In rhombus TIGE, diagonals TG and IE intersect at R. The perimeter

of TIGE is 68, and TG = 16.

R

G

E

What is the length of diagonal IEP

(1) 15

(3) 34

(2) 30

(4) 52

Answer:

1863M

Step-by-step explanation:

split into smaller rectangles

(31 * 23) * 2 = 713 *2 = 1426

31-12 = 19

19 * 23 = 437

1426 + 437

The expected winnings for this game are given as follows:

$171.67.

The expected value of a distribution is obtained as the sum of each outcome multiplied by it's respective probability.

The probability of rolling a two and getting heads is of:

P = 1/6 x 1/2 = 1/12.

Hence the probability of winning $1,000 is:

P(X = 1000) = 1/12.

The probability of rolling a four or a six and getting heads is of:

P = 2/6 x 1/2 = 2/12.

Hence the probability of winning $500 is of:

P(X = 500) = 2/12.

The probability of rolling an even number and tails is of:

P = 3/6 x 1/2 = 3/12.

The probability of rolling and odd number and heads is of:

P = 3/6 x 1/2 = 3/12.

Hence the probability of winning $10 is of:

P(X = 10) = 6/12.

Then the probability of losing, that is, earning $0, is of:

P(X = 0) = 1 - (1/12 + 2/12 + 6/12) = 3/12.

Then the distribution is given as follows:

Then the expected value of the distribution is of:

E(X) = 0 x 3/12 + 10 x 6/12 + 500 x 2/12 + 1000 x 1/12 = $171.67.

The problem asks for the expected winnings of the game.

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Hey there!

2x + 2 = -4(x - 5)

2x + 2 = -4(x) - 4(-5)

2x + 2 = -4x + 20

ADD 4x to BOTH SIDES

2x + 2 + 4x = -4x + 20 + 4x

SIMPLIFY IT!

6x + 2 = 20

SUBTRACT 18 to BOTH SIDES

6x + 2 - 2 = 20 - 2

CANCEL out: 2 - 2 because it give you 0

KEEP: 20 - 2 because it help solve for the x-value

NEW EQUATION: 6x = 20 - 2

SIMPLIFY IT!

6x = 18

DIVIDE 6 to BOTH SIDES

6x/6 = 18/6

CANCEL out: 6/6 because it give you 1

KEE: 18/6 because it help solve for the x-value

NEW EQUATION: x = 18/6

SIMPLIFY IT!

x = 3

Therefore, your answer is: x = 3

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

(a) To solve the given differential equation, we can use an integrating factor. the integrating factor is r(x) = 1 / |x^7|. b) The general solution to the given differential equation is given by: y(x) = e^(∫(7/x) dx) * [∫(7x / (x^7 |x^7|)) dx + C]

a) The integrating factor, denoted as r(x), is defined as:

r(x) = e^(∫(x) dx)

In this case, we have dx/dy = 7y - 7x. So, rewriting it in the form of dy/dx, we get:

dy/dx = (7y - 7x) / x

Comparing this with the standard form dy/dx + P(x)y = Q(x), we have P(x) = -7/x and Q(x) = 7y/x.

Now, let's calculate the integrating factor r(x):

r(x) = e^(∫(-7/x) dx)

= e^(-7ln|x|)

= e^(ln|x^(-7)|)

= |x^(-7)|

= 1 / |x^7|

Therefore, the integrating factor is r(x) = 1 / |x^7|.

(b) Now that we have the integrating factor, we can multiply both sides of the differential equation by r(x) to obtain the new equation:

1 / |x^7| * dy/dx = (7y - 7x) / x

Simplifying further:

dy/dx = (7y - 7x) / (x |x^7|)

Next, we integrate both sides with respect to x:

∫dy = ∫(7y - 7x) / (x |x^7|) dx

Integrating the right side requires using the method of partial fractions, which results in a complex integration process. Therefore, it is not feasible to provide the detailed solution in this format. However, we can write down the general solution in terms of an arbitrary constant.

The general solution to the given differential equation is given by:

y(x) = e^(∫(7/x) dx) * [∫(7x / (x^7 |x^7|)) dx + C]

Note that the integral of (7x / (x^7 |x^7|)) requires careful handling and substitution, resulting in a complex expression. The arbitrary constant C represents the constant of integration.

(c) To solve the initial value problem y(1) = 9, we substitute x = 1 and y = 9 into the general solution obtained in part (b). However, due to the complexity of the general solution, it is not possible to provide a direct solution in this format. The evaluation of the integral and the substitution process is extensive and requires detailed calculations.

