a solid metal prism has a rectangular base with sides of 4 inches and a height of 6 inches. a hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism.
What is the approximate volume of the remaining solid, in cubic inches?
a. 19 cubic inches b. 77 cubic inches c. 96 cubic inches d. 93 cubic inches

The distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.

Distance can be calculated using a variety of methods, depending on the context. For example, the distance between two points in a straight line can be calculated using the Pythagorean theorem in two dimensions or the distance formula in three dimensions. In more complex situations, such as when the two points are not in a straight line, distance may be calculated using other mathematical methods or by estimating the distance based on contextual information.

Distance is often used in everyday life to describe how far apart objects or locations are from each other, such as the distance between two cities, the distance from home to work, or the distance between two landmarks. It is also used in many scientific fields to describe the separation between celestial objects, the distances traveled by particles in a chemical reaction, or the distances between neurons in the brain.

We can solve this problem using the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:

a/sin A = b/sin B = c/sin C

Let's label the distance from point A to the boat as a, the distance from point B to the boat as b, and the distance from point C to the opposite bank as c. We are given that AB = 50 meters, angle ABC = 68 degrees, and angle BCA = 73 degrees. We want to find a and b.

First, we can find the measure of angle ACB by using the fact that the sum of angles in a triangle is 180 degrees:

angle ACB = 180 - angle ABC - angle BCA

angle ACB = 180 - 68 - 73

angle ACB = 39 degrees

Next, we can use the Law of Sines to find a and b:

a/sin 68 = c/sin 39

b/sin 73 = c/sin 39

Solving for c in both equations gives:

c = a sin 39 / sin 68

c = b sin 39 / sin 73

We can set these two equations equal to each other and solve for b:

a sin 39 / sin 68 = b sin 39 / sin 73

b = a (sin 39 / sin 73) * (sin 68 / sin 39)

b = a (sin 68 / sin 73)

We know that a + b = 50, so we can substitute the expression for b into this equation:

a + a (sin 68 / sin 73) = 50

Solving for a gives:

a = 50 / (1 + sin 68 / sin 73)

a ≈ 23.3 meters

Substituting this value of a into the expression for b gives:

b ≈ 26.7 meters

So the distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.

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The complete question is

Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if angle ABC=68 degree and angle BCA=73 degree. Round to the nearest foot.

In this context, the p-value represents the probability of observing the data or a more extreme result, assuming that the null hypothesis (the retention rate is still 4%) is true.

In other words, it measures the strength of evidence against the null hypothesis. A small p-value indicates that the observed result is unlikely to have occurred by chance alone, while a large p-value suggests that the null hypothesis cannot be rejected.

In this case, the calculated p-value of 0.075 suggests that there is some evidence to reject the null hypothesis that the retention rate is still 4%.

However, since the p-value is above the conventional threshold of 0.05, we cannot conclude with certainty that the new programs have significantly increased the retention rate. Instead, we can say that there is some indication that the programs may have been effective, but further investigation is needed to determine if this is true.

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A future interest in real property typically exists in conjunction with a present interest in that same property at the time the future interest is granted.

What is a future interest?

Future interests are created when a property owner grants an interest in their property that will take effect at a later time, such as after their death or the expiration of a lease.

These interests are typically created in the form of a trust or a will, and they can be used to ensure that property is distributed according to the owner's wishes, to provide for the future needs of family members, or to protect property from creditors or other claims.

Examples of future interests include remainders, reversions, and executory interests.

Complete questin:

A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?

1) future interest

2) protect property

3) both a and b

4) None of these

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Thus, the distance travelled by the airplane from point A to point B is found as:  1159.93 ft.

Let the distance travelled between A and B be 'x'.

Height h = 6900 feet.

The figure is attached.

