Geometry Help!!

For triangle TRI the following facts are given:
Segment AN || Segment RI
AT = 8cm
AR = 2cm
TN = 12cm
(a) use a two-column or paragraph format to prove triangle TAN ~ triangle TRI
(b) use the side splitting theorem to find NI.

divide 52.5o by 7

52.50 / 7 = 7.50 per hour

Answer:

The unit rate is 235 calories per hour.

Step-by-step explanation:

General house cleaning (sweeping the floor vacuuming laundry) can burn 470 calories every two hour determine the unit rate.

Unit rate means we have to find the calories burned in 1 hour.

Hence, calories burned in 1 hour = [tex]\frac{470}{2}= 235[/tex]

Answer :

The unit rate is 235 calories per hour.

The equation of the circle passing through the point (−5, −2) and center at (−2, 3) is  [tex]\bold{( x +2 )^2 + ( y - 3 )^2 = 34}[/tex]

The general equation of the circle whose center at (h, k) and radius r is,

[tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]

For given example,

the circle passing through the point (−5, −2) whose center is at (−2, 3).

The radius of the circle is the distance between point (-5, -2) and the center (-2, 3).

Using distance formula the radius of a circle would be,

⇒ [tex]r=\sqrt{(-2-3)^2 + (-5-(-2))^2}[/tex]

⇒ [tex]r=\sqrt{(-5)^2+(-3)^2}[/tex]

⇒ [tex]r=\sqrt{25+9}[/tex]

⇒ [tex]r=\sqrt{34}[/tex] units

Let center (h, k) = (-2, 3)

Using the general form of the circle,

⇒ [tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]

⇒ [tex]( x - (-2) )^2 + ( y - 3 )^2 = (\sqrt{34})^2[/tex]

⇒ [tex]( x +2 )^2 + ( y - 3 )^2 = 34[/tex]

Therefore, the equation of the circle passing through the point (−5, −2) whose center is at (−2,3) would be [tex]\bold{( x +2 )^2 + ( y - 3 )^2 = 34}[/tex]

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y/9 +5 =0

 subtract 5 from each side

y/9 = -5

 multiply both sides by 9

y = -5 * 9

y = -45

Alex broke 3 glasses during the unpacking of the glasses.

As mentioned in the question, Alex was hired to unpack 576 items of glass wear, at five cents per piece unpacked. For every item broken in the process, however, Alex had to pay $1.98. At the end of the job, Alex received $22.71.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The total amount earned for 576 glasses is given as,
= 576 × 0.05
= $28.80.

Amount earned = $22.71
Amount paid by Alex for the broken glass = $28.80 - $22.71 = 6.09
Total glass broked = 6.09 / 1.98 ≈ 3

Thus, Alex broke 3 glasses during the unpacking of the glasses.

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Final answer:

Each student gets 1/4 of a pizza when 12 students share 3 pizzas equally. This is because 3 pizzas divided by 12 students results in each student receiving 1/4 of a pizza.

Explanation:

To determine the fraction of the pizza each student gets when 12 students share 3 pizzas equally, you'd divide the total number of pizzas by the number of students. Here's the step-by-step breakdown:

Understanding fractions can be similar to figuring out slices of pie or the number of quarters in a dollar.

The complete list of possible pairs of rodents from the choices woodchuck, prairie dog, beaver, and chipmunk includes six combinations, showcasing an application of combinatorics in mathematics to determine all possible selections.

The question involves determining the complete list of possible pairs of rodents that radio listeners could choose from four options: woodchuck, prairie dog, beaver, and chipmunk. This is a matter of combinatorics, a branch of mathematics focused on counting, arrangement, and combination of sets of elements. Since each listener picks two favorites and the order in which they pick them does not matter (choosing a beaver and a woodchuck is the same as choosing a woodchuck and a beaver), we use combinations to find the total number of possible pairs.

Mathematically, the number of ways to choose 2 favorites out of 4 is given by the combination formula C(n, r) = n! / r!(n-r)!, where n is the total number of options and r is the number being chosen. Here, n=4 and r=2, resulting in C(4, 2) = 4! / 2!(4-2)! = 6, which matches our list of 6 possible pairs.

Answer:

False; True; True.

Step-by-step explanation:

In this situation, the y-intercept would represent the amount of money in her account at x=0 weeks, or the beginning of the year.  This is not the x-intercept, so the first statement is false.

The slope is the rate of change.  This would describe how her account changes every week, so this represents the amount of money she deposits into her account each week.  This means the second statement is true.

The line goes through the point (4, 0).  Since x is the number of weeks, this would represent the amount in her account after 4 weeks.  Since the y-value is 0, this means she no longer has an overdraft balance after 4 weeks.  This means the second statement is true.

Following are the response to the given points:

Therefore, the final answer is "false, true, and true".

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To express 645,300 in expanded form using exponents, it is written as [tex]6x10^{5} + 4x10^{4} + 5x10^{3}+ 3x10^{2}[/tex]x, breaking down each digit by its place value and expressing each as a power of 10.