In conclusion, the general solution to the given differential equation is y(x) = e^(∫(7/x) dx) * [∫(7x / (x^7 |x^7|)) dx + C]. To solve the specific initial value problem y(1) = 9, the general solution needs to be evaluated at x = 1, but the detailed calculation is beyond the scope of this format.

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Thus,  the directional derivative of g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j is -108.

To find the directional derivative of the function g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j, we need to use the formula for directional derivative:

dvg(6, 0) = ∇g(6, 0) ⋅ v

where ∇g is the gradient of g, which is given by:

∇g = (∂g/∂u)i + (∂g/∂v)j
   = (2ue^(-v))i - (u^2e^(-v))j

Evaluating the gradient at (6, 0), we get:

∇g(6, 0) = (2(6)e^(0))i - ((6)^2e^(0))j
         = 12i - 36j

Now we can substitute these values into the formula for directional derivative:

dvg(6, 0) = ∇g(6, 0) ⋅ v
         = (12i - 36j) ⋅ (3i + 4j)
         = 36 - 144
         = -108

Therefore, the directional derivative of g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j is -108.

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Answer:

  a14 = -40,960

Step-by-step explanation:

The sequence has a first term of 5 and a common ratio of -10/5 = -2, so the n-th term is given by ...

  an = a1·r^(n-1)

  an = 5·(-2)^(n-1)

The 14th term is then ...

  a14 = 5·(-2)^(14-1) = -5·2^13 = -5·8192

  a14 = -40,960

a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

Answer:

Value of x = 20°

Angle B = 60°

Exterior angle to B = 300°

Step-by-step explanation:

Given:

Angles of triangle.

A = 2x

B = 3x

C = 4x

We know that,

A + B + C = 180°

2x + 3x + 4x = 180°

9x = 180°

x = 20°

Value of x = 20°

Angle B = 3x

Angle B = 3(20°)

Angle B = 60°

Exterior angle to B = 360° - 60°

Exterior angle to B = 300°

Answer:

c!!!!!!!!!!!!!!!!!!!

The exact values are tan(t) = 2√5/5 and sec²(t) = 45/25. sec²(t) = 9/5. To find the exact values of tan(t) and sec²(t) with sin(t) = 2/3 and the terminal point in quadrant I, we can follow these steps:

1. Use the Pythagorean identity: sin²(t) + cos²(t) = 1.
2. Calculate cos(t): cos²(t) = 1 - sin²(t) = 1 - (2/3)² = 1 - 4/9 = 5/9, and since the terminal point is in quadrant I, cos(t) is positive, so cos(t) = √(5/9) = √5/3.
3. Calculate tan(t): tan(t) = sin(t)/cos(t) = (2/3) / (√5/3) = 2/√5, and rationalize the denominator, we get tan(t) = 2√5/5.
4. Calculate sec(t): sec(t) = 1/cos(t) = 1/(√5/3) = 3/√5, and rationalize the denominator, we get sec(t) = 3√5/5.
5. Calculate sec²(t): sec²(t) = (3√5/5)² = 9 * 5 / 25 = 45/25.
So, the exact values are tan(t) = 2√5/5 and sec²(t) = 45/25.

First, we know that sin(t) = 2/3, which means that in the unit circle, the y-coordinate of the terminal point is 2/3. Since the terminal point is in quadrant i, we also know that the x-coordinate is positive.
Using the Pythagorean theorem, we can find the radius of the unit circle:
r² = x² + y²
r² = 1²
r = 1
Now we can find the x-coordinate of the terminal point:
x = sqrt(r² - y²)
x = sqrt(1² - (2/3)²)
x = sqrt(5/9)
x = sqrt(5)/3
So now we know that the terminal point is at (sqrt(5)/3, 2/3).

To find tan(t), we use the formula:
tan(t) = y/x
Plugging in our values, we get:
tan(t) = (2/3) / (sqrt(5)/3)
tan(t) = 2 / sqrt(5)
tan(t) = (2 / sqrt(5)) * (sqrt(5) / sqrt(5))
tan(t) = 2sqrt(5) / 5
So tan(t) = 2sqrt(5) / 5.

To find sec²(t), we use the formula:
sec²(t) = 1 / cos²(t)
Since sin(t) = 2/3, we can use the Pythagorean identity to find cos(t):
cos²(t) = 1 - sin²(t)
cos²(t) = 1 - (2/3)²
cos²(t) = 1 - 4/9
cos²(t) = 5/9
Now we can find sec²(t):
sec²(t) = 1 / (5/9)
sec²(t) = 9/5
So sec²(t) = 9/5.

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Answer:

The polynomial that represents the area of a rhombus is \(A = 2\cdot P^{2}-8\).