Using the tan function:

tan Ф = opposite side/ hypotenuse

In right triangle BCE.

tan 27 = 6900 / y

y = 6900 / tan 27

y = 15281.80

In right triangle ACD

tan 16 = 6900 /(x + y)

x + y = 6900/tan 16

x = 26873.72 - 15281.80

x = 1159.93

Thus, the distance travelled by the airplane from point A to point B is found as:  1159.93 ft.

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The value of x in the right triangle when calculated is approximately 13.8 units

Given the right-angled triangle

The side length x can be calculated using the following sine ratio

So, we have

sin(39) = x/22

To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.

First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.

Then, we can set up the equation:

0.6293 = x/22

To solve for x, we can multiply both sides by 22:

0.6293 * 22 = x

13.8446 = x

Rewrite as

x = 13.8446

Approximate the value of x

x = 13.8

Therefore, x is approximately 13.8 in the triangle

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Answer:

x = 10, -4

Step-by-step explanation:

(x – 3)² = 49

x - 3 = √49

x - 3 = ± 7

x = 10, -4

Looking at options,  10 and -4 is the answer.

Answer:

Step-by-step explanation:

Let's call the length of the shorter leg of the isosceles trapezoid "a" and the length of the longer leg "b".

From the problem, we know that:

a = 0.1x - 0.5 (length of one leg is 0.1.x - 0.5 meters)

b = 0.3x - 2.1 (length of the other leg is 0.3.x-2.1 meters)

Since we know that the trapezoid is isosceles, we know that a = b. So we can set the two expressions equal to each other:

0.1x - 0.5 = 0.3x - 2.1

Now we can solve for x:

0.2x = 1.6

x = 8

Now that we know x, we can substitute it back into the expressions for a and b to find their lengths:

a = 0.1(8) - 0.5 = 0.3 meters

b = 0.3(8) - 2.1 = 0.3 meters

Therefore, each of the legs of the solar panel are 0.3 meters long.

Answer:

Step-by-step explanation:

Replacing it

True, conditional formulas can be used to exclude data from analysis if certain conditions are met. These formulas, often found in spreadsheet software and programming languages, allow you to set specific criteria that must be met in order for the data to be included or excluded from your analysis.

This can be useful in situations where you need to focus on specific subsets of data, or to remove outliers or irrelevant information from your dataset.

By incorporating conditional logic in your formulas, you can ensure that only relevant and useful data is included in your analysis, making it more accurate and efficient. Overall, the use of conditional formulas can greatly enhance your data analysis by providing a flexible and powerful tool to filter and process your data based on specific requirements.

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Answer:

8.17

Step-by-step explanation:

43x19/100 equals 8.17

the amount of sand in the top cone when the height of the sand is only 1 inch is (h-1)/h times the amount of sand in the top cone originally.

the cones are similar, their volumes are proportional to the cube of their heights. Let's denote the height of the top cone as h, and the radius of the top and bottom bases as r. Then, the volume of the top cone can be expressed as:

V₁ = (1/3)π[tex]r^2[/tex]h

If the height of the sand in the top cone is reduced to 1 inch, then the height of the remaining sand in the top cone is (h-1) inches. The volume of the remaining sand in the top cone can be expressed as:

V₂ = (1/3)π[tex]r^2[/tex](h-1)

To compare the amount of sand in the top cone in these two scenarios, we can take the ratio of their volumes:

V₂/V₁ = [(1/3)π[tex]r^2[/tex](h-1)] / [(1/3)π[tex]r^2[/tex]h] = (h-1)/h

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The fact that the overall frequency of an event can be determined by multiplying together the frequencies of the independently occurring factors related to that event is called a frequency multiplier. Also called as multiplication rule.

             The multiplication rule states that the overall probability of a sequence of events happening jointly is the product of the probabilities of the individual events.

                  In probability, the multiplication rule is used to calculate the joint probability of two independent events that occur together.

              In probability scenarios, the factors are the set of conditions that influence the probability of a certain occurrence, event, or outcome.

