Evaluate the expression when x= 14 and y= 6.x+y^2/x-2ySimplify your answer as much as possible.

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Jenny's Average swimming speed is 1.5 km/h.

Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.

We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.

Thus, the distance she swam is S * 1 = S km.

Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.

Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.

Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.

She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.

The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.

Therefore, we can write the equation:

S + 8S + 28S = 55.5.

Simplifying the equation, we get:

37S = 55.5.

To solve for S, we divide both sides of the equation by 37:

S = 55.5 / 37 = 1.5.

Thus, Jenny's average swimming speed is 1.5 km/h.

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Answer:

It should be C

Step-by-step explanation:

Answer:

Air conditioners are rated by the number of British Thermal Units (BTU) of heat they can remove per hour. Another common rating term for air conditioning size is the "ton," which is 12,000 BTU per hour.

Each air conditioner has an energy-efficiency rating that lists how many BTUs per hour are removed or “pulled out” for each watt of power it draws.

The efficiency rating for room conditioners is the Energy Efficiency Ratio, or EER.

The efficiency rating for central air conditioners, is the Seasonal Energy Efficiency Ratio, or SEER.

These ratings are posted on an Energy Guide Label, which must be conspicuously attached to all new air conditioners. Energy Star-labeled appliances mean that they have high EER and SEER ratings

Answer:

151.9 or 15.2

Step-by-step explanation:

Answer: b

Step-by-step explanation:

3^2 + x^2 = 9^2

9 + x^2 = 81

x^2 = 72

x = sqrt(72)

Answer:

23/72 or .3194

Step-by-step explanation:

Answer:

0.31944444444

Step-by-step explanation:

The centroid of the triangle is (2,4).

Given that the triangle whose vertices are A (1, 2) B(3, 7) and C (2, 3)​.

The center point of the object is centroid. The intersection of the three medians of a triangle is called the centroid of the triangle. It is also defined as the intersection of the three medians.

Let the given vertices of a triangle be A(1,2) and B (3,7) let the third vertex be C (2,3)

Let the centroid be G.

Centroid=[(x₁+x₂+x₃)/3,(y₁+y₂+y₃)/3]

Here, x₁=1, x₂=3, x₃=2, y₁=2, y₂=7 and y₃=3

Now, we want to substitute the values in the formula, we get

G=[(1+3+2)/3,(2+7+3)/3]

G=[6/3,12/3]

G=[2,4]

Hence, the centroid of the triangle whose vertices are A (1, 2) B(3, 7) and C (2, 3)​ is (2,4).

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Answer:

y = x - 3

Step-by-step explanation:

ok so r has the cornets of (4,1) and (6,3)

x - 3 = y

4 - 3 = 1

6 - 3 = 3

Option D is the correct synthetic division of (x^2-4x+7) divided by (x-2)

Synthetic division is a shorthand procedure used to divide a polynomial by a linear factor of (x - a) form, in which "a" is constant. This method gives an expedient way to locate the quotient and remainder without carrying out long division.

x - 2 | x^2 - 4x + 7

            x^2 - 2x

           ---------

                 -2x + 7

                 -2x + 4

                 -------

                        3

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Answer:

A parabola                    

Explanation:

Answer:

$56 I think

Step-by-step explanation:

because 30% of 80 is 24 and 80-24=56

According to the information, the maximum infection rate is:  k * 2500 * (5000 - 2500) = 6250k = 40

To address this problem, we can use the law of the infection rate, which states that the infection rate is directly proportional to the product of the number of people infected and the number of people not infected. Therefore, we can write:

where "k" is a constant of proportionality. Since we want to find the number of people infected that produces the maximum infection rate, we can consider the infection rate as a function of the variable "x" representing the number of people infected. Therefore, we can write:

To find the value of "x" that maximizes the infection rate, we can derive this function and set the derivative equal to zero:

This implies that 5000 - 2x = 0, and therefore:

Therefore, the number of infected people that produces the maximum daily rate of infection is 2,500.

However, we must verify that this result is consistent with the information given in the problem. We know that when there are 1,000 people infected, the flu spreads at the rate of 40 new cases per day. Therefore, if we add 1,500 more infected people (for a total of 2,500), the infection rate would be:

If the infection rate is 40 new cases per day, we have:

which implies that:

Therefore, the maximum infection rate is:

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Answer:

8*5=40

160/40=4

to recheck

V= LxWxH

V=8*5*4

V=160

Step-by-step explanation:

GOOD LUCK

Answer:

0.2835 = 28.35% probability that exactly two of them require warranty repairs.

Step-by-step explanation:

For each TV, there are only two possible outcomes. Either they require warranty repairs, or they do not. The probability of a TV requiring warranty repairs is independent of any other TV, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

10% require repair to be done under the warranty during the first year service.

This means that \(p = 0.1\)

A particular dealership sells 18 such TV per week.

This means that \(n = 18\)

a) What is the probability that exactly two of them require warranty repairs?

This is \(P(X = 2)\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{18,2}.(0.1)^{2}.(0.9)^{16} = 0.2835\)

0.2835 = 28.35% probability that exactly two of them require warranty repairs.

Applying the angles of intersecting chords theorem, the value of x in the first figure is: x = 7.

If two chords of a circle intersect, the angles of intersecting chords theorem states that, the measure of the angle formed equals 1/2(sum of the measure of the arcs which are intercepted.

Thus, we can use the angles of intersecting chords theorem to find missing angles or value of x in the questions given.

For example, let's find the value of x in the first figure given:

12x + 5 = 1/2(83 + 95)

12x + 5 = 89

12x = 89 - 5

12x = 84

x = 7

Using same strategy, you can solve the rest of the problem given.

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Answer:

5\(ft^2\) is the area of the original piece of fabric.

Step-by-step explanation:

0.625 x 8 = 5

Answer:

The slope is a value that describes the steepness and direction of a line

Step-by-step explanation:

I think ts either 2 or nagtive 2

Answer:

gradient (slope) = 2

Step-by-step explanation:

gradient (slope) = difference of y-coordinates / difference of x-coordinates = (y₂-y₁)/(x₂-x₁)

Pick two points, ex: (0,1) and (-2,0)

= (0-1)/((-2)-0)

= -1/-2

= 1/2

Answer:

300

Step-by-step explanation:

45 minutes is 15% of x

45 = 0.15x

0.15x = 45

x = 45/0.15

x = 300

Answer: 300

So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

Answer:

1/15

Step-by-step explanation:

\(7/24 * 8/35\)

\(1/3*1/5=1/15\)

Step-by-step explanation:

\( \frac{7}{24} \times \frac{8}{35} \\ \\ = \frac{1}{3} \times \frac{1}{5} \\ \\ = \frac{1}{15} \)

Answer:

24 inches

Step-by-step explanation:

Answer:

7.5 or 7 1/2

Step-by-step explanation:

since in the original you divide by 4 and multiply by 5,

the same rule applies for the second.

6/4=1.5x5=7.5

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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Step-by-step explanation:

1 plus 1 equals 2

It's addition so u just add

1 + 1 = 2

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