The measures of the angles of a triangle are shown in the figure below. Solve for x.

Answer:

95.5

Step-by-step explanation:

∠4 is the exterior angle of the triangle

The exterior angle formed by extending the side of a triangle is the sum of the alternate interior angles

Here the alternate interior angles are ∠1 and ∠2

So

m∠4 = m∠1 +  m∠3
        = 13.5 + 82
        = 95.5

Population: All American households.

Sample: The 1780 American households surveyed.

Individuals: The American households participating in the survey.

In the given scenario, we have a survey of 1780 American households that found 59% of the households own a computer. Let's identify the population, sample, and individuals in the study:

Population: The population refers to the entire group or larger set of individuals that we are interested in. In this case, the population would be all American households.

Sample: The sample is a subset of the population that is chosen to represent the population accurately. In this situation, the survey includes 1780 American households. Therefore, the sample is the 1780 households that were surveyed.

Individuals: The individuals in the study are the specific units or elements being surveyed or examined. In this case, the individuals are the American households that participated in the survey. Each household represents an individual within the study.

To summarize:

Population: All American households.

Sample: The 1780 American households surveyed.

Individuals: The American households participating in the survey.

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The ladder and the top of the building form a right triangle

The building is 20.8 feet tall

The given parameters are:

The height (h) of the building is calculated using the following Pythagoras theorem

L^2 = b^2 + h^2

So, we have:

39^2 = 33^2 + h^2

Evaluate the exponent

1521 = 1089 + h^2

Rewrite as:

h^2 = 1521 - 1089

h^2 = 432

Take the square root of both sides

h = 20.8

Hence, the building is 20.8 feet tall

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Answer:

2 people left more than 15%.

The corresponding range of the domain is (11, -4, -29)

The function is given as:

5x + y = 1

Make y the subject

y = 1 - 5x

The domain is given as:

(-2,1,6)

Substitute these values in y = 1 - 5x

y = 1 - 5(-2) = 11

y = 1 - 5(1) = -4

y = 1 - 5(6) = -29

Hence, the corresponding range of the domain is (11, -4, -29)

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The measure of the other side of the triangle is approximately 7.5 meters.

To find the measure of the other side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.  In this case, we are given the length of one side and the hypotenuse:
Side 1: 4 m
Hypotenuse: 8.5 m

So, in this case, we can write:

8.5^2 = 4^2 + x^2

where x is the length of the other side we are trying to find.

Simplifying the equation, we get:

72.25 = 16 + x^2

Subtracting 16 from both sides, we get:

56.25 = x^2

Taking the square root of both sides, we get:

x = 7.5

Therefore, the measure of the other side of the triangle is 7.5 meters.

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Answer:

600 centimeters

Step-by-step explanation:

one meter is 100 centimeters so 6 meters is 600 centimeters :)

1 meter is 100 centimeters so 6 meter is 600 centimeters

By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25

The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1

Let us solve this problem by applying the Kuhn-Tucker theorem.

Let us first write down the Lagrangian function:

L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)

Then, we find the first order conditions for a maximum:

Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0

Ly = x - 8λ₁y - 2λ₁x = 0

Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0

Lλ₂ = 2x - y + 1 = 0

The complementary slackness conditions are:

λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0

λ₂(2x - y + 1) = 0

Now, we solve for the above equations one by one:

From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1

Substitute this in equation (1), we get:

8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0

Simplifying, we get:

10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)

From equation (2), we can write x = 8λ₁y + 2λ₁x

Substitute this in equation (1), we get:

8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0

Simplifying, we get:

-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)

Solving equations (4) and (5) for λ₁ and λ₂, we get:

λ₁ = 1/20 and λ₂ = 9/100

Then, substituting these values in the first order conditions, we get:

x = 2/5 and y = 9/5

Therefore, the maximum value of xy is:

2/5 x 9/5 = 18/25

Hence, the required answer is 18/25.

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2x-3=7

The answer would be 5.

Answer:

x=5

Step-by-step explanation:

2x−3=7

Add 3 to both sides.

2x=7+3

Add 7 and 3 to get 10.

2x=10

Divide both sides by 2.

x=10/2

Divide 10 by 2 to get 5.

x=5

m=2

because in the other equation, the digit next to x is 2 so m must be 2

Answer:

9 feet

Step-by-step explanation:

Answer:

raitonal maybe

Step-by-step explanation:

sorry if its wrong

Answer:

Natural numbers are real, rational, whole, an integer too so it could be: 1,2,3,4,5,6,7,8,9...

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

C would also be the correct answer but its not rounded to the nearest tenth.

Answer:

$156

Step-by-step explanation:

(9600 + 5376 )/ (8 * 12) = 156

Answer:

$156

Step-by-step explanation:

interest for 8 years = $5376

convert 8 years to months

1 year = 12 month

8 years = 8*12

=96 months

monthly

now monthly interest = $5376/96

=$56

now find amount that he has to pay monthly

=$9600/96

=$100

monthly payment with interest = $100 + $56

=$156

Take the square root of each side.

