Which of the following are not congruence theorems for right triangles? Check all that apply.

A. LA
B. HL
C. AA
D. HA
E. HH
F. LL

By the principle of mathematical induction, we have shown that for all positive integers n, n^3 + 2n is divisible by 3.

Proof by Induction: n^3 + 2n is divisible by 3 for all positive integers n.

Base Case:

For n = 1, n^3 + 2n = 1^3 + 2(1) = 3, which is divisible by 3.

Induction Hypothesis:

Assume that for some positive integer k, k^3 + 2k is divisible by 3. We can write this as: k^3 + 2k = 3m, where m is an integer.

Induction Step:

We need to show that (k + 1)^3 + 2(k + 1) is divisible by 3. Expanding the expression:

(k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2

= (k^3 + 2k) + (3k^2 + 3k + 3)

Substituting the induction hypothesis:

= 3m + 3(k^2 + k + 1)

= 3(m + k^2 + k + 1)

Since k^2 + k + 1 is an integer (sum of three integers), and m is an integer, their sum (m + k^2 + k + 1) is also an integer. Therefore, (k + 1)^3 + 2(k + 1) is divisible by 3.

A function is denoted as y = f (x), where x is the argument or input of the function. This means that from  f(6) follows that x= 6, and to get the answer we should replace x with 6.

f(6)=6^2÷ 3 + 6= 36÷ 3 + 6= 12+6= 18

f(6)=18

Answer:

The value of f(6) is, 18

Step-by-step explanation:

Given the function:

[tex]f(x) = x^2 \div 3+ x[/tex]               .....[1]

We have to find the value of [tex]f(6)[/tex].

Put x = 6 in [1] we have;

[tex]f(6) = 6^2 \div 3+ 6[/tex]

⇒[tex]f(6) = 36 \div 3 +6[/tex]

⇒[tex]f(6) = \frac{36}{3}+6[/tex]

Simplify:

[tex]f(6) = 12 +6 = 18[/tex]

Therefore, the value of f(6) is, 18

Donald earned a commission of $739.26 last week.

To calculate the commission amount earned by Donald last week, we need to find the sales above his weekly quota first. Sales above the quota is calculated by subtracting the weekly quota from the total sales. In this case, $32,480 - $12,500 = $19,980. Next, we can calculate the commission amount by multiplying the sales above the quota by the commission rate. The commission amount earned by Donald last week is $19,980 * 0.037 = $739.26.

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Answer:

it is the distance of a circle

Step-by-step explanation:

It is a true statement that it is guaranteed that ΔABC ≈ ΔXYZ in the diagram given.

In this context, all triangles have 180 degrees altogether in as much they have a standard size of the shape.

The triangles have the sames standard size although the letters of the angles are different.

Therefore, the statement is a true statement.

Read more about triangles angle

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Answer:

D. $15061.98

Step-by-step explanation:

In order to calculate the proceeds we will using the following computation:

Principal + {Principal * Discounted rate * Frequency of a year on Maturity Date}

15,000 + {15,000 * 5% * (30/365)}

Hence, the proceeds of note would be $15,061.98

To find the sprinter's unit rate of feet per second, divide the total distance by the time. In this case, the sprinter's unit rate is approximately 31 feet per second.

To find the sprinter's unit rate of feet per second, we need to divide the total distance the sprinter can run by the time it takes. In this case, the sprinter can run 279 feet in 9 seconds. So the unit rate is 279 feet divided by 9 seconds, which is approximately 31 feet per second.

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Answer : The north middle school have fewer than 750 students.

Step-by-step explanation:

Let the number of students in south middle school be, x

and the number of students in north middle school be, y

Given:

Number students in south middle school = x = 750

and,

North middle school has 13/15 times as many students as South. That means,

[tex]y=\frac{13}{15}\times x[/tex]   ........(1)

Now put the value of 'x' in expression 1, we get:

[tex]y=\frac{13}{15}\times 750[/tex]

[tex]y=650[/tex]

Thus, number of students in north middle school = y = 650

From this we conclude that north middle school have fewer than 750 students.

Hence, the north middle school have fewer than 750 students.

A Jeweler has 36 inches of silver chain. She needs 5 times much to make some necklaces and 3 times that amount to make some bracelets. How much does the jeweler need to make her necklaces and bracelets

Step-by-step explanation:

The equation of a line with an undefined slope passing through the point (2, 5) can be written as x = 2.

