8) For a given area of a triangle, the base varies inversely as its height. When the height is
10 in the base is 5 in. Find the base if the height is increased to 20 in.

76 is m<BFD in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

 m<AFC + m<BFD = 180°

   (7x-8)° +   m<AFC = 180°

   (5x+6)° +  m<BFD =  180°

(7x-8)° = (5x+6)

 2x = 12

    x = 14

m<BFD=(5x+6)°

       = 5 * 14 + 6

        = 70 + 6

          = 76

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The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.

Let us assume the number of coach tickets purchased is x.

And the number of first-class tickets purchased is y.

Now,

Including Sarah, a total of 11 people took the trip.

Thus,

[tex]x + y = 11 [/tex]

The cost of coach tickets and first-class tickets are $210 and $1200 respectively.

The total budget for airfare for the trip is $10,230.

Therefore,

210x + 1200y = 102309

21x + 120y = 1023

Solving both the equations, we get.

x=3

y=8

Thus, The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.

The length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.

The angles of a triangle are the angles formed by its sides. The sum of the angles of a triangle is always 180 degrees, which is a fundamental property of this shape. There are different types of triangles, based on their side lengths and angle measures. For example:

A scalene triangle has three sides of different lengths and three different angles.

An isosceles triangle has two sides of equal length and two equal angles.

An equilateral triangle has three sides of equal length and three equal angles.

A right triangle has one angle that measures 90 degrees (a right angle), and the side opposite to it is called the hypotenuse.

Triangles have many important properties and applications in mathematics, physics, and engineering. They can be used to calculate distances, angles, areas, volumes, and many other quantities. Triangles are also used in the construction of buildings, bridges, and other structures, as well as in art, design, and other fields.

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

sin(42) = opposite/hypotenuse

sin(42) = x/5

To solve for x, we can multiply both sides by 5 and simplify:

x = 5*sin(42)

x ≈ 3.4 (rounded to the nearest tenth)

Therefore, the length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.

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Answer:

y = 8 is the smaller number.

Step-by-step explanation:

Sove the system by adding the two equations together, one on top of the other. Add from the top, down.



x + y = 20

x - y = 4

________

2x = 24

Divide by 2.

x = 12

Put this back into either original equation.

x + y = 20

12 + y = 20

Subtract 12.

y = 8

The numbers are 12 and 8.

8 is the smaller number.

Answer:

To solve this problem, we can use the central limit theorem and the standard normal distribution.

The central limit theorem states that the distribution of sample means is approximately normal, with a mean equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Let X be the systolic blood pressure of an individual in the population. We know that X is normally distributed with a mean of 120 and a standard deviation of 8.

Let Y be the sample mean blood pressure of a sample of 20 individuals. Then Y is also normally distributed, with a mean of 120 and a standard deviation of 8 / sqrt(20) = 1.7889.

We want to find the probability that the sample mean blood pressure is greater than 123. We can standardize this value using the standard normal distribution as follows:

Z = (Y - 120) / (8 / sqrt(20))

P(Y > 123) = P(Z > (123 - 120) / (8 / sqrt(20)))

= P(Z > 1.3363)

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 1.3363 is approximately 0.0918.

Therefore, the probability that the mean blood pressure for a sample of 20 people will be greater than 123 is approximately 0.0918.

Theoretical probability is the likelihood of an event occurring based on mathematical reasoning or analysis, rather than on empirical or experimental data.

Probability refers to the likelihood of a particular event or outcome occurring. It is a measure of the chance of an event happening, and is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, physics, engineering, and finance, to make predictions and inform decision-making.

Here,

It is calculated using the laws of probability and assumes that all outcomes are equally likely to occur. Theoretical probability is often used in situations where it is not possible or practical to conduct experiments or collect data, such as in mathematical or statistical modeling.

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Since AB and CD are parallel lines cut by a transversal GH, we know that the corresponding angles are equal. Therefore, LDFE = 35°

what is  parallel lines ?

Parallel lines are two or more lines in a plane that never meet or intersect, no matter how far they are extended. They always maintain the same distance between them and remain equidistant at every point along their length.

In the given question,

Parallel lines are two or more lines in a plane that never meet or intersect, no matter how far they are extended. They always maintain the same distance between them and remain equidistant at every point along their length.

Corresponding angles are pairs of angles that are in the same relative position at the intersection of two lines that are crossed by a third line, called a transversal. More specifically, corresponding angles are formed when a transversal intersects two parallel lines.

