of 3 units right on x axis and 5 unit upward on y axis; T3,5.

Image = (24 + 3, -28 + 5)

Image = (27, -23)

Thus, the final image of the given points after the given translation and dilation is  (27, -23).

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As per the reference document attached thereby along with the question statement, if (∠SOX = 160°), [∠1 = (x + 14)], and [∠2 = (3x – 10)], then the measure of ∠2 in degrees will be 113°

As per the reference document attached thereby along with the question statement, (∠SOX = 160°), and it's constituent angles

[∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)],

And we are required to determine the measure of ∠2.

Since, [(∠SOW + ∠WOX) = ∠SOX],

Therefore, [{(x + 14) + (3x – 10)} = 160°]

Or, [{(x + 3x) + (14 - 10)} = 160°]

Or, [(4x - 4) = 160°]

Or, [4x = (160 + 4)°]

Or, (4x = 164°)

Or, [x = (164/4)°]

Or, (x = 41°)

Or, [(3x – 10) = {(3 * 41) - 10}°]

Or, [∠2 = (123 - 10)°]

Or, (∠2 = 113°)

That is, if (∠SOX = 160°), and it's constituent angles (∠1) and (∠2) measure as [∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)], then the measure of ∠2 in degrees will be 113°

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Applying the inscribed angle theorem, we have:

a. x = 55° b. x = 60°  c. x = 92°    d. x = 84°

These theorem states that:

Inscribed angle measure = 1/2(central angle) or measure of intercepted arc.

Intercepted arc measure = central angle measure.

Therefore, we have:

a. x = 180 - 35 - 90 [tangent theorem]

x = 55°

b. x = 1/2(120) [inscribed angle theorem]

x = 60°

c. x = 2(46) [inscribed angle theorem]

x = 92°

d. m(FE) = 2(42) = 84°

m(EB) = 180 - FE = 180 - 84

m(EB) = 96°

m(AB) = 180 - m(EB) = 180 - 96

m(AB) = 84°

x = m(AB) = 84° [central angle theorem]

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Answer:182.5

Step-by-step explanation: 67.4 + 43 = 110.4

110.4 + 30 + 42.10

110.4 + 30 = 140.4

140.4 + 42.10

140.4 + 42.10 = 182.5

182.5

Round 182.5 → 182 (Decimals: 0)

find dy/dx

x= t sin(t); (Given in the question)

y= t²+8t; (Given in the question)

then, x= t sin(t)

dx/dt = sin t + t cos t ;

y= t²+8t

dy/dt = 2t + 8;

then, dy/dx = dy/dt x dx/dt

dy/dx = (2t+8)/(sin t + t cos t)

dy/dx = 2(t+4)/(sin t + t cos t)

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Answer:

y = 4x - 12

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

let the denominator of the fraction be x , then the fraction is

\(\frac{x-5}{x}\)

increasing the numerator and denominator by 4

\(\frac{x-5+4}{x+4}\) = \(\frac{x-1}{x+4}\)

this fraction is then equal to 3 times ( triple ) the value of the fraction, so

\(\frac{x-1}{x+4}\) = \(\frac{3(x-5)}{x}\) ( cross- multiplying )

3(x - 5)(x + 4) = x(x - 1) ← expand factors on left using FOIL

3(x² - x - 20) = x(x - 1) ← distribute parenthesis on both sides

3x² - 3x - 60 = x² - x ( subtract x² - x from both sides )

2x² - 2x - 60 = 0 ( divide through by 2 )

x² - x - 30 = 0 ← in standard form

(x - 6)(x + 5) = 0

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 5 = 0 ⇒ x = - 5

however, x > 0 , then x = 6

original fraction

= \(\frac{x-5}{x}\) = \(\frac{6-5}{6}\) = \(\frac{1}{6}\)

Answer:

-4

Step-by-step explanation:

hope this helps with the work

The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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The  total distance it flies, rounded to the nearest mile is: d. 1,692 miles .

First distance= 550 miles (given)

Second distance=483 miles (given)

Now let find the third distance

Let x represent the third distance

Hence:

x/sin79 = 550/sin55

x= 659.1

Now let calculate the total distance

Total distance=550+483+659.1

Total distance= 1692.1

Total distance= 1692 miles (rounded)

Therefore the correct option is d.

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By taking the quotient between the total number of hours and the number of shifts each shift is 1.5 hours long.

We know that Paolo worked (2 + 3/4) hours this week, and that is equivalent to (1 + 5/6) shifts.

To find the number of hours that each shift takes, we need to take the quotient between the total number of hours and the number of shifts:

\(\frac{(2 + 3/4)h}{1 + 5/6} = 1.5 h\)

This means that each shift is 1.5 hours long.

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