a student wants to show that the product of three consecutive positive integers is divisible by 6. unfortunately, they are not convinced that one of these integers must be divisible by 3 (they skipped every lecture during the number theory unit). using induction, write a proof that never uses the fact that one of the integers must be divisible by 3.

The length of TS is 30.

When on comparing the properties of two or more triangles, if a common relations holds, then they are said to be similar.

Note that similarity is NOT congruency.

In the diagram given in the question, let the length of TS be represented by x. So that;

TS/ QS = SU/ SR

But, we have;

TS = x

SU = TS - 6 = x - 6

So that;

x/ 55 = (x - 6)/ 44

44x = 55(x - 6)

      = 55x - 330

330 = 55x - 44x

330 = 11x

x = 330/ 11

 = 30

x = 30

Therefore, the length of TS is 30.

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Answer:

correct

Step-by-step explanation:

he is correct because the transformation is a translation and under the translation the image and preimage are congruent.

the measure of the sides are preserved, and the peasure of the angles are preserved so if all the corsponding sides and angles are congruent the hexagons are congruent too

Answer:

(x, y) -----> ( - x , y - 10 )

Step-by-step explanation:

Titus is not correct.

There are two transformations will correctly prove FEDCBA ≅ F'E'D'C'B'A'

First transformation is Reflection over y-axis , then translation 10 units down.

The final formula is ( - x , y - 10 )

Linear equations are a subset of non-linear equations, and the equation 3xy = 9 is a non-linear equation.

The equation 3xy = 9 is not a linear equation. It is a non-linear equation. Linear equations are first-degree equations, meaning that the exponent of all variables is 1. A linear equation is represented in the form y = mx + b, where m and b are constants.

The variables in linear equations are not raised to powers higher than 1, making it easier to graph them. In contrast, non-linear equations are any equations that cannot be written in the form y = mx + b. Non-linear equations have at least one variable with an exponent that is greater than or equal to 2. Non-linear equations are harder to graph than linear equations.

The answer is false, the equation 3xy = 9 is a non-linear equation, not a linear equation. Non-linear equations are any equations that cannot be written in the form y = mx + b. They have at least one variable with an exponent that is greater than or equal to 2.

Linear equations are a subset of non-linear equations, and the equation 3xy = 9 is a non-linear equation.

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Answer:

x∈(-∞,3]

Step-by-step explanation:

2x-6<=5*3-5x

2x-6<=15-5x

+5x        +5x

7x-6<=15

+6       +6

7x<=21

:7     :7

x<=3

x∈(-∞,3]

Answer:

j=816 inch

Step-by-step explanation:

J^+K^+L^=180° (sum of int. angles of triangle)

L^+11+63=180

L^=106°

j/sinJ=l/sinL

j/sin63=880/sin106

j*sin106/sin106=880*sin63/sin106

j=815.6

j=816 inch

Answer: D

Step-by-step explanation: The answer is the z score that is farthest from the mean is - 2.00. The Z-score is the number of standard deviations a random value is from the population mean.

The z-score values which represents represents the location farthest from the mean is z=-2.00. (D)

In a standard normal distribution, the z-score represents the number of standard deviations a given value is from the mean.

The larger the absolute value of the z-score, the farther the value is from the mean. In this case, we're asked to identify the location farthest from the mean among the given choices.

By looking at the absolute value of each z-score, we can determine which value is the farthest from the mean. The absolute value of a z-score indicates how far away a given value is from the mean, regardless of whether it's above or below the mean.

In this case, the absolute value of the z-score "D. z = -2.00" is the largest among the choices, indicating that this value is the farthest from the mean. Hence, "D. z = -2.00" is the answer.

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It should be noted that the relationship between the balance and the number of withdrawals is linear, because there is a constant amount of $10 per withdrawal.

To confirm this, we can calculate the differences in balance for each pair of withdrawals:

Between withdrawals 3 and 2: 170 - 140 = 30

Based on the information, the starting amount is $200.

The equation to illustrate the withdrawal will be:

= 200 - 10w

where w = withdrawal.

These differences are constant, which means the rate of change of the balance is constant too.

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Answer:

(n+7)x2

Step-by-step explanation:

We can actually deduce here that the value of y after the given statement has been coded and executed, given that x = 3 is: 27.

In Mathematics, value is actually known to be a number or digit or what a number represents in a mathematical expression. Values help us to know numbers and figures.