Corresponding angles are congruent, which means they have the same measure or degree of angle

Since AB and CD are parallel lines cut by a transversal GH, we know that the corresponding angles are equal. Therefore,

LAEG = LDFE

So, LDFE = 35°. .

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Answer:

Step-by-step explanation:

b

The vertical shape of the graph will be the same as that of the first rocket, assuming both rockets have the same initial velocity and acceleration.

1.I agree with Serena that we can draw the graphs for the other two rockets by shifting the functions. We can use the same equation and just adjust the values of the horizontal and vertical shifts.

2. The equation f(t) = -6t² represents a quadratic function, which has a parabolic shape when graphed. If we apply a transformation to this function, such as a vertical or horizontal shift, the shape of the graph will change accordingly.

3. The term 82.14 likely represents the maximum height achieved by the rocket, since the equation f(t) = -6t² gives the height of the rocket as a function of time. The value of h(t) = 82.14 corresponds to a specific time when the rocket reaches its maximum height.

4. If the second rocket is launched 3 seconds after the first one, the graph of the second rocket will be shifted horizontally by 3 units to the right compared to the graph of the first rocket. This represents a time delay of 3 seconds between the two launches.

5. The equation of the second rocket would be f(t) = -6(t-3)², assuming that the second rocket has the same initial velocity and acceleration as the first rocket but is launched 3 seconds later.

6. Since the third rocket is launched 3 seconds after the second rocket and from a tall platform, its graph will be shifted horizontally to the right by 6 units compared to the graph of the first rocket.

9. A: Based on the graph, the third rocket was launched at approximately 5:20 PM.

B: Based on the graph, the first rocket lands at approximately 5:15 PM.

C: Based on the graph, all three rockets are in the air between approximately 5:10 PM and 5:25 PM, so the approximate interval during which all three rockets are in the air is 15 minutes.

Therefore,  spends an additional 6 seconds in the air before landing. The vertical shape of the graph will depend on the specifics of the rocket's launch and trajectory.

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Answer:

Only the set of ordered pairs is one-to-one

Step-by-step explanation:

You have three right

The last one:
A function is one-to-one if and only if, for every value of y there is only one value of x

The mapping diagram is not one-to-one since for two values of x, x = -3 and x = 5 we get the same y value of 6

The set of ordered pairs is a one-to=-one since for every value of y there is a unique value for x

The inequality that has a dashed boundary line when graphed is:

y > 3x + 1

In mathematics, an inequality is a statement that two quantities are not equal or do not have the same value. In other words, it is a statement that compares two values, expressing that one value is greater than, less than, or not equal to the other value. An inequality is denoted by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

In mathematics, a dashed boundary refers to a boundary line that is graphed as a dashed line rather than a solid line. The use of a dashed line is typically used to indicate that the boundary itself is not included in the set of solutions of an inequality or equation.

In the given question,

The inequality that has a dashed boundary line when graphed is:

y > 3x + 1

The reason for this is that when graphed, the boundary line of the inequality y > 3x + 1 is a straight line, but it is dashed instead of solid. This is because the inequality is strict, meaning that the boundary line itself is not included in the set of solutions. On the other hand, if the inequality had been y ≥ 3x + 1, the boundary line would have been a solid line because the inequality is non-strict and includes the boundary line itself as a solution.

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Answer:

Step-by-step explanation:

9. sin 18 = x/21

 x = 21* sin 18

  x = 6.5

10. tan 55 = 29/x

  x* tan 55 = 29

x = 29/tan 55

x = 20.3

11. sin 23 = x/25

  x = 25 * sin 23

  x = 9.8

12. sin 47 = 33/x

  x * sin 47 = 33

 x = 33/sin 47

  x = 45.1

Answer:

Step-by-step explanation:

rate of the plane be x

distance traveled by plane = 420 miles

time taken by plane = 420/x

distance traveled by car =120 miles

rate of car = x-120

time taken by car = 120 / x-100

the time taken by both are same

420/x = 120/ x-100

420(x-100)=120x

420x-42000 = 120x

420x-120x=42000

300x= 42000

x=42000/300

x=140 mph the speed of the plane

The probability that one-half of the selected people will have high blood pressure is given as follows:

P(X = 13) = 0.0004684.

The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.

The mass probability formula is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters, along with their meaning, are listed as follows:

The parameter values for this problem are given as follows:

n = 26, p = 0.2.

One-half of 26 is of 13, hence the probability is given as follows:

P(X = 13) = 26!/(13! x 13!) x (0.2)^13 x (0.8)^13

P(X = 13) = 0.0004684.