These factors are used to calculate the probability of an event. The likelihood of the occurrence of an event is based on these factors.

             The multiplication rule can be used to calculate the overall frequency of an event by multiplying the frequency of each factor independently related to the event.

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Total of 3 hours are needed to complete the job.

The required equation that can be used to answer this question is: 31x = 568 − 475, where x is the number of hours of labor that was needed to complete the job.

Here's how you can solve it:Samantha recently hired a mechanic to do some necessary work. On the final bill, Samantha was charged a total of $568. $475 was listed for parts and the rest for labor.

If the hourly rate for labor was $31, how many hours of labor were needed to complete the job?Solution:Let x be the number of hours of labor needed to complete the job.

Labor cost = $31/hourTotal labor cost = 31x dollars. Total cost of the job = $568.

Cost of parts = $475.

Labor cost = Total cost − Cost of parts.

31x = 568 − 47531x = 93x = 3

Therefore, 3 hours of labor was needed to complete the job.

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Answer:

To solve the inequality x^2-5x-36>0, we need to find the values of x for which the expression is greater than zero.

One way to do this is by factoring the quadratic expression:

x^2-5x-36 = (x-9)(x+4)

The expression is positive when either both factors are positive or both factors are negative.

When both factors are positive: x-9 > 0 and x+4 > 0

Solving for x, we get x > 9 and x > -4. Therefore, x > 9.

When both factors are negative: x-9 < 0 and x+4 < 0

Solving for x, we get x < 9 and x < -4. Therefore, x < -4.

Now, we have two intervals: x < -4 and x > 9. To check whether the expression is positive within these intervals, we can pick a value within each interval and plug it into the expression.

Let's choose x = -5 (within x < -4) and x = 10 (within x > 9).

For x = -5:

x^2-5x-36 = (-5)^2-5(-5)-36

= 25+25-36

= 14

Since 14 is greater than zero, the expression is positive when x = -5.

For x = 10:

x^2-5x-36 = 10^2-5(10)-36

= 100-50-36

= 14

Since 14 is greater than zero, the expression is also positive when x = 10.

Therefore, the solution to the inequality x^2-5x-36>0 is x < -4 or x > 9, which can be written in interval notation as (-∞,-4) ∪ (9,∞).

Answer:

10km/hr

Step-by-step explanation:

The speed of the wind is approximately 6.93 km/hr.

We have,

Let's call the speed of the wind "w" (in km/hr).

When the airship is flying with the wind, its speed relative to the ground is the sum of its speed in calm weather (50 km/hr) and the speed of the wind (w km/hr). So the airship's speed with the wind is 50 + w km/hr.

When the airship is flying against the wind, its speed relative to the ground is the difference between its speed in calm weather (50 km/hr) and the speed of the wind (w km/hr).

So the airship's speed against the wind is 50 - w km/hr.

The distance flown by airship in each direction is the same (150 km).

Let's use the formula for distance, rate, and time:

distance = rate x time

For the first leg of the trip (flying with the wind), we have:

distance = (50 + w) x time

distance = (50 + w) x t(1)

where t(1) is the time taken for the first leg of the trip.

For the second leg of the trip (flying against the wind), we have:

distance = (50 - w) x time

distance = (50 - w) x t(2)

where t(2) is the time taken for the second leg of the trip.

The total time for the round trip is given as 6 hours and 15 minutes, or 6.25 hours.

So we have:

t(1) + t(2) = 6.25

We also know that the distance flown in each direction is 150 km. So we have:

(50 + w) x t(10 = 150

(50 - w) x t(2) = 150

Now we can solve this system of equations for w:

t(1) = 150 / (50 + w)

t(2) = 150 / (50 - w)

t(1) + t(2) = 6.25

Substituting the first two equations into the third equation, we get:

150 / (50 + w) + 150 / (50 - w) = 6.25

Multiplying both sides by (50 + w)(50 - w), we get:

150(50 - w) + 150(50 + w) = 6.25(50 + w)(50 - w)

Expanding and simplifying, we get:

7500 - 150w + 7500 + 150w = 15625 - 312.5w²

Simplifying further, we get:

15000 = 312.5w²

Dividing both sides by 312.5, we get:

w² = 48

Taking the square root of both sides, we get:

w = ±√(48)

Since the speed of the wind cannot be negative, we take the positive square root:

w = √(48) ≈ 6.93 km/hr

Therefore,

The speed of the wind is approximately 6.93 km/hr.

