What is the greatest possible length of a side of a triangle whose perimeter is 1000 and all of whose sides have integral lengths?

The values of x and y on solving the two simultaneous equations are x = 1 and y = 3.

The simultaneous equations to be solved are 4x + 2y = 10 and x + 2y = 7.

Rearranging the above equations, we have,

- 4x - 2y = - 10 -----(A)

x + 2y = 7  -------(B)

Solving them, we have, -3x = -3

x = 1 ------(C)

Substituting (C) in (B), we have,

1 + 2y = 7

2y = 6

y = 3 ------(D)

Now, let us substitute the x and y values in (A) and (B) and then check.

4x + 2y = 10

4 + 2(3) = 10

A is checked.

x + 2y = 7

1 + 2(3) = 7

B is checked.

Thus, the values of x and y are checked to be correct.

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The distance between G and H on the number line  -12 and -2 is -10.

What is Distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language .

The phrase is widely used metaphorically to refer to a measurement of the degree of difference between two similar objects since spatial cognition is a rich source of conceptual metaphors in human thought.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.  

What is number line?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that each real number and each point on a number line relate to one another.

We are given two point G and H which are represented on number line;

The value G = -12 and H = -2

We have to find the distance between them;

So , we can simply subtract these two values of  G and H to get the distance between them;

distance = -12-(-2)

             = -12 + 2

             = -10

Therefore, the distance between G and H on the number line  -12 and -2 is -10.

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Answer:

x ≥ 10

Step-by-step explanation:

A solid dot on 10 means 10 is included.

An arrow pointing to the right of 10 means all numbers greater than 10 are included.

Answer: x ≥ 10

Answer:10 =< x

Step-by-step explanation:
Shaded circle means include that number so it is a <= or >= sign
Goes to x.
Think about it a bit, not quite sure if 50 is involved in this inequality

a) Equation would be 5x + (x - 6) + (x - 6) = 180°

b) m∠1 = 180° and  m∠2 = 30°

What is the measure of angle?

The term "degree measure" refers to the measurement of an angle in degrees. Because one entire revolution equals 360°, it is divided into 360 parts. Each stage of the revolution represents a degree.

a) The angle measures in a triangle must add up to 180°.

Therefore, the equation to find x is:

        5x + (x - 6) + (x - 6) = 180°

b) Solving for x, we get:

x = 36

Therefore, angle m∠1 = (5x) = (5 * 36) = 180° (major angle)

angle m∠2 = (x - 6) = (36 - 6) = 30° (minor angle)

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Answer: Ordinal numbers are a designation of something's place in a series by a number, such as first or third.  Ordinal numbers can function as pronouns, nouns, and adjectives.

Answer:

Step-by-step explanation:

It means what place something is in. For example the ordinal of 1 is 1st 2 is 2nd and 3 is 3rd and so on. I hope this helps.

The area, in square inches, will be 156.25π

You would require the radius in order to get the circle's area. You would enter the circumference (25) into the equation for the circle's circumference, which looks like this:

C = 2πr

25π = 2πr

Then you would figure out how to solve for r. (the radius)

25π = 2πr

12.5π = πr

12.5 = r  

After that, you would enter the radius into the equation for a circle's area.

A = π(r^2)

A = 12.5^2π

A = 156.25π

Due to the fact that meters were used as the unit of measurement, your response would be 156.25 meters.

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The range of the ticket prices after the discount is used is 1.

The difference between the lowest and highest values, is considered as range.

Given that, groups of 25 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age.

The range of a data is given by, difference of lowest element and largest element.

Here, 20% discount is to be given, and ticket price ranges from $10 to $15

20% of 10 = 2

And

20% of 15 = 3

Therefore, range = 3-2

= 1

Hence, the range of the ticket prices after the discount is used is 1.

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Answer:-√ 5

Step-by-step explanation:

4√ 20 = 8√ 5
3√ 45 = 9√ 5
8√ 5 - 9√ 5 = -√ 5

There are a total of 10 slips.

8 slip with 3 on it

2 slips with 9  on it

value = Probability of 3 x 3 + Probability of 9 x 9.

=  (8 / 11)  x 3 + (2/ 11)  x 9

24 / 11 + 24 / 11 = 4.36

probability

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

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Answer:

2

Step-by-step explanation:

count the grids, A is 4, B is 8, so scale =2

The initial fee charged to customers for using the gym, given the graph showing the charges to customers is $ 20.