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The conversion of 1/12in to milliters  can be expressed as 2.117mm

Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. As an illustration, if you had 1,000 interactions and 50 conversions, your conversion rate would be 5% because 50 x 1,000 = 5%.

The proportion of users who perform the intended action is known as the conversion rate. The proportion of website visitors who make a purchase there serves as the prototypical illustration of conversion rate.

We can  1/12in to milliters by using the conversion rate, which 1inch = 25.4mm,and this can be used to make the conversion as:

If  1inch = 25.4mm

 1/12 = X mm

Xmm =  (1/12 *25.4mm)/ 1inch

=2.117mm

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complete question:

How much is 1/12in to milliters?

Therefore, the total purchase price is $734.78.

Profit is the financial gain obtained by subtracting the cost (or expenses) of producing and selling goods or services from the revenue generated from their sale. In other words, profit is the amount of money that is left over after all expenses have been paid, including the cost of goods sold, operating expenses, taxes, and any other costs associated with running a business.

Profit can be calculated using the following formula:

Profit = Revenue - Cost

by the question.

To calculate the total purchase price, we need to calculate the tax and add it to the sum of the prices of the diamond necklace and the gold pendant.

The tax on the diamond necklace is:

572.95 * 0.065 = 37.24

The tax on the gold pendant is:

113.76 * 0.065 = 7.40

The total tax is the sum of these two taxes:

37.24 + 7.40 = 44.64

We also need to add the city tax, which is 0.5 percent of the total price:

(572.95 + 113.76) * 0.005 = 3.43

The total purchase price is the sum of the prices of the diamond necklace and the gold pendant, the state tax, and the city tax:

572.95 + 113.76 + 44.64 + 3.43 = 734.78

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The x- and y-intercepts as required to be determined in the task content are; (-4/3, 0) and (0, -4).

As evident in the task content; the given function is; f(x) = - 3x - 4.

The x-intercept represents the value of x when f(x) = 0.

0 = -3x - 4

3x = -4

x = -4 / 3.

The y-intercept represents the value of f(0); hence, we have that;

f (x) = -3(0) - 4

f(0) = -4.

Ultimately, the points which correctly represents the x- and y-intercepts are; (-4/3, 0) and (0, -4).

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Answer:

34

Step-by-step explanation:

16x-12= 9x-11 + 9x-11

16×-12=18x-22

10=2x

5=x

WT= 9x-11=9(5)-11

WT=45-11

WT=34

Answer:

Second one

Step-by-step explanation:

Answer:

A:0 Noone goes higher than 40. b: 5 miles

The upper and lower interval estimate are often describe as associated with a specific level of confidence.

In statistics, interval estimate is the process of determining the interval, or range of values, within which a parameter—such as the mean (average) of a population—is most likely to fall.

The interval encompassing a population parameter is determined by computing the statistic from values obtained from a random sample chosen from the population and by using the understanding (derived from probability theory) of how accurately sample properties reflect those of the full population.

The possibility that the estimated confidence interval estimate will include the genuine population parameter is frequently referred to as the confidence level.

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Therefore , the solution of the given problem of unitary method comes out to be 14.7 dollars  before taxation, assuming he bought 650 feet of the cheaper rope.

The job can be completed by bringing together what was learned and applying this variable technique, that also includes all supplementary data from two people that utilized a specific tactic. To put it another way, if the desired outcome materialises, either the entity stated in the calculation will be recognised, or both expression essential processes will truly skip the colour. For forty pencils, a refundable charge of Rupees ($1.01) might be required.

Here,

To evaluate the prices, we need to use the same units.

Since 0.9144 metres make up one yard, we can convert the cost of the rope at the hardware shop to dollars per metre as follows:

=> 0.89 dollars/yard * 1 yard/0.9144 meters = 0.97 dollars/meter

b) We must change the units to yards or metres in order to evaluate the costs of 650 feet of rope. 650 feet is equivalent to 3 yards, which is:

=> 650 feet x 3 feet per yard = 216.67 yards

The hardware store's price for the cord is:

=>  192.5 dollars ($0.89/yard x 216.67 yards)

At the timber yard, the price of the rope is:

=>  (216.67 yards * 0.9144 meters/yard) * 0.94 dollars/meter = 177.8 dollars.

Jim would therefore save:

=>  192.5 dollars - 177.8 dollars = 14.7 dollars.

before taxation, assuming he bought 650 feet of the cheaper rope.

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The value of m∠1 is 103°. The solution has been obtained by using the angle sum property.

What is the angle sum property?