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The national average for energy usage per home in BTU is approximately 90 BTU.

BTU stands for British Thermal Unit, which is the amount of energy required to raise the temperature of one pound of water by one degree Fahrenheit. It is used to quantify the amount of energy consumed by heating or cooling equipment.In California, people use 63 BTU of energy per home, which is 30% less than the national average. Therefore, to calculate the average BTU consumption for American households, we will use the following formula: National average BTU = California BTU / (1 - 30%)

Let's solve for the national average BTU: National average BTU = 63 BTU / (1 - 0.30)

National average BTU = 63 BTU / 0.70National average BTU = 90 BTU

Therefore, the average American household uses 90 BTU of energy per home.

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Answer:

China's top ten famous flowers are: the queen of flowers - plum blossom, the king of flowers - peony, frost blooming - chrysanthemum, gentleman's flower - orchid, the queen of flowers - rose, blooming flowers - Rhododendron, delicate flowers - camellia, water hibiscus - lotus, ten miles of fragrance - osmanthus, Lingbo fairy - daffodil 10 kinds of precious and beautiful local flowers.

Plum blossom is known as the "top ten famous flowers in China". These ten kinds of flowers respectively contain different levels of Chinese spiritual and cultural deposits, with profound and strong historical connotation. They are unique in the flower industry, marking the extraordinary significance of Chinese traditional culture. However, among China's top 10 traditional famous flowers, only the plum blossom, osmanthus and lotus have international registration rights.

To solve an equation with multiple unknowns, you need to have as many equations as there are unknowns.the solution to the system of equations is  [tex]x = 13/11 and z = 37/11.[/tex]

For the equation you provided, [tex]-x - 4z = -15[/tex]  , there are two unknowns: x and z. To solve for both, you need another equation that involves x and z.

If you have another equation that involves x and z, you can use a method like substitution or elimination to solve for both variables simultaneously.

For example, let's say you have the equation  [tex]2x + 3z = 7.[/tex] You can use substitution to solve for one variable in terms of the other and substitute the result into the other equation.

To solve for x, rearrange the first equation to get x in terms of z:

[tex]-x - 4z = -15[/tex]

[tex]x = -15 + 4z[/tex]

Substitute the expression for x into the second equation:

[tex]2x + 3z = 7[/tex]

[tex]2(-15 + 4z) + 3z = 7[/tex]

Distribute the 2:

[tex]-30 + 8z + 3z = 7[/tex]

Simplify:

[tex]11z = 37[/tex]

Solve for z:

[tex]z = 37/11[/tex]

Substitute the value of z back into the equation for x:

[tex]x = -15 + 4z[/tex]

[tex]x = -15 + 4(37/11)[/tex]

[tex]x = -15 + 148/11[/tex]

Simplify:

[tex]x = 13/11[/tex]

Therefore, the solution to the system of equations is x = 13/11 and z = 37/11.

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The numerical value of x in the expression (x+5) and 2(x-4) is 61.

The sum of angles on a straight line equals 180 degrees.

From the figure in the image:

We know that the sum of angles on a straight line equals 180 degrees.

Since angle GDC and its supplement are on a straight line.

Hence;

Angle GDC + Supplemetary angle to GDC = 180

Plug in the given values and solve for x.