The options that complete the question are:

We see here that the expression given is:

Set y = pow(x,x)

We see here that x=3

Thus, pow(3,3) = 3×3×3 = 27 (when coded and executed).

Thus, the answer is 27.

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Answer:

First, while this can be solved by calculating each individual area, let's do it in a smarter way.

Notice that there are two outer parts shaded, and two inner parts shaded.

When we add all of those, we get half of the larger circle.

So we only need to calculate the area of the larger circle and then divide it by two.

Remember that the area of a circle is:

A = pi*r^2

where:

pi = 3.1416

r = radius of the circle.

In the image, we can see that the diameter of the larger circle is 8ft.

And we know that r is half of the diameter, then:

r = 8ft/2 = 4ft

Now we can replace those values in the area of the larger circle and get:

A = 3.1416*(4ft)^2 = 50.27 ft^2

Half of that is:

A/2 = 21.14 ft^2.

That is the area of the shaded regions.

For a balloon mortgage, the monthly payments are usually lower, but there is a final "balloon" payment due at the end of the term.

a. Property Taxes:

The assessed value of the building is $500,000, and the property tax rate is 2.415%. To calculate the property taxes, we multiply the assessed value by the tax rate:

Property taxes = Assessed value * Tax rate

Property taxes = $500,000 * 2.415% (convert percentage to decimal)

Property taxes = $500,000 * 0.02415

Property taxes = $12,075

Therefore, the property taxes on the assessed value of the building will be $12,075.

b. Monthly Mortgage Payment:

To calculate the monthly mortgage payment, we need to consider the loan amount, interest rate, and loan term. The down payment is 20%, so the loan amount will be 80% of the market value of the building:

Loan amount = Market value * (1 - Down payment percentage)

Loan amount = $457,350 * (1 - 20%) (convert percentage to decimal)

Loan amount = $457,350 * 0.8

Loan amount = $365,880

We can now use this loan amount, along with the mortgage interest rate and loan term, to calculate the monthly payment using the formula for a fixed-rate mortgage:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

The monthly interest rate is the annual interest rate divided by 12, and the total number of months is the loan term multiplied by 12.

Annual interest rate = 4.55% (convert percentage to decimal)

Monthly interest rate = 4.55% / 12

Loan term = 30 years

Total number of months = 30 * 12

Now, let's calculate the monthly payment:

Monthly payment = ($365,880 * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

c. Total Interest Paid:

To calculate the total interest paid over the life of the loan, we multiply the monthly payment by the total number of months and subtract the loan amount:

Total interest paid = (Monthly payment * Total number of months) - Loan amount

d. Closing Costs:

The closing costs can vary, but a common range is between 2% and 5% of the purchase price. To calculate the range for closing costs, we'll use these percentages:

Minimum closing costs = Purchase price * 2%

Maximum closing costs = Purchase price * 5%

e. Balloon Mortgage Payment:

For a balloon mortgage, the monthly payments are usually lower, but there is a final "balloon" payment due at the end of the term. To calculate the monthly payment for the balloon mortgage, we'll use the loan amount, interest rate, and loan term:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

Now, let's calculate the monthly payment for the balloon mortgage.

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Answer: 9:25 ?

Step-by-step explanation:

4.5 × 2 = 9

12.5 × 2 = 25

4.5:12.5 ratio simplified is 9:25

Answer:

38.73 cm

Step-by-step explanation:

Given:

Solution:

S² = (R - r)^2xh^2

(40)^2=(30-20)^2+h^2

1600=(10)^2+h^2

1600-100=h^2

h=√1500

h=10√15

h=38.73 (rounded to the nearest tenth)

Answer:

14.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mean is 3.5

There are 720 different choices if order matters and there are 120 different choices if order does not matter.

a) If order matters,

The player can choose the first number in 10 ways (any of the digits 0-9), the second number in 9 ways (since one digit has already been chosen), and the third number in 8 ways (since two digits have already been chosen).

So the total number of choices is:

10 x 9 x 8 = 720

Therefore, there are 720 different choices if order matters.

b) If order does not matter,

We need to divide the number of choices by the number of ways the three numbers can be arranged.

Since there are 3 numbers, they can be arranged in 3! = 6 ways.

So the number of choices when order does not matter is:

(10 x 9 x 8) / 6 = 120

Therefore, there are 120 different choices if order does not matter.