Step-by-step explanation:

The area formula for the rhombus is defined below:

\(A = \frac{D\cdot d}{2}\) (1)

Where:

\(A\) - Area of the rhombus.

\(D\) - Greater diagonal.

\(d\) - Lesser diagonal.

If we know that \(d = (2\cdot P -4)\) and \(D = (2\cdot P + 4)\), then the area formula of the rhombus:

\(A = \frac{(2\cdot P - 4)\cdot (2\cdot P +4)}{2}\)

\(A = \frac{4\cdot P^{2}-16}{2}\)

\(A = 2\cdot P^{2}-8\)

The polynomial that represents the area of a rhombus is \(A = 2\cdot P^{2}-8\).

Assume, Steve walks at a constant pace, he will be in his house after 5 hours

Given the Parameters :

The distance walked in 1 hour = 15 miles - 12 miles = 3 miles

Recall :

Steve's speed = 3 miles ÷ 1 hour = 3mi/hr

Time taken to reach his destination :

Time taken = distance / speed

Time = (15 ÷ 3) = 5 hours

Therefore, It will take Steve 5 hours to reach his destination.

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Answer: $2 per candle

Step-by-step explanation:

Dollars to candles

4 to 2

is equivalent to

2 to 1

$2 per candle

The ratio of candles to dollars is 1/2.

$2 per candle.

Option B is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The following coordinates are from the graph.

(2, 4), (4, 8), (8, 16).

The x-coordinates denote the number of candles.

The y-coordinate denotes the cost.

Now,

(2, 4) means 2 candles cost $4.

(4, 8) means 4 candles cost $8.

(8, 16) means 8 candles cost $16.

The ratio of candles to dollars.

= 2/4

= 1/2

This means,

The cost of one candle is $2.

Thus,

The cost of one candle is $2.

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The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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Answer: y=-x+5 and y=-14 \(2x+2y=10 subtract 2x from both sides\\2x+2y-2x=10-2x \\2y=10-2x divide both sides by 2\\y=5-x rewriting using the commutative property\\y=-x+5\)

Step-by-step explanation:

Slope Intercept form is y=mx+b

Equation A:

Answer:

Use The Distributive Property of Equality

Step-by-step explanation:

In order to combine all the like terms you first need to get rid of those parentheses

you do this by doing the distributive property of

\(-6(3x+10)\)

This will get you

\(-18x -60\)

Now you can combine like terms and them move the variable and constants to different sides.

Answer = Use The Distributive Property of Equality

Plz mark me brainliest!

Hope this helps.

The area between the curves y = x^3 - 12x^2 + 35x and y = -x^3 + 12x^2 - 35x is to be determined. These two curves intersect at three points, and the area between them can be calculated by finding the definite integral of their difference.

To find the area between the curves, we need to determine the points where they intersect. Equating the two equations, we get x^3 - 12x^2 + 35x = -x^3 + 12x^2 - 35x. Simplifying this equation, we find 2x^3 - 24x^2 + 70x = 0. Factoring out 2x, we obtain 2x(x^2 - 12x + 35) = 0. This equation gives us three solutions: x = 0, x = 5, and x = 7. These values indicate the limits of integration for calculating the area.

Next, we need to find the positive difference between the two curves. This can be done by subtracting the equation of the lower curve from the equation of the upper curve, resulting in (x^3 - 12x^2 + 35x) - (-x^3 + 12x^2 - 35x). Simplifying further, we get 2x^3 - 24x^2 + 70x. Integrating this expression between the limits of x = 0 and x = 7, we can determine the area enclosed by the curves.

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Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

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Answer: 8 six packs because its cheaper

Step-by-step explanation:

8x2.1=$16.80 and 6x3.12=$18.72

(a)The range of the given set of measurements is 4.

(b)The sample mean of the given set of measurements is approximately 5.625.

(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.

(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.

To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.

Range = Largest value - Smallest value

Range = 8 - 4

Range = 4

The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.

(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.

To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.

Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45

Sample mean = Sum of measurements / Total number of measurements

Sample mean = 45 / 8

Sample mean ≈ 5.625

The sample mean represents the average value of the measurements and provides a measure of central tendency.

(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.

To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.

Squared difference for each measurement:

(4 - 5.625)^2 = 2.890625

(4 - 5.625)^2 = 2.890625

(7 - 5.625)^2 = 1.890625

(6 - 5.625)^2 = 0.140625

(4 - 5.625)^2 = 2.890625

(6 - 5.625)^2 = 0.140625

(6 - 5.625)^2 = 0.140625

(8 - 5.625)^2 = 5.390625

Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375

Sample variance = Sum of squared differences / (Total number of measurements - 1)

Sample variance = 16.364375 / (8 - 1)

Sample variance ≈ 2.337768

The standard deviation, denoted as s, is the square root of the sample variance.