( x + 5 ) + 2( x - 4 ) = 180

Apply distributive property.

x + 5 + 2x - 8 = 180

Collect like terms

x + 2x - 8 + 5 = 180

3x - 3 = 180

3x = 180 + 3

3x = 183

x = 183/3

x = 61

Therefore, the value of x is 61.

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The probability that a dessert chosen at random contains nuts given that it contains chocolate is 34.9%.

The likelihood of any event A happening when another event B related to A has already happened is known as conditional probability. This implies that the likelihood of event A relies on event B.

The conditional probability symbol is P(A|B). Conditional probability P(A|B) is crucial for any exam that is part of a competition. The concept of conditional probability P(A|B), formula, and examples with solutions are all covered in this article. The Bayes theorem predicts the likelihood that an event connected to any condition would occur. For the situation of conditional probability, this theorem is taken into account.

Let A : a certain cafe contains chocolates

B: a dessert contains Nuts

P(A) = 86% = 0.86

P(AB) = 30% = 0.3

[tex]P(B|A) =\frac{P(AB)}{P(A)}[/tex]

= 0.3/0.86

= 34.9 %

So the answer is 34.9%

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the relationship between test scores and the student-teacher ratio can be modeled as a linear function: The right choice is D) lessen test scores by 4.56 for each school locale.

In view of the data in the inquiry, the relationship between test scores and the understudy educator proportion can be numerically composed as follows:

x = 698.9 - 2.28y .................... (1)

Where,

x = test scores

y = understudy educator proportion

The slant of (- 2.28) shows the sum by which x will change at whatever point there is an adjustment of y.

Hence, when there is a reduction in the understudy educator proportion by 2 (for example y = 2), we will have:

Change in x = - 2.28 * 2 = - 4.56

The negative sign thusly shows that the test scores will decrease by 4.56 for each school area. Accordingly, the right choice is D) lessen test scores by 4.56 for each school locale.

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the complete question is:

Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student teacher ratio by 2 will: A) reduce test scores by 2.28 on average) result in a test score of 698.9C) reduce test scores by 2.56 on average) reduce test scores by 4.56 for every school district.

Jennifer needs to sample at least 151 vets to achieve a standard error of the mean of 3.42 years or less.

The variability or uncertainty of a sample statistic, like the mean or proportion, is measured by standard error. It represents the sample distribution's standard deviation for that statistic. In other words, it calculates the amount by which chance is likely to cause the sample statistic to deviate from the actual population parameter.

The calculation of the standard error is based on the particular statistic being produced as well as the characteristics of the sampled population. For instance, the population's standard deviation is divided by the square root of the sample size to determine the standard error of the mean. If p is the estimated proportion based on the sample, then the standard error of a proportion is determined as (p * (1 - p)) divided by the square root of the sample size.

A population parameter estimate that has a lower standard error is more accurate. Inferential statistics frequently employ the standard error to compute confidence intervals and test population parameter-related hypotheses.

The formula for the standard error of the mean can be used to get the approximate number of veterans Jennifer needs to sample:

[tex]SE = / \sqrt{n}[/tex]

where n: sample size, delta: age standard deviation, and SE: standard error of the mean.

In this instance, we are aware that = 22 years and SE = 3.42 years. As we solve for n, we obtain:

[tex]n = (delta / SE)^2 n = (22 / 3.42)^2 \sn = 150.39[/tex]

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n/8⋅л=56. You’re welcome!

Each number occupies 7.7 inches² of  the dartboard.

In geοmetry, area is the amοunt οf space a flat shape, like a pοlygοn, circle οr ellipse, takes up οn a plane. The area οf a shape is always measured in square units. Tο find the area οf simple shapes like a square οr the area οf a rectangle, yοu οnly need its width, w, and length, l (οr base, b). The area is length times width:

First we need the area of the dartboard

Area = πr²

here r = d/2 = 14/2 = 7

Area of dartboard = πr²

[tex]$ \rm = \frac{22}{7 } \times 7 \times 7[/tex]

= 22 × 7

= 154 inches²

Now, its is said that each number occupies 1/20 of the board,

Then area of each number =  154 ×  1/20

                                             = 7.7 inches²

Thus, Each number occupies 7.7 inches² of  the dartboard.