The angle sum property of a triangle states that the sum of the three internal angles of a triangle is 180 degrees.

We are given that m∠5 = 142° and m∠4 = 65°.

Since m∠5 and m∠2 lie on a straight line so, they form a linear pair.

So,

⇒ m∠5 + m∠2 = 180°

⇒ 142° + m∠2 = 180°

⇒ m∠2 = 38°

We know that sum of angles of a triangle is 180°.

So,

⇒ m∠3 + m∠4 + m∠2 = 180°

⇒ m∠3 + 65° + 38° = 180°

⇒ m∠3 + 103° = 180°

⇒ m∠3 = 77°

Now, since m∠3 and m∠1 lie on a straight line so, they form a linear pair.

So,

⇒ m∠3 + m∠1 = 180°

⇒ 77° + m∠1 = 180°

⇒ m∠1 = 103°

Hence, the value of m∠1 is 103°.

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The complete question and the figure has been attached below.

Question: Find m∠1 if m∠5 = 142° and m∠4 = 65°.

The amount that she needs to pay on her debt to reach a 25% debt-to-credit ratio is given as follows:

$2,535.

The amount that she needs to pay on her debt reach a 25% debt-to-credit ratio is obtained applying the proportions in the context of the problem.

She has a credit limit of $7,950.00, hence 25% of her credit limit is obtained as follows:

0.25 x 7950 = $1987.5.

She current has $4,522.50 on debts, hence the amount that she needs to pay for the debts to be reduced to $1987.5 is given as follows:

4522.5 - 1987.5 = $2,535.

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Answer:

Step-by-step explanation:

because we know 1 hour is 60 min so 3 hours would be 60x3=180 then you do 3x23.7=71 12x11.2=134 so in total he has 23.7 per hour and 11.2 for 3 hours

The company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

What is the Gaussian method?

The Gaussian method, also known as Gaussian elimination or row reduction, is a technique for solving systems of linear equations. It involves performing a sequence of operations on the rows of a matrix to transform it into an equivalent matrix that is in row echelon form or reduced row echelon form.

To use the Gaussian method, we need to set up a system of linear equations based on the given information. Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem produced per month, respectively. Then we have:

Machining department: 1200x + 1800y + 3000z = 1050(60)

Inspection department: 2400x + 1200y = 1160(60)

Assembly department: 600x + 3000y = 830(60)

Simplifying these equations, we get:

Machining department: 20x + 30y + 50z = 3150

Inspection department: 8x + 4y = 232

Assembly department: x + 5y = 139

Now we can use the Gaussian method to solve for x, y, and z:

Step 1: Write the augmented matrix:

| 20 30 50 | 3150 |

| 8 4 0 | 232 |

| 1 5 0 | 139 |

Step 2: Use row operations to get the matrix in row echelon form:

R2 → R2 - 4/5 R3

R1 → R1 - 20R3

| 0 -2 50 | 850 |

| 0 2 -4   | -28 |

| 1 5 0     | 139 |

R2→ -1/2 R2

R1 → R1 + R2

| 0 1 -25 | 407 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R1→ R1 - R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R3→ R3 - 5R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R1→ -1/23 R1

| 0 0 1 | -17 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R2 → R2 + 2R3

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 10 | 65 |

R3 → R3 - 10R1

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 0 | 235 |

Step 3: Read off the solution from the row echelon form:

z = -17

y = 96

x = 235

Therefore, the company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

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Based on the image, we can break 9 × 4 into two expressions as 4 groups of 9 or 9 groups of 4. This equals 36.

It should be noted that to break 9 x 4 up into two expressions, you can use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac.

So, we can rewrite 9 x 4 as:

9 x 4 = 9 x (3 + 1)

Using the distributive property, we can expand this expression as:

9 x (3 + 1) = (9 x 3) + (9 x 1)

Simplifying, we get:

9 x 4 = 27 + 9

Therefore, we have broken up 9 x 4 into two expressions: 27 and 9. This will give 36.

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Callie will need a total of 112 feet of fence for the triangle DFG.

We can find the amount of fence needed by finding the relationship between both triangles and find the missing side.

The sum of all the sides of the triangle will be known as the perimeter of the triangle. we can use this knowledge to find the amount of fence needed.

Both triangles are similar and are in the ratio of 1:7To find the missing side of triangle DFG, we multiply the corresponding side of triangle BAC by 7 to find the missing side.

This will give us 7 x 7 = 49ft

To find the amount of fence needed for triangle DFG we add all the sides of triangle DFG which will be 49 + 35 + 28.

The total will be 112ft.

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