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Answer:

Not similar

Step-by-step explanation:

In triangle MLN & WXY,

Right angles - > 1

There is nothing common in these 2 triangles other than (1)

Therefore,

Not similar

Answer:

2 cos (x + pi/2)

Step-by-step explanation:

Of the choices given, this looks like a cos curve that is shifted to the Left by pi / 2  and   multiplied to give an amplitude of 2

Answer:

1. clockwise

2. counterclockwise

Step-by-step explanation:

If a figure rotates to the right, it is called \( \boxed{\purple{\bold {clockwise}}} \) rotation and if the figure rotates to the left, it is called \( \boxed{\red{\bold {counterclockwise}}} \) rotation.

Answer:

y = 2 v2, 2 square root 2

Step-by-step explanation:

since it's a right triangle with a 45°, that means the other angle is also 45°

which makes both sides the same

Pythagoras

4^2 = y^2 + y^2

16 = 2 y^2

16/2 = y^2

8 = y ^2

v8 = y

2 v2 = y

note: (v = square root)

Answer:

\(2\sqrt{2\)

Step-by-step explanation:

The ratios of a 45 - 45 - 90 triangle is \(1:1:\sqrt{2}\)

To get 4 for the hypotenuse, you need to mulitpy \(\sqrt{2}\) by \(\sqrt{8}\).

\(\sqrt{2}\) x \(\sqrt{8}\) = \(\sqrt{16}\)

Simplify.

\(\sqrt{16} = 4\)

If you simplify the \(\sqrt{8}\), it equals \(2\sqrt{2}\).

Since the ratio is \(1:1:\sqrt{2}\)

The sides will be \(2\sqrt{2}:2\sqrt{2}:4\)

By applying Pythagoras' theorem, the length of x is equal to 10 units.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:

x² = y² + z²

x² = 8² + 6²

x² = 64 + 36

x = √100

x = 10 units.

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Answer:

Step-by-step explanation:

150 90x 100/60

Answer:

22 inches is the answer

Answer:

I think it is 52 degrease

Step-by-step explanation:

Answer:

Taylor will charge more by $15

Step-by-step explanation:

Given

Taylor

First Hour = $15

Hourly Rate = $10

Lucy:

\(f(x) = \left \{ {{20x,\ 0 \le \ x \ \le 2} \atop {10x, x>2}} \right.\)

For a dog walk of 2.5 hours.

Taylor's charges is:

\(Charges = First\ Hour + Hourly\ Rate * 2.5\)

\(Charges = \$15 + \$10 * 2.5\)

\(Charges = \$15 + \$25\)

\(Charges = \$40\)

Lucy's charges is:

Here, we consider

\(f(x) = 10x\) Because \(x > 2\)

i.e 2.5 > 2

So, Lucy's charges is:

\(Charges = 10 * \$2.5\)

\(Charges = \$25\)

By comparison;

Taylor will charge more by $15

The difference is calculated by:

\(Difference = \$40 - \$25\)

\(Difference = \$15\)

Using an arithmetic sequence, it is found that:

i) They collected 300 bottles on June 25th.

ii) The day was July 18th.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

\(a_n = a_1 + (n - 1)d\)

In which \(a_1\) is the first term.

In this problem, the sequence is: {417 ,404 ,391, .........}, hence the first term is \(a_1 = 417\), the common difference is d = -13, and the equation is:

\(a_n = 417 - 13(n - 1)\)

Item i)

They started on June 15th, hence June 25th is the 10th day, thus:

\(a_{10} = 417 - 13(9) = 300\)

They collected 300 bottles on June 25th.

Item ii)

This is n days after June 15th, for which \(a_n = 1\), hence:

\(a_n = 417 - 13(n - 1)\)

\(1 = 430 - 13n\)

\(13n = 429\)

\(n = 33\)

33 days after June 15th is July 18th.

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Form A

H(t) = -8(t – 2)² + 37

Form B

H(t)= -8t² + 32t + 5

a. From form A, the vertex of the parabola is at (2, 37). This means that the maximum height is 37 feet and it's reached after 2 seconds.

b. The initial height corresponds to t = 0 seconds. Replacing t = 0 into form B:

H(0)= -8(0)² + 32(0) + 5 = 5 ft

That is, the initial height was 5 ft

The construction that uses the compass for only one step in addition to drawing the circle itself is A. an equilateral triangle inscribed in a circle.

It should be noted that a compass simply means a device that's used to show cardinal directions. It's also used in mathematics to draw shapes.

In this case, the construction that uses the compass for only one step in addition to drawing the circle itself is an equilateral triangle inscribed in a circle.

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