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Answer:

first box (pies): 3, 6, 9, 12, 15, 18, 33

-> increments of 3

2nd box [cost ($)]: 11, 22, 33, 44, 55, 66, 121

-> increment of 11

Step-by-step explanation:

$44 ÷ 12 pies = $3.67 per 1 pie

3 × $3.67 = $11.01

same process: (number of pies) × $3.67 ≈ COST

Answer:

Step-by-step explanation:

So start off with 66 x 33. That will equal 2,178. Divide 2,178 by 18, like this: 2,178/18. That will equal 121. that will mean that 33 = 121. So 9 = 33 because 9 x 44 = 396 so you will divide that by 12 meaning that 9 equals 33. So now you will multiply 9 and 22 and then divide that answer by 33 making 6 = 22. now divide 22 by 6. That will equal 3.67. So 3.67 is the cost of one pie.

For the boxes above 12 and 44 it will be 16 = 59.

I hope it helped

The roots of the given quadratic equation are x= 4, [tex]\frac{-3}{2}[/tex]

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0The roots of a quadratic equation are found using the quadratic formula. In place of the factorization method, this formula aids in evaluating the quadratic equations' solutions. The quadratic formula aids in identifying the problem's fictitious roots when a quadratic equation lacks actual roots. Shreedhara Acharya's formula is another name for the quadratic formula.

2x² - 5x​ -12 = 0

The Shridharacharya formula or quadratic formula -

[tex]x=\frac{-b\ +-\sqrt{b^2-4ac}}{2a}[/tex]

we have a=2, b=-5 and c=-12

[tex]x=\frac{5+-\sqrt{5^2-4*2*12}}{2*2}\\\\x=\frac{5+-\sqrt{25+96}}{4}\\\\x=\frac{5+\sqrt{121}}{4}\\\\x=\frac{5+-11}{4}\\now, \\x=\frac{5+11}{4}=\frac{16}{4}\\x=4\\x=\frac{5-11}{4}\\x=-6/4\\x=-3/2[/tex]

The mistake in your solution is we have the value of b=-5 so , when we put the value of b in a formula then -5 will be 5.

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Answer:

B. y = (x+1)(x-3)

Step-by-step explanation:

Bbecause when y intersect the x axis, y = 0

so (x+1)(x-3) = 0, which we get x = -1 and x = 3

As shown in the graph this is true, because the function does indeed also intersect with the x axis at x = -1 and x = 3 as well.

In the given right angled triangle, using Pythagorean theorem, the value of x is 12.73 units.

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the length of the squares on the other two sides add up to the length of the square whose side is the hypotenuse, or the side across from the right angle. This theory can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:

a² + b² =c²

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.

In the given right angled triangle, using Pythagorean theorem,

x² = (9[tex]\sqrt{2}[/tex] )²+ (9[tex]\sqrt{2}[/tex] )²

x² = 81×2

x = [tex]\sqrt{162}[/tex]

x = 12.73 units

Therefore, the value of x will be 12.73 units.

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Answer:

The first one...............

If the system has infinite solutions, it means that the two equations are not independent, but rather one equation is a multiple of the other. In other words, the second equation must be a multiple of y = 7x + 8.

One possible equation that completes the system is:

14y = 98x + 112

To check that this equation works, we can substitute y = 7x + 8 into the equation:

14(7x + 8) = 98x + 112

98x + 112 = 98x + 112

As we can see, the equation is true for any value of x, which means that it is satisfied for any value of y that corresponds to y = 7x + 8.

Therefore, the system of equations that has y = 7x + 8 as one of its equations and has infinite solutions is:

y = 7x + 8

14y = 98x + 112