Sample standard deviation = √(Sample variance)

Sample standard deviation = √(2.337768)

Sample standard deviation ≈ 1.529

These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.

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Answer:

4x^2+44x+121

Step-by-step explanation:

See the image below.

Answer:

7.3

Step-by-step explanation:

i think

stan kim namjoon as thx

Answer:

3¹²

Step-by-step explanation:

First lets simplify:

(3⁵)² would be 3¹⁰

and 3⁻² would stay the same:

Now;

\(\frac{3^{10} }{3^{-2} }\)

Now keep the base same and subtract exponents:

10 - (-2) = 12

=> Therefore the answer would be 3¹²

Hope this helps!

Answer:

3¹²

Step-by-step explanation:

This kinda Questions can be done using the Law of exponents as ,

So using these properties we have ,

→ (3⁵)² / 3-²

→ 3¹⁰ / 3 -²

→ 3¹²

Answer:

the first one

Step-by-step explanation:

Answer:

\(x = 4\)

\(2x + 2(x + 4) \times \frac{1}{2} = 2(x + 4) \\ 2x + x + 4 = 2(x + 4) \\ 3x + 4 = 2(x + 4) \\ 3x + 4 = 2x + 8 \\ 3x + 4 - 2x = 8 \\ x + 4 = 8 \\ x = 8 - 4 \\ x = 4\)

The probability of the spinner stopping on a blue section on the first spin and then a red section on the second spin is 3/49.

To find the probability of the spinner stopping on a blue section on the first spin and then a red section on the second spin, we need to multiply the probabilities of each event happening independently.

Step 1: Find the probability of landing on a blue section on the first spin.

There is 1 blue section out of 7 total sections, so the probability is 1/7.

Step 2: Find the probability of landing on a red section on the second spin.

There are 3 red sections out of 7 total sections, so the probability is 3/7.

Step 3: Multiply the probabilities from step 1 and step 2.

(1/7) * (3/7) = 3/49.

So, the probability of the spinner stopping on a blue section on the first spin and then a red section on the second spin is 3/49.

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Answer:

3

Step-by-step explanation:

The pattern is dividing 4 each time.

192/4=48

48/4=12

12/4=3

Hope this helps! Plz give brainliest!

Answer:it would be 3 1/4 pounds of blueberries

Step-by-step explanation:

(a) If S is a compact subset of a metric space X, then S is closed and bounded.

The statement is true.

To prove that if S is a compact subset of a metric space X, then S is closed and bounded, we need to show two properties: closedness and boundedness.

Closedness:

Let's prove that S is closed. To do this, we will show that every limit point of S belongs to S.

Suppose x is a limit point of S. This means that every open ball centered at x contains points of S other than x itself.

Since S is compact, it is also sequentially compact. Therefore, there exists a sequence (x_n) in S that converges to x.

Since S is sequentially compact, every sequence in S has a convergent subsequence that converges to a point in S. In particular, the sequence (x_n) has a subsequence (x_{n_k}) that converges to x.

Since S is sequentially compact, the limit of any convergent subsequence of S must be in S. Therefore, x, being the limit of the subsequence (x_{n_k}), belongs to S. This shows that every limit point of S is in S, hence S is closed.

Boundedness:

Let's prove that S is bounded. We will show that there exists a positive number M such that every point in S lies within a ball of radius M centered at some point in X.

Suppose for the sake of contradiction, that S is unbounded. Then, for every positive integer n, there exists a point x_n in S such that the distance between x_n and any fixed point in X is greater than n. Therefore, we have a sequence (x_n) in S that is unbounded.

Since S is compact, it is also sequentially compact. Therefore, there exists a subsequence (x_{n_k}) of (x_n) that converges to a point x in X.

Since the distance between x_{n_k} and any fixed point in X is greater than or equal to n_k, and n_k is an increasing sequence of positive integers, the limit x must be at an infinite distance from any fixed point in X, which contradicts the fact that x is in X.

Hence, our assumption that S is unbounded is false. Therefore, S must be bounded.

We have shown that if S is a compact subset of a metric space X, then S is closed and bounded. Thus, the statement is true.

(b)  A closed, bounded subset S of a metric space X is compact.

True.

A closed, bounded subset S of a metric space X is indeed compact. This is known as the Heine-Borel theorem.

The Heine-Borel theorem states that in a metric space, a subset is compact if and only if it is closed and bounded.

In this case, since S is closed and bounded, it satisfies the conditions of the Heine-Borel theorem and therefore must be compact.

A closed, bounded subset S of a metric space X is compact.

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