The area of a square room can be expressed as 196x12y10z6 square feet . hajime is installing a wallpaper border along the perimeter of the room. what is the perimeter? 52x6|y5z3| feet 52x10y8z4 feet 56x10y8z4 feet 56x6|y5z3| feet

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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The value of angle x rounded to the nearest tenth of a degree is 53.6°.

How can trigonometric ratios be used to find the angle in a right triangle?

Trigonometric ratios are used to relate the sides of a right triangle to its angles. In a right triangle, one of the angles is always 90 degrees, which is the right angle. The three primary trigonometric ratios are sine, cosine, and tangent, which are defined as follows:

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Cosine (cos): The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

To find the value of an angle in a right triangle, we can use the inverse trigonometric functions, also known as arc functions or anti trigonometric functions. These functions are denoted as \(sin^{-1}\), \(cos^{-1}\) , and  \(tan^{-1}\) , and they are used to find the angle whose trigonometric ratio is known.

Finding the value of x :

We can use the trigonometric ratio of sine to solve for x.

sin(x) = opposite/hypotenuse = MN/LN

\(sin(x) = 83/92\)

Taking the inverse sine of both sides:

\(x = sin^{-1}(83/92)\)

Using a calculator, we get:

\(x \approx 53.6^{o}\)

Therefore, the value of x rounded to the nearest tenth of a degree is 53.6°.

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To continue the pattern, you can buy 6 cupcakes this week.

Let's break down the pattern and the calculation step by step.

The pattern you mentioned is that you want to gradually reduce the number of cupcakes you buy each week. In this case, we start with 12 cupcakes two weeks ago and then bought 9 cupcakes last week.

To continue this pattern, we need to determine how many cupcakes to buy this week.

To calculate this, we can use the following logic:

Start with the number of cupcakes you bought last week (9 cupcakes).

Subtract the difference between the number of cupcakes you bought two weeks ago and last week (12 - 9 = 3 cupcakes).

The result of this subtraction will give you the number of cupcakes to buy this week.

Applying this calculation:

9 cupcakes - 3 cupcakes = 6 cupcakes

Therefore, to continue the pattern of gradually reducing the number of cupcakes, you should buy 6 cupcakes this week.

Your question is incomplete but most probably your full question was

I'm trying to cut down on how many cupcakes I buy. Two weeks ago I bought 12 cupcakes and then last week I bought 9. Please help me continue this pattern

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The expression which is equivalent to 8x²√375x + 2³√3x^7 if x = 0 is; 0.

According to the task content, the expression given is; 8x²√375x + 2³√3x^7.

On this note, it follows that when x=0 is substituted into the expression; the evaluation amounts to zero, 0.

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The correlation coefficient that indicates the strongest relationship between two variables is a. -1.0.

The correlation coefficient is a numerical measure that quantifies the relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

In this case, a correlation coefficient of -1.0 represents a perfect negative correlation, meaning that the two variables have a strong, linear relationship where as one variable increases, the other decreases in a perfectly predictable manner. This indicates a very strong and consistent inverse relationship between the variables.

In comparison, a correlation coefficient of 0.80 indicates a strong positive correlation, but it is not as strong as a perfect negative correlation of -1.0. A correlation coefficient of 0.1 suggests a weak positive correlation, while a correlation coefficient of -0.45 indicates a moderate negative correlation.

Therefore, out of the given options, the correlation coefficient of -1.0 represents the strongest relationship between two variables.

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Answer:

6-5 = 7-6

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

g(-4)=2(-4)^2+4(-4)-8

g(-4)=8

f(8)=2(8)-4

f(8)=12

Answer:

C.

represent 0

hope it helps

Of all the network cabling options, "fiber optic cable" offers the longest possible segment length.

Fiber optic cable offers the longest possible segment length among network cabling options due to its unique characteristics. Fiber optic cables are made of glass or plastic fibers that transmit data as pulses of light. This technology allows for much higher bandwidth and data transmission rates compared to traditional copper cables. Additionally, fiber optic cables have low signal loss, resistance to electromagnetic interference, and can transmit data over long distances without degradation. These properties make fiber optic cables ideal for long-distance communication, such as in telecommunications networks or data centers, where maintaining signal integrity over extended segments is crucial.

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Answer:

D line

Step-by-step explanation:

The 4i word should be eliminated since we want (3+4i)z to be a genuine number. Then, to ensure that the imaginary terms cancel out when z is multiplied together, we can make z of the form (n-4/3 ni).

Answer:

60

Step-by-step explanation:

i did -15 -45 and it is 60

2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

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Answer:

mn(5mn² + 9) ;

2mn(1 - 1/2mn²)

Step-by-step explanation:

Given:

5m²n³ +9mn

(8mn - 4m²n³ ÷ 4)​

5m²n³ + 9mn

mn(5mn² + 9)

(8mn - 4m²n³ ÷ 4)​

8mn/ 4 - 4m²n³ / 4

2mn - m²n³

2mn(1 - 1/2mn²)

Answer:

-2/1

Step-by-step explanation:

Answer:

-2/1

Step-by-step explanation:

The first fill in the blank is 6 1/2

The second one is 7 1/5

So, she ended up buying fewer apples

Can I have a brainliest?