To write the number 645,300 in expanded form using exponents, we break down each digit according to its place value and then express each of these as a power of 10. The place values for the number 645,300 are as follows:

600,000 which is 6 times 100,000

40,000 which is 4 times 10,000

5,000 which is 5 times 1,000

300 which is 3 times 100

Now we express these place values using exponents:

645,300 = [tex]6x10^{5} + 4x10^{4} + 5x10^{3}+ 3x10^{2}[/tex]

This notation shows the number 645,300 written as the sum of each digit multiplied by the appropriate power of 10 based on its position in the number.

3/4  is the probability that any veteran game player will like the new computer game.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Given,

New computer game has been developed and 80 veteran game players will test its market potential.  

In this sixty players liked the game.

We need to find the probability that any veteran game player will like the new computer game.

To find the probability we just need to divide sixty by 80.

60/80

3/4

Hence 3/4  is the probability that any veteran game player will like the new computer game.

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Answer:

the answer is t = 20.625

Step-by-step explanation:

To begin, you would need to find the displacement of the first car and the equation to find that is d = 1/2at^2. So you would plug in what you have from the problem into the equation: d = (1/2)3(6)^2 and d is equal to 54 m. THIS IS YOUR DISPLACEMENT FOR THE FIRST CAR.

Next, you need to find the velocity of the car and the equation would be v = at. Plug in what you know from the problem: v = 3(6) which is 18. THIS IS YOUR INITIAL VELOCITY.

Next, we need to find out the distance of the 2nd car and we would use d = 1/2at^2. Plug in what you now from the problem: d = (1/2)5t^2 which would be d = 2.5t^2.

Next, you would equal these two equations together: 2.5t^2 = 1.5t^2 + 18t +54.  All these values are from when we solved them from above, and once you solve it you will get 20.625. (SOLVE FOR T)

Priscilla and Herb can address 10,000 envelopes together in approximately 44.44 hours, when we combine their individual work rates of 100 and 125 envelopes per hour respectively.

Priscilla and Herb are addressing envelopes for a firm, and we need to determine how long it would take them to address 10,000 envelopes if they work together. Priscilla can address 10,000 envelopes in 100 hours, and Herb can do the same in 80 hours.

To solve this, we can calculate each person's work rate and then combine these work rates to get the rate at which they complete the task together.

First, we calculate their work rates:

Working together, their combined rate would be:

Combined rate = Priscilla's rate + Herb's rate

Combined rate = 100 envelopes/hour + 125 envelopes/hour

Combined rate = 225 envelopes per hour

To address 10,000 envelopes at this combined rate, we can divide the total number of envelopes by their combined rate:

Time to address 10,000 envelopes together = 10,000 envelopes / 225 envelopes/hour

Time to address 10,000 envelopes together = approximately 44.44 hours

Answer:

Answer when we  round off 446,221 to the nearest ten is 446,220

Step-by-step explanation:

We need to round off 446,221 to the nearest ten.

Nearest ten to the 446,221 can be 446,220 or 446,230

Difference between 446,221 and 446,220 = 446,221 - 446,220 = 1

Difference between 446,221 and 446,230 = 446,230 - 446,221 = 9

Here the difference is minimum for 446,220

Answer when we  round off 446,221 to the nearest ten is 446,220

Answer:3/13

Step-by-step explanation:

Just took test

To calculate the balance after 6 years with compound interest, use the formula Balance = Principal * (1 + Interest Rate)^Time. Substituting the values, we find the balance to be approximately $2,243.89.

To calculate the balance after 6 years, we need to use the formula for compound interest:

Given that the principal (initial investment) is $1600 and the interest rate is 6.5%, we can substitute these values into the formula:

Calculating this, we find that the balance after 6 years is approximately $2,243.89.

The balance after 6 years is approximately $2105.69.

To find the balance after 6 years, we can use the formula for compound interest:

Balance = Principal(1 + Interest Rate)^Ti

Plugging in the given values, we have:

Balance = $1600(1 + 0.065)^6

Simplifying, we get:

Balance = $1600(1.065)^6

Calculating, we find that the balance after 6 years is approximately $oxed{2105.69}.

Answer: s=-1

Explanation:

We can re-write the equation as follows:

[tex]\frac{1}{64}=(4^{2s-1})(16^{2s+2})[/tex]

Let's rewrite the terms on the left and on the right as follows:

[tex]2^{-6} = ((2^2)^{2s-1})((2^4)^{2s+2})[/tex]

So we have

[tex]2^{-6} = (2^{2(2s-1)})(2^{4(2s+2)})[/tex]

Now we can use the following rule:

[tex]x^{a+b}=x^a x^b[/tex]

to rewrite the term on the right:

[tex](2^{2(2s-1)})(2^{4(2s+2)})=2^{2(2s-1)+4(2s+2)}[/tex]

So now we have

[tex]2^{-6}=2^{2(2s-1)+4(2s+2)}[/tex]

and since the bases are the same, we can just equalize the exponents:

[tex]-6=2(2s-1)+4(2s+2)[/tex]

[tex]-6=4s-2+8s+8\\-12 = 12 s\\s=-1[/tex]