When the slope of a line is undefined, it means that the line is vertical. In a vertical line, the x-coordinate remains constant while the y-coordinate can take any value.

So, for this line passing through the point (2, 5), the x-coordinate will always be 2, regardless of the value of y. Therefore, we can represent this line with the equation x = 2.

once you have that relation, then you can replace the variables by the numbers given. by similar triangles that relation is

Answer:

Domain is {x| 1<=x <5}

Step-by-step explanation:

The graph of the piecewise function f(x) is shown.

In the given graph of piecewise function

Domain is the set of x values for which the function is defined

first graph is from x= 1 to 3, 3 is excluded

second graph is from x= 3 to 5, 5 is excluded

So the graph of x values is from x=1 to 5 ( 5 excluded because we have open circle at 5)

Domain is {x| 1<=x <5}

Final answer:

For the function f(x) = (sinx)/x to be continuous at x = 0, the value of k must be 1, which is the limit of the function as x approaches 0.

Explanation:

The student is asking about the continuity of a given function at x = 0. To determine what the value of k must be for the function f(x) = (sinx)/x when x is approaching 0, we need to look at the limit of the function as x approaches 0.

Although the function is not defined at x = 0 due to division by zero, we know that the limit of (sin x)/x as x approaches 0 is 1. This can be proven using L'Hospital's rule or the squeezing theorem. Hence, for the function to be continuous at x = 0, the value of k must also be 1.

Explanation of how to expand and simplify the given quadratic expression Hence answer is 4a²x² + abx² + 1/4b²x²,

Solve the equation: (2ax + 1/2 bx)²

Expanding the given expression:

(2ax + 1/2 bx)²

= (2ax)² + (2ax) (1/2 bx) + (1/2 bx)²

= 4a²x² + 2abx² + 1/4b²x²

= 4a²x² + abx² + 1/4b²x²

Answer: 4a²x² + abx² + 1/4b²x²

Final answer:

To find the relative minimum of the function, we first calculate its first derivative and set it to zero to find critical points. A single critical point is found at x = -9/2. Using the Second Derivative Test, we conclude that there is a relative minimum at (-9/2, -97/4) since the function's second derivative is positive, indicating the function is concave up at this point.

Explanation:

To find the relative extrema of the function f(x) = x2 + 9x − 4, we first need to determine its critical points. This is done by finding the derivative of f(x) and setting it equal to zero.

The derivative of the function, f'(x), can be calculated as follows:

f'(x) = 2x + 9

Setting the derivative equal to zero gives us:

2x + 9 = 0
x = -9/2

Now, we apply the Second Derivative Test to determine if this critical point is a relative maximum or minimum. The second derivative is:

f''(x) = 2

Since the second derivative is positive, the function is concave up at x = -9/2. Therefore, the function has a relative minimum at this point.

To find the y-coordinate, we substitute x = -9/2 into the original function:

f(-9/2) = (-9/2)2 + 9*(-9/2) − 4

Simplifying this, we get:

y = 81/4 - 81/2 - 4
y = 81/4 - 162/4 - 16/4
y = -97/4

Therefore, the relative minimum is (-9/2, -97/4). There is no relative maximum since the function is a parabola that opens upwards.

The volume of the ball bearing, which is a sphere, would be approximately 8.18 cm³. This is calculated using the formula for the volume of a sphere and the given diameter, which is halved to get the radius for the calculation

The volume of a sphere can be calculated using the formula V = 4/3 * π * r³, where r is the radius of the sphere. In this case, the diameter of the ball bearing is 2.5 cm, so the radius would be half of that (diameter/2), which is 1.25 cm. Substituting the radius value to the volume formula, we get: V = 4/3 * π * (1.25cm)³ = 4/3 * 3.14 * 1.95cm³ = approximately 8.18 cm³, rounded to the nearest hundredth.

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Answer:

126 is the answer please give me brainliest.

Step-by-step explanation:

Answer:

[tex]6x^2,3xy,4z[/tex]

Step-by-step explanation:

We are given that an expression

[tex]6x^2+3xy+4z[/tex]

We have to find the variable terms in the given expression.

Variable term: The term which contains variable is called variable term.

Constant term:The term which does not contain variable is called constant term.

To find the variable terms we will find the terms which contains variable.

We can see that in the given expression

There are three terms which contain variables.

Hence, the variable terms are

[tex]6x^2,3xy,4z[/tex]