To find the initial membership fee, you should look at the y - intercept of the graph.

The y - intercept is the point where the x vale is 0 and this case this point shows the cost when the customers have not worked out in the gym for any hour yet.

This y - intercept is therefore $ 20 as this is the point on the graph where the value of x is 0.

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The question is:

What is the initial fee charged to customers for using the gym?

There are other methods to write a division issue, such as using a / or a to denote "divided by." As a result, in the equation 473 / 2 = 1 the divisor is the quotient, the remainder is 236, and the divisor is 2.

Divide the dividend's first digit, which should be on the left, by the divisor, then write the result as the quotient on top. Write the difference below after subtracting the outcome from the digit. Bring down the dividend's next digit (if present).

Long division strategy: lengthy division techniques. The same symbols are used for long division as they are for short division: dividend (the number being divided) under the "bus stop," divisor (the number the dividend is being divided by), quotient (the solution) on top, and each place value aligned with the dividend.

Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

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The complete question is "Divide the given numbers 473 and 6 using our free online Long Division Calculator and determine the Quotient and Remainder as Q 78 R 5 instantly without any hurdles."

Answer:

A. 500 people will go out to the park when its 100F is incorrect.

Three letters will be selected from five letters. The number of possible selections is 10.

A combination is a method of picking elements from a collection where the order of selection is irrelevant. Assume we have three numbers P, Q, and R. The number of ways we can choose two numbers from each set is determined by combination.

Suppose we want to pick k elements from a set of n elements, then the number ways it can be chosen is:

C(n,k) = n! / k! (n-k)!

Where n! is n factorial.

In this case, there are 5 letters and we want to select three letters. Hence, k = 3, and n = 5.

C(5,3) = 5! / 3! (5-3)!

C(5,3) = 5! / (3! 2!) = 10

Thus, there are 10 possible selections.

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The value of d in the given angles using the concept of complementary angles is; d = 13

Complementary angles are defined as angles that add up to 90 degrees.

Now, we are told that one angle measures 18°, and another angle measures (6d − 6)°. This tells us that;

(6d - 6) + 18 = 90

Expanding the bracket gives us;

6d - 6 + 18 = 90

6d + 12 = 90

6d = 90 - 12

6d = 78

Use division property of equality to divide both sides by 6 to get;

6d/6 = 78/6

d = 13

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The equation of a circle with center located at (5,2) and that is tangent to the y-axis is given as follows:

C. x² + y² - 10x - 4y + 4 = 0.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

Considering the center, we have that:

(x - 5)² + (y - 2)² = r².

The circle is tangent to the y-axis, meaning that it passes through the point (0, 2), thus the radius is obtained as follows:

r² = 25.

Then the equation in standard form is given as follows:

x² - 10x + 25 + y² - 4y + 4 - 25 = 0.

x² + y² - 10x - 4y + 4 = 0.

Meaning that option C is correct.

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Answer:

-20

Step-by-step explanation:

A rectangular prism has a volume of  2x ^ 3 + 19x ^ 2 + 24x

the volume of the rectangular prism is

The area contained by an object's limits in three-dimensional space is referred to as its volume.

Thus, a rectangular prism having the following dimensions: 2x length, (x2) width, and (x + 2) height

L x B x H = volume

= x× (x +8 )(2x + 3)

= x(x + 8)(2x + 3)

(2x + 3) * x ^ 2 + 8x(2x + 3)

2x ^ 3 + 19x ^ 2 + 24x

The area contained by an object's limits in three-dimensional space is referred to as its volume.

A rectangular prism's volume is thus 2x ^ 3 + 19x ^ 2 + 24x

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From the trigonometric function sec θ = 13/12, two more functions are derived -

Option C: cos θ = 12/13

Option D: tan θ = 5/12

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The given trigonometric function is -

sec θ = 13/12

Sec function is written as the ratio of hypotenuse to adjacent.

sec θ = 1/cos θ

Cos function is written as the ratio of adjacent to hypotenuse.

cos θ = 12/13

To find the opposite, apply the Pythagoras theorem -

(Opposite)² = (Hypotenuse)² - (Adjacent)²

(Opposite)² = (13)² - (12)²

(Opposite)² = 169 - 144

Opposite = √25

Opposite = 5

Tan function is written as the ratio of opposite to adjacent.

tan θ = 5/12

Therefore, from sec function, cos and tan function are obtained.