Answer:

The first fill in the blank is 6 1/2

The second one is 7 1/5

She ended up buying fewer apples

Step-by-step explanation:

Answer:

she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)

Answer: 4

Step-by-step explanation:

24 divided by 5 is 20 with a remainder of 4.

24 divided by 5 is with a remainder of 4.

Here, we have,

given that,

divide 24 by 5

so, we have,

24 ÷ 5

using the rules of division we get,

24/5

= 20+4 /5

as we have,

5 | 24 | 4

    20

---------------

      4

so, we get,

24 divided by 5 is with a remainder of 4.

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The equation of the plane passing through (0, -1, 4) that is orthogonal to the planes 5x + 4y - 4z = 0 and -x + 2y + 5z = 7 can be found using the cross product of the normal vectors of the given planes.

Step 1: Find the normal vectors of the given planes.
For the first plane, 5x + 4y - 4z = 0, the coefficients of x, y, and z form the normal vector (5, 4, -4).
For the second plane, -x + 2y + 5z = 7, the coefficients of x, y, and z form the normal vector (-1, 2, 5).

Step 2: Take the cross-product of the normal vectors.
To find the cross product, multiply the corresponding components and subtract the products of the other components. This will give us the direction vector of the plane we're looking for.
Cross product: (5, 4, -4) × (-1, 2, 5) = (6, -29, -14)

Step 3: Use the direction vector and the given point to find the equation of the plane.
The equation of a plane can be written as Ax + By + Cz + D = 0, where (A, B, C) is the direction vector and (x, y, z) is any point on the plane.
Using the point (0, -1, 4) and the direction vector (6, -29, -14), we can substitute these values into the equation to find D.
6(0) - 29(-1) - 14(4) + D = 0
29 - 56 - 56 + D = 0
D = 83

Therefore, the equation of the plane passing through (0, -1, 4) and orthogonal to the planes 5x + 4y - 4z = 0 and -x + 2y + 5z = 7 is:
6x - 29y - 14z + 83 = 0.

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Answer:

If you typed it correctly then the answer is 12.12 .

But if you meant 36 divided by 3 then the answer is just 12.

Step-by-step explanation:

There are 8,640 ways the five people can be seated in the eight empty seats.

To determine the number of ways the five people can be seated in eight empty seats, we can use the concept of permutations.

Since the order in which the people are seated matters, we need to calculate the number of permutations of five people taken from eight seats.

The formula for permutations is given by:

P(n, r) = n! / (n - r)!

where n represents the total number of items and r represents the number of items taken at a time.

In this case, we have 8 empty seats (n) and want to seat 5 people (r). Therefore, we can calculate the number of ways as:

P(8, 5) = 8! / (8 - 5)!

= 8! / 3!

= (8 * 7 * 6 * 5 * 4 * 3!) / 3!

= 8 * 7 * 6 * 5 * 4

= 8,640

Hence, there are 8,640 ways the five people can be seated in the eight empty seats.

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The statements are true about the given expressions include the following:

In order to determine whether these expressions are equivalent, we would evaluate the two expressions based on each of the statements:

"When x = 2, both expressions have a value of 18"

7x + 4 = 7(2) + 4 = 14 + 4 = 18.

3x + 5 + 4x - 1 = 3(2) + 5 + 4(2) - 1 = 6 + 5 + 6 - 1 = 18.

"The expressions are only equivalent for x = 4 and x = 6." is false has demonstrated above.

"The expressions have equivalent values for any value of x." is true.

Let x = 1;

7x + 4 = 7(1) + 4 = 7 + 4 = 11.

3x + 5 + 4x - 1 = 3(1) + 5 + 4(1) - 1 = 3 + 5 + 4 - 1 = 11.

Let x = 10;

7x + 4 = 7(10) + 4 = 70 + 4 = 74.

3x + 5 + 4x - 1 = 3(10) + 5 + 4(10) - 1 = 30 + 5 + 40 - 1 = 74.

"The expressions should have been evaluated with one odd value and one even value." is false because all values of x are solutions.

"When x = 0, the first expression has a value of 4 and the second expression has a value of 5." is false because the two expressions are equivalent expressions.

In conclusion, "The expressions have equivalent values if x = 8." is true because the two expressions are equivalent expressions.

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To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.

We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.

According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by

x = (-b +/- √(b² - 4ac)) / (2a)

In this formula, if we add "ax² = y," we obtain

x = (-0 +/- √(0² - 4ay)) / (2a)

which simplifies to

x = √(-4ay) / (2a)

If a = 4, the equation becomes

x = √(-16y) / 8

The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.

