Given that x is a whole number, Niram conjectured that x3>x2 .
What value is a counterexample to Niram's conjecture?
(a) −2
(b) 1/10
(c) 1
(d) 5

The two numbers that represent the lengths of the legs of the right triangle are 2 and 5.

Trigonometry is the study of the relationship between the ratios of the sides of a right-angled triangle and their angles. The trigonometric ratios used to examine this relationship are sine, cosine, tangent, cotangent, secant, and cosecant.

Given:

A right triangle has an acute angle measure of 22°.

Using Trigonometry

tan [tex]\theta[/tex] = opposite/adjacent

tan 22° = 2/5

            = 0.40

Thus, the lengths of the legs of the right triangle are 2 and 5.

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Final answer:

To calculate the fraction of a 10-hour shift that 6 hours represents, you divide 6 by 10 and simplify the resulting fraction, which is 6/10, to 3/5. Therefore, 6 hours is 3/5 of the work shift.

Explanation:

If an employee works a 10-hour shift, and you want to find out what fraction of the shift is represented by 6 hours, you divide 6 by the total hours in the shift which is 10. So, we write this as the fraction 6/10.

Now, simplifying the fraction, both the numerator (6) and the denominator (10) can be divided by 2. This gives us 3/5. Therefore, 6 hours represent 3/5 of the employee's 10-hour work shift.

To relate this to a concept you might already be familiar with, consider that 60 minutes make up 1 hour. If we write this as a ratio, it would be 60 minutes / 60 minutes, which simplifies to 1. Similarly, when we talk about fractions of an hour, like in the question, we're essentially looking for the number of parts of the shift that are being taken up by 6 hours in a 10-hour slot, which is 3/5.

Answer: 80x130

Step-by-step explanation:

The percentage of red marbles in a bag is 65%.

Given that, a bag of marbles contains 7 blue marbles and 13 red marbles.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, total number of marbles in a bag

= 7+13 =20

Now, percentage of red marbles

= 13/20 × 100

= 65%

Therefore, the percentage of red marbles in a bag is 65%.

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Answer:

no its not

Step-by-step explanation:

simplest form for 22/33 is 2/3

Sara travels a distance of 12 feet below sea level when she jumped into the sea.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have been given that Sara was on a cliff 25 feet above sea level. she jumped into the sea and descended a total of 37 feet.

To determine the number of feet below sea level travel by Sara

The number of feet below sea level = total descended -  cliff of a number of feet above sea level.

Here total descent is 37 feet and the cliff is 25 feet above sea level.

Substitute the value in the above equation,

The number of feet below sea level = 37 - 25

The number of feet below sea level = 12 feet

Therefore, she travels a distance of 12 feet below sea level.

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The value of F(4) in the given function is: f(4) = 7

The domain of a function is defined as the set of all possible input values that makes the function possible while the range is defined as the set of all possible output values for which the function is possible.

We are given the function as:

f(x) = 3x - 5

Thus f(4) will be gotten as:

f(4) = 3(4) - 5

f(4) = 7

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Final answer:

To solve for the number of dimes and quarters Michael has, we use two equations: 0.10d + 0.25q = 4.40 for the total value, and d + q = 20 for the total quantity of coins.

Explanation:

To find the number of dimes, d, and the number of quarters, q, Michael has, we need two equations to form a system. The first equation will represent the total amount of money in terms of dimes and quarters, and the second one will represent the total number of coins.

The value of a dime is $0.10 and the value of a quarter is $0.25. The total amount of money, $4.40, can be represented as 0.10d + 0.25q = 4.40. This is the value equation.

Since there are 20 coins in total, the second equation will simply be the count of both types of coins together: d + q = 20. This is the quantity equation.

The system of equations to find the number of dimes and quarters is:

0.10d + 0.25q = 4.40 (value equation)

d + q = 20 (quantity equation)

Kelvin found the correct equation and solution.

Brittany write incorrect equation because difference of a number and 20 can be written as, x - 20 where, x is a number; but Brittany can be written as 20 - x.

Here,

Kevin and Brittany write an equation to represent the following relationship, and both students solve their equation.

And, condition is given as,

5 times the difference of a number and 20 is the same as half the sum of 4 more than 4 times a number.

What is linear equation?

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1.

Now, according to given condition,

5 times the difference of a number and 20 is written as,

[tex]5 ( x - 20 )[/tex]

And, half the sum of 4 more than 4 times a number, is written as

[tex]\frac{1}{2} ( 4x + 4)[/tex]

Now, both equation are equal

[tex]5 ( x - 20 ) = \frac{1}{2} ( 4x + 4)\\5x - 100 = 2x + 2\\3x = 102\\x = 34[/tex]

Hence, Kelvin found the correct equation and solution.

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The question is missing critical information as it lacks the proportion or number related to the shaded part of the model. Without this detail or a visual representation, it's not possible to determine the accuracy of Gary or John's statements.

The question provided seems to be missing critical information, specifically the proportion or number that Gary and John are referring to when they mention how much of a model is shaded. In a typical mathematics problem regarding fractions or percentages, students would be asked to determine if statements about the shaded portion of a model are correct. Without the visual model or additional context indicating the proportion of the model that is shaded, it's impossible to conclude which student, Gary or John, is correct.

In order to answer correctly, we would need either a clear description of the model and its shaded parts or, preferably, a visual representation. Then, we would analyze the shaded portion to assess which statement about the fraction or percentage shaded is accurate. If we had this information, we could illustrate the process of comparing the given fraction or percentage with the actual shaded section of the model.

Unfortunately, without the necessary details, we can neither confirm if Gary, John, or both are correct, nor can we properly address the question.

Answer:   n6 + 7mn5 + 14m2n4 - 5m3n3 - 6m6

Step-by-step explanation:

The required ratio of 2 frogs to 5 turtles is given as 2 / 5 or 2:5.

As mentioned in the question ratio of the 2 frogs and 5 turtles is to be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The ratio of the two terms is given as a / b or a: b
Let a =  number of frogs ad b = number of turtles,
Now, put the values of a and b in a/b or a:b
So,
The ratio is given as,
= 2/5 or 2:5

Thus, the required ratio of 2 frogs to 5 turtles is given as 2 / 5 or 2:5.

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The only situation in which two angles are both congruent and complementary is when their measures are both 45°:

Two angles are complementary if their sum is 90°, and they are congruent if their measures are the same, say n. Therefore, to find two congruent angles which are complementary, we solve the following equation:

n+n=2n

2n = 90

2n/2 = 90/2

n=45

Two angles that are both congruent and complementary can be found in right angles.

Two angles that are both congruent and complementary can be found in the case of right angles. When two angles are right angles, they are both congruent (having the same measure) and complementary (adding up to 90 degrees).

The length of rectangular field  would be: 750ft

Its the sum of length of the sides used to made the given figure.

Given the rectangle perimeter (2,000 ft) and the ratio of rectangle length : width (3:1).

The equation of this question should be:

3 rectangle width = rectangle length

rectangle width = 1/3 rectangle length

The rectangle perimeter = 2,000ft

Using the formula of perimeter of rectangle = 2(length+width)

Now, Length of rectangular field is calculated as;

2,000ft  = 2 (length+width)

2,000ft /2 = 1/3 length + length

length = 750ft

Hence, The length of rectangular field  would be: 750ft

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