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Answer: b to the power of 3 / 8 Have a nice day!

The fourth option represents the reflection over the x-axis of f(x)=√x. The graph has been attached below. The solution has been obtained by the concept of reflections.

What is reflection?

A flip is the term for a reflection in geometry. The shape is mirrored in a reflection. The line of reflection is a line across which an image will reflect. A reflection is the shape's mirror image. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way.

We are given the function f(x)=√x.

When we replace x with -x, then the graph of the resulting equation i.e.

f(x)=√-x is captured by reflecting the graph of f(x)=√x vertically across the x-axis.

Thus, the reflection of the function f(x)=√x is a vertical reflection across the x-axis.

Hence, the graph below represents the reflection of the function f(x)=√x which is the fourth option.

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The required money will the businessperson have when they convert the money to U.S. dollars is 5220.96 dollar.

Commodities and services can be exchanged using money. Currency is defined as a unit of account that is issued by a government and is accepted at face value. When bartering, products and services were directly exchanged for one another.

We know that

1 US dollar = 6.4651 yuan

To find US dollar value of given yuan

1 yuan = 1/6.4651 US dollar

337 54 yuan = 337 54/6.4651  = 5220.96 dollar

Thus, required dollars are 5220.96.

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Answer:

the answer is 52.21 all u gotta do is divide 337.54 by 6.4651 and u get 52.20955592334225 and just round it and u get the answer which is 52.21

Step-by-step explanation:

Answer:

X < 250

Step-by-step explanation:

Inequalities:

> Greater/More than

< Less/Fewer than

= Equal to

>= Greater than/More than OR equal to

<= Less than/Fewer than OR equal to

Since it says fewer than, we'll use <

X in this case will be the actual number of people.

We know fewer than 250 will attend, making the inequality

X < 250

The probabilities for this problem are given as follows:

It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The bounds for this problem are given as follows:

a = 2, b = 70.

Hence the probability of less than 30 seconds is given as follows:

P(X < 30) = (30 - 2)/(70 - 2)

P(X < 30) = 0.4118 = 41.18%.

The uniform distribution is a continuous distribution, meaning that the probability of an exact value is of 0.

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Simon's target number of laps will be 80.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, his coach tells him to swim a target number of laps and Simon swims 45 laps before practice is canceled due to a thunderstorm. Simon still has 35 laps left to reach his target number

Let the target number be x. This will be:

x - 45 = 35

x = 45 + 35

x = 80.

The Target number is 80

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Answer: 7x - 140

The expression 7(x-20) is a product of 7 and a grouping of x-20. To simplify this expression, we use the distributive property, which states that we can multiply the 7 by each term inside the grouping. So, 7(x-20) becomes 7x - 140. This is because 7x is the product of 7 and x, and 140 is the product of 7 and 20.

Step-by-step explanation:

Answer:

C) 11

Step-by-step explanation:

Exterior angles in a triangle = the sum of the interior angles of the triangle

Here, the exterior angle is ∠BCT while the interior angles are ∠CAB and ∠ABC

Using the above theorem we can say that ∠BCT = ∠CAB + ∠ABC

Plugging in the given expressions and values of the angles we acquire

9x + 6 = 3x + 2 + 70

==> combine like terms

9x + 6 = 3x + 72

==> subtract 3x from both sides

6x + 6 = 72

==> subtract 6 from both sides

6x = 66

==> divide both sides by 6

x = 11

The probability that  a product attains a good review is 0.6125

The given information can be tabulated as follows.

Success type          High             Moderate              Low            Total

                               0.40                   0.35                 0.25             1

Good reviews          0.95                    0.60                0.10

Combined prob       0.4*0.95             0.35*0.6          0.25*0.1

                                0.38                    0.21                  0.025       0.6125

A)the likelihood that a product will receive a favorable review = Prob it is successful and receives a favorable review + Prob it is moderately successful and receives a favorable review + Prob it is unsuccessful and receives a favorable review = 0.6125

B) If a new design receives positive feedback, there is a 0.62 percent chance that it will be a highly successful product.

C) Chance of not receiving a favorable review: (0.40*0.05)

+0.35(0.4) +(0.25)*0.9\s= 0.385

Prob for successful but not receiving a favorable evaluation is 0.40(0.05) = 0.02; required prob is 0.0519.

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