\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)

Answer:

5y - 2

Step-by-step explanation:

1/3 ( 15y - 6 ) = (15y - 6) / 3 = 5y - 2

Done! Hope you learned how to do this/understood this and have a great day! Please mark me as brainliest, vote 5.0 on my answer and thank me to show some support! Bye!

The mean of the z scores after converting the pulse rates to z scores is 0, and the standard deviation of the z scores is 1. The units of the corresponding z scores are dimensionless.

The process of converting the pulse rates to z scores involves subtracting the mean and dividing by the standard deviation. This transformation standardizes the data and makes it comparable across different distributions. In the case of z scores, the mean is always 0, and the standard deviation is always 1. Therefore, the mean and standard deviation of the z scores in this scenario are 0 and 1, respectively.

Since z scores are calculated by subtracting the mean and dividing by the standard deviation, the resulting values are dimensionless. They represent the number of standard deviations away from the mean. Therefore, the units of the corresponding z scores are neither "beats per minute," "beats," nor "minutes per beat." They are simply numerical values without specific units.

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Therefore , the solution of the given problem of triangle is we can conclude that the best approximation of w is 4.0 cm .

Having three sides and three vertices, triangles are polygons. The angles of a triangle are formed by connecting its three sides together at one point. The triangle contains three angles with a total angle of 180 degrees.

Here,

First, we may change the notation of our triangle to fit the law of sines: sin(W)/W =sin(U)/u

Now that W = 39, U = 31, and u = can swap out the values in our previous expression, we may deduce this from our diagram:

W = sin(39)/sin(W) (U)

sin(39)/ W = sin(31) /3.3

Finally, we can solve for w:

3.3sin(39) /W = sin(31)

3.3sin(39) = w sin (31)

3.3sin(39) /w= sin(31)

w = 4.03224

Which rounds to w= 4.0

Therefore , the solution of the given problem is we can conclude that the best approximation of w is 4.0 cm .

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Therefore , the solution of the given problem of triangle is we can conclude that the best approximation of w is 4.0 cm .

Having three sides and three vertices, triangles are polygons. The angles of a triangle are formed by connecting its three sides together at one point. The triangle contains three angles with a total angle of 180 degrees.

Here,

First, we may change the notation of our triangle to fit the law of sines: sin(W)/W =sin(U)/u

Now that W = 39, U = 31, and u = can swap out the values in our previous expression, we may deduce this from our diagram:

W = sin(39)/sin(W) (U)

sin(39)/ W = sin(31) /3.3

Finally, we can solve for w:

3.3sin(39) /W = sin(31)

3.3sin(39) = w sin (31)

3.3sin(39) /w= sin(31)

w = 4.03224

Which rounds to w= 4.0

Therefore , the solution of the given problem is we can conclude that the best approximation of w is 4.0 cm .

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9514 1404 393

Answer:

  86.6 inches

Step-by-step explanation:

The side length of an equilateral triangle is 2/√3 times the altitude. So, the perimeter is ...

  P = 3s = 3(25)(2/√3) = 50√3 ≈ 86.6 . . . . inches

Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

Any three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.

Here,

Because angles 1 and 2 are close to one another, they are neighboring angles.

A They share a side and are near to each other, making them neighboring angles.

B. The angles are complimentary (add to 90 degrees) False—Angle 2 has a 90 degree angle.

C. They are additional angles. (add to 180) They do not create a straight line, which is untrue.

D. Vertical angles describe them. (Contrary angles) False, they are not created through the intersection of lines.

Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

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The probability that a randomly selected score will be less than 89 is 0.9821.

The probability that a randomly selected score will be less than 89 can be found using the z-score formula.
The z-score formula is:
z = (x - μ) / σ
Where x is the score we are interested in, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Plugging in the values given in the question, we get:
z = (89 - 72.8) / 7.7
z = 16.2 / 7.7
z = 2.10
Now we can use a z-table to find the probability that a randomly selected score will be less than 89.
Looking up a z-score of 2.10 on a z-table, we find that the probability is 0.9821.

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Answer:

They ate 3/4 of the pizza. 1/4 of it was left.

Step-by-step explanation:

Answer:

They ate 3/4 of the pizza.

Bilal had 1/4 of the pizza

Step-by-step explanation:

The requried, pair of lines that are parallel is 6y=9x+7 and 2y = 3x + 4.

A) The slope of the first line is 2, and the slope of the second line is -1/2. Since the slopes are negative reciprocals of each other, the lines are perpendicular.

B) The slope of the first line is 3/2, and the slope of the second line is 3/2. Since the slopes are equal, the lines are parallel.

C) By rearranging the equations to slope-intercept form, we find that the slopes of lines are 5/7 and -5/7. Since the slopes are unequal, the lines are not parallel.

D) These are not equations of lines that are parallel.

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Answer:

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

Parallel lines have equal slopes, perpendicular lines have negative reciprocal slopes.