The equation has a single solution provided by any other value of a.

x = √(-4ay) / (2a)

For example, if a = 3, the equation becomes

x = √(-12y) / 6

Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.

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Given that we have a random sample 1, 2, ..., n such that the i's follow an unknown distribution with mean = 5 and variance 5² = 25. We need to find the value of z such that P(X-bar − < 1) ≅ 0.95, assuming the sample size > 30.

By Central Limit Theorem, the sample mean follows a normal distribution with mean µ = 5 and variance σ²  = (25/n). We are given that n > 30, so we can use the standard normal distribution to approximate the sampling distribution of the sample mean.

Using the standard normal distribution, we have:

P(Z < (X-bar − µ)/(σ/√n)) = P(Z < (X-bar − 5)/(5/√n)) = 0.95

From the standard normal distribution table, we can find that the z-score corresponding to the 95th percentile is 1.96.

So, we have:

(Z < (X-bar − 5)/(5/√n)) = 0.95

1.96 = (X-bar − 5)/(5/√n)

Solving for n, we get:

n = (1.96*5/1)² ≈ 96.04

Since n must be an integer, we round up to n = 97.

Therefore, for a sample size of at least 97, the value of X-bar − 5 divided by the standard error of the sample mean is less than 1 with probability approximately 0.95.

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Yes, line is used to define an angle.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The common point is referred to as the vertex.

The length of the angle formed when two rays or arms intersect at a common vertex is known as an angle measure in geometry.

A straight line is a straight angle.

Therefore, two lines are used to define an angle.

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The uncertainty in the best estimate for the length of the side of the block is approximately 0.0447 mm.

To determine the uncertainty in the best estimate for the length of the block side, we can consider the range of values obtained from the measurements. Since the uncertainty represents the possible deviation from the true value, the range of measurements can be used to estimate the uncertainty in the best estimate

To find the standard deviation represents the average amount of variation or spread among the measurements , we use the formula σ = Δb / √n, where σ is the standard deviation, Δb is the uncertainty in each measurement, and n is the number of measurements.

In this case, Δb = 0.1 mm and n = 5. Plugging these values into the formula, we get σ = 0.1 / √5 ≈ 0.0447 mm.

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97.04 mg Initial mass = 48 mg, Mass after 7 weeks = 48 mg * (1/2)^(12.25) Half-life of the goo in minutes = 120 / (log(37/296) / log(1/2)) The artifact was made approximately 22920 years ago.

Question 26:

The half-life of Radium-226 is 1590 years. To determine how many milligrams will remain after 3000 years, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where:

N(t) is the remaining amount after time t,

N₀ is the initial amount,

t is the elapsed time, and

T is the half-life.

Given that the initial amount is 200 mg, the elapsed time is 3000 years, and the half-life is 1590 years, we can substitute these values into the formula:

N(3000) = 200 * (1/2)^(3000/1590).

Calculating this, we find:

N(3000) ≈ 200 * (1/2)^(1.8862) ≈ 200 * 0.4852 ≈ 97.04.

Therefore, approximately 97.04 mg of Radium-226 will remain after 3000 years.

Question 27:

The half-life of Palladium-100 is 4 days. We can use the half-life formula again to determine the initial mass and the mass after 7 weeks.

1. Initial mass:

After 12 days, the sample of Palladium-100 has been reduced to 6 mg. We need to determine how many half-lives have passed in 12 days to find the initial mass.

t = (12 days) / (4 days/half-life) = 3 half-lives.

Let's denote the initial mass as M₀. We can use the formula:

M(t) = M₀ * (1/2)^(t/T).

Substituting the values, we have:

6 mg = M₀ * (1/2)^(3).

Solving for M₀:

M₀ = 6 mg * 2^3 = 48 mg.

Therefore, the initial mass of the sample was 48 mg.

2. Mass after 7 weeks (49 days):

To find the mass after 7 weeks, we need to determine how many half-lives have passed in 49 days:

t = (49 days) / (4 days/half-life) = 12.25 half-lives.

Using the formula, we can calculate the mass after 7 weeks:

M(49 days) = M₀ * (1/2)^(12.25).

Substituting the initial mass we found earlier:

M(49 days) = 48 mg * (1/2)^(12.25).

Calculating this value will give us the mass after 7 weeks.

Question 28:

To find the half-life of the radioactive goo, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where N(t) is the remaining amount at time t, N₀ is the initial amount, t is the elapsed time, and T is the half-life.

Given that the initial amount is 296 grams and the amount after 120 minutes is 37 grams, we can substitute these values into the formula:

37 g = 296 g * (1/2)^(120/T).

To find the half-life T, we can rearrange the equation:

(1/2)^(120/T) = 37/296.

Taking the logarithm of both sides, we have:

120/T * log(1/2) = log(37/296).

Solving for T:

T = 120 / (log(37/296) / log(1/2)).

Calculate the value of T using this equation to find the half-life of the radioactive goo in minutes.

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