Find the slopes of lines and compare.

y = 2x + 1,

4y = - 2x - 5  ⇒ y = (- 2/4)x - 5/4  ⇒ y = (-1/2)x - 5/4

These slopes are negative reciprocals, so lines are perpendicular.

6y = 9x + 7  ⇒ y = (9/6)x + 7/6  ⇒ y = (3/2)x + 7/6,

2y = 3x + 4  ⇒ y = (3/2)x + 2,

The slopes are equal, so lines are parallel.

5x - 7y = 12 ⇒ 7y = 5x - 12 ⇒ y = (5/7)x - 12/7,

10x + 14y = 9 ⇒ 14y = - 10x + 9 ⇒ y = (-10/14)x + 9 ⇒ y = (- 5/7)x + 9,

This is neither parallel nor perpendicular

x = 1,

y = - 5,

The lines are perpendicular

Take 1 cm of 5th, 6th and 7th shelves, it comes out to be = 210

Now,

5 - 2 = 3 book in the shelves

6 - 3 = 3 book in the shelves

7 - 4 = 3 book in the shelves

3 books are in common, so, 210 - 3 = 207 book Lizzie have.

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In order to divide these numbers, first let's start with a 0 in the unit place, since 9.2 is smaller than 52.063.

Then, we multiply 9.2 by 10, this way we will calculate the tenths place.

Now, dividing 92 by 52.063, we have 1 as the result.

The remainder will be 92 - 52.063 = 39.937.

Again, let's multiply the remainder by 10, so now we will calculate the hundredths of the result.

Dividing 399.37 by 52.063 we have 7.

The remainder is 399.37 - 7*52.063 = 34.929.

Multiplying by 10, we have 349.29, and now we calculate the thousandths.

Dividing 349.29 by 52.063 we have 6.

Until now, the result of the division is 0.176.

Rounding to the nearest hundredth, we have 0.18 as the result of the division.

Answer:

x+y = 36

x-y = 10

Add these two equations to get

2x = 46

x = 23

Sub x=23 into either equation, I like the first.

23 + y = 36

y = 13

23,13 are the pair.

Answer:

First Option

Step-by-step explanation:

Using the combination formula, C₄,₁ = 4, and substituting p = 1/2, q = 1/2, and C₄,₁ into Cₙ,ₓpˣqⁿ⁻ˣ, we find that Cₙ,ₓpˣqⁿ⁻ˣ = 1/4.



To evaluate Cₙ,ₓpˣqⁿ⁻ˣ, we can use the combination formula and substitute the given values. The combination formula is given by:

Cₙ,ₓ = n! / (x!(n - x)!)

where n! represents the factorial of n.

Given:

n = 4

x = 1

p = 1/2

First, let's calculate q, which is the complement of p:

q = 1 - p

 = 1 - 1/2

 = 1/2

Now, let's substitute the values into the combination formula:

C₄,₁ = 4! / (1!(4 - 1)!)

     = 4! / (1! * 3!)

Calculating the factorials:

4! = 4 * 3 * 2 * 1 = 24

1! = 1

3! = 3 * 2 * 1 = 6

Substituting the factorials back into the formula:

C₄,₁ = 24 / (1 * 6)

     = 4

Now, let's substitute p, q, and C₄,₁ into Cₙ,ₓpˣqⁿ⁻ˣ:

Cₙ,ₓpˣqⁿ⁻ˣ = C₄,₁ * pˣ * q^(n - x)

           = 4 * (1/2)^1 * (1/2)^(4 - 1)

           = 4 * (1/2) * (1/2)^3

           = 4 * 1/2 * 1/8

           = 4/16

           = 1/4

Therefore, Cₙ,ₓpˣqⁿ⁻ˣ evaluates to 1/4.

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The first step to isolate the variable term on one side of the equation is to move all constant terms to the other side by adding or subtracting the appropriate terms.

To isolate the variable term on one side of the equation, the first step is to gather all terms containing the variable on one side and move all constant terms to the other side.

In the given equation:

2/3x = -1/2x + 5

We have variable terms on both sides: 2/3x and -1/2x. To isolate the variable term, we can start by moving the -1/2x term to the left side by adding 1/2x to both sides of the equation.

Adding 1/2x to both sides:

(2/3x) + (1/2x) = (-1/2x) + (1/2x) + 5

Simplifying the left side:

(2/3x + 1/2x) = 5

To combine the fractions, we need a common denominator. The common denominator of 3 and 2 is 6, so we can rewrite the left side:

(4/6x + 3/6x) = 5

Combining like terms on the left side:

(7/6x) = 5

Now, the variable term 7/6x is isolated on one side of the equation. To completely isolate the variable, we can multiply both sides of the equation by the reciprocal of the coefficient of x, which in this case is 6/7.

Multiplying both sides by 6/7:

(6/7) * (7/6x) = (5) * (6/7)

Simplifying:

1x = 30/7

The variable x is now isolated on the left side, and the equation simplifies to:

x = 30/7

Moving all constant terms to the opposite side of the equation by appropriately adding or deleting terms is the first step towards isolating the variable term on one